‘Adaptive plastic responses to metal contamination in a multistress context: a field experiment in fish’
Quentin PETITJEAN[q.petitjean1@gmail.com], Pascal LAFFAILLE, Annie PERRAULT, Myriam COUSSEAU, Séverine JEAN, Lisa JACQUIN
25/06/2022
1 Load libraries
packageList <- c("lme4", # To build linear mixed effect model with binomial family
"car", # To perform logit and power transformations and obtain p-value from linear mixed effect model
"MuMIn", # To perform automated model selection based on AIC and compute conditional and marginal R square for mixed effect model
"bimixt", # To transform data using bimixt::boxcox transformation (power transformation)
"dplyr", # To manage the database (e.g., left_join, count)
"tidyr", # To manage the database (e.g., separate)
"performance", # check model performances
"kableExtra") # To draw table
for(i in packageList){
if(require(i, character.only = TRUE)){
install.packages(i)
}
}
for(i in packageList){
library(i, character.only = TRUE)
}2 Load Some custom functions (making tables and drawing plots)
# load some custom functions used to draw the plots included within the MS
source("https://raw.githubusercontent.com/qpetitjean/Adaptive-plastic-responses-of-fish-in-a-multistress-context/main/Rscript/SourcePlots_PlasticResponsesFishMS.R")
# load some custom functions used to draw the statistic tables included within the MS
source("https://raw.githubusercontent.com/qpetitjean/Adaptive-plastic-responses-of-fish-in-a-multistress-context/main/Rscript/SourceTables_PlasticResponsesFishMS.R")3 Load the dataset
dat1 <- read.csv2("https://raw.githubusercontent.com/qpetitjean/Adaptive-plastic-responses-of-fish-in-a-multistress-context/main/Dataset/Dataset_Petitjeanetal-Adaptive_plastic_responses_of_fish_in_multistress_context.csv", dec = ".", sep = ";")
# specify that the cage Id is a factor instead of numeric to use it as random intercept in mixed effect models
dat1[["CageSiteID"]] <- as.factor(dat1[["CageSiteID"]])
# Add merged treatments variables
dat1$CxOxI = paste(dat1$TransplantContam, dat1$OriginSite, dat1$Injection, sep = "_")
dat1$CxO2xI = paste(dat1$TransplantContam,
dat1$OriginContam,
dat1$Injection,
sep = "_")
dat1$CxO = paste(dat1$TransplantContam, dat1$OriginSite, sep = "_")
dat1$CxO2 = paste(dat1$TransplantContam, dat1$OriginContam, sep = "_")
dat1$CxI = paste(dat1$TransplantContam, dat1$Injection, sep = "_")
dat1$O2xI = paste(dat1$OriginContam, dat1$Injection, sep = "_")
head(dat1,5)## ColorMark IndID Escaped OriginSite CagingSite OriginContam SitesPair
## 1 UNMARKED 1 No AUSCOR ARIMAS HC AUSCOR_ARIMAS
## 2 WHITE_GREEN 2 No AUSCOR ARIMAS HC AUSCOR_ARIMAS
## 3 PINK_ORANGE 3 No AUSCOR ARIMAS HC AUSCOR_ARIMAS
## 4 PINK_RED 4 No AUSCOR ARIMAS HC AUSCOR_ARIMAS
## 5 PINK_GREEN 5 No AUSCOR ARIMAS HC AUSCOR_ARIMAS
## CageID CageSiteID TransplantContam Transplant Injection Treatment
## 1 6 6 LC HC_LC AMIX HC_LC_AMIX
## 2 6 6 LC HC_LC AMIX HC_LC_AMIX
## 3 6 6 LC HC_LC PBS HC_LC_PBS
## 4 6 6 LC HC_LC AMIX HC_LC_AMIX
## 5 6 6 LC HC_LC PBS HC_LC_PBS
## WeightStart SizeStart Weight7D Size7D Weight9D Size9D WeightEnd SizeEnd
## 1 4.9 7.6 4.7 7.5 4.6 7.5 4.5 7.5
## 2 6.0 7.8 5.9 7.6 5.5 8.0 5.6 7.9
## 3 7.6 8.9 7.3 8.7 7.2 8.6 7.1 8.7
## 4 4.3 7.0 3.9 6.9 3.7 7.0 3.7 6.8
## 5 5.7 8.0 5.5 7.5 5.4 7.5 5.2 7.7
## DailyMassChange Death DeathDate MarkDate InjectionDate EuthanasiaDate
## 1 -0.5830904 0 <NA> 10/09/2018 17/09/2018 24/09/2018
## 2 -0.4761905 0 <NA> 10/09/2018 17/09/2018 24/09/2018
## 3 -0.4699248 0 <NA> 10/09/2018 17/09/2018 24/09/2018
## 4 -0.9966777 0 <NA> 10/09/2018 17/09/2018 24/09/2018
## 5 -0.6265664 0 <NA> 10/09/2018 17/09/2018 24/09/2018
## DaysAlive InjectionTime Pcaud1D7 Pcaud2D7 Pcaud3D7 MeanPcaudD7 PcaudDate
## 1 14 09:45:00 2.012 2.014 2.018 2.014667 19/09/2018
## 2 14 09:45:00 2.022 2.012 2.006 2.013333 19/09/2018
## 3 14 09:45:00 2.210 2.198 2.184 2.197333 19/09/2018
## 4 14 09:45:00 2.020 2.002 2.000 2.007333 19/09/2018
## 5 14 09:45:00 2.022 2.028 2.016 2.022000 19/09/2018
## PcaudTime Pcaud1D9 Pcaud2D9 Pcaud3D9 MeanPcaudD9 IR IRTime
## 1 12:30:00 2.286 2.266 2.282 2.278000 13.0708140 47.88542
## 2 12:30:00 2.422 2.412 2.404 2.412667 19.8344371 47.88542
## 3 12:30:00 2.710 2.724 2.728 2.720667 23.8167476 47.88542
## 4 12:30:00 2.020 2.012 2.036 2.022667 0.7638658 47.88542
## 5 12:30:00 1.630 1.654 1.626 1.636667 -19.0570392 47.88542
## GonadsWeight Sex LiverWeight GSI HSI Lymphocytes Monocytes
## 1 0.079 F 0.051 1.7555556 1.1333333 NA NA
## 2 0.074 F 0.056 1.3214286 1.0000000 91 8
## 3 0.174 F 0.029 2.4507042 0.4084507 93 3
## 4 0.052 F 0.022 1.4054054 0.5945946 87 13
## 5 0.012 M 0.030 0.2307692 0.5769231 NA NA
## Neutrophils mMH2O2 mMHCLO MuscleCarbohydrate MuscleProtein MuscleLipid
## 1 NA NA NA 37.34316 759.5371 1901.281
## 2 1 NA NA 40.93106 1547.8848 5235.155
## 3 4 4.500544 NA 44.72313 1265.5788 6348.720
## 4 0 NA NA 19.59270 1287.4869 3870.738
## 5 NA NA NA 29.53739 1024.9727 1745.356
## AvailableEnerJ CqActb DeltaCtCat DeltaCtCasp3 DeltaCtGpx DeltaCtMtl
## 1 2698.161 24.41974 0.07138744 0.005951188 0.3118747 0.6621643
## 2 6823.971 26.45246 0.03845321 0.026903646 0.6009854 9.4992353
## 3 7659.022 25.32390 0.03655256 0.006485931 0.6950857 14.5623734
## 4 5177.818 25.37811 0.03377133 0.006698988 0.2555632 0.7285995
## 5 2799.866 24.00830 0.04684323 0.007794697 0.3911237 2.4443257
## DeltaCtPcx DeltaCtPygl MuscleAl MuscleCr MuscleCo MuscleNi MuscleCu
## 1 0.037076525 0.10068714 26.497849 0.35363824 0.022987203 0.2452521 10.917660
## 2 0.006979170 0.03752741 1.313570 0.12796698 0.011615140 1.6162667 4.794625
## 3 0.017903927 0.06595523 3.016400 0.11952862 0.011496152 0.0322936 5.239017
## 4 0.007300098 0.03637586 3.657936 0.05860145 0.009343916 0.3097805 1.422597
## 5 0.020840611 0.06521035 11.235868 0.29147406 0.017189684 0.2715557 3.836860
## MuscleZn MuscleAs MuscleCd CxOxI CxO2xI CxO CxO2
## 1 212.00439 0.5486982 0.013927432 LC_AUSCOR_AMIX LC_HC_AMIX LC_AUSCOR LC_HC
## 2 78.75929 0.6634702 0.009095777 LC_AUSCOR_AMIX LC_HC_AMIX LC_AUSCOR LC_HC
## 3 84.98429 0.3719471 0.003173364 LC_AUSCOR_PBS LC_HC_PBS LC_AUSCOR LC_HC
## 4 108.06563 0.4981519 0.001854870 LC_AUSCOR_AMIX LC_HC_AMIX LC_AUSCOR LC_HC
## 5 143.04142 0.4685862 0.004087401 LC_AUSCOR_PBS LC_HC_PBS LC_AUSCOR LC_HC
## CxI O2xI
## 1 LC_AMIX HC_AMIX
## 2 LC_AMIX HC_AMIX
## 3 LC_PBS HC_PBS
## 4 LC_AMIX HC_AMIX
## 5 LC_PBS HC_PBS4 Check sample size per treatments
4.1 Including escaped fish
tab1 <- data.frame(table(dat1$OriginSite, dat1$CagingSite, dat1$OriginContam, dat1$TransplantContam, dat1$Injection))
names(tab1) <- c("Origin site", "Transplant site", "Contamination level in origin site", "Contamination level in transplant site", "Immune challenge", "Sample size")
tab1 <- tab1[which(tab1[["Sample size"]]>0),]
tab1 <- tab1[order(tab1[["Origin site"]], tab1[["Transplant site"]]),]
rownames(tab1) <- NULL
kableExtra::kable_classic(kableExtra::kbl(tab1), bootstrap_options = c("striped", "hover", "condensed", "responsive"), full_width = F, html_font = "arial", font_size = 10)| Origin site | Transplant site | Contamination level in origin site | Contamination level in transplant site | Immune challenge | Sample size |
|---|---|---|---|---|---|
| ARIMAS | ARIMAS | LC | LC | AMIX | 18 |
| ARIMAS | ARIMAS | LC | LC | PBS | 15 |
| ARIMAS | AUSCOR | LC | HC | AMIX | 21 |
| ARIMAS | AUSCOR | LC | HC | PBS | 18 |
| AUSCOR | ARIMAS | HC | LC | AMIX | 18 |
| AUSCOR | ARIMAS | HC | LC | PBS | 17 |
| AUSCOR | AUSCOR | HC | HC | AMIX | 16 |
| AUSCOR | AUSCOR | HC | HC | PBS | 17 |
| CELFIG | CELFIG | LC | LC | AMIX | 17 |
| CELFIG | CELFIG | LC | LC | PBS | 16 |
| CELFIG | RIOU | LC | HC | AMIX | 17 |
| CELFIG | RIOU | LC | HC | PBS | 17 |
| RIOU | CELFIG | HC | LC | AMIX | 17 |
| RIOU | CELFIG | HC | LC | PBS | 16 |
| RIOU | RIOU | HC | HC | AMIX | 18 |
| RIOU | RIOU | HC | HC | PBS | 16 |
# total sample size:
sum(tab1[["Sample size"]])## [1] 2744.2 Excluding escaped fish
dat1bis = dat1[dat1$Escaped == "No", ]
tab2 <- data.frame(table(dat1bis$OriginSite, dat1bis$CagingSite, dat1bis$OriginContam, dat1bis$TransplantContam, dat1bis$Injection))
names(tab2) <- c("Origin site", "Transplant site", "Contamination level in origin site", "Contamination level in transplant site", "Immune challenge", "Sample size")
tab2 <- tab2[which(tab2[["Sample size"]]>0),]
tab2 <- tab2[order(tab2[["Origin site"]], tab2[["Transplant site"]]),]
rownames(tab2) <- NULL
kableExtra::kable_classic(kableExtra::kbl(tab2), bootstrap_options = c("striped", "hover", "condensed", "responsive"), full_width = F, html_font = "arial", font_size = 10)| Origin site | Transplant site | Contamination level in origin site | Contamination level in transplant site | Immune challenge | Sample size |
|---|---|---|---|---|---|
| ARIMAS | ARIMAS | LC | LC | AMIX | 18 |
| ARIMAS | ARIMAS | LC | LC | PBS | 15 |
| ARIMAS | AUSCOR | LC | HC | AMIX | 20 |
| ARIMAS | AUSCOR | LC | HC | PBS | 18 |
| AUSCOR | ARIMAS | HC | LC | AMIX | 18 |
| AUSCOR | ARIMAS | HC | LC | PBS | 17 |
| AUSCOR | AUSCOR | HC | HC | AMIX | 15 |
| AUSCOR | AUSCOR | HC | HC | PBS | 14 |
| CELFIG | CELFIG | LC | LC | AMIX | 17 |
| CELFIG | CELFIG | LC | LC | PBS | 16 |
| CELFIG | RIOU | LC | HC | AMIX | 17 |
| CELFIG | RIOU | LC | HC | PBS | 17 |
| RIOU | CELFIG | HC | LC | AMIX | 17 |
| RIOU | CELFIG | HC | LC | PBS | 15 |
| RIOU | RIOU | HC | HC | AMIX | 18 |
| RIOU | RIOU | HC | HC | PBS | 16 |
# total sample size:
sum(tab2[["Sample size"]])## [1] 2685 Test some basics
here we will test the design of the experiment.
A quick reminder:
- Treatments (fixed effects):
- TransplantContam (transplant treatment either High contamination-HC
or Low contamination-LC)
- OriginContam (Origin of the population either High contamination-HC
or Low contamination-LC)
- Injection (control saline: PBS, antigen mixture: AMIX)
- TransplantContam (transplant treatment either High contamination-HC
or Low contamination-LC)
- Covariates :
- SizeEnd (Fish size at the end of the experiment)
- Sex (Fish sex determined by visual inspection at the end of the
experiment)
- SizeEnd (Fish size at the end of the experiment)
- Blocks (random effects):
- CagingSite (The name of the study site where fish are caged, either
ARIMAS, AUSCOR, CELFIG or RIOU)
- CageSiteID (The ID number ranging from 1 to 6 corresponding to the
number of the cage within each study site)
- OriginSite (The name of the site where each population were sampled
= population ID)
- CagingSite (The name of the study site where fish are caged, either
ARIMAS, AUSCOR, CELFIG or RIOU)
5.1 Test Distribution of
fish sex among cages
sex determination was performed at the end of the experiment: visual inspection of the gonads
dat2 = dat1[is.na(dat1$Sex) == F, ]
sexTabCage = table(dat2$CageID, dat2$Sex)
sexTabOrigin = table(dat2$OriginContam, dat2$Sex)
sexTabTransplant = table(dat2$TransplantContam, dat2$Sex)
sexTabInj = table(dat2$Injection, dat2$Sex)
sexTabTriple = table(dat2$CxO2xI, dat2$Sex)5.1.1 Visualize the data
par(mfrow=c(3,2))
plot(sexTabCage, main = "Cage number", ylab = "sex")
plot(sexTabOrigin, main = "Origin site", ylab = "sex")
plot(sexTabTransplant, main = "Transplant site", ylab = "sex")
plot(sexTabInj, main = "Injection", ylab = "sex")
plot(sexTabTriple, main = "All_treatments", ylab = "sex")
### Test sex distribution among cages using Chi square test
chi = chisq.test(sexTabCage)## Warning in chisq.test(sexTabCage): Chi-squared approximation may be incorrectcontrib <- 100 * chi$residuals ^ 2 / chi$statistic
chi##
## Pearson's Chi-squared test
##
## data: sexTabCage
## X-squared = 31.578, df = 23, p-value = 0.1093While some cages contains more female than male, the global pattern
is not significant
since Chi-squared approximation may be incorrect, run fisher exact test
to confirm this result :
fisher.test(sexTabCage, simulate.p.value = TRUE)##
## Fisher's Exact Test for Count Data with simulated p-value (based on
## 2000 replicates)
##
## data: sexTabCage
## p-value = 0.07696
## alternative hypothesis: two.sidedFisher test is non-significant, which confirm the result of the Chisquare-test
5.1.2 What about sex distribution among treatments: origin ?
chi = chisq.test(sexTabOrigin)
contrib <- 100 * chi$residuals ^ 2 / chi$statistic
chi##
## Pearson's Chi-squared test with Yates' continuity correction
##
## data: sexTabOrigin
## X-squared = 0.11037, df = 1, p-value = 0.7397As observed on the plot and as confirmed by chisquare test,
distribution of male and female is balanced among populations origin
5.1.3 What about sex distribution among treatments: TransplantContam ?
chi = chisq.test(sexTabTransplant)
contrib <- 100 * chi$residuals ^ 2 / chi$statistic
chi##
## Pearson's Chi-squared test with Yates' continuity correction
##
## data: sexTabTransplant
## X-squared = 0.11037, df = 1, p-value = 0.7397As observed on the plot and as confirmed by chisquare test,
distribution of male and female is balanced between TransplantContam
treatments
5.1.4 What about sex distribution among treatments: Injection ?
chi = chisq.test(sexTabInj)
contrib <- 100 * chi$residuals ^ 2 / chi$statistic
chi##
## Pearson's Chi-squared test with Yates' continuity correction
##
## data: sexTabInj
## X-squared = 1.3894, df = 1, p-value = 0.2385As observed on the plot and as confirmed by chisquare test,
distribution of male and female is balanced between Injection
treatments
5.1.5 What about sex distribution among treatments: triple combination of treatments ?
chi = chisq.test(sexTabTriple)
contrib <- 100 * chi$residuals ^ 2 / chi$statistic
chi##
## Pearson's Chi-squared test
##
## data: sexTabTriple
## X-squared = 7.7457, df = 7, p-value = 0.3556As observed on the plot and as confirmed by chisquare test,
distribution of male and female is more or less balanced among
treatments
5.2 Test distribution of fish weight among treatments (at the beginning of the experiment, using WeightStart)
Visualize the data
dat2 <- dat1[is.na(dat1$WeightStart) == F, ]
par(mfrow = c(2, 2))
hist(log(dat2$WeightStart),
main = "WeightStart distribution (log-transformed)")
boxplot(log(WeightStart) ~ OriginContam,
data = dat2,
main = "WeightStart vs. \nContam. level at origin site (log-transformed)")
boxplot(log(WeightStart) ~ TransplantContam,
data = dat2,
main = "WeightStart vs. \nContam. level at transplant site (log-transformed)")
boxplot(log(WeightStart) ~ Injection,
data = dat2,
main = "WeightStart vs. \nimmune challenge (log-transformed)")
Create the full model
mod1 <- lme4::lmer(
log(WeightStart) ~ TransplantContam * OriginContam * Injection +
(1 | CagingSite / CageSiteID) + (1 | OriginSite),
data = dat2
)
performance::check_model(mod1)
car::Anova(mod1, type = "3")## Analysis of Deviance Table (Type III Wald chisquare tests)
##
## Response: log(WeightStart)
## Chisq Df Pr(>Chisq)
## (Intercept) 49.1325 1 2.392e-12 ***
## TransplantContam 0.7673 1 0.3810
## OriginContam 0.0335 1 0.8548
## Injection 0.2716 1 0.6023
## TransplantContam:OriginContam 0.0575 1 0.8104
## TransplantContam:Injection 0.0075 1 0.9308
## OriginContam:Injection 0.0177 1 0.8941
## TransplantContam:OriginContam:Injection 0.0003 1 0.9871
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1summary(mod1)## Linear mixed model fit by REML ['lmerMod']
## Formula: log(WeightStart) ~ TransplantContam * OriginContam * Injection +
## (1 | CagingSite/CageSiteID) + (1 | OriginSite)
## Data: dat2
##
## REML criterion at convergence: 233.5
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -2.79246 -0.64175 -0.02739 0.62911 2.92879
##
## Random effects:
## Groups Name Variance Std.Dev.
## CageSiteID:CagingSite (Intercept) 0.005362 0.07323
## CagingSite (Intercept) 0.009039 0.09507
## OriginSite (Intercept) 0.238754 0.48863
## Residual 0.117980 0.34348
## Number of obs: 274, groups:
## CageSiteID:CagingSite, 24; CagingSite, 4; OriginSite, 4
##
## Fixed effects:
## Estimate Std. Error t value
## (Intercept) 2.510397 0.358144 7.009
## TransplantContamLC -0.116490 0.132982 -0.876
## OriginContamLC -0.090998 0.497147 -0.183
## InjectionPBS 0.043809 0.084066 0.521
## TransplantContamLC:OriginContamLC 0.031222 0.130154 0.240
## TransplantContamLC:InjectionPBS -0.010287 0.118470 -0.087
## OriginContamLC:InjectionPBS -0.015510 0.116522 -0.133
## TransplantContamLC:OriginContamLC:InjectionPBS -0.002688 0.166541 -0.016
##
## Correlation of Fixed Effects:
## (Intr) TrnCLC OrgCLC InjPBS TrCLC:OCLC TCLC:I OCLC:I
## TrnsplntCLC -0.187
## OrignCntmLC -0.695 0.066
## InjectinPBS -0.116 0.312 0.083
## TrnCLC:OCLC 0.094 -0.500 -0.130 -0.319
## TrnCLC:IPBS 0.082 -0.436 -0.059 -0.710 0.445
## OrgCLC:IPBS 0.083 -0.225 -0.114 -0.722 0.436 0.512
## TCLC:OCLC:I -0.058 0.310 0.080 0.505 -0.617 -0.712 -0.700now, refine the model using AIC
mod1 =lme4::lmer(
log(WeightStart) ~ TransplantContam * OriginContam * Injection +
(1 | CagingSite / CageSiteID) + (1 | OriginSite),
data = dat2,
REML = FALSE,
na.action = "na.fail"
)
MuMIn::dredge(mod1, rank = "AIC")## Global model call: lme4::lmer(formula = log(WeightStart) ~ TransplantContam * OriginContam *
## Injection + (1 | CagingSite/CageSiteID) + (1 | OriginSite),
## data = dat2, REML = FALSE, na.action = "na.fail")
## ---
## Model selection table
## (Int) Inj OrC TrC Inj:OrC Inj:TrC OrC:TrC Inj:OrC:TrC df logLik AIC
## 1 2.429 5 -108.035 226.1
## 5 2.483 + 6 -107.337 226.7
## 2 2.414 + 6 -107.764 227.5
## 3 2.471 + 6 -108.007 228.0
## 6 2.468 + + 7 -107.065 228.1
## 7 2.524 + + 7 -107.308 228.6
## 4 2.456 + + 7 -107.736 229.5
## 8 2.509 + + + 8 -107.037 230.1
## 22 2.465 + + + 8 -107.056 230.1
## 39 2.532 + + + 8 -107.264 230.5
## 12 2.452 + + + 8 -107.715 231.4
## 40 2.517 + + + + 9 -106.992 232.0
## 16 2.505 + + + + 9 -107.015 232.0
## 24 2.507 + + + + 9 -107.027 232.1
## 48 2.513 + + + + + 10 -106.970 233.9
## 56 2.514 + + + + + 10 -106.983 234.0
## 32 2.502 + + + + + 10 -107.004 234.0
## 64 2.510 + + + + + + 11 -106.961 235.9
## 128 2.510 + + + + + + + 12 -106.961 237.9
## delta weight
## 1 0.00 0.245
## 5 0.60 0.181
## 2 1.46 0.118
## 3 1.94 0.093
## 6 2.06 0.087
## 7 2.55 0.069
## 4 3.40 0.045
## 8 4.00 0.033
## 22 4.04 0.032
## 39 4.46 0.026
## 12 5.36 0.017
## 40 5.91 0.013
## 16 5.96 0.012
## 24 5.98 0.012
## 48 7.87 0.005
## 56 7.90 0.005
## 32 7.94 0.005
## 64 9.85 0.002
## 128 11.85 0.001
## Models ranked by AIC(x)
## Random terms (all models):
## '1 | CagingSite/CageSiteID', '1 | OriginSite'The best model is the null model meaning that fish mass were not
significantly different among treatments
run the model with simple treatments effect to obtain NS p-value
(reported in material & methods)
mod2 = lme4::lmer(
log(WeightStart) ~ TransplantContam + OriginContam + Injection +
(1 | CagingSite / CageSiteID) + (1 | OriginSite),
data = dat2,
)
car::Anova(mod2, type = "3")## Analysis of Deviance Table (Type III Wald chisquare tests)
##
## Response: log(WeightStart)
## Chisq Df Pr(>Chisq)
## (Intercept) 49.8378 1 1.67e-12 ***
## TransplantContam 0.9723 1 0.3241
## OriginContam 0.0290 1 0.8649
## Injection 0.5419 1 0.4617
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1summary(mod2)## Linear mixed model fit by REML ['lmerMod']
## Formula: log(WeightStart) ~ TransplantContam + OriginContam + Injection +
## (1 | CagingSite/CageSiteID) + (1 | OriginSite)
## Data: dat2
##
## REML criterion at convergence: 222.9
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -2.77716 -0.63120 -0.03151 0.63460 2.92805
##
## Random effects:
## Groups Name Variance Std.Dev.
## CageSiteID:CagingSite (Intercept) 0.004712 0.06864
## CagingSite (Intercept) 0.009156 0.09569
## OriginSite (Intercept) 0.238929 0.48880
## Residual 0.116574 0.34143
## Number of obs: 274, groups:
## CageSiteID:CagingSite, 24; CagingSite, 4; OriginSite, 4
##
## Fixed effects:
## Estimate Std. Error t value
## (Intercept) 2.50934 0.35545 7.060
## TransplantContamLC -0.10643 0.10793 -0.986
## OriginContamLC -0.08362 0.49135 -0.170
## InjectionPBS 0.03044 0.04135 0.736
##
## Correlation of Fixed Effects:
## (Intr) TrnCLC OrgCLC
## TrnsplntCLC -0.152
## OrignCntmLC -0.691 0.001
## InjectinPBS -0.057 0.004 0.001Compute mean and Sd of fish Weight (reported in material & methods)
mean(dat2$WeightStart)## [1] 12.93686sd(dat2$WeightStart)## [1] 6.9338315.3 Test Distribution of fish size among treatments (at the beginning of the experiment, using SizeStart)
Visualize the data
dat2 = dat1[is.na(dat1$SizeStart) == F, ]
par(mfrow = c(2, 2))
hist(log(dat2$SizeStart),
main = "SizeStart distribution (log-transformed)")
boxplot(log(SizeStart) ~ OriginContam,
data = dat2,
main = "SizeStart vs. \nContam. level at origin site (log-transformed)")
boxplot(log(SizeStart) ~ TransplantContam,
data = dat2,
main = "SizeStart vs. \nContam. level at transplant site (log-transformed)")
boxplot(log(SizeStart) ~ Injection,
data = dat2,
main = "SizeStart vs. \nimmune challenge (log-transformed)")
Create the full model
mod1 <- lme4::lmer(
log(SizeStart) ~ TransplantContam * OriginContam * Injection +
(1 | CagingSite / CageSiteID) + (1 | OriginSite),
data = dat2
)
performance::check_model(mod1)
car::Anova(mod1, type = "3")## Analysis of Deviance Table (Type III Wald chisquare tests)
##
## Response: log(SizeStart)
## Chisq Df Pr(>Chisq)
## (Intercept) 509.4453 1 <2e-16 ***
## TransplantContam 0.8929 1 0.3447
## OriginContam 0.0191 1 0.8900
## Injection 0.1480 1 0.7005
## TransplantContam:OriginContam 0.0666 1 0.7964
## TransplantContam:Injection 0.0073 1 0.9318
## OriginContam:Injection 0.1812 1 0.6703
## TransplantContam:OriginContam:Injection 0.0679 1 0.7945
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1summary(mod1)## Linear mixed model fit by REML ['lmerMod']
## Formula: log(SizeStart) ~ TransplantContam * OriginContam * Injection +
## (1 | CagingSite/CageSiteID) + (1 | OriginSite)
## Data: dat2
##
## REML criterion at convergence: -336.1
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -3.01022 -0.72980 -0.01529 0.62898 2.69373
##
## Random effects:
## Groups Name Variance Std.Dev.
## CageSiteID:CagingSite (Intercept) 0.0002450 0.01565
## CagingSite (Intercept) 0.0007335 0.02708
## OriginSite (Intercept) 0.0192863 0.13888
## Residual 0.0141330 0.11888
## Number of obs: 274, groups:
## CageSiteID:CagingSite, 24; CagingSite, 4; OriginSite, 4
##
## Fixed effects:
## Estimate Std. Error t value
## (Intercept) 2.309201 0.102309 22.571
## TransplantContamLC -0.038222 0.040448 -0.945
## OriginContamLC -0.019636 0.141983 -0.138
## InjectionPBS 0.011188 0.029083 0.385
## TransplantContamLC:OriginContamLC 0.010833 0.041983 0.258
## TransplantContamLC:InjectionPBS -0.003507 0.040977 -0.086
## OriginContamLC:InjectionPBS -0.017157 0.040302 -0.426
## TransplantContamLC:OriginContamLC:InjectionPBS 0.015005 0.057604 0.260
##
## Correlation of Fixed Effects:
## (Intr) TrnCLC OrgCLC InjPBS TrCLC:OCLC TCLC:I OCLC:I
## TrnsplntCLC -0.199
## OrignCntmLC -0.695 0.080
## InjectinPBS -0.140 0.354 0.101
## TrnCLC:OCLC 0.107 -0.532 -0.146 -0.342
## TrnCLC:IPBS 0.099 -0.496 -0.072 -0.710 0.478
## OrgCLC:IPBS 0.101 -0.256 -0.138 -0.722 0.468 0.512
## TCLC:OCLC:I -0.071 0.353 0.097 0.505 -0.662 -0.712 -0.700now, refine the model using AIC
mod1 =lme4::lmer(
log(SizeStart) ~ TransplantContam * OriginContam * Injection +
(1 | CagingSite / CageSiteID) + (1 | OriginSite),
data = dat2,
REML = FALSE,
na.action = "na.fail"
)
MuMIn::dredge(mod1, rank = "AIC")## Global model call: lme4::lmer(formula = log(SizeStart) ~ TransplantContam * OriginContam *
## Injection + (1 | CagingSite/CageSiteID) + (1 | OriginSite),
## data = dat2, REML = FALSE, na.action = "na.fail")
## ---
## Model selection table
## (Int) Inj OrC TrC Inj:OrC Inj:TrC OrC:TrC Inj:OrC:TrC df logLik AIC
## 1 2.285 5 185.981 -362.0
## 5 2.301 + 6 186.677 -361.4
## 2 2.283 + 6 186.029 -360.1
## 3 2.295 + 6 185.999 -360.0
## 6 2.299 + + 7 186.724 -359.4
## 7 2.310 + + 7 186.695 -359.4
## 4 2.292 + + 7 186.047 -358.1
## 39 2.315 + + + 8 186.863 -357.7
## 8 2.308 + + + 8 186.742 -357.5
## 22 2.300 + + + 8 186.736 -357.5
## 12 2.290 + + + 8 186.110 -356.2
## 40 2.312 + + + + 9 186.911 -355.8
## 16 2.305 + + + + 9 186.808 -355.6
## 24 2.309 + + + + 9 186.754 -355.5
## 48 2.310 + + + + + 10 186.976 -354.0
## 56 2.314 + + + + + 10 186.924 -353.8
## 32 2.306 + + + + + 10 186.817 -353.6
## 64 2.311 + + + + + + 11 186.986 -352.0
## 128 2.309 + + + + + + + 12 187.024 -350.0
## delta weight
## 1 0.00 0.265
## 5 0.61 0.195
## 2 1.90 0.102
## 3 1.96 0.099
## 6 2.51 0.075
## 7 2.57 0.073
## 4 3.87 0.038
## 39 4.24 0.032
## 8 4.48 0.028
## 22 4.49 0.028
## 12 5.74 0.015
## 40 6.14 0.012
## 16 6.35 0.011
## 24 6.46 0.010
## 48 8.01 0.005
## 56 8.12 0.005
## 32 8.33 0.004
## 64 9.99 0.002
## 128 11.91 0.001
## Models ranked by AIC(x)
## Random terms (all models):
## '1 | CagingSite/CageSiteID', '1 | OriginSite'The best model is the null model meaning that fish mass were not
significantly different among treatments
run the model with simple treatments effect to obtain NS p-value
(reported in material & methods)
mod2 = lme4::lmer(
log(SizeStart) ~ TransplantContam + OriginContam + Injection +
(1 | CagingSite / CageSiteID) + (1 | OriginSite),
data = dat2,
)
car::Anova(mod2, type = "3")## Analysis of Deviance Table (Type III Wald chisquare tests)
##
## Response: log(SizeStart)
## Chisq Df Pr(>Chisq)
## (Intercept) 519.3942 1 <2e-16 ***
## TransplantContam 0.9642 1 0.3261
## OriginContam 0.0186 1 0.8916
## Injection 0.0953 1 0.7575
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1summary(mod2)## Linear mixed model fit by REML ['lmerMod']
## Formula: log(SizeStart) ~ TransplantContam + OriginContam + Injection +
## (1 | CagingSite/CageSiteID) + (1 | OriginSite)
## Data: dat2
##
## REML criterion at convergence: -355
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -3.00146 -0.72982 -0.02693 0.63527 2.70416
##
## Random effects:
## Groups Name Variance Std.Dev.
## CageSiteID:CagingSite (Intercept) 0.0002086 0.01444
## CagingSite (Intercept) 0.0007474 0.02734
## OriginSite (Intercept) 0.0193006 0.13893
## Residual 0.0139709 0.11820
## Number of obs: 274, groups:
## CageSiteID:CagingSite, 24; CagingSite, 4; OriginSite, 4
##
## Fixed effects:
## Estimate Std. Error t value
## (Intercept) 2.307936 0.101269 22.790
## TransplantContamLC -0.030846 0.031412 -0.982
## OriginContamLC -0.019052 0.139785 -0.136
## InjectionPBS 0.004417 0.014307 0.309
##
## Correlation of Fixed Effects:
## (Intr) TrnCLC OrgCLC
## TrnsplntCLC -0.156
## OrignCntmLC -0.691 0.001
## InjectinPBS -0.070 0.004 0.001Compute mean and Sd of fish size (reported in material & methods)
mean(dat2$SizeStart)## [1] 9.962044sd(dat2$SizeStart)## [1] 1.5890715.4 Test for Crowding
5.4.1 Compute mean and Sd of fish density per liter (reported in material & methods)
- At the start of the experiment
Crowd = aggregate(dat1$WeightStart, list(dat1$CageID), sum)
Crowd$dens = Crowd$x / 130 # 130 is the volume of the cages in liters
mean(Crowd$dens) # expressed in grams of fish per liter of water within the cage## [1] 1.136122sd(Crowd$dens)## [1] 0.4599962- At the end of the experiment
dat2 = dat1[is.na(dat1$Death) == F, ]
dat2 = dat2[-c(which(dat2$Death == 1)), ]
Crowd2 = aggregate(dat2$WeightEnd, list(dat2$CageID), function(x)
sum(x, na.rm = T))
Crowd2$dens = Crowd2$x / 130 # 130 is the volume of the cages in liters
mean(Crowd2$dens)## [1] 0.9001603sd(Crowd2$dens)## [1] 0.37838535.4.2 Test for the difference between start and end of the experiment
CrowdTest = cbind(Crowd$dens, Crowd2$dens)
chi = chisq.test(CrowdTest)## Warning in chisq.test(CrowdTest): Chi-squared approximation may be incorrectcontrib <- 100 * chi$residuals ^ 2 / chi$statistic
chi##
## Pearson's Chi-squared test
##
## data: CrowdTest
## X-squared = 0.47726, df = 23, p-value = 1# Here the test confirmed that density of fish is not significantly different among cages
# but since Chi-squared approximation may be incorrect, run fisher exact test to confirm this result :
fisher.test(round(CrowdTest, 1)*10, simulate.p.value = TRUE) # Round values to the first decimal and multiply by 10 to have integer only (necessary for fisher-test)##
## Fisher's Exact Test for Count Data with simulated p-value (based on
## 2000 replicates)
##
## data: round(CrowdTest, 1) * 10
## p-value = 1
## alternative hypothesis: two.sidedFisher test is non-significant, confirming the result of the Chisquare-test: The density of fish is not significantly different among cages between the start and end of the experiment, hence, While there was some death in several cages, the global pattern is not significant
5.5 Check Toxic Unit (TU) consistency among studies and between the start and end of the experiment
Retrieve the TU reported in PETITJEAN et al. 2020 a,b (based on water agency database)
Tu2020 = c(-0.9,-0.9,-0.3, 1.3)Retrieve the global TU reported in the present study
based on water samples collected in this study, both at the start and
end of the experiment
TuStart = c(-0.4,-0.5,-0.1, 1.1)
TuEnd = c(-0.3,-0.7, 0.3, 0.9)
TuGlobal = c(-0.4,-0.6, 0.2, 1.0)
Tutab = cbind(Tu2020, TuGlobal)
Tutab2 = cbind(TuStart, TuEnd)5.5.1 Visualize
par(mfrow = c(1, 2))
plot(Tutab,
xlab = "TU2020",
ylab = "TUGlobal",
main = "Global TU vs. previous studies")
plot(Tutab2,
xlab = "TuStart",
ylab = "TuEnd",
main = "TU measured at the end of this study \n vs. \n TU measured at the start of this study")
5.5.2 Test the difference among global and TU reported in this study and reported in PETITJEAN et al. 2020 a,b
chi = chisq.test(Tutab + 1) # add 1 to each values to ensure TU is positive (necessary for chi-test)## Warning in chisq.test(Tutab + 1): Chi-squared approximation may be incorrectcontrib <- 100 * chi$residuals ^ 2 / chi$statistic
chi##
## Pearson's Chi-squared test
##
## data: Tutab + 1
## X-squared = 0.56483, df = 3, p-value = 0.9044# Here the test confirmed that Toxic units are not significantly different among studies
# but since Chi-squared approximation may be incorrect, run fisher exact test to confirm this result :
fisher.test((Tutab + 1)*10, simulate.p.value = TRUE) # add 1 to each values to ensure TU is positive and multiply by 10 to have integer only (necessary for fisher-test)##
## Fisher's Exact Test for Count Data with simulated p-value (based on
## 2000 replicates)
##
## data: (Tutab + 1) * 10
## p-value = 0.1489
## alternative hypothesis: two.sidedFisher test is non-significant, confirming the result of the Chisquare-test: The toxic units are not significantly different among studies
5.5.3 Test the difference in Toxic Unit between the start and the end of the experiment
chi = chisq.test(Tutab2 + 1) # add 1 to each values to ensure TU is positive (necessary for chi-test)## Warning in chisq.test(Tutab2 + 1): Chi-squared approximation may be incorrectcontrib <- 100 * chi$residuals ^ 2 / chi$statistic
chi##
## Pearson's Chi-squared test
##
## data: Tutab2 + 1
## X-squared = 0.13923, df = 3, p-value = 0.9867# Here the test confirmed that Toxic units are not significantly different between the start and the end of the experiment
# but since Chi-squared approximation may be incorrect, run fisher exact test to confirm this result :
fisher.test((Tutab2 + 1)*10, simulate.p.value = TRUE) # add 1 to each values to ensure TU is positive and multiply by 10 to have integer only (necessary for fisher-test)##
## Fisher's Exact Test for Count Data with simulated p-value (based on
## 2000 replicates)
##
## data: (Tutab2 + 1) * 10
## p-value = 0.7096
## alternative hypothesis: two.sidedFisher test is non-significant, confirming the result of the Chisquare-test: the toxic units are not significantly different between the start and the end of the experiment
6 Data analyses
A quick reminder:
- Treatments (fixed effects):
- TransplantContam (transplant treatment either High contamination-HC
or Low contamination-LC)
- OriginContam (Origin of the population either High contamination-HC
or Low contamination-LC)
- Injection (control saline: PBS, antigen mixture: AMIX)
- TransplantContam (transplant treatment either High contamination-HC
or Low contamination-LC)
- Covariates :
- SizeEnd (Fish size at the end of the experiment)
- Sex (Fish sex determined by visual inspection at the end of the
experiment)
- SizeEnd (Fish size at the end of the experiment)
- Blocks (random effects):
- CagingSite (The name of the study site where fish are caged, either
ARIMAS, AUSCOR, CELFIG or RIOU)
- CageSiteID (The ID number ranging from 1 to 6 corresponding to the
number of the cage within each study site)
- OriginSite (The name of the site where each population were sampled
= population ID)
- CagingSite (The name of the study site where fish are caged, either
ARIMAS, AUSCOR, CELFIG or RIOU)
Here we used The identity of the cage nested within the study site as
random effects
to consider possible shared conditions within the cage and the study
site.
Best models were selected by backward selection procedure, eliminating non-significant interactions and variables (i.e., p-value > 0.05).
When interactions were found significant, we analyzed differences between groups using pairwise t-test with false discovery rate adjustment (Benjamini and Hochberg, 1995) or two-sample fisher’s exact test for count data (i.e., survival) (Agresti, 2007), respectively.
In addition, when interactions between the level of contamination in the transplant site and the origin of the population (i.e., HC or LC) were significant, we tested whether slopes were parallel among replicates populations by comparing models including the level of contamination in transplant site (i.e., HC or LC) and the identity of the origin of the population (i.e., ARIMAS, AUSCOR or CELFIG, RIOU) with models including the interaction between the level of contamination in transplant site and the identity of the origin of the population according to (Jacquin et al., 2016).
NB: The results retrieved from the following refined models are reported in Table 3 of the manuscript. The table 3 can also be found in the section “Summary of the best models (Table 3 from the manuscript)”
6.1 Survival
dat2 = dat1[is.na(dat1$Death) == F, ]
par(mfrow = c(1,2))
plot(dat2$Death)
hist(dat2$Death)
The data are binomial, so use glmer function from lme4 package to
construct the full model: ### Use GLMER with family binomial
modfull <-
lme4::glmer(
Death ~ (TransplantContam + OriginContam + Injection) ^ 3 + (1 | CagingSite / CageSiteID) + (1| OriginSite),
data = dat2,
family = binomial(link = "logit"),
na.action = na.fail
)
performance::check_model(modfull)
car::Anova(modfull, type = "3")## Analysis of Deviance Table (Type III Wald chisquare tests)
##
## Response: Death
## Chisq Df Pr(>Chisq)
## (Intercept) 0.0083 1 0.9273
## TransplantContam 0.0062 1 0.9373
## OriginContam 0.0072 1 0.9326
## Injection 0.0000 1 0.9997
## TransplantContam:OriginContam 0.0077 1 0.9303
## TransplantContam:Injection 0.0023 1 0.9621
## OriginContam:Injection 0.0000 1 0.9989
## TransplantContam:OriginContam:Injection 0.0024 1 0.9612summary(modfull)## Generalized linear mixed model fit by maximum likelihood (Laplace
## Approximation) [glmerMod]
## Family: binomial ( logit )
## Formula: Death ~ (TransplantContam + OriginContam + Injection)^3 + (1 |
## CagingSite/CageSiteID) + (1 | OriginSite)
## Data: dat2
##
## AIC BIC logLik deviance df.resid
## 136.3 175.8 -57.2 114.3 257
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -0.7322 -0.2658 -0.1625 0.0000 5.7648
##
## Random effects:
## Groups Name Variance Std.Dev.
## CageSiteID:CagingSite (Intercept) 2.912e-01 5.396e-01
## CagingSite (Intercept) 1.310e-10 1.144e-05
## OriginSite (Intercept) 0.000e+00 0.000e+00
## Number of obs: 268, groups:
## CageSiteID:CagingSite, 24; CagingSite, 4; OriginSite, 4
##
## Fixed effects:
## Estimate Std. Error z value
## (Intercept) -21.4406 235.0225 -0.091
## TransplantContamLC 18.4876 235.0224 0.079
## OriginContamLC 19.8733 235.0222 0.085
## InjectionPBS -0.1350 406.2111 0.000
## TransplantContamLC:OriginContamLC -20.5680 235.0231 -0.088
## TransplantContamLC:InjectionPBS -18.6017 391.4285 -0.048
## OriginContamLC:InjectionPBS 0.5503 406.2112 0.001
## TransplantContamLC:OriginContamLC:InjectionPBS 19.0396 391.4280 0.049
## Pr(>|z|)
## (Intercept) 0.927
## TransplantContamLC 0.937
## OriginContamLC 0.933
## InjectionPBS 1.000
## TransplantContamLC:OriginContamLC 0.930
## TransplantContamLC:InjectionPBS 0.962
## OriginContamLC:InjectionPBS 0.999
## TransplantContamLC:OriginContamLC:InjectionPBS 0.961
##
## Correlation of Fixed Effects:
## (Intr) TrnCLC OrgCLC InjPBS TrCLC:OCLC TCLC:I OCLC:I
## TrnsplntCLC -1.000
## OrignCntmLC -1.000 1.000
## InjectinPBS -0.020 0.020 0.020
## TrnCLC:OCLC 1.000 -1.000 -1.000 -0.020
## TrnCLC:IPBS -0.019 0.019 0.019 -0.148 -0.019
## OrgCLC:IPBS 0.020 -0.020 -0.020 -1.000 0.020 0.148
## TCLC:OCLC:I 0.019 -0.019 -0.019 0.148 0.019 -1.000 -0.148
## optimizer (Nelder_Mead) convergence code: 0 (OK)
## boundary (singular) fit: see ?isSingularMuMIn::r.squaredGLMM(modfull)## R2m R2c
## theoretical 0.9595305 0.9628213
## delta 0.8477609 0.8506684The model returns a singular fit, the random structure seems too complex for the data since “OriginSite” have a variance of zero. To solve this, we can use two alternative methods:
6.1.1 Use classic glm with family binomial (remove random effects)
modfull <-
glm(
Death ~ (TransplantContam + OriginContam + Injection) ^ 3,
data = dat2,
family = "binomial"
)
car::Anova(modfull, type = "3")## Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred
## Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred## Analysis of Deviance Table (Type III tests)
##
## Response: Death
## LR Chisq Df Pr(>Chisq)
## TransplantContam 2.7138 1 0.099486 .
## OriginContam 9.6183 1 0.001927 **
## Injection 0.0000 1 1.000000
## TransplantContam:OriginContam 6.2985 1 0.012084 *
## TransplantContam:Injection 0.0000 1 1.000000
## OriginContam:Injection 0.0000 1 0.999960
## TransplantContam:OriginContam:Injection 0.0000 1 1.000000
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1summary(modfull)##
## Call:
## glm(formula = Death ~ (TransplantContam + OriginContam + Injection)^3,
## family = "binomial", data = dat2)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -0.77104 -0.36522 -0.24078 -0.00008 2.66659
##
## Coefficients:
## Estimate Std. Error z value
## (Intercept) -1.957e+01 1.872e+03 -0.010
## TransplantContamLC 1.676e+01 1.872e+03 0.009
## OriginContamLC 1.811e+01 1.872e+03 0.010
## InjectionPBS -9.667e-09 2.713e+03 0.000
## TransplantContamLC:OriginContamLC -1.883e+01 1.872e+03 -0.010
## TransplantContamLC:InjectionPBS -1.676e+01 3.313e+03 -0.005
## OriginContamLC:InjectionPBS 3.944e-01 2.713e+03 0.000
## TransplantContamLC:OriginContamLC:InjectionPBS 1.722e+01 3.313e+03 0.005
## Pr(>|z|)
## (Intercept) 0.992
## TransplantContamLC 0.993
## OriginContamLC 0.992
## InjectionPBS 1.000
## TransplantContamLC:OriginContamLC 0.992
## TransplantContamLC:InjectionPBS 0.996
## OriginContamLC:InjectionPBS 1.000
## TransplantContamLC:OriginContamLC:InjectionPBS 0.996
##
## (Dispersion parameter for binomial family taken to be 1)
##
## Null deviance: 147.26 on 267 degrees of freedom
## Residual deviance: 115.04 on 260 degrees of freedom
## AIC: 131.04
##
## Number of Fisher Scoring iterations: 186.1.1.1 Refine the model
mod2 <-
glm(
Death ~ (TransplantContam + OriginContam + Injection) ^ 2,
data = dat2,
family = "binomial"
)## Warning: glm.fit: fitted probabilities numerically 0 or 1 occurredcar::Anova(mod2, type = "3")## Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred## Analysis of Deviance Table (Type III tests)
##
## Response: Death
## LR Chisq Df Pr(>Chisq)
## TransplantContam 2.7138 1 0.099486 .
## OriginContam 9.6183 1 0.001927 **
## Injection 2.2948 1 0.129805
## TransplantContam:OriginContam 6.2985 1 0.012084 *
## TransplantContam:Injection 0.1140 1 0.735627
## OriginContam:Injection 3.0363 1 0.081423 .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1summary(mod2)##
## Call:
## glm(formula = Death ~ (TransplantContam + OriginContam + Injection)^2,
## family = "binomial", data = dat2)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -0.77104 -0.36522 -0.24078 -0.00007 2.66659
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -19.6981 1999.7748 -0.010 0.992
## TransplantContamLC 16.8947 1999.7749 0.008 0.993
## OriginContamLC 18.2428 1999.7748 0.009 0.993
## InjectionPBS -17.3332 2011.2531 -0.009 0.993
## TransplantContamLC:OriginContamLC -18.9658 1999.7752 -0.009 0.992
## TransplantContamLC:InjectionPBS 0.4578 1.3746 0.333 0.739
## OriginContamLC:InjectionPBS 17.7276 2011.2531 0.009 0.993
##
## (Dispersion parameter for binomial family taken to be 1)
##
## Null deviance: 147.26 on 267 degrees of freedom
## Residual deviance: 115.04 on 261 degrees of freedom
## AIC: 129.04
##
## Number of Fisher Scoring iterations: 196.1.1.2 Refine the model
mod3 <-
glm(
Death ~ (TransplantContam + OriginContam) ^ 2 + Injection,
data = dat2,
family = "binomial"
)
car::Anova(mod3, type = "3")## Analysis of Deviance Table (Type III tests)
##
## Response: Death
## LR Chisq Df Pr(>Chisq)
## TransplantContam 2.6805 1 0.10159
## OriginContam 21.9792 1 2.756e-06 ***
## Injection 0.1708 1 0.67940
## TransplantContam:OriginContam 6.5855 1 0.01028 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1summary(mod3)##
## Call:
## glm(formula = Death ~ (TransplantContam + OriginContam)^2 + Injection,
## family = "binomial", data = dat2)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -0.74070 -0.32045 -0.25853 -0.00008 2.68644
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -19.6644 1353.9148 -0.015 0.988
## TransplantContamLC 16.0834 1353.9150 0.012 0.991
## OriginContamLC 18.3121 1353.9148 0.014 0.989
## InjectionPBS 0.1991 0.4821 0.413 0.680
## TransplantContamLC:OriginContamLC -17.8737 1353.9152 -0.013 0.989
##
## (Dispersion parameter for binomial family taken to be 1)
##
## Null deviance: 147.26 on 267 degrees of freedom
## Residual deviance: 118.50 on 263 degrees of freedom
## AIC: 128.5
##
## Number of Fisher Scoring iterations: 186.1.1.3 Refine the model
mod4 <-
glm(Death ~ (TransplantContam + OriginContam) ^ 2,
data = dat2,
family = "binomial")
performance::check_model(mod4)
car::Anova(mod4, type = "3")## Analysis of Deviance Table (Type III tests)
##
## Response: Death
## LR Chisq Df Pr(>Chisq)
## TransplantContam 2.6807 1 0.10157
## OriginContam 21.9923 1 2.738e-06 ***
## TransplantContam:OriginContam 6.5915 1 0.01025 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1summary(mod4)##
## Call:
## glm(formula = Death ~ (TransplantContam + OriginContam)^2, family = "binomial",
## data = dat2)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -0.70896 -0.30502 -0.24619 -0.00008 2.65011
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -19.57 1354.88 -0.014 0.988
## TransplantContamLC 16.08 1354.88 0.012 0.991
## OriginContamLC 18.31 1354.88 0.014 0.989
## TransplantContamLC:OriginContamLC -17.88 1354.88 -0.013 0.989
##
## (Dispersion parameter for binomial family taken to be 1)
##
## Null deviance: 147.26 on 267 degrees of freedom
## Residual deviance: 118.67 on 264 degrees of freedom
## AIC: 126.67
##
## Number of Fisher Scoring iterations: 18modSurvival <- mod4Here the interaction between fish origin and the transplant site is significant. Alternatively, we can compute a survival rate per cage and build model with survival transformed to logit
6.1.2 Build model with survival transformed to logit
NB: here we used the CagingSite as random effect only since survival is computed for each cage so that there is no need to add the cageSiteID.
6.1.2.1 Create a new dataset containing survival rate within each cage
dat2$CageIDInj <- paste(dat2$CageID, dat2$Injection, sep = "_")
n = as.data.frame(dplyr::count(dat2, CageIDInj))
names(n)[1] <- "CageIDInj"
names(n)[2] <- "n"
alive <-
as.data.frame(dplyr::count(dat2[dat2$Death == "0", ], CageIDInj))
dead <-
as.data.frame(dplyr::count(dat2[dat2$Death == "1", ], CageIDInj))
DeathSum <- dplyr::left_join(alive, dead, by = "CageIDInj")
DeathSum$n.y[is.na(DeathSum$n.y)] <- 0
DeathSum <- dplyr::left_join(DeathSum, n, by = "CageIDInj")
names(DeathSum)[2] <- "alive"
names(DeathSum)[3] <- "dead"
DeathSum$survival <- DeathSum$alive / DeathSum$n
DeathSum <- dplyr::left_join(DeathSum,
dat2[match(DeathSum$CageIDInj, dat2$CageIDInj), c(
"CageIDInj",
"CageID",
"OriginSite",
"OriginContam",
"SitesPair",
"CageSiteID",
"CagingSite",
"TransplantContam",
"Injection",
"CxOxI",
"CxO2xI",
"CxO",
"O2xI"
)], by = "CageIDInj")6.1.2.2 Build the full model
modfull <-
lme4::lmer(
car::logit(survival) ~ (TransplantContam + OriginContam + Injection) ^ 3 +
(1 | CagingSite) + (1 | OriginSite),
data = DeathSum,
na.action = na.exclude
)## Warning in car::logit(survival): proportions remapped to (0.025, 0.975)
## Warning in car::logit(survival): proportions remapped to (0.025, 0.975)
## Warning in car::logit(survival): proportions remapped to (0.025, 0.975)car::Anova(modfull, type = "3")## Analysis of Deviance Table (Type III Wald chisquare tests)
##
## Response: car::logit(survival)
## Chisq Df Pr(>Chisq)
## (Intercept) 78.0809 1 < 2.2e-16 ***
## TransplantContam 0.6331 1 0.426220
## OriginContam 8.6911 1 0.003198 **
## Injection 0.0000 1 1.000000
## TransplantContam:OriginContam 4.8891 1 0.027026 *
## TransplantContam:Injection 0.3166 1 0.573688
## OriginContam:Injection 0.1793 1 0.671964
## TransplantContam:OriginContam:Injection 0.1893 1 0.663535
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1summary(modfull)## Linear mixed model fit by REML ['lmerMod']
## Formula:
## car::logit(survival) ~ (TransplantContam + OriginContam + Injection)^3 +
## (1 | CagingSite) + (1 | OriginSite)
## Data: DeathSum
##
## REML criterion at convergence: 129.1
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -2.2969 -0.1086 0.0000 0.4594 2.0478
##
## Random effects:
## Groups Name Variance Std.Dev.
## CagingSite (Intercept) 0.000 0.000
## OriginSite (Intercept) 0.000 0.000
## Residual 1.031 1.016
## Number of obs: 48, groups: CagingSite, 4; OriginSite, 4
##
## Fixed effects:
## Estimate Std. Error t value
## (Intercept) 3.664e+00 4.146e-01 8.836
## TransplantContamLC -4.665e-01 5.863e-01 -0.796
## OriginContamLC -1.729e+00 5.863e-01 -2.948
## InjectionPBS -1.602e-15 5.863e-01 0.000
## TransplantContamLC:OriginContamLC 1.833e+00 8.292e-01 2.211
## TransplantContamLC:InjectionPBS 4.665e-01 8.292e-01 0.563
## OriginContamLC:InjectionPBS -3.511e-01 8.292e-01 -0.423
## TransplantContamLC:OriginContamLC:InjectionPBS -5.102e-01 1.173e+00 -0.435
##
## Correlation of Fixed Effects:
## (Intr) TrnCLC OrgCLC InjPBS TrCLC:OCLC TCLC:I OCLC:I
## TrnsplntCLC -0.707
## OrignCntmLC -0.707 0.500
## InjectinPBS -0.707 0.500 0.500
## TrnCLC:OCLC 0.500 -0.707 -0.707 -0.354
## TrnCLC:IPBS 0.500 -0.707 -0.354 -0.707 0.500
## OrgCLC:IPBS 0.500 -0.354 -0.707 -0.707 0.500 0.500
## TCLC:OCLC:I -0.354 0.500 0.500 0.500 -0.707 -0.707 -0.707
## optimizer (nloptwrap) convergence code: 0 (OK)
## boundary (singular) fit: see ?isSingular6.1.2.3 Refine the model
mod2 <-
lme4::lmer(
car::logit(survival) ~ (TransplantContam + OriginContam + Injection) ^ 2+
(1 | CagingSite) + (1 | OriginSite),
data = DeathSum,
na.action = na.exclude
)## Warning in car::logit(survival): proportions remapped to (0.025, 0.975)
## Warning in car::logit(survival): proportions remapped to (0.025, 0.975)
## Warning in car::logit(survival): proportions remapped to (0.025, 0.975)car::Anova(mod2, type="3")## Analysis of Deviance Table (Type III Wald chisquare tests)
##
## Response: car::logit(survival)
## Chisq Df Pr(>Chisq)
## (Intercept) 87.8938 1 < 2.2e-16 ***
## TransplantContam 0.4547 1 0.500121
## OriginContam 10.1418 1 0.001449 **
## Injection 0.0644 1 0.799735
## TransplantContam:OriginContam 7.3930 1 0.006548 **
## TransplantContam:Injection 0.1327 1 0.715665
## OriginContam:Injection 1.0905 1 0.296361
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1summary(mod2)## Linear mixed model fit by REML ['lmerMod']
## Formula:
## car::logit(survival) ~ (TransplantContam + OriginContam + Injection)^2 +
## (1 | CagingSite) + (1 | OriginSite)
## Data: DeathSum
##
## REML criterion at convergence: 131.4
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -2.38339 -0.17309 0.06342 0.42306 2.13179
##
## Random effects:
## Groups Name Variance Std.Dev.
## CagingSite (Intercept) 0.000 0.000
## OriginSite (Intercept) 0.000 0.000
## Residual 1.011 1.005
## Number of obs: 48, groups: CagingSite, 4; OriginSite, 4
##
## Fixed effects:
## Estimate Std. Error t value
## (Intercept) 3.5998 0.3840 9.375
## TransplantContamLC -0.3390 0.5027 -0.674
## OriginContamLC -1.6010 0.5027 -3.185
## InjectionPBS 0.1275 0.5027 0.254
## TransplantContamLC:OriginContamLC 1.5784 0.5805 2.719
## TransplantContamLC:InjectionPBS 0.2115 0.5805 0.364
## OriginContamLC:InjectionPBS -0.6062 0.5805 -1.044
##
## Correlation of Fixed Effects:
## (Intr) TrnCLC OrgCLC InjPBS TCLC:O TCLC:I
## TrnsplntCLC -0.655
## OrignCntmLC -0.655 0.333
## InjectinPBS -0.655 0.333 0.333
## TrnCLC:OCLC 0.378 -0.577 -0.577 0.000
## TrnCLC:IPBS 0.378 -0.577 0.000 -0.577 0.000
## OrgCLC:IPBS 0.378 0.000 -0.577 -0.577 0.000 0.000
## optimizer (nloptwrap) convergence code: 0 (OK)
## boundary (singular) fit: see ?isSingular6.1.2.4 Refine the model
mod3 <-
lme4::lmer(
car::logit(survival) ~ (TransplantContam + OriginContam) ^ 2 + Injection +
(1 | CagingSite) + (1 | OriginSite),
data = DeathSum,
na.action = na.exclude
)## Warning in car::logit(survival): proportions remapped to (0.025, 0.975)
## Warning in car::logit(survival): proportions remapped to (0.025, 0.975)
## Warning in car::logit(survival): proportions remapped to (0.025, 0.975)car::Anova(mod3, type = "3")## Analysis of Deviance Table (Type III Wald chisquare tests)
##
## Response: car::logit(survival)
## Chisq Df Pr(>Chisq)
## (Intercept) 132.2805 1 < 2.2e-16 ***
## TransplantContam 0.3289 1 0.566321
## OriginContam 21.9139 1 2.852e-06 ***
## Injection 0.0590 1 0.808152
## TransplantContam:OriginContam 7.5290 1 0.006071 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1summary(mod3)## Linear mixed model fit by REML ['lmerMod']
## Formula: car::logit(survival) ~ (TransplantContam + OriginContam)^2 +
## Injection + (1 | CagingSite) + (1 | OriginSite)
## Data: DeathSum
##
## REML criterion at convergence: 134.1
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -2.6104 -0.1017 0.1171 0.5260 1.9462
##
## Random effects:
## Groups Name Variance Std.Dev.
## CagingSite (Intercept) 0.0000 0.0000
## OriginSite (Intercept) 0.0000 0.0000
## Residual 0.9927 0.9963
## Number of obs: 48, groups: CagingSite, 4; OriginSite, 4
##
## Fixed effects:
## Estimate Std. Error t value
## (Intercept) 3.69848 0.32157 11.501
## TransplantContamLC -0.23327 0.40676 -0.573
## OriginContamLC -1.90412 0.40676 -4.681
## InjectionPBS -0.06984 0.28762 -0.243
## TransplantContamLC:OriginContamLC 1.57841 0.57524 2.744
##
## Correlation of Fixed Effects:
## (Intr) TrnCLC OrgCLC InjPBS
## TrnsplntCLC -0.632
## OrignCntmLC -0.632 0.500
## InjectinPBS -0.447 0.000 0.000
## TrnCLC:OCLC 0.447 -0.707 -0.707 0.000
## optimizer (nloptwrap) convergence code: 0 (OK)
## boundary (singular) fit: see ?isSingular6.1.2.5 Refine the model
mod4 <-
lme4::lmer(
car::logit(survival) ~ (TransplantContam + OriginContam) ^ 2 +
(1 | CagingSite) + (1 | OriginSite),
data = DeathSum,
na.action = na.exclude
)## Warning in car::logit(survival): proportions remapped to (0.025, 0.975)
## Warning in car::logit(survival): proportions remapped to (0.025, 0.975)
## Warning in car::logit(survival): proportions remapped to (0.025, 0.975)performance::check_model(mod4)
car::Anova(mod4, type = "3")## Analysis of Deviance Table (Type III Wald chisquare tests)
##
## Response: car::logit(survival)
## Chisq Df Pr(>Chisq)
## (Intercept) 165.7888 1 < 2.2e-16 ***
## TransplantContam 0.3361 1 0.562109
## OriginContam 22.3928 1 2.222e-06 ***
## TransplantContam:OriginContam 7.6935 1 0.005542 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1summary(mod4)## Linear mixed model fit by REML ['lmerMod']
## Formula: car::logit(survival) ~ (TransplantContam + OriginContam)^2 +
## (1 | CagingSite) + (1 | OriginSite)
## Data: DeathSum
##
## REML criterion at convergence: 133.5
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -2.60333 -0.06735 0.11833 0.56713 1.93187
##
## Random effects:
## Groups Name Variance Std.Dev.
## CagingSite (Intercept) 0.0000 0.0000
## OriginSite (Intercept) 0.0000 0.0000
## Residual 0.9715 0.9856
## Number of obs: 48, groups: CagingSite, 4; OriginSite, 4
##
## Fixed effects:
## Estimate Std. Error t value
## (Intercept) 3.6636 0.2845 12.876
## TransplantContamLC -0.2333 0.4024 -0.580
## OriginContamLC -1.9041 0.4024 -4.732
## TransplantContamLC:OriginContamLC 1.5784 0.5691 2.774
##
## Correlation of Fixed Effects:
## (Intr) TrnCLC OrgCLC
## TrnsplntCLC -0.707
## OrignCntmLC -0.707 0.500
## TrnCLC:OCLC 0.500 -0.707 -0.707
## optimizer (nloptwrap) convergence code: 0 (OK)
## boundary (singular) fit: see ?isSingularAlthough, this last method also result in singular fit (“CagingSite” and “OriginSite” random effects variance is estimated as zero), here the interaction between fish origin and the transplant site is significant. Both simplified methods give similar results, hence the results of the more straightforward method (glm) are reported in the statistic table (table 3). Also, because an interaction is significant, perform a posthoc test.
6.1.3 Posthoc test (test for equality of proportions)
# create two matrix containing fish survival rate according to their origin and transplant sites
DeathSum$CxO2 = paste(DeathSum$TransplantContam, DeathSum$OriginContam, sep =
"_")
a = aggregate(DeathSum$alive, list(DeathSum$CxO2), sum)
b = aggregate(DeathSum$dead, list(DeathSum$CxO2), sum)
# create the matrix for Low contamination origin
OriginLC = matrix(
c(b[b$Group.1 == "LC_LC", 2], a[a$Group.1 == "LC_LC", 2], b[b$Group.1 == "HC_LC", 2], a[a$Group.1 == "HC_LC", 2]),
nrow = 2,
ncol = 2,
dimnames = list(c("Dead", "Alive"), c("LC", "HC"))
)
OriginLC## LC HC
## Dead 3 16
## Alive 63 56# create the matrix for High contamination origin
OriginHC = matrix(
c(b[b$Group.1 == "LC_HC", 2], a[a$Group.1 == "LC_HC", 2], b[b$Group.1 == "HC_HC", 2], a[a$Group.1 == "HC_HC", 2]),
nrow = 2,
ncol = 2,
dimnames = list(c("Dead", "Alive"), c("LC", "HC"))
)
OriginHC## LC HC
## Dead 2 0
## Alive 65 63# run test for equality of proportions on each matrix
fisher.test(OriginLC, conf.level = 0.95)##
## Fisher's Exact Test for Count Data
##
## data: OriginLC
## p-value = 0.002728
## alternative hypothesis: true odds ratio is not equal to 1
## 95 percent confidence interval:
## 0.02990582 0.63312320
## sample estimates:
## odds ratio
## 0.1685805fisher.test(OriginHC, conf.level = 0.95)##
## Fisher's Exact Test for Count Data
##
## data: OriginHC
## p-value = 0.4966
## alternative hypothesis: true odds ratio is not equal to 1
## 95 percent confidence interval:
## 0.1769481 Inf
## sample estimates:
## odds ratio
## InfHere fish from Low Contamination, display a significant decrease in survival when exposed to High Contamination site. On the contrary, fish from High contamination site do not display a significant change in survival according to transplant site.
Also,because interaction between the contamination in origin and transplant site of fish is significant We test for parallel response between replicate populations.
6.1.4 Test for parallel responses between replicate populations (from the same origin)
6.1.4.1 For Populations from High contamination sites (AUSCOR and RIOU)
dat3 <- dat2[which(dat2$OriginSite %in% c("AUSCOR", "RIOU")),]
## build the null model
mod.null <-
glm(Death ~ TransplantContam + OriginSite,
data = dat3)
## build the model with the site of origin in interaction with the level of contamination in transplant sites
mod.par <-
glm(Death ~ TransplantContam * OriginSite,
data = dat3)
anova(mod.null, mod.par, test = "LRT")## Analysis of Deviance Table
##
## Model 1: Death ~ TransplantContam + OriginSite
## Model 2: Death ~ TransplantContam * OriginSite
## Resid. Df Resid. Dev Df Deviance Pr(>Chi)
## 1 127 1.9121
## 2 126 1.8857 1 0.026394 0.1842coef(mod.par)## (Intercept) TransplantContamLC
## 5.355515e-17 5.714286e-02
## OriginSiteRIOU TransplantContamLC:OriginSiteRIOU
## -4.878627e-18 -5.714286e-02summary(mod.par)##
## Call:
## glm(formula = Death ~ TransplantContam * OriginSite, data = dat3)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -0.05714 -0.04286 0.00000 0.00000 0.94286
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 5.356e-17 2.272e-02 0.000 1.0000
## TransplantContamLC 5.714e-02 3.072e-02 1.860 0.0652 .
## OriginSiteRIOU -4.879e-18 3.092e-02 0.000 1.0000
## TransplantContamLC:OriginSiteRIOU -5.714e-02 4.303e-02 -1.328 0.1866
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for gaussian family taken to be 0.01496599)
##
## Null deviance: 1.9692 on 129 degrees of freedom
## Residual deviance: 1.8857 on 126 degrees of freedom
## AIC: -171.4
##
## Number of Fisher Scoring iterations: 2The null model and the model including the site of origin in interaction with the level of contaminant in transplant sites are not significantly different, we hence cannot reject the null hypothesis: the slopes of HC populations are parallel.
6.1.4.2 For Populations from Low contamination sites (ARIMAS and CELFIG)
dat4 <- dat2[which(dat2$OriginSite %in% c("ARIMAS", "CELFIG")),]
## build the null model
mod.null <-
glm(Death ~ TransplantContam + OriginSite,
data = dat4)
## build the model with the site of origin in interaction with the level of contamination in transplant sites
mod.par <-
glm(Death ~ TransplantContam * OriginSite,
data = dat4)
anova(mod.null, mod.par, test = "LRT")## Analysis of Deviance Table
##
## Model 1: Death ~ TransplantContam + OriginSite
## Model 2: Death ~ TransplantContam * OriginSite
## Resid. Df Resid. Dev Df Deviance Pr(>Chi)
## 1 135 15.308
## 2 134 15.276 1 0.032262 0.5947coef(mod.par)## (Intercept) TransplantContamLC
## 0.23684211 -0.20653907
## OriginSiteCELFIG TransplantContamLC:OriginSiteCELFIG
## -0.03095975 0.06126278summary(mod.par)##
## Call:
## glm(formula = Death ~ TransplantContam * OriginSite, data = dat4)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -0.23684 -0.20588 -0.06061 -0.03030 0.96970
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.23684 0.05477 4.324 2.97e-05 ***
## TransplantContamLC -0.20654 0.08034 -2.571 0.0112 *
## OriginSiteCELFIG -0.03096 0.07970 -0.388 0.6983
## TransplantContamLC:OriginSiteCELFIG 0.06126 0.11516 0.532 0.5956
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for gaussian family taken to be 0.113998)
##
## Null deviance: 16.384 on 137 degrees of freedom
## Residual deviance: 15.276 on 134 degrees of freedom
## AIC: 97.891
##
## Number of Fisher Scoring iterations: 2The null model and the model including the site of origin in interaction with the level of contaminant in transplant sites are not significantly different, we hence cannot reject the null hypothesis: the slopes of LC populations are parallel.
6.1.5 Visualize
The plot reported below correspond to the figure 2A from the manuscript
par(mfrow=c(1,1))
Survivplot()
6.2 Metal bioaccumulation
6.2.1 Create a global index of metal accumulation: Zn, Cd, Cu
dat2 = dat1[is.na(dat1$MuscleCd) == F, ]
dat2$Cdscaled = scale(log(dat2$MuscleCd), center = T, scale = T)
dat2$Cuscaled = scale(log(dat2$MuscleCu), center = T, scale = T)
dat2$Znscaled = scale(log(dat2$MuscleZn), center = T, scale = T)
dat2$Bioacc = dat2$Cdscaled + dat2$Cuscaled + dat2$Znscaled
hist(dat2$Bioacc)
6.2.2 Visualize
par(mfrow=c(2,3))
boxplot(Bioacc ~ OriginContam, data = dat2)
boxplot(Bioacc ~ TransplantContam, data = dat2)
boxplot(Bioacc ~ Injection, data = dat2)
boxplot(Bioacc ~ TransplantContam * Injection, data = dat2)
boxplot(Bioacc ~ TransplantContam * OriginContam, data = dat2)
boxplot(Bioacc ~ TransplantContam * OriginContam * Injection, data = dat2)
6.2.3 Build the full model
modfull <-
lme4::lmer(
Bioacc ~ (TransplantContam + OriginContam + Injection) ^ 3 + SizeEnd +
(1 | CagingSite / CageSiteID) + (1| OriginSite),
data = dat2,
na.action = na.exclude
)
car::Anova(modfull, type = "3")## Analysis of Deviance Table (Type III Wald chisquare tests)
##
## Response: Bioacc
## Chisq Df Pr(>Chisq)
## (Intercept) 0.2687 1 0.6042
## TransplantContam 0.0320 1 0.8580
## OriginContam 0.7147 1 0.3979
## Injection 0.0171 1 0.8961
## SizeEnd 0.8024 1 0.3704
## TransplantContam:OriginContam 1.5238 1 0.2170
## TransplantContam:Injection 1.1853 1 0.2763
## OriginContam:Injection 0.1581 1 0.6909
## TransplantContam:OriginContam:Injection 0.4158 1 0.5191summary(modfull)## Linear mixed model fit by REML ['lmerMod']
## Formula: Bioacc ~ (TransplantContam + OriginContam + Injection)^3 + SizeEnd +
## (1 | CagingSite/CageSiteID) + (1 | OriginSite)
## Data: dat2
##
## REML criterion at convergence: 998.1
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -2.5929 -0.6166 0.0019 0.6315 3.6126
##
## Random effects:
## Groups Name Variance Std.Dev.
## CageSiteID:CagingSite (Intercept) 0.06108 0.2471
## CagingSite (Intercept) 1.62483 1.2747
## OriginSite (Intercept) 0.00000 0.0000
## Residual 3.17253 1.7812
## Number of obs: 248, groups:
## CageSiteID:CagingSite, 24; CagingSite, 4; OriginSite, 4
##
## Fixed effects:
## Estimate Std. Error t value
## (Intercept) -0.64621 1.24654 -0.518
## TransplantContamLC 0.24267 1.35588 0.179
## OriginContamLC 0.39650 0.46902 0.845
## InjectionPBS 0.05873 0.44959 0.131
## SizeEnd 0.07050 0.07871 0.896
## TransplantContamLC:OriginContamLC -0.80902 0.65538 -1.234
## TransplantContamLC:InjectionPBS -0.68677 0.63080 -1.089
## OriginContamLC:InjectionPBS 0.25975 0.65322 0.398
## TransplantContamLC:OriginContamLC:InjectionPBS -0.58575 0.90841 -0.645
##
## Correlation of Fixed Effects:
## (Intr) TrnCLC OrgCLC InjPBS SizEnd TrCLC:OCLC TCLC:I OCLC:I
## TrnsplntCLC -0.554
## OrignCntmLC -0.212 0.169
## InjectinPBS -0.180 0.158 0.457
## SizeEnd -0.639 0.017 0.047 0.013
## TrnCLC:OCLC 0.123 -0.240 -0.714 -0.326 0.013
## TrnCLC:IPBS 0.117 -0.225 -0.325 -0.712 0.008 0.466
## OrgCLC:IPBS 0.125 -0.109 -0.648 -0.688 -0.011 0.463 0.490
## TCLC:OCLC:I -0.081 0.156 0.466 0.495 -0.006 -0.652 -0.694 -0.719
## optimizer (nloptwrap) convergence code: 0 (OK)
## boundary (singular) fit: see ?isSingular6.2.4 Refining the model
mod2 <-
lme4::lmer(
Bioacc ~ (TransplantContam + OriginContam + Injection) ^ 2 + SizeEnd+
(1 | CagingSite / CageSiteID) + (1| OriginSite),
data = dat2,
na.action = na.exclude
)
car::Anova(mod2, type = "3")## Analysis of Deviance Table (Type III Wald chisquare tests)
##
## Response: Bioacc
## Chisq Df Pr(>Chisq)
## (Intercept) 0.3280 1 0.56683
## TransplantContam 0.0802 1 0.77698
## OriginContam 1.6806 1 0.19484
## Injection 0.2684 1 0.60444
## SizeEnd 0.7970 1 0.37199
## TransplantContam:OriginContam 4.7839 1 0.02873 *
## TransplantContam:Injection 4.5674 1 0.03259 *
## OriginContam:Injection 0.0090 1 0.92439
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1summary(mod2)## Linear mixed model fit by REML ['lmerMod']
## Formula: Bioacc ~ (TransplantContam + OriginContam + Injection)^2 + SizeEnd +
## (1 | CagingSite/CageSiteID) + (1 | OriginSite)
## Data: dat2
##
## REML criterion at convergence: 1000.2
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -2.6406 -0.6315 -0.0083 0.6140 3.6553
##
## Random effects:
## Groups Name Variance Std.Dev.
## CageSiteID:CagingSite (Intercept) 6.007e-02 2.451e-01
## CagingSite (Intercept) 1.622e+00 1.274e+00
## OriginSite (Intercept) 1.265e-09 3.557e-05
## Residual 3.165e+00 1.779e+00
## Number of obs: 248, groups:
## CageSiteID:CagingSite, 24; CagingSite, 4; OriginSite, 4
##
## Fixed effects:
## Estimate Std. Error t value
## (Intercept) -0.71077 1.24102 -0.573
## TransplantContamLC 0.37903 1.33812 0.283
## OriginContamLC 0.53707 0.41428 1.296
## InjectionPBS 0.20217 0.39028 0.518
## SizeEnd 0.07015 0.07858 0.893
## TransplantContamLC:OriginContamLC -1.08431 0.49575 -2.187
## TransplantContamLC:InjectionPBS -0.96917 0.45349 -2.137
## OriginContamLC:InjectionPBS -0.04305 0.45353 -0.095
##
## Correlation of Fixed Effects:
## (Intr) TrnCLC OrgCLC InjPBS SizEnd TCLC:O TCLC:I
## TrnsplntCLC -0.550
## OrignCntmLC -0.198 0.110
## InjectinPBS -0.162 0.094 0.295
## SizeEnd -0.641 0.018 0.056 0.019
## TrnCLC:OCLC 0.092 -0.184 -0.611 -0.006 0.011
## TrnCLC:IPBS 0.085 -0.164 -0.003 -0.590 0.005 0.024
## OrgCLC:IPBS 0.097 0.005 -0.510 -0.551 -0.023 -0.010 -0.018
## optimizer (nloptwrap) convergence code: 0 (OK)
## boundary (singular) fit: see ?isSingular6.2.5 Refining the model
mod3 <-
lme4::lmer(
Bioacc ~ (TransplantContam + OriginContam) ^ 2 + (TransplantContam + Injection) ^ 2 + SizeEnd +
(1 | CagingSite / CageSiteID) + (1| OriginSite),
data = dat2,
na.action = na.exclude
)
car::Anova(mod3, type = "3")## Analysis of Deviance Table (Type III Wald chisquare tests)
##
## Response: Bioacc
## Chisq Df Pr(>Chisq)
## (Intercept) 0.3213 1 0.57080
## TransplantContam 0.0806 1 0.77648
## OriginContam 2.1094 1 0.14639
## Injection 0.3124 1 0.57618
## SizeEnd 0.7964 1 0.37217
## TransplantContam:OriginContam 4.7930 1 0.02858 *
## TransplantContam:Injection 4.5959 1 0.03205 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1summary(mod3)## Linear mixed model fit by REML ['lmerMod']
## Formula: Bioacc ~ (TransplantContam + OriginContam)^2 + (TransplantContam +
## Injection)^2 + SizeEnd + (1 | CagingSite/CageSiteID) + (1 |
## OriginSite)
## Data: dat2
##
## REML criterion at convergence: 1000.4
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -2.6527 -0.6343 -0.0135 0.6174 3.6569
##
## Random effects:
## Groups Name Variance Std.Dev.
## CageSiteID:CagingSite (Intercept) 0.06142 0.2478
## CagingSite (Intercept) 1.62265 1.2738
## OriginSite (Intercept) 0.00000 0.0000
## Residual 3.15118 1.7752
## Number of obs: 248, groups:
## CageSiteID:CagingSite, 24; CagingSite, 4; OriginSite, 4
##
## Fixed effects:
## Estimate Std. Error t value
## (Intercept) -0.69980 1.23449 -0.567
## TransplantContamLC 0.37990 1.33810 0.284
## OriginContamLC 0.51742 0.35625 1.452
## InjectionPBS 0.18171 0.32508 0.559
## SizeEnd 0.07001 0.07845 0.892
## TransplantContamLC:OriginContamLC -1.08527 0.49572 -2.189
## TransplantContamLC:InjectionPBS -0.96988 0.45241 -2.144
##
## Correlation of Fixed Effects:
## (Intr) TrnCLC OrgCLC InjPBS SizEnd TCLC:O
## TrnsplntCLC -0.554
## OrignCntmLC -0.173 0.130
## InjectinPBS -0.130 0.116 0.019
## SizeEnd -0.642 0.018 0.051 0.007
## TrnCLC:OCLC 0.094 -0.184 -0.716 -0.014 0.011
## TrnCLC:IPBS 0.087 -0.163 -0.013 -0.718 0.005 0.024
## optimizer (nloptwrap) convergence code: 0 (OK)
## boundary (singular) fit: see ?isSingular6.2.6 Refining the model
mod4 <-
lme4::lmer(
Bioacc ~ (TransplantContam + OriginContam) ^ 2 + (TransplantContam + Injection) ^ 2 +
(1 | CagingSite / CageSiteID) + (1| OriginSite),
data = dat2,
na.action = na.exclude
)
car::Anova(mod4, type = "3")## Analysis of Deviance Table (Type III Wald chisquare tests)
##
## Response: Bioacc
## Chisq Df Pr(>Chisq)
## (Intercept) 0.0001 1 0.99345
## TransplantContam 0.0699 1 0.79149
## OriginContam 2.0077 1 0.15650
## Injection 0.3065 1 0.57987
## TransplantContam:OriginContam 4.9131 1 0.02665 *
## TransplantContam:Injection 4.6157 1 0.03168 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1summary(mod4)## Linear mixed model fit by REML ['lmerMod']
## Formula: Bioacc ~ (TransplantContam + OriginContam)^2 + (TransplantContam +
## Injection)^2 + (1 | CagingSite/CageSiteID) + (1 | OriginSite)
## Data: dat2
##
## REML criterion at convergence: 998
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -2.7307 -0.6338 0.0011 0.6105 3.6689
##
## Random effects:
## Groups Name Variance Std.Dev.
## CageSiteID:CagingSite (Intercept) 0.05418 0.2328
## CagingSite (Intercept) 1.66493 1.2903
## OriginSite (Intercept) 0.00000 0.0000
## Residual 3.15254 1.7755
## Number of obs: 248, groups:
## CageSiteID:CagingSite, 24; CagingSite, 4; OriginSite, 4
##
## Fixed effects:
## Estimate Std. Error t value
## (Intercept) 0.007861 0.957003 0.008
## TransplantContamLC 0.357625 1.352719 0.264
## OriginContamLC 0.499324 0.352393 1.417
## InjectionPBS 0.179984 0.325128 0.554
## TransplantContamLC:OriginContamLC -1.087981 0.490846 -2.217
## TransplantContamLC:InjectionPBS -0.972115 0.452478 -2.148
##
## Correlation of Fixed Effects:
## (Intr) TrnCLC OrgCLC InjPBS TCLC:O
## TrnsplntCLC -0.707
## OrignCntmLC -0.180 0.127
## InjectinPBS -0.162 0.114 0.019
## TrnCLC:OCLC 0.129 -0.180 -0.718 -0.014
## TrnCLC:IPBS 0.116 -0.162 -0.014 -0.719 0.024
## optimizer (nloptwrap) convergence code: 0 (OK)
## boundary (singular) fit: see ?isSingularmodBioacc <- mod4
RmodBioacc <- MuMIn::r.squaredGLMM(modBioacc)Now that we have identified the best model, add sex as covariate to check whether results are sensitive NB: sample size is reduced when adding sex variable within the model, for this reason the sex effect on results is checked on the final model
6.2.7 Test for the sex effect
dat2 = dat2[is.na(dat2$Sex) == F, ]
modSex <-
lme4::lmer(
Bioacc ~ (TransplantContam + OriginContam) ^ 2 + (TransplantContam + Injection) ^ 2 + Sex +
(1 | CagingSite / CageSiteID) + (1| OriginSite),
data = dat2,
na.action = na.exclude
)
car::Anova(modSex, type = "3")## Analysis of Deviance Table (Type III Wald chisquare tests)
##
## Response: Bioacc
## Chisq Df Pr(>Chisq)
## (Intercept) 0.0049 1 0.94411
## TransplantContam 0.0543 1 0.81582
## OriginContam 1.9330 1 0.16443
## Injection 0.2676 1 0.60495
## Sex 0.9997 1 0.31737
## TransplantContam:OriginContam 4.3526 1 0.03695 *
## TransplantContam:Injection 4.2714 1 0.03876 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1summary(modSex)## Linear mixed model fit by REML ['lmerMod']
## Formula: Bioacc ~ (TransplantContam + OriginContam)^2 + (TransplantContam +
## Injection)^2 + Sex + (1 | CagingSite/CageSiteID) + (1 | OriginSite)
## Data: dat2
##
## REML criterion at convergence: 994.4
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -2.8057 -0.6443 0.0424 0.5911 3.5562
##
## Random effects:
## Groups Name Variance Std.Dev.
## CageSiteID:CagingSite (Intercept) 0.08238 0.287
## CagingSite (Intercept) 1.61475 1.271
## OriginSite (Intercept) 0.00000 0.000
## Residual 3.14100 1.772
## Number of obs: 247, groups:
## CageSiteID:CagingSite, 24; CagingSite, 4; OriginSite, 4
##
## Fixed effects:
## Estimate Std. Error t value
## (Intercept) -0.0666 0.9500 -0.070
## TransplantContamLC 0.3116 1.3380 0.233
## OriginContamLC 0.5101 0.3669 1.390
## InjectionPBS 0.1686 0.3260 0.517
## SexM 0.2379 0.2379 1.000
## TransplantContamLC:OriginContamLC -1.0691 0.5124 -2.086
## TransplantContamLC:InjectionPBS -0.9358 0.4528 -2.067
##
## Correlation of Fixed Effects:
## (Intr) TrnCLC OrgCLC InjPBS SexM TCLC:O
## TrnsplntCLC -0.702
## OrignCntmLC -0.181 0.133
## InjectinPBS -0.166 0.115 0.009
## SexM -0.088 -0.029 -0.053 0.037
## TrnCLC:OCLC 0.124 -0.190 -0.719 -0.004 0.099
## TrnCLC:IPBS 0.115 -0.164 -0.010 -0.718 0.030 0.022
## optimizer (nloptwrap) convergence code: 0 (OK)
## boundary (singular) fit: see ?isSingularAdding the sex as covariate does no change the significance of the interactions, also sex effect is non-significant. The mod4 is thus the best model.
6.2.8 Posthoc test (pairwise t-test)
The interactions between fish origin and the transplant as well as between transplant and injection treatments are significant. Hence, perform posthoc test (pairwise t-test) according to significant interactions
pairwise.t.test(dat2$Bioacc, dat2$CxI, p.adjust.method = "fdr")##
## Pairwise comparisons using t tests with pooled SD
##
## data: dat2$Bioacc and dat2$CxI
##
## HC_AMIX HC_PBS LC_AMIX
## HC_PBS 0.749 - -
## LC_AMIX 0.640 0.530 -
## LC_PBS 0.012 0.011 0.040
##
## P value adjustment method: fdrHere, fish from low contamination site and injected with a saline control solution, has bioaccumulated significantly less metals than the fish exposed to other treatment, even compared to LC exposed in Low contamination site and injected to the antigen mixture, suggesting that the antigen mixture could affect bioaccumulation in fish muscle.
pairwise.t.test(dat2$Bioacc, dat2$CxO2, p.adjust.method = "fdr")##
## Pairwise comparisons using t tests with pooled SD
##
## data: dat2$Bioacc and dat2$CxO2
##
## HC_HC HC_LC LC_HC
## HC_LC 0.32 - -
## LC_HC 0.57 0.18 -
## LC_LC 0.11 0.01 0.18
##
## P value adjustment method: fdrHere fish from Low Contamination, display a significant increase in the amount of metal bioaccumulated in their muscle when exposed to High Contamination site compared to when they are exposed in low contamination site. On the contrary, the metal levels is constant in HC fish, whatever the site of transplantation.
Also,because interaction between the contamination in origin and transplant site of fish is significant We test for parallel response between replicate populations.
6.2.9 Test for parallel responses between replicate populations (from the same origin)
6.2.9.1 For Populations from High contamination sites (AUSCOR and RIOU)
dat3 <- dat2[which(dat2$OriginSite %in% c("AUSCOR", "RIOU")),]
## build the null model
mod.null <-
glm(Bioacc ~ TransplantContam + OriginSite,
data = dat3)
## build the model with the site of origin in interaction with the level of contam in transplant sites
mod.par <-
glm(Bioacc ~ TransplantContam * OriginSite,
data = dat3)
anova(mod.null, mod.par, test = "LRT")## Analysis of Deviance Table
##
## Model 1: Bioacc ~ TransplantContam + OriginSite
## Model 2: Bioacc ~ TransplantContam * OriginSite
## Resid. Df Resid. Dev Df Deviance Pr(>Chi)
## 1 125 405.31
## 2 124 393.62 1 11.688 0.05501 .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1coef(mod.par)## (Intercept) TransplantContamLC
## -0.5641966 -0.7376128
## OriginSiteRIOU TransplantContamLC:OriginSiteRIOU
## 1.3456317 1.2108581summary(mod.par)##
## Call:
## glm(formula = Bioacc ~ TransplantContam * OriginSite, data = dat3)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -3.9865 -0.8885 0.0204 0.9680 6.3792
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -0.5642 0.3308 -1.705 0.09064 .
## TransplantContamLC -0.7376 0.4535 -1.627 0.10638
## OriginSiteRIOU 1.3456 0.4504 2.988 0.00339 **
## TransplantContamLC:OriginSiteRIOU 1.2109 0.6310 1.919 0.05731 .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for gaussian family taken to be 3.174371)
##
## Null deviance: 529.49 on 127 degrees of freedom
## Residual deviance: 393.62 on 124 degrees of freedom
## AIC: 517.04
##
## Number of Fisher Scoring iterations: 2The null model and the model including the site of origin in interaction with the level of contaminant in transplant sites are not significantly different, we hence cannot reject the null hypothesis: the slopes of HC populations are parallel.
6.2.9.2 For Populations from Low contamination sites (ARIMAS and CELFIG)
# We test for parallel response between replicate LC populations (ARIMAS and CELFIG)
dat4 <- dat2[which(dat2$OriginSite %in% c("ARIMAS", "CELFIG")),]
## build the null model
mod.null <-
glm(Bioacc ~ TransplantContam + OriginSite,
data = dat4)
## build the model with the site of origin in interaction with the level of contam in transplant sites
mod.par <-
glm(Bioacc ~ TransplantContam * OriginSite,
data = dat4)
anova(mod.null, mod.par, test = "LRT")## Analysis of Deviance Table
##
## Model 1: Bioacc ~ TransplantContam + OriginSite
## Model 2: Bioacc ~ TransplantContam * OriginSite
## Resid. Df Resid. Dev Df Deviance Pr(>Chi)
## 1 116 382.81
## 2 115 382.09 1 0.72023 0.6415coef(mod.par)## (Intercept) TransplantContamLC
## -0.3383157 -1.0450200
## OriginSiteCELFIG TransplantContamLC:OriginSiteCELFIG
## 1.8961427 -0.3118520summary(mod.par)##
## Call:
## glm(formula = Bioacc ~ TransplantContam * OriginSite, data = dat4)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -5.1336 -1.1292 -0.1314 1.1556 6.0411
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -0.3383 0.3385 -1.000 0.319645
## TransplantContamLC -1.0450 0.4673 -2.236 0.027271 *
## OriginSiteCELFIG 1.8961 0.4875 3.890 0.000168 ***
## TransplantContamLC:OriginSiteCELFIG -0.3119 0.6698 -0.466 0.642389
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for gaussian family taken to be 3.322503)
##
## Null deviance: 513.14 on 118 degrees of freedom
## Residual deviance: 382.09 on 115 degrees of freedom
## AIC: 486.52
##
## Number of Fisher Scoring iterations: 2The null model and the model including the site of origin in interaction with the level of contaminant in transplant sites are not significantly different, we hence cannot reject the null hypothesis: the slopes of LC populations are parallel.
6.2.10 Visualize
The plot reported below correspond to the figure 3 and the figure 2B from the manuscript
BioaccPlot3()
BioaccPlot1()
6.3 Oxidative Stress Index
6.3.1 Create a global index of oxidative stress (Costantini and Dell’Omo, 2006)
dat2 = dat1[is.na(dat1$mMHCLO) == F, ]
dat2 = dat2[is.na(dat2$mMH2O2) == F, ]
dat2$ratOXI = dat2$mMH2O2 * 1000 / dat2$mMHCLO
hist(log(dat2$ratOXI + 1))
6.3.2 Visualize
par(mfrow=c(2,3))
boxplot(log(dat2$ratOXI + 1) ~ OriginContam, data = dat2)
boxplot(log(dat2$ratOXI + 1) ~ TransplantContam, data = dat2)
boxplot(log(dat2$ratOXI + 1) ~ Injection, data = dat2)
boxplot(log(dat2$ratOXI + 1) ~ TransplantContam * Injection, data = dat2, cex.axis = 0.8)
boxplot(log(dat2$ratOXI + 1) ~ TransplantContam * OriginContam, data = dat2)
boxplot(log(dat2$ratOXI + 1) ~ TransplantContam * OriginContam * Injection, data = dat2, cex.axis = 0.8, las = 2)
6.3.3 Build the full model
modfull <-
lme4::lmer(
log(ratOXI + 1) ~ (TransplantContam + OriginContam + Injection) ^ 3 + SizeEnd +
(1 | CagingSite / CageSiteID) + (1| OriginSite),
data = dat2,
na.action = na.exclude
)
car::Anova(modfull, type = "3")## Analysis of Deviance Table (Type III Wald chisquare tests)
##
## Response: log(ratOXI + 1)
## Chisq Df Pr(>Chisq)
## (Intercept) 69.2314 1 < 2.2e-16 ***
## TransplantContam 0.3238 1 0.569314
## OriginContam 0.0007 1 0.979569
## Injection 0.0786 1 0.779203
## SizeEnd 8.7427 1 0.003108 **
## TransplantContam:OriginContam 0.0505 1 0.822210
## TransplantContam:Injection 1.3823 1 0.239711
## OriginContam:Injection 0.0913 1 0.762495
## TransplantContam:OriginContam:Injection 0.0696 1 0.791853
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1summary(modfull)## Linear mixed model fit by REML ['lmerMod']
## Formula: log(ratOXI + 1) ~ (TransplantContam + OriginContam + Injection)^3 +
## SizeEnd + (1 | CagingSite/CageSiteID) + (1 | OriginSite)
## Data: dat2
##
## REML criterion at convergence: 275.1
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -3.3106 -0.5139 0.0337 0.6605 1.9304
##
## Random effects:
## Groups Name Variance Std.Dev.
## CageSiteID:CagingSite (Intercept) 0.02445 0.1564
## CagingSite (Intercept) 0.00000 0.0000
## OriginSite (Intercept) 0.07611 0.2759
## Residual 0.25584 0.5058
## Number of obs: 166, groups:
## CageSiteID:CagingSite, 24; CagingSite, 4; OriginSite, 4
##
## Fixed effects:
## Estimate Std. Error t value
## (Intercept) 3.453200 0.415021 8.321
## TransplantContamLC 0.101436 0.178251 0.569
## OriginContamLC -0.008508 0.332223 -0.026
## InjectionPBS -0.042766 0.152541 -0.280
## SizeEnd -0.100495 0.033988 -2.957
## TransplantContamLC:OriginContamLC -0.057986 0.258055 -0.225
## TransplantContamLC:InjectionPBS 0.249744 0.212420 1.176
## OriginContamLC:InjectionPBS 0.068667 0.227218 0.302
## TransplantContamLC:OriginContamLC:InjectionPBS -0.084638 0.320713 -0.264
##
## Correlation of Fixed Effects:
## (Intr) TrnCLC OrgCLC InjPBS SizEnd TrCLC:OCLC TCLC:I OCLC:I
## TrnsplntCLC -0.205
## OrignCntmLC -0.414 0.278
## InjectinPBS -0.162 0.457 0.244
## SizeEnd -0.826 -0.022 0.021 -0.042
## TrnCLC:OCLC 0.136 -0.691 -0.397 -0.316 0.023
## TrnCLC:IPBS 0.080 -0.620 -0.174 -0.719 0.073 0.429
## OrgCLC:IPBS 0.124 -0.306 -0.339 -0.671 0.010 0.436 0.482
## TCLC:OCLC:I -0.066 0.410 0.240 0.476 -0.032 -0.602 -0.661 -0.709
## optimizer (nloptwrap) convergence code: 0 (OK)
## boundary (singular) fit: see ?isSingular6.3.4 Refining the model
mod2 <-
lme4::lmer(
log(ratOXI + 1) ~ (TransplantContam + OriginContam + Injection) ^ 2 + SizeEnd +
(1 | CagingSite / CageSiteID) + (1| OriginSite),
data = dat2,
na.action = na.exclude
)
car::Anova(mod2, type = "3")## Analysis of Deviance Table (Type III Wald chisquare tests)
##
## Response: log(ratOXI + 1)
## Chisq Df Pr(>Chisq)
## (Intercept) 69.5593 1 < 2e-16 ***
## TransplantContam 0.5469 1 0.45958
## OriginContam 0.0015 1 0.96941
## Injection 0.0323 1 0.85744
## SizeEnd 8.8570 1 0.00292 **
## TransplantContam:OriginContam 0.2313 1 0.63054
## TransplantContam:Injection 1.8062 1 0.17896
## OriginContam:Injection 0.0270 1 0.86949
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1summary(mod2)## Linear mixed model fit by REML ['lmerMod']
## Formula: log(ratOXI + 1) ~ (TransplantContam + OriginContam + Injection)^2 +
## SizeEnd + (1 | CagingSite/CageSiteID) + (1 | OriginSite)
## Data: dat2
##
## REML criterion at convergence: 274.7
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -3.3431 -0.5207 0.0314 0.6552 1.9356
##
## Random effects:
## Groups Name Variance Std.Dev.
## CageSiteID:CagingSite (Intercept) 2.488e-02 1.577e-01
## CagingSite (Intercept) 2.116e-10 1.455e-05
## OriginSite (Intercept) 7.611e-02 2.759e-01
## Residual 2.540e-01 5.040e-01
## Number of obs: 166, groups:
## CageSiteID:CagingSite, 24; CagingSite, 4; OriginSite, 4
##
## Fixed effects:
## Estimate Std. Error t value
## (Intercept) 3.44615 0.41320 8.340
## TransplantContamLC 0.12028 0.16264 0.740
## OriginContamLC 0.01237 0.32251 0.038
## InjectionPBS -0.02402 0.13371 -0.180
## SizeEnd -0.10078 0.03386 -2.976
## TransplantContamLC:OriginContamLC -0.09921 0.20628 -0.481
## TransplantContamLC:InjectionPBS 0.21346 0.15883 1.344
## OriginContamLC:InjectionPBS 0.02625 0.15977 0.164
##
## Correlation of Fixed Effects:
## (Intr) TrnCLC OrgCLC InjPBS SizEnd TCLC:O TCLC:I
## TrnsplntCLC -0.196
## OrignCntmLC -0.412 0.204
## InjectinPBS -0.148 0.325 0.152
## SizeEnd -0.830 -0.010 0.030 -0.031
## TrnCLC:OCLC 0.121 -0.610 -0.326 -0.042 0.004
## TrnCLC:IPBS 0.048 -0.508 -0.020 -0.614 0.069 0.051
## OrgCLC:IPBS 0.109 -0.025 -0.245 -0.537 -0.018 0.016 0.025
## optimizer (nloptwrap) convergence code: 0 (OK)
## boundary (singular) fit: see ?isSingular6.3.5 Refining the model
mod3 <-
lme4::lmer(
log(ratOXI + 1) ~ (TransplantContam + OriginContam + Injection) ^ 2 + SizeEnd +
(1 | CagingSite / CageSiteID) + (1| OriginSite),
data = dat2,
na.action = na.exclude
)
car::Anova(mod3, type = "3")## Analysis of Deviance Table (Type III Wald chisquare tests)
##
## Response: log(ratOXI + 1)
## Chisq Df Pr(>Chisq)
## (Intercept) 69.5593 1 < 2e-16 ***
## TransplantContam 0.5469 1 0.45958
## OriginContam 0.0015 1 0.96941
## Injection 0.0323 1 0.85744
## SizeEnd 8.8570 1 0.00292 **
## TransplantContam:OriginContam 0.2313 1 0.63054
## TransplantContam:Injection 1.8062 1 0.17896
## OriginContam:Injection 0.0270 1 0.86949
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1summary(mod3)## Linear mixed model fit by REML ['lmerMod']
## Formula: log(ratOXI + 1) ~ (TransplantContam + OriginContam + Injection)^2 +
## SizeEnd + (1 | CagingSite/CageSiteID) + (1 | OriginSite)
## Data: dat2
##
## REML criterion at convergence: 274.7
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -3.3431 -0.5207 0.0314 0.6552 1.9356
##
## Random effects:
## Groups Name Variance Std.Dev.
## CageSiteID:CagingSite (Intercept) 2.488e-02 1.577e-01
## CagingSite (Intercept) 2.116e-10 1.455e-05
## OriginSite (Intercept) 7.611e-02 2.759e-01
## Residual 2.540e-01 5.040e-01
## Number of obs: 166, groups:
## CageSiteID:CagingSite, 24; CagingSite, 4; OriginSite, 4
##
## Fixed effects:
## Estimate Std. Error t value
## (Intercept) 3.44615 0.41320 8.340
## TransplantContamLC 0.12028 0.16264 0.740
## OriginContamLC 0.01237 0.32251 0.038
## InjectionPBS -0.02402 0.13371 -0.180
## SizeEnd -0.10078 0.03386 -2.976
## TransplantContamLC:OriginContamLC -0.09921 0.20628 -0.481
## TransplantContamLC:InjectionPBS 0.21346 0.15883 1.344
## OriginContamLC:InjectionPBS 0.02625 0.15977 0.164
##
## Correlation of Fixed Effects:
## (Intr) TrnCLC OrgCLC InjPBS SizEnd TCLC:O TCLC:I
## TrnsplntCLC -0.196
## OrignCntmLC -0.412 0.204
## InjectinPBS -0.148 0.325 0.152
## SizeEnd -0.830 -0.010 0.030 -0.031
## TrnCLC:OCLC 0.121 -0.610 -0.326 -0.042 0.004
## TrnCLC:IPBS 0.048 -0.508 -0.020 -0.614 0.069 0.051
## OrgCLC:IPBS 0.109 -0.025 -0.245 -0.537 -0.018 0.016 0.025
## optimizer (nloptwrap) convergence code: 0 (OK)
## boundary (singular) fit: see ?isSingular6.3.6 Refining the model
mod4 <-
lme4::lmer(
log(ratOXI + 1) ~ TransplantContam + OriginContam + Injection + SizeEnd +
(1 | CagingSite / CageSiteID) + (1| OriginSite),
data = dat2,
na.action = na.exclude
)
car::Anova(mod4, type = "3")## Analysis of Deviance Table (Type III Wald chisquare tests)
##
## Response: log(ratOXI + 1)
## Chisq Df Pr(>Chisq)
## (Intercept) 71.3344 1 < 2.2e-16 ***
## TransplantContam 3.5864 1 0.058255 .
## OriginContam 0.0053 1 0.942076
## Injection 1.4256 1 0.232490
## SizeEnd 9.5099 1 0.002044 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1summary(mod4)## Linear mixed model fit by REML ['lmerMod']
## Formula: log(ratOXI + 1) ~ TransplantContam + OriginContam + Injection +
## SizeEnd + (1 | CagingSite/CageSiteID) + (1 | OriginSite)
## Data: dat2
##
## REML criterion at convergence: 271.7
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -3.1871 -0.5425 0.0135 0.6022 2.0323
##
## Random effects:
## Groups Name Variance Std.Dev.
## CageSiteID:CagingSite (Intercept) 1.667e-02 1.291e-01
## CagingSite (Intercept) 3.888e-11 6.236e-06
## OriginSite (Intercept) 7.776e-02 2.789e-01
## Residual 2.567e-01 5.066e-01
## Number of obs: 166, groups:
## CageSiteID:CagingSite, 24; CagingSite, 4; OriginSite, 4
##
## Fixed effects:
## Estimate Std. Error t value
## (Intercept) 3.44289 0.40764 8.446
## TransplantContamLC 0.18166 0.09593 1.894
## OriginContamLC -0.02147 0.29548 -0.073
## InjectionPBS 0.09488 0.07947 1.194
## SizeEnd -0.10427 0.03381 -3.084
##
## Correlation of Fixed Effects:
## (Intr) TrnCLC OrgCLC InjPBS
## TrnsplntCLC -0.158
## OrignCntmLC -0.386 0.004
## InjectinPBS -0.106 0.017 0.020
## SizeEnd -0.846 0.043 0.030 0.003
## optimizer (nloptwrap) convergence code: 0 (OK)
## boundary (singular) fit: see ?isSingular6.3.7 Refining the model
mod5 <-
lme4::lmer(
log(ratOXI + 1) ~ SizeEnd +
(1 | CagingSite / CageSiteID) + (1| OriginSite),
data = dat2,
na.action = na.exclude
)
performance::check_model(mod5)
car::Anova(mod5, type = "3")## Analysis of Deviance Table (Type III Wald chisquare tests)
##
## Response: log(ratOXI + 1)
## Chisq Df Pr(>Chisq)
## (Intercept) 99.4348 1 < 2.2e-16 ***
## SizeEnd 9.2082 1 0.002409 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1summary(mod5)## Linear mixed model fit by REML ['lmerMod']
## Formula: log(ratOXI + 1) ~ SizeEnd + (1 | CagingSite/CageSiteID) + (1 |
## OriginSite)
## Data: dat2
##
## REML criterion at convergence: 269
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -3.3526 -0.4999 0.0010 0.6396 1.8761
##
## Random effects:
## Groups Name Variance Std.Dev.
## CageSiteID:CagingSite (Intercept) 0.01830 0.1353
## CagingSite (Intercept) 0.01190 0.1091
## OriginSite (Intercept) 0.03728 0.1931
## Residual 0.25728 0.5072
## Number of obs: 166, groups:
## CageSiteID:CagingSite, 24; CagingSite, 4; OriginSite, 4
##
## Fixed effects:
## Estimate Std. Error t value
## (Intercept) 3.53866 0.35487 9.972
## SizeEnd -0.10109 0.03331 -3.034
##
## Correlation of Fixed Effects:
## (Intr)
## SizeEnd -0.940modRatOx <- mod5
RmodRatOx <- MuMIn::r.squaredGLMM(modRatOx)The treatments has no effect on oxidative stress index but the oxidative stress index is lower in bigger fish Represent the relation between fish size and oxidative stress index
plot(log(ratOXI + 1) ~ SizeEnd, data = dat2)
abline(b = -0.10109, a = 3.53866, col = "red")
Now that we have identified the best model, add sex as covariate to check whether results are sensitive NB: sample size is reduced when adding sex variable within the model, for this reason the sex effect on results is checked on the final model
6.3.8 Test for the sex effect
dat2 = dat2[is.na(dat2$Sex) == F, ]
mod5 <-
lme4::lmer(
log(ratOXI + 1) ~ SizeEnd + Sex +
(1 | CagingSite / CageSiteID) + (1| OriginSite),
data = dat2,
na.action = na.exclude
)
performance::check_model(mod5)
car::Anova(mod5, type = "3")## Analysis of Deviance Table (Type III Wald chisquare tests)
##
## Response: log(ratOXI + 1)
## Chisq Df Pr(>Chisq)
## (Intercept) 99.176 1 < 2.2e-16 ***
## SizeEnd 9.413 1 0.002155 **
## Sex 0.145 1 0.703328
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1summary(mod5)## Linear mixed model fit by REML ['lmerMod']
## Formula: log(ratOXI + 1) ~ SizeEnd + Sex + (1 | CagingSite/CageSiteID) +
## (1 | OriginSite)
## Data: dat2
##
## REML criterion at convergence: 269.6
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -3.2988 -0.5140 0.0161 0.6177 1.9481
##
## Random effects:
## Groups Name Variance Std.Dev.
## CageSiteID:CagingSite (Intercept) 0.01693 0.1301
## CagingSite (Intercept) 0.01374 0.1172
## OriginSite (Intercept) 0.03700 0.1924
## Residual 0.25788 0.5078
## Number of obs: 165, groups:
## CageSiteID:CagingSite, 24; CagingSite, 4; OriginSite, 4
##
## Fixed effects:
## Estimate Std. Error t value
## (Intercept) 3.53925 0.35539 9.959
## SizeEnd -0.10284 0.03352 -3.068
## SexM 0.03204 0.08413 0.381
##
## Correlation of Fixed Effects:
## (Intr) SizEnd
## SizeEnd -0.934
## SexM 0.006 -0.109The sex effect is non-significant. The mod5 is thus the best model. Here, there is no interaction, and hence no posthoc test nor parallelism test to conduct
6.4 Oxidative damage
6.4.1 Check the data
dat2 = dat1[is.na(dat1$mMH2O2) == F, ]
hist(log(dat2$mMH2O2 + 1))
6.4.2 Visualize
par(mfrow=c(2,3))
boxplot(log(dat2$mMH2O2 + 1) ~ OriginContam, data = dat2)
boxplot(log(dat2$mMH2O2 + 1) ~ TransplantContam, data = dat2)
boxplot(log(dat2$mMH2O2 + 1) ~ Injection, data = dat2)
boxplot(log(dat2$mMH2O2 + 1) ~ TransplantContam * Injection, data = dat2)
boxplot(log(dat2$mMH2O2 + 1) ~ TransplantContam * OriginContam, data = dat2)
boxplot(log(dat2$mMH2O2 + 1) ~ TransplantContam * OriginContam * Injection, data = dat2)
6.4.3 Build the full model
modfull <-
lme4::lmer(
log(mMH2O2 + 1) ~ (TransplantContam + OriginContam + Injection) ^ 3 + SizeEnd +
(1 | CagingSite / CageSiteID) + (1| OriginSite),
data = dat2,
na.action = na.exclude
)
car::Anova(modfull, type = "3")## Analysis of Deviance Table (Type III Wald chisquare tests)
##
## Response: log(mMH2O2 + 1)
## Chisq Df Pr(>Chisq)
## (Intercept) 54.8494 1 1.301e-13 ***
## TransplantContam 0.0387 1 0.843997
## OriginContam 0.5331 1 0.465301
## Injection 3.0090 1 0.082804 .
## SizeEnd 12.6086 1 0.000384 ***
## TransplantContam:OriginContam 0.1036 1 0.747597
## TransplantContam:Injection 5.9362 1 0.014833 *
## OriginContam:Injection 2.2515 1 0.133487
## TransplantContam:OriginContam:Injection 3.4945 1 0.061573 .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1summary(modfull)## Linear mixed model fit by REML ['lmerMod']
## Formula: log(mMH2O2 + 1) ~ (TransplantContam + OriginContam + Injection)^3 +
## SizeEnd + (1 | CagingSite/CageSiteID) + (1 | OriginSite)
## Data: dat2
##
## REML criterion at convergence: 166.4
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -2.56602 -0.62429 0.00728 0.64432 2.55410
##
## Random effects:
## Groups Name Variance Std.Dev.
## CageSiteID:CagingSite (Intercept) 0.01557 0.1248
## CagingSite (Intercept) 0.00000 0.0000
## OriginSite (Intercept) 0.04218 0.2054
## Residual 0.11756 0.3429
## Number of obs: 179, groups:
## CageSiteID:CagingSite, 24; CagingSite, 4; OriginSite, 4
##
## Fixed effects:
## Estimate Std. Error t value
## (Intercept) 2.11280 0.28528 7.406
## TransplantContamLC -0.02420 0.12299 -0.197
## OriginContamLC -0.17654 0.24178 -0.730
## InjectionPBS -0.17080 0.09846 -1.735
## SizeEnd -0.08067 0.02272 -3.551
## TransplantContamLC:OriginContamLC 0.05790 0.17991 0.322
## TransplantContamLC:InjectionPBS 0.33987 0.13949 2.436
## OriginContamLC:InjectionPBS 0.22025 0.14679 1.500
## TransplantContamLC:OriginContamLC:InjectionPBS -0.38945 0.20834 -1.869
##
## Correlation of Fixed Effects:
## (Intr) TrnCLC OrgCLC InjPBS SizEnd TrCLC:OCLC TCLC:I OCLC:I
## TrnsplntCLC -0.200
## OrignCntmLC -0.433 0.247
## InjectinPBS -0.141 0.391 0.198
## SizeEnd -0.806 -0.012 0.024 -0.034
## TrnCLC:OCLC 0.133 -0.684 -0.372 -0.267 0.013
## TrnCLC:IPBS 0.061 -0.575 -0.138 -0.707 0.071 0.394
## OrgCLC:IPBS 0.101 -0.262 -0.303 -0.670 0.014 0.408 0.474
## TCLC:OCLC:I -0.067 0.385 0.214 0.472 -0.015 -0.580 -0.667 -0.705
## optimizer (nloptwrap) convergence code: 0 (OK)
## boundary (singular) fit: see ?isSingular6.4.4 Refining the model
mod2 <-
lme4::lmer(
log(mMH2O2 + 1) ~ (TransplantContam + OriginContam + Injection) ^ 2 + SizeEnd +
(1 | CagingSite / CageSiteID) + (1| OriginSite),
data = dat2,
na.action = na.exclude
)
car::Anova(mod2, type = "3")## Analysis of Deviance Table (Type III Wald chisquare tests)
##
## Response: log(mMH2O2 + 1)
## Chisq Df Pr(>Chisq)
## (Intercept) 53.0417 1 3.265e-13 ***
## TransplantContam 0.3188 1 0.5723230
## OriginContam 0.1176 1 0.7316722
## Injection 0.9171 1 0.3382448
## SizeEnd 12.5772 1 0.0003905 ***
## TransplantContam:OriginContam 0.8666 1 0.3518981
## TransplantContam:Injection 2.5028 1 0.1136463
## OriginContam:Injection 0.0655 1 0.7980361
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1summary(mod2)## Linear mixed model fit by REML ['lmerMod']
## Formula: log(mMH2O2 + 1) ~ (TransplantContam + OriginContam + Injection)^2 +
## SizeEnd + (1 | CagingSite/CageSiteID) + (1 | OriginSite)
## Data: dat2
##
## REML criterion at convergence: 168.6
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -2.69555 -0.59671 0.00027 0.63658 2.41208
##
## Random effects:
## Groups Name Variance Std.Dev.
## CageSiteID:CagingSite (Intercept) 1.560e-02 1.249e-01
## CagingSite (Intercept) 3.708e-10 1.926e-05
## OriginSite (Intercept) 4.090e-02 2.022e-01
## Residual 1.194e-01 3.456e-01
## Number of obs: 179, groups:
## CageSiteID:CagingSite, 24; CagingSite, 4; OriginSite, 4
##
## Fixed effects:
## Estimate Std. Error t value
## (Intercept) 2.07527 0.28495 7.283
## TransplantContamLC 0.06441 0.11408 0.565
## OriginContamLC -0.08016 0.23376 -0.343
## InjectionPBS -0.08375 0.08746 -0.958
## SizeEnd -0.08111 0.02287 -3.546
## TransplantContamLC:OriginContamLC -0.13701 0.14718 -0.931
## TransplantContamLC:InjectionPBS 0.16564 0.10470 1.582
## OriginContamLC:InjectionPBS 0.02685 0.10493 0.256
##
## Correlation of Fixed Effects:
## (Intr) TrnCLC OrgCLC InjPBS SizEnd TCLC:O TCLC:I
## TrnsplntCLC -0.190
## OrignCntmLC -0.425 0.186
## InjectinPBS -0.125 0.257 0.115
## SizeEnd -0.814 -0.007 0.029 -0.030
## TrnCLC:OCLC 0.116 -0.612 -0.316 0.010 0.006
## TrnCLC:IPBS 0.022 -0.465 0.007 -0.597 0.081 0.011
## OrgCLC:IPBS 0.078 0.014 -0.225 -0.540 0.004 -0.002 0.007
## optimizer (nloptwrap) convergence code: 0 (OK)
## boundary (singular) fit: see ?isSingular6.4.5 Refining the model
mod3 <-
lme4::lmer(
log(mMH2O2 + 1) ~ (TransplantContam + Injection) ^ 2 + OriginContam + SizeEnd +
(1 | CagingSite / CageSiteID) + (1| OriginSite),
data = dat2,
na.action = na.exclude
)
car::Anova(mod3, type = "3")## Analysis of Deviance Table (Type III Wald chisquare tests)
##
## Response: log(mMH2O2 + 1)
## Chisq Df Pr(>Chisq)
## (Intercept) 55.5203 1 9.25e-14 ***
## TransplantContam 0.0000 1 0.9989045
## Injection 0.9161 1 0.3384952
## OriginContam 0.3939 1 0.5302729
## SizeEnd 12.6114 1 0.0003834 ***
## TransplantContam:Injection 2.5040 1 0.1135540
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1summary(mod3)## Linear mixed model fit by REML ['lmerMod']
## Formula: log(mMH2O2 + 1) ~ (TransplantContam + Injection)^2 + OriginContam +
## SizeEnd + (1 | CagingSite/CageSiteID) + (1 | OriginSite)
## Data: dat2
##
## REML criterion at convergence: 164.9
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -2.6627 -0.6294 0.0190 0.6121 2.3592
##
## Random effects:
## Groups Name Variance Std.Dev.
## CageSiteID:CagingSite (Intercept) 1.450e-02 1.204e-01
## CagingSite (Intercept) 5.086e-11 7.132e-06
## OriginSite (Intercept) 4.131e-02 2.032e-01
## Residual 1.191e-01 3.451e-01
## Number of obs: 179, groups:
## CageSiteID:CagingSite, 24; CagingSite, 4; OriginSite, 4
##
## Fixed effects:
## Estimate Std. Error t value
## (Intercept) 2.1004046 0.2818883 7.451
## TransplantContamLC 0.0001223 0.0890673 0.001
## InjectionPBS -0.0703594 0.0735099 -0.957
## OriginContamLC -0.1355283 0.2159505 -0.628
## SizeEnd -0.0810685 0.0228282 -3.551
## TransplantContamLC:InjectionPBS 0.1653988 0.1045228 1.582
##
## Correlation of Fixed Effects:
## (Intr) TrnCLC InjPBS OrgCLC SizEnd
## TrnsplntCLC -0.151
## InjectinPBS -0.101 0.411
## OrignCntmLC -0.407 -0.006 -0.005
## SizeEnd -0.822 -0.005 -0.033 0.034
## TrnCLC:IPBS 0.021 -0.586 -0.706 0.013 0.082
## optimizer (nloptwrap) convergence code: 0 (OK)
## boundary (singular) fit: see ?isSingular6.4.6 Refining the model
mod4 <-
lme4::lmer(
log(mMH2O2 + 1) ~ TransplantContam + Injection + OriginContam + SizeEnd +
(1 | CagingSite / CageSiteID) + (1| OriginSite),
data = dat2,
na.action = na.exclude
)
car::Anova(mod4, type = "3")## Analysis of Deviance Table (Type III Wald chisquare tests)
##
## Response: log(mMH2O2 + 1)
## Chisq Df Pr(>Chisq)
## (Intercept) 54.5200 1 1.539e-13 ***
## TransplantContam 1.4266 1 0.2323242
## Injection 0.0508 1 0.8216143
## OriginContam 0.4177 1 0.5180867
## SizeEnd 13.4376 1 0.0002466 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1summary(mod4)## Linear mixed model fit by REML ['lmerMod']
## Formula: log(mMH2O2 + 1) ~ TransplantContam + Injection + OriginContam +
## SizeEnd + (1 | CagingSite/CageSiteID) + (1 | OriginSite)
## Data: dat2
##
## REML criterion at convergence: 164.6
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -2.50161 -0.62349 -0.00387 0.65442 2.23814
##
## Random effects:
## Groups Name Variance Std.Dev.
## CageSiteID:CagingSite (Intercept) 0.01254 0.1120
## CagingSite (Intercept) 0.00000 0.0000
## OriginSite (Intercept) 0.04173 0.2043
## Residual 0.12105 0.3479
## Number of obs: 179, groups:
## CageSiteID:CagingSite, 24; CagingSite, 4; OriginSite, 4
##
## Fixed effects:
## Estimate Std. Error t value
## (Intercept) 2.09001 0.28305 7.384
## TransplantContamLC 0.08377 0.07014 1.194
## InjectionPBS 0.01183 0.05248 0.225
## OriginContamLC -0.13976 0.21624 -0.646
## SizeEnd -0.08393 0.02290 -3.666
##
## Correlation of Fixed Effects:
## (Intr) TrnCLC InjPBS OrgCLC
## TrnsplntCLC -0.169
## InjectinPBS -0.123 -0.004
## OrignCntmLC -0.407 0.001 0.006
## SizeEnd -0.828 0.055 0.034 0.033
## optimizer (nloptwrap) convergence code: 0 (OK)
## boundary (singular) fit: see ?isSingular6.4.7 Refining the model
mod5 <-
lme4::lmer(
log(mMH2O2 + 1) ~ SizeEnd +
(1 | CagingSite / CageSiteID) + (1| OriginSite),
data = dat2,
na.action = na.exclude
)
performance::check_model(mod5)
car::Anova(mod5, type = "3")## Analysis of Deviance Table (Type III Wald chisquare tests)
##
## Response: log(mMH2O2 + 1)
## Chisq Df Pr(>Chisq)
## (Intercept) 70.728 1 < 2.2e-16 ***
## SizeEnd 13.668 1 0.0002182 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1summary(mod5)## Linear mixed model fit by REML ['lmerMod']
## Formula: log(mMH2O2 + 1) ~ SizeEnd + (1 | CagingSite/CageSiteID) + (1 |
## OriginSite)
## Data: dat2
##
## REML criterion at convergence: 157.7
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -2.61419 -0.65373 0.00172 0.62497 2.21411
##
## Random effects:
## Groups Name Variance Std.Dev.
## CageSiteID:CagingSite (Intercept) 1.400e-02 1.183e-01
## CagingSite (Intercept) 4.228e-11 6.502e-06
## OriginSite (Intercept) 3.266e-02 1.807e-01
## Residual 1.199e-01 3.463e-01
## Number of obs: 179, groups:
## CageSiteID:CagingSite, 24; CagingSite, 4; OriginSite, 4
##
## Fixed effects:
## Estimate Std. Error t value
## (Intercept) 2.06737 0.24582 8.410
## SizeEnd -0.08377 0.02266 -3.697
##
## Correlation of Fixed Effects:
## (Intr)
## SizeEnd -0.918
## optimizer (nloptwrap) convergence code: 0 (OK)
## boundary (singular) fit: see ?isSingularmodOXDam <- mod5
RmodOXDam <- MuMIn::r.squaredGLMM(modOXDam)The treatments has no effect on oxidative damage but the oxidative damage are lower in bigger fish Represent the relation between fish size and oxidative damage
plot(log(mMH2O2 + 1) ~ SizeEnd, data = dat2)
abline(b = -0.08377, a = 2.06737, col = "red")
Now that we have identified the best model, add sex as covariate to check whether results are sensitive NB: sample size is reduced when adding sex variable within the model, for this reason the sex effect on results is checked on the final model
6.4.8 Test for the sex effect
dat2 = dat2[is.na(dat2$Sex) == F, ]
modSex <-
lme4::lmer(
log(mMH2O2 + 1) ~ SizeEnd + Sex +
(1 | CagingSite / CageSiteID) + (1| OriginSite),
data = dat2,
na.action = na.exclude
)
car::Anova(modSex, type = "3")## Analysis of Deviance Table (Type III Wald chisquare tests)
##
## Response: log(mMH2O2 + 1)
## Chisq Df Pr(>Chisq)
## (Intercept) 70.9360 1 < 2.2e-16 ***
## SizeEnd 13.8796 1 0.0001949 ***
## Sex 0.0402 1 0.8411112
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1summary(modSex)## Linear mixed model fit by REML ['lmerMod']
## Formula: log(mMH2O2 + 1) ~ SizeEnd + Sex + (1 | CagingSite/CageSiteID) +
## (1 | OriginSite)
## Data: dat2
##
## REML criterion at convergence: 158.3
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -2.50997 -0.63249 0.01078 0.65634 2.33837
##
## Random effects:
## Groups Name Variance Std.Dev.
## CageSiteID:CagingSite (Intercept) 0.01358 0.1165
## CagingSite (Intercept) 0.00000 0.0000
## OriginSite (Intercept) 0.03354 0.1831
## Residual 0.11895 0.3449
## Number of obs: 178, groups:
## CageSiteID:CagingSite, 24; CagingSite, 4; OriginSite, 4
##
## Fixed effects:
## Estimate Std. Error t value
## (Intercept) 2.06736 0.24546 8.422
## SizeEnd -0.08459 0.02271 -3.726
## SexM 0.01120 0.05585 0.200
##
## Correlation of Fixed Effects:
## (Intr) SizEnd
## SizeEnd -0.912
## SexM 0.005 -0.107
## optimizer (nloptwrap) convergence code: 0 (OK)
## boundary (singular) fit: see ?isSingularThe sex effect is non-significant. The mod5 is thus the best model. Here, there is no interaction, and hence no posthoc test nor parallelism test to conduct
6.5 Antiox. Capacity
6.5.1 Check the data
dat2 = dat1[is.na(dat1$mMHCLO) == F, ]
# transform variable to approx. normality
dat2$mMHCLO.p <-
bimixt::boxcox(dat2$mMHCLO, car::powerTransform(dat2$mMHCLO)$lambda)
plot(dat2$mMHCLO.p, dat2$mMHCLO)
hist(dat2$mMHCLO.p)
6.5.2 Visualize
par(mfrow=c(2,3))
boxplot(mMHCLO.p ~ OriginContam, data = dat2)
boxplot(mMHCLO.p ~ TransplantContam, data = dat2)
boxplot(mMHCLO.p ~ Injection, data = dat2)
boxplot(mMHCLO.p ~ TransplantContam * Injection, data = dat2)
boxplot(mMHCLO.p ~ TransplantContam * OriginContam, data = dat2)
boxplot(mMHCLO.p ~ TransplantContam * OriginContam * Injection, data = dat2)
6.5.3 Build the full model
modfull <-
lme4::lmer(
mMHCLO.p ~ (TransplantContam + OriginContam + Injection) ^ 3 + SizeEnd +
(1 | CagingSite / CageSiteID) + (1| OriginSite),
data = dat2,
na.action = na.exclude
)
car::Anova(modfull, type = "3")## Analysis of Deviance Table (Type III Wald chisquare tests)
##
## Response: mMHCLO.p
## Chisq Df Pr(>Chisq)
## (Intercept) 233.3662 1 < 2e-16 ***
## TransplantContam 0.4058 1 0.52413
## OriginContam 2.9468 1 0.08605 .
## Injection 1.7544 1 0.18532
## SizeEnd 0.3068 1 0.57967
## TransplantContam:OriginContam 0.0314 1 0.85939
## TransplantContam:Injection 0.6411 1 0.42330
## OriginContam:Injection 2.4429 1 0.11806
## TransplantContam:OriginContam:Injection 3.0174 1 0.08238 .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1summary(modfull)## Linear mixed model fit by REML ['lmerMod']
## Formula: mMHCLO.p ~ (TransplantContam + OriginContam + Injection)^3 +
## SizeEnd + (1 | CagingSite/CageSiteID) + (1 | OriginSite)
## Data: dat2
##
## REML criterion at convergence: 541.7
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -2.7540 -0.5760 0.1430 0.6006 5.3445
##
## Random effects:
## Groups Name Variance Std.Dev.
## CageSiteID:CagingSite (Intercept) 1.662e-10 1.289e-05
## CagingSite (Intercept) 0.000e+00 0.000e+00
## OriginSite (Intercept) 4.487e-02 2.118e-01
## Residual 1.419e+00 1.191e+00
## Number of obs: 169, groups:
## CageSiteID:CagingSite, 24; CagingSite, 4; OriginSite, 4
##
## Fixed effects:
## Estimate Std. Error t value
## (Intercept) 11.99105 0.78494 15.276
## TransplantContamLC -0.22155 0.34781 -0.637
## OriginContamLC -0.72751 0.42380 -1.717
## InjectionPBS -0.46049 0.34766 -1.325
## SizeEnd -0.03909 0.07057 -0.554
## TransplantContamLC:OriginContamLC 0.09041 0.51039 0.177
## TransplantContamLC:InjectionPBS 0.39216 0.48976 0.801
## OriginContamLC:InjectionPBS 0.82024 0.52479 1.563
## TransplantContamLC:OriginContamLC:InjectionPBS -1.28948 0.74234 -1.737
##
## Correlation of Fixed Effects:
## (Intr) TrnCLC OrgCLC InjPBS SizEnd TrCLC:OCLC TCLC:I OCLC:I
## TrnsplntCLC -0.222
## OrignCntmLC -0.311 0.417
## InjectinPBS -0.227 0.510 0.420
## SizeEnd -0.929 -0.003 0.061 0.001
## TrnCLC:OCLC 0.122 -0.682 -0.614 -0.347 0.034
## TrnCLC:IPBS 0.113 -0.710 -0.293 -0.709 0.051 0.486
## OrgCLC:IPBS 0.166 -0.338 -0.598 -0.662 -0.017 0.495 0.469
## TCLC:OCLC:I -0.074 0.469 0.421 0.468 -0.033 -0.688 -0.660 -0.706
## optimizer (nloptwrap) convergence code: 0 (OK)
## boundary (singular) fit: see ?isSingular6.5.4 Refining the model
mod2 <-
lme4::lmer(
mMHCLO.p~ (TransplantContam + OriginContam + Injection) ^ 2 + SizeEnd +
(1 | CagingSite / CageSiteID) + (1| OriginSite),
data = dat2,
na.action = na.exclude
)
car::Anova(mod2, type = "3")## Analysis of Deviance Table (Type III Wald chisquare tests)
##
## Response: mMHCLO.p
## Chisq Df Pr(>Chisq)
## (Intercept) 230.6349 1 <2e-16 ***
## TransplantContam 0.0392 1 0.8430
## OriginContam 1.1930 1 0.2747
## Injection 0.3317 1 0.5646
## SizeEnd 0.3452 1 0.5569
## TransplantContam:OriginContam 1.9466 1 0.1630
## TransplantContam:Injection 0.2054 1 0.6504
## OriginContam:Injection 0.2239 1 0.6361
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1summary(mod2)## Linear mixed model fit by REML ['lmerMod']
## Formula: mMHCLO.p ~ (TransplantContam + OriginContam + Injection)^2 +
## SizeEnd + (1 | CagingSite/CageSiteID) + (1 | OriginSite)
## Data: dat2
##
## REML criterion at convergence: 545.9
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -2.8958 -0.5804 0.1787 0.6118 5.4241
##
## Random effects:
## Groups Name Variance Std.Dev.
## CageSiteID:CagingSite (Intercept) 0.00000 0.0000
## CagingSite (Intercept) 0.00000 0.0000
## OriginSite (Intercept) 0.03975 0.1994
## Residual 1.43820 1.1992
## Number of obs: 169, groups:
## CageSiteID:CagingSite, 24; CagingSite, 4; OriginSite, 4
##
## Fixed effects:
## Estimate Std. Error t value
## (Intercept) 11.87136 0.78170 15.187
## TransplantContamLC 0.06125 0.30928 0.198
## OriginContamLC -0.41438 0.37938 -1.092
## InjectionPBS -0.17813 0.30927 -0.576
## SizeEnd -0.04141 0.07049 -0.588
## TransplantContamLC:OriginContamLC -0.52047 0.37304 -1.395
## TransplantContamLC:InjectionPBS -0.16791 0.37048 -0.453
## OriginContamLC:InjectionPBS 0.17703 0.37413 0.473
##
## Correlation of Fixed Effects:
## (Intr) TrnCLC OrgCLC InjPBS SizEnd TCLC:O TCLC:I
## TrnsplntCLC -0.214
## OrignCntmLC -0.307 0.280
## InjectinPBS -0.220 0.372 0.283
## SizeEnd -0.936 0.013 0.084 0.019
## TrnCLC:OCLC 0.098 -0.560 -0.502 -0.040 0.016
## TrnCLC:IPBS 0.086 -0.604 -0.023 -0.603 0.038 0.059
## OrgCLC:IPBS 0.162 -0.011 -0.478 -0.531 -0.058 0.018 0.006
## optimizer (nloptwrap) convergence code: 0 (OK)
## boundary (singular) fit: see ?isSingular6.5.5 Refining the model
mod3 <-
lme4::lmer(
mMHCLO.p ~ (TransplantContam + OriginContam ) ^ 2 + Injection + SizeEnd +
(1 | CagingSite / CageSiteID) + (1| OriginSite),
data = dat2,
na.action = na.exclude
)
car::Anova(mod3, type = "3")## Analysis of Deviance Table (Type III Wald chisquare tests)
##
## Response: mMHCLO.p
## Chisq Df Pr(>Chisq)
## (Intercept) 240.1201 1 <2e-16 ***
## TransplantContam 0.0083 1 0.9274
## OriginContam 1.0066 1 0.3157
## Injection 1.0082 1 0.3153
## SizeEnd 0.2955 1 0.5867
## TransplantContam:OriginContam 1.9226 1 0.1656
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1summary(mod3)## Linear mixed model fit by REML ['lmerMod']
## Formula: mMHCLO.p ~ (TransplantContam + OriginContam)^2 + Injection +
## SizeEnd + (1 | CagingSite/CageSiteID) + (1 | OriginSite)
## Data: dat2
##
## REML criterion at convergence: 546.1
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -2.9016 -0.5463 0.1922 0.6084 5.4537
##
## Random effects:
## Groups Name Variance Std.Dev.
## CageSiteID:CagingSite (Intercept) 0.0000 0.0000
## CagingSite (Intercept) 0.0000 0.0000
## OriginSite (Intercept) 0.0387 0.1967
## Residual 1.4245 1.1935
## Number of obs: 169, groups:
## CageSiteID:CagingSite, 24; CagingSite, 4; OriginSite, 4
##
## Fixed effects:
## Estimate Std. Error t value
## (Intercept) 11.83934 0.76403 15.496
## TransplantContamLC -0.02235 0.24524 -0.091
## OriginContamLC -0.33167 0.33057 -1.003
## InjectionPBS -0.18506 0.18430 -1.004
## SizeEnd -0.03801 0.06992 -0.544
## TransplantContamLC:OriginContamLC -0.51381 0.37056 -1.387
##
## Correlation of Fixed Effects:
## (Intr) TrnCLC OrgCLC InjPBS SizEnd
## TrnsplntCLC -0.205
## OrignCntmLC -0.264 0.376
## InjectinPBS -0.142 0.008 0.034
## SizeEnd -0.948 0.045 0.065 0.019
## TrnCLC:OCLC 0.092 -0.660 -0.564 0.008 0.015
## optimizer (nloptwrap) convergence code: 0 (OK)
## boundary (singular) fit: see ?isSingular6.5.6 Refining the model
mod4 <-
lme4::lmer(
mMHCLO.p ~ TransplantContam + Injection + OriginContam + SizeEnd +
(1 | CagingSite / CageSiteID) + (1| OriginSite),
data = dat2,
na.action = na.exclude
)
car::Anova(mod4, type = "3")## Analysis of Deviance Table (Type III Wald chisquare tests)
##
## Response: mMHCLO.p
## Chisq Df Pr(>Chisq)
## (Intercept) 241.0178 1 < 2e-16 ***
## TransplantContam 1.7770 1 0.18252
## Injection 0.9884 1 0.32012
## OriginContam 4.2989 1 0.03814 *
## SizeEnd 0.3013 1 0.58308
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1summary(mod4)## Linear mixed model fit by REML ['lmerMod']
## Formula: mMHCLO.p ~ TransplantContam + Injection + OriginContam + SizeEnd +
## (1 | CagingSite/CageSiteID) + (1 | OriginSite)
## Data: dat2
##
## REML criterion at convergence: 547.8
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -2.9991 -0.5639 0.1525 0.6239 5.3481
##
## Random effects:
## Groups Name Variance Std.Dev.
## CageSiteID:CagingSite (Intercept) 0.00000 0.000
## CagingSite (Intercept) 0.00000 0.000
## OriginSite (Intercept) 0.04579 0.214
## Residual 1.43108 1.196
## Number of obs: 169, groups:
## CageSiteID:CagingSite, 24; CagingSite, 4; OriginSite, 4
##
## Fixed effects:
## Estimate Std. Error t value
## (Intercept) 11.95948 0.77035 15.525
## TransplantContamLC -0.24628 0.18475 -1.333
## InjectionPBS -0.18366 0.18473 -0.994
## OriginContamLC -0.59335 0.28618 -2.073
## SizeEnd -0.03880 0.07069 -0.549
##
## Correlation of Fixed Effects:
## (Intr) TrnCLC InjPBS OrgCLC
## TrnsplntCLC -0.192
## InjectinPBS -0.142 0.018
## OrignCntmLC -0.261 0.006 0.044
## SizeEnd -0.952 0.074 0.019 0.085
## optimizer (nloptwrap) convergence code: 0 (OK)
## boundary (singular) fit: see ?isSingular6.5.7 Refining the model
mod5 <-
lme4::lmer(
mMHCLO.p ~ OriginContam +
(1 | CagingSite / CageSiteID) + (1| OriginSite),
data = dat2,
na.action = na.exclude
)
performance::check_model(mod5)
car::Anova(mod5, type = "3")## Analysis of Deviance Table (Type III Wald chisquare tests)
##
## Response: mMHCLO.p
## Chisq Df Pr(>Chisq)
## (Intercept) 4829.6889 1 < 2e-16 ***
## OriginContam 5.5915 1 0.01805 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1summary(mod5)## Linear mixed model fit by REML ['lmerMod']
## Formula: mMHCLO.p ~ OriginContam + (1 | CagingSite/CageSiteID) + (1 |
## OriginSite)
## Data: dat2
##
## REML criterion at convergence: 544.1
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -3.1941 -0.5074 0.2039 0.6000 5.5700
##
## Random effects:
## Groups Name Variance Std.Dev.
## CageSiteID:CagingSite (Intercept) 0.000000 0.00000
## CagingSite (Intercept) 0.003901 0.06246
## OriginSite (Intercept) 0.020520 0.14325
## Residual 1.433492 1.19729
## Number of obs: 169, groups:
## CageSiteID:CagingSite, 24; CagingSite, 4; OriginSite, 4
##
## Fixed effects:
## Estimate Std. Error t value
## (Intercept) 11.3444 0.1632 69.496
## OriginContamLC -0.5580 0.2360 -2.365
##
## Correlation of Fixed Effects:
## (Intr)
## OrignCntmLC -0.667
## optimizer (nloptwrap) convergence code: 0 (OK)
## boundary (singular) fit: see ?isSingularmodantiOx <- mod5
RmodantiOx <- MuMIn::r.squaredGLMM(modantiOx)The origin of the fish affects the non-enzymatic antioxidant capacity (measured in plasma), With HC fish having higher non-enzymatic antioxidant capacity than fish from LC sites (see boxplot and table below).
boxplot(mMHCLO.p ~ OriginContam, data = dat2)
# compute mean and Se for LC and HC groups (on raw antioxidant capacity data - not transformed)
meanVal <-
data.frame(
mean = c(mean(dat2$mMHCLO[which(dat2$OriginContam == "LC")]),
mean(dat2$mMHCLO[which(dat2$OriginContam == "HC")])),
Se = c(
sd(dat2$mMHCLO[which(dat2$OriginContam == "LC")]) / sqrt(length(dat2$mMHCLO[which(dat2$OriginContam == "LC")])),
sd(dat2$mMHCLO[which(dat2$OriginContam == "HC")]) / sqrt(length(dat2$mMHCLO[which(dat2$OriginContam == "HC")]))
),
row.names = c("LC", "HC")
)
kableExtra::kable_classic(
kableExtra::kbl(meanVal),
bootstrap_options = c("striped", "hover", "condensed", "responsive"),
full_width = F,
html_font = "arial",
font_size = 10
)| mean | Se | |
|---|---|---|
| LC | 195.3241 | 6.786571 |
| HC | 223.7893 | 8.853048 |
Now that we have identified the best model, add sex as covariate to check whether results are sensitive NB: sample size is reduced when adding sex variable within the model, for this reason the sex effect on results is checked on the final model
6.5.8 Test for the sex effect
dat2 = dat2[is.na(dat2$Sex) == F, ]
modSex <-
lme4::lmer(
mMHCLO.p ~ OriginContam + Sex +
(1 | CagingSite / CageSiteID) + (1| OriginSite),
data = dat2,
na.action = na.exclude
)
car::Anova(modSex, type = "3")## Analysis of Deviance Table (Type III Wald chisquare tests)
##
## Response: mMHCLO.p
## Chisq Df Pr(>Chisq)
## (Intercept) 5096.4526 1 < 2e-16 ***
## OriginContam 7.5057 1 0.00615 **
## Sex 0.5553 1 0.45615
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1summary(modSex)## Linear mixed model fit by REML ['lmerMod']
## Formula: mMHCLO.p ~ OriginContam + Sex + (1 | CagingSite/CageSiteID) +
## (1 | OriginSite)
## Data: dat2
##
## REML criterion at convergence: 542
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -3.1498 -0.5333 0.1974 0.5922 5.5104
##
## Random effects:
## Groups Name Variance Std.Dev.
## CageSiteID:CagingSite (Intercept) 1.642e-09 4.052e-05
## CagingSite (Intercept) 4.225e-03 6.500e-02
## OriginSite (Intercept) 6.740e-03 8.210e-02
## Residual 1.443e+00 1.201e+00
## Number of obs: 168, groups:
## CageSiteID:CagingSite, 24; CagingSite, 4; OriginSite, 4
##
## Fixed effects:
## Estimate Std. Error t value
## (Intercept) 11.4000 0.1597 71.389
## OriginContamLC -0.5620 0.2051 -2.740
## SexM -0.1414 0.1897 -0.745
##
## Correlation of Fixed Effects:
## (Intr) OrgCLC
## OrignCntmLC -0.571
## SexM -0.473 -0.002
## optimizer (nloptwrap) convergence code: 0 (OK)
## boundary (singular) fit: see ?isSingularThe sex effect is non-significant. The mod5 is thus the best model. Here, there is no interaction, and hence no posthoc test nor parallelism test to conduct
6.6 local inflammatory Response
6.6.1 Check the data
dat2 = dat1[is.na(dat1$IR) == F, ]
hist(dat2$IR)
6.6.2 Visualize
par(mfrow=c(2,3))
boxplot(IR ~ OriginContam, data = dat2)
boxplot(IR ~ TransplantContam, data = dat2)
boxplot(IR ~ Injection, data = dat2)
boxplot(IR ~ TransplantContam * Injection, data = dat2)
boxplot(IR ~ TransplantContam * OriginContam, data = dat2)
boxplot(IR ~ TransplantContam * OriginContam * Injection, data = dat2)
6.6.3 Build the full model
modfull <-
lme4::lmer(
IR ~ (TransplantContam + OriginContam + Injection) ^ 3 + SizeEnd + IRTime +
(1 | CagingSite / CageSiteID) + (1| OriginSite),
data = dat2,
na.action = na.exclude
)
car::Anova(modfull, type = "3")## Analysis of Deviance Table (Type III Wald chisquare tests)
##
## Response: IR
## Chisq Df Pr(>Chisq)
## (Intercept) 2.0173 1 0.1555
## TransplantContam 1.5175 1 0.2180
## OriginContam 2.5784 1 0.1083
## Injection 49.8556 1 1.655e-12 ***
## SizeEnd 0.4385 1 0.5079
## IRTime 2.0751 1 0.1497
## TransplantContam:OriginContam 0.3677 1 0.5443
## TransplantContam:Injection 0.3178 1 0.5729
## OriginContam:Injection 0.0781 1 0.7799
## TransplantContam:OriginContam:Injection 0.1481 1 0.7004
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1summary(modfull)## Linear mixed model fit by REML ['lmerMod']
## Formula: IR ~ (TransplantContam + OriginContam + Injection)^3 + SizeEnd +
## IRTime + (1 | CagingSite/CageSiteID) + (1 | OriginSite)
## Data: dat2
##
## REML criterion at convergence: 1939.2
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -2.61224 -0.67264 -0.07626 0.66819 2.77716
##
## Random effects:
## Groups Name Variance Std.Dev.
## CageSiteID:CagingSite (Intercept) 1.013e+01 3.182e+00
## CagingSite (Intercept) 1.495e+01 3.867e+00
## OriginSite (Intercept) 2.309e-08 1.519e-04
## Residual 1.735e+02 1.317e+01
## Number of obs: 247, groups:
## CageSiteID:CagingSite, 24; CagingSite, 4; OriginSite, 4
##
## Fixed effects:
## Estimate Std. Error t value
## (Intercept) -1603.1248 1128.7057 -1.420
## TransplantContamLC -8.5645 6.9524 -1.232
## OriginContamLC -6.1207 3.8118 -1.606
## InjectionPBS -23.5048 3.3289 -7.061
## SizeEnd 0.4180 0.6313 0.662
## IRTime 34.0555 23.6410 1.441
## TransplantContamLC:OriginContamLC 3.3518 5.5275 0.606
## TransplantContamLC:InjectionPBS 2.6322 4.6689 0.564
## OriginContamLC:InjectionPBS -1.3575 4.8572 -0.279
## TransplantContamLC:OriginContamLC:InjectionPBS -2.5928 6.7380 -0.385
##
## Correlation of Fixed Effects:
## (Intr) TrnCLC OrgCLC InjPBS SizEnd IRTime TrCLC:OCLC TCLC:I OCLC:I
## TrnsplntCLC 0.632
## OrignCntmLC 0.040 0.291
## InjectinPBS 0.038 0.252 0.417
## SizeEnd 0.217 0.165 0.055 0.022
## IRTime -1.000 -0.634 -0.042 -0.039 -0.222
## TrnCLC:OCLC 0.277 -0.187 -0.675 -0.275 0.070 -0.276
## TrnCLC:IPBS -0.022 -0.339 -0.296 -0.713 0.001 0.023 0.402
## OrgCLC:IPBS -0.041 -0.183 -0.599 -0.686 -0.023 0.042 0.400 0.489
## TCLC:OCLC:I 0.027 0.242 0.431 0.494 0.004 -0.027 -0.568 -0.693 -0.721
## optimizer (nloptwrap) convergence code: 0 (OK)
## boundary (singular) fit: see ?isSingular6.6.4 Refining the model
mod2 <-
lme4::lmer(
IR~ (TransplantContam + OriginContam + Injection) ^ 2 + SizeEnd + IRTime +
(1 | CagingSite / CageSiteID) + (1| OriginSite),
data = dat2,
na.action = na.exclude
)
car::Anova(mod2, type = "3")## Analysis of Deviance Table (Type III Wald chisquare tests)
##
## Response: IR
## Chisq Df Pr(>Chisq)
## (Intercept) 1.9876 1 0.1586
## TransplantContam 1.3775 1 0.2405
## OriginContam 2.5466 1 0.1105
## Injection 62.7080 1 2.397e-15 ***
## SizeEnd 0.4401 1 0.5071
## IRTime 2.0443 1 0.1528
## TransplantContam:OriginContam 0.2225 1 0.6372
## TransplantContam:Injection 0.1702 1 0.6799
## OriginContam:Injection 0.6470 1 0.4212
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1summary(mod2)## Linear mixed model fit by REML ['lmerMod']
## Formula: IR ~ (TransplantContam + OriginContam + Injection)^2 + SizeEnd +
## IRTime + (1 | CagingSite/CageSiteID) + (1 | OriginSite)
## Data: dat2
##
## REML criterion at convergence: 1945
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -2.63906 -0.68254 -0.06801 0.67242 2.80334
##
## Random effects:
## Groups Name Variance Std.Dev.
## CageSiteID:CagingSite (Intercept) 1.024e+01 3.199e+00
## CagingSite (Intercept) 1.492e+01 3.863e+00
## OriginSite (Intercept) 2.530e-10 1.591e-05
## Residual 1.728e+02 1.314e+01
## Number of obs: 247, groups:
## CageSiteID:CagingSite, 24; CagingSite, 4; OriginSite, 4
##
## Fixed effects:
## Estimate Std. Error t value
## (Intercept) -1590.5868 1128.2249 -1.410
## TransplantContamLC -7.9146 6.7435 -1.174
## OriginContamLC -5.4893 3.4398 -1.596
## InjectionPBS -22.8716 2.8882 -7.919
## SizeEnd 0.4183 0.6306 0.663
## IRTime 33.7869 23.6305 1.430
## TransplantContamLC:OriginContamLC 2.1474 4.5529 0.472
## TransplantContamLC:InjectionPBS 1.3857 3.3590 0.413
## OriginContamLC:InjectionPBS -2.7037 3.3613 -0.804
##
## Correlation of Fixed Effects:
## (Intr) TrnCLC OrgCLC InjPBS SizEnd IRTime TCLC:O TCLC:I
## TrnsplntCLC 0.645
## OrignCntmLC 0.032 0.213
## InjectinPBS 0.028 0.157 0.259
## SizeEnd 0.216 0.169 0.059 0.023
## IRTime -1.000 -0.647 -0.033 -0.030 -0.221
## TrnCLC:OCLC 0.355 -0.063 -0.579 0.008 0.088 -0.354
## TrnCLC:IPBS -0.006 -0.245 0.004 -0.591 0.005 0.006 0.014
## OrgCLC:IPBS -0.032 -0.012 -0.460 -0.547 -0.029 0.033 -0.017 -0.021
## optimizer (nloptwrap) convergence code: 0 (OK)
## boundary (singular) fit: see ?isSingular6.6.5 Refining the model
mod3 <-
lme4::lmer(
IR ~ (TransplantContam + OriginContam) ^ 2 + (TransplantContam + Injection) ^ 2 + SizeEnd + IRTime +
(1 | CagingSite / CageSiteID) + (1| OriginSite),
data = dat2,
na.action = na.exclude
)
car::Anova(mod3, type = "3")## Analysis of Deviance Table (Type III Wald chisquare tests)
##
## Response: IR
## Chisq Df Pr(>Chisq)
## (Intercept) 2.0589 1 0.15132
## TransplantContam 1.4011 1 0.23654
## OriginContam 4.8898 1 0.02702 *
## Injection 99.9115 1 < 2e-16 ***
## SizeEnd 0.4089 1 0.52255
## IRTime 2.1186 1 0.14551
## TransplantContam:OriginContam 0.2101 1 0.64666
## TransplantContam:Injection 0.1563 1 0.69256
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1summary(mod3)## Linear mixed model fit by REML ['lmerMod']
## Formula: IR ~ (TransplantContam + OriginContam)^2 + (TransplantContam +
## Injection)^2 + SizeEnd + IRTime + (1 | CagingSite/CageSiteID) +
## (1 | OriginSite)
## Data: dat2
##
## REML criterion at convergence: 1949.9
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -2.6898 -0.6877 -0.0809 0.6640 2.7638
##
## Random effects:
## Groups Name Variance Std.Dev.
## CageSiteID:CagingSite (Intercept) 10.34 3.215
## CagingSite (Intercept) 14.86 3.855
## OriginSite (Intercept) 0.00 0.000
## Residual 172.45 13.132
## Number of obs: 247, groups:
## CageSiteID:CagingSite, 24; CagingSite, 4; OriginSite, 4
##
## Fixed effects:
## Estimate Std. Error t value
## (Intercept) -1618.3861 1127.8888 -1.435
## TransplantContamLC -7.9789 6.7407 -1.184
## OriginContamLC -6.7624 3.0581 -2.211
## InjectionPBS -24.1425 2.4153 -9.996
## SizeEnd 0.4030 0.6302 0.639
## IRTime 34.3843 23.6227 1.456
## TransplantContamLC:OriginContamLC 2.0892 4.5577 0.458
## TransplantContamLC:InjectionPBS 1.3266 3.3553 0.395
##
## Correlation of Fixed Effects:
## (Intr) TrnCLC OrgCLC InjPBS SizEnd IRTime TCLC:O
## TrnsplntCLC 0.645
## OrignCntmLC 0.019 0.234
## InjectinPBS 0.013 0.180 0.010
## SizeEnd 0.215 0.168 0.051 0.009
## IRTime -1.000 -0.647 -0.021 -0.014 -0.220
## TrnCLC:OCLC 0.354 -0.064 -0.661 -0.001 0.087 -0.354
## TrnCLC:IPBS -0.006 -0.245 -0.007 -0.720 0.004 0.007 0.013
## optimizer (nloptwrap) convergence code: 0 (OK)
## boundary (singular) fit: see ?isSingular6.6.6 Refining the model
mod4 <-
lme4::lmer(
IR ~ TransplantContam + Injection + OriginContam + SizeEnd + IRTime +
(1 | CagingSite / CageSiteID) + (1| OriginSite),
data = dat2,
na.action = na.exclude
)
car::Anova(mod4, type = "3")## Analysis of Deviance Table (Type III Wald chisquare tests)
##
## Response: IR
## Chisq Df Pr(>Chisq)
## (Intercept) 3.0220 1 0.082145 .
## TransplantContam 1.2373 1 0.265988
## Injection 196.5979 1 < 2.2e-16 ***
## OriginContam 6.7803 1 0.009217 **
## SizeEnd 0.3747 1 0.540431
## IRTime 3.0957 1 0.078499 .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1summary(mod4)## Linear mixed model fit by REML ['lmerMod']
## Formula: IR ~ TransplantContam + Injection + OriginContam + SizeEnd +
## IRTime + (1 | CagingSite/CageSiteID) + (1 | OriginSite)
## Data: dat2
##
## REML criterion at convergence: 1959.4
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -2.74699 -0.69578 -0.05167 0.67464 2.83876
##
## Random effects:
## Groups Name Variance Std.Dev.
## CageSiteID:CagingSite (Intercept) 9.211 3.035
## CagingSite (Intercept) 14.842 3.853
## OriginSite (Intercept) 0.000 0.000
## Residual 171.806 13.107
## Number of obs: 247, groups:
## CageSiteID:CagingSite, 24; CagingSite, 4; OriginSite, 4
##
## Fixed effects:
## Estimate Std. Error t value
## (Intercept) -1805.6127 1038.6776 -1.738
## TransplantContamLC -7.1777 6.4527 -1.112
## InjectionPBS -23.4627 1.6734 -14.021
## OriginContamLC -5.8468 2.2454 -2.604
## SizeEnd 0.3811 0.6225 0.612
## IRTime 38.2893 21.7619 1.759
##
## Correlation of Fixed Effects:
## (Intr) TrnCLC InjPBS OrgCLC SizEnd
## TrnsplntCLC 0.732
## InjectinPBS 0.008 0.005
## OrignCntmLC 0.364 0.266 0.021
## SizeEnd 0.201 0.183 0.015 0.148
## IRTime -1.000 -0.734 -0.009 -0.365 -0.207
## optimizer (nloptwrap) convergence code: 0 (OK)
## boundary (singular) fit: see ?isSingular6.6.7 Refining the model
mod5 <-
lme4::lmer(
IR ~ OriginContam + Injection + IRTime +
(1 | CagingSite / CageSiteID) + (1| OriginSite),
data = dat2,
na.action = na.exclude
)## Warning in checkConv(attr(opt, "derivs"), opt$par, ctrl = control$checkConv, :
## unable to evaluate scaled gradient## Warning in checkConv(attr(opt, "derivs"), opt$par, ctrl = control$checkConv, :
## Model failed to converge: degenerate Hessian with 1 negative eigenvaluesperformance::check_model(mod5)
car::Anova(mod5, type = "3")## Analysis of Deviance Table (Type III Wald chisquare tests)
##
## Response: IR
## Chisq Df Pr(>Chisq)
## (Intercept) 1.7985 1 0.17990
## OriginContam 5.9245 1 0.01493 *
## Injection 199.6451 1 < 2e-16 ***
## IRTime 1.9059 1 0.16742
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1summary(mod5)## Linear mixed model fit by REML ['lmerMod']
## Formula:
## IR ~ OriginContam + Injection + IRTime + (1 | CagingSite/CageSiteID) +
## (1 | OriginSite)
## Data: dat2
##
## REML criterion at convergence: 1983.3
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -2.69902 -0.68555 -0.06849 0.67737 2.85502
##
## Random effects:
## Groups Name Variance Std.Dev.
## CageSiteID:CagingSite (Intercept) 9.957e+00 3.155436
## CagingSite (Intercept) 1.626e+01 4.032053
## OriginSite (Intercept) 1.502e-05 0.003876
## Residual 1.709e+02 13.072306
## Number of obs: 249, groups:
## CageSiteID:CagingSite, 24; CagingSite, 4; OriginSite, 4
##
## Fixed effects:
## Estimate Std. Error t value
## (Intercept) -968.190 721.950 -1.341
## OriginContamLC -5.297 2.176 -2.434
## InjectionPBS -23.495 1.663 -14.130
## IRTime 20.809 15.073 1.381
##
## Correlation of Fixed Effects:
## (Intr) OrgCLC InjPBS
## OrignCntmLC 0.254
## InjectinPBS 0.004 0.024
## IRTime -1.000 -0.255 -0.005
## optimizer (nloptwrap) convergence code: 0 (OK)
## unable to evaluate scaled gradient
## Model failed to converge: degenerate Hessian with 1 negative eigenvalues6.6.8 Refining the model
mod6 <-
lme4::lmer(
IR ~ Injection +
(1 | CagingSite / CageSiteID) + (1| OriginSite),
data = dat2,
na.action = na.exclude
)
performance::check_model(mod6)
car::Anova(mod6, type = "3")## Analysis of Deviance Table (Type III Wald chisquare tests)
##
## Response: IR
## Chisq Df Pr(>Chisq)
## (Intercept) 116.67 1 < 2.2e-16 ***
## Injection 198.82 1 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1summary(mod6)## Linear mixed model fit by REML ['lmerMod']
## Formula: IR ~ Injection + (1 | CagingSite/CageSiteID) + (1 | OriginSite)
## Data: dat2
##
## REML criterion at convergence: 1998.1
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -2.6216 -0.6995 -0.0447 0.6676 2.7812
##
## Random effects:
## Groups Name Variance Std.Dev.
## CageSiteID:CagingSite (Intercept) 11.357 3.370
## CagingSite (Intercept) 7.254 2.693
## OriginSite (Intercept) 9.178 3.030
## Residual 170.910 13.073
## Number of obs: 249, groups:
## CageSiteID:CagingSite, 24; CagingSite, 4; OriginSite, 4
##
## Fixed effects:
## Estimate Std. Error t value
## (Intercept) 26.195 2.425 10.8
## InjectionPBS -23.448 1.663 -14.1
##
## Correlation of Fixed Effects:
## (Intr)
## InjectinPBS -0.322modIR <- mod6
RmodIR <- MuMIn::r.squaredGLMM(modIR)The immune challenge led to a significant skin swelling, and hence triggered the local immune response.
boxplot(IR ~ Injection, data = dat2)
# compute mean and Se for LC and HC groups (on raw antioxidant capacity data - not transformed)
meanVal <-
data.frame(
mean = c(mean(dat2$IR[which(dat2$Injection == "PBS")]),
mean(dat2$IR[which(dat2$Injection == "AMIX")])),
Se = c(
sd(dat2$IR[which(dat2$Injection == "PBS")]) / sqrt(length(dat2$IR[which(dat2$Injection == "PBS")])),
sd(dat2$IR[which(dat2$Injection == "AMIX")]) / sqrt(length(dat2$IR[which(dat2$Injection == "AMIX")]))
),
row.names = c("PBS", "AMIX")
)
kableExtra::kable_classic(
kableExtra::kbl(meanVal),
bootstrap_options = c("striped", "hover", "condensed", "responsive"),
full_width = F,
html_font = "arial",
font_size = 10
)| mean | Se | |
|---|---|---|
| PBS | 2.806122 | 1.288356 |
| AMIX | 26.255052 | 1.214435 |
Now that we have identified the best model, add sex as covariate to check whether results are sensitive NB: sample size is reduced when adding sex variable within the model, for this reason the sex effect on results is checked on the final model
6.6.9 Test for the sex effect
dat2 = dat2[is.na(dat2$Sex) == F, ]
modSex <-
lme4::lmer(
IR ~ Injection + Sex +
(1 | CagingSite / CageSiteID) + (1| OriginSite),
data = dat2,
na.action = na.exclude
)
car::Anova(modSex, type = "3")## Analysis of Deviance Table (Type III Wald chisquare tests)
##
## Response: IR
## Chisq Df Pr(>Chisq)
## (Intercept) 109.9042 1 <2e-16 ***
## Injection 195.5905 1 <2e-16 ***
## Sex 0.0782 1 0.7798
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1summary(modSex)## Linear mixed model fit by REML ['lmerMod']
## Formula: IR ~ Injection + Sex + (1 | CagingSite/CageSiteID) + (1 | OriginSite)
## Data: dat2
##
## REML criterion at convergence: 1979.6
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -2.62888 -0.68051 -0.04432 0.66882 2.78725
##
## Random effects:
## Groups Name Variance Std.Dev.
## CageSiteID:CagingSite (Intercept) 12.217 3.495
## CagingSite (Intercept) 6.526 2.555
## OriginSite (Intercept) 9.260 3.043
## Residual 171.764 13.106
## Number of obs: 247, groups:
## CageSiteID:CagingSite, 24; CagingSite, 4; OriginSite, 4
##
## Fixed effects:
## Estimate Std. Error t value
## (Intercept) 26.3880 2.5171 10.48
## InjectionPBS -23.4780 1.6788 -13.98
## SexM -0.4957 1.7726 -0.28
##
## Correlation of Fixed Effects:
## (Intr) InjPBS
## InjectinPBS -0.337
## SexM -0.295 0.081The sex effect is non-significant. The mod6 is thus the best model. Here, there is no interaction, and hence no posthoc test nor parallelism test to conduct
6.7 NL inflammatory Response
6.7.1 compute NL ratio
# compute NL ratio
dat2 = dat1[is.na(dat1$Lymphocytes) == F, ]
dat2 = dat2[is.na(dat2$Neutrophils) == F, ]
dat2$NLRatio = dat2$Neutrophils / dat2$Lymphocytes
# transform variable to approx. normality
dat2$NLRatio.p <-
bimixt::boxcox(dat2$NLRatio + 1, car::powerTransform(dat2$NLRatio + 1)$lambda)6.7.2 Visualize
par(mfrow=c(2,3))
boxplot(NLRatio.p ~ OriginContam, data = dat2)
boxplot(NLRatio.p ~ TransplantContam, data = dat2)
boxplot(NLRatio.p ~ Injection, data = dat2)
boxplot(NLRatio.p ~ TransplantContam * Injection, data = dat2)
boxplot(NLRatio.p ~ TransplantContam * OriginContam, data = dat2)
boxplot(NLRatio.p ~ TransplantContam * OriginContam * Injection, data = dat2)
6.7.3 Build the full model
modfull <-
lme4::lmer(
NLRatio.p ~ (TransplantContam + OriginContam + Injection) ^ 3 + SizeEnd +
(1 | CagingSite / CageSiteID) + (1| OriginSite),
data = dat2,
na.action = na.exclude
)
car::Anova(modfull, type = "3")## Analysis of Deviance Table (Type III Wald chisquare tests)
##
## Response: NLRatio.p
## Chisq Df Pr(>Chisq)
## (Intercept) 0.3430 1 0.558086
## TransplantContam 0.7926 1 0.373303
## OriginContam 2.7926 1 0.094703 .
## Injection 0.0309 1 0.860455
## SizeEnd 7.0077 1 0.008116 **
## TransplantContam:OriginContam 6.5866 1 0.010275 *
## TransplantContam:Injection 0.1674 1 0.682424
## OriginContam:Injection 2.1609 1 0.141565
## TransplantContam:OriginContam:Injection 2.0030 1 0.156987
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1summary(modfull)## Linear mixed model fit by REML ['lmerMod']
## Formula: NLRatio.p ~ (TransplantContam + OriginContam + Injection)^3 +
## SizeEnd + (1 | CagingSite/CageSiteID) + (1 | OriginSite)
## Data: dat2
##
## REML criterion at convergence: -977.9
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -2.37113 -0.70032 -0.04037 0.62365 2.54298
##
## Random effects:
## Groups Name Variance Std.Dev.
## CageSiteID:CagingSite (Intercept) 1.114e-05 3.337e-03
## CagingSite (Intercept) 1.699e-12 1.304e-06
## OriginSite (Intercept) 5.993e-05 7.742e-03
## Residual 5.743e-04 2.396e-02
## Number of obs: 229, groups:
## CageSiteID:CagingSite, 24; CagingSite, 4; OriginSite, 4
##
## Fixed effects:
## Estimate Std. Error t value
## (Intercept) 0.008906 0.015206 0.586
## TransplantContamLC -0.005651 0.006348 -0.890
## OriginContamLC -0.016786 0.010045 -1.671
## InjectionPBS -0.001071 0.006094 -0.176
## SizeEnd 0.003564 0.001346 2.647
## TransplantContamLC:OriginContamLC 0.023390 0.009114 2.566
## TransplantContamLC:InjectionPBS -0.003557 0.008693 -0.409
## OriginContamLC:InjectionPBS 0.013173 0.008961 1.470
## TransplantContamLC:OriginContamLC:InjectionPBS -0.018051 0.012754 -1.415
##
## Correlation of Fixed Effects:
## (Intr) TrnCLC OrgCLC InjPBS SizEnd TrCLC:OCLC TCLC:I OCLC:I
## TrnsplntCLC -0.227
## OrignCntmLC -0.343 0.312
## InjectinPBS -0.195 0.464 0.294
## SizeEnd -0.886 0.024 0.018 0.001
## TrnCLC:OCLC 0.121 -0.695 -0.446 -0.323 0.026
## TrnCLC:IPBS 0.131 -0.662 -0.205 -0.701 0.005 0.461
## OrgCLC:IPBS 0.135 -0.316 -0.412 -0.680 -0.003 0.454 0.476
## TCLC:OCLC:I -0.097 0.451 0.289 0.477 0.005 -0.650 -0.682 -0.702
## optimizer (nloptwrap) convergence code: 0 (OK)
## boundary (singular) fit: see ?isSingular6.7.4 Refining the model
mod2 <-
lme4::lmer(
NLRatio.p ~ (TransplantContam + OriginContam + Injection) ^ 2 + SizeEnd +
(1 | CagingSite / CageSiteID) + (1| OriginSite),
data = dat2,
na.action = na.exclude
)
car::Anova(mod2, type = "3")## Analysis of Deviance Table (Type III Wald chisquare tests)
##
## Response: NLRatio.p
## Chisq Df Pr(>Chisq)
## (Intercept) 0.1801 1 0.671308
## TransplantContam 0.0842 1 0.771721
## OriginContam 1.8013 1 0.179559
## Injection 0.3106 1 0.577334
## SizeEnd 7.2018 1 0.007283 **
## TransplantContam:OriginContam 4.9634 1 0.025889 *
## TransplantContam:Injection 3.4759 1 0.062269 .
## OriginContam:Injection 0.4586 1 0.498268
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1summary(mod2)## Linear mixed model fit by REML ['lmerMod']
## Formula: NLRatio.p ~ (TransplantContam + OriginContam + Injection)^2 +
## SizeEnd + (1 | CagingSite/CageSiteID) + (1 | OriginSite)
## Data: dat2
##
## REML criterion at convergence: -982.8
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -2.44899 -0.72905 -0.04652 0.62828 2.62195
##
## Random effects:
## Groups Name Variance Std.Dev.
## CageSiteID:CagingSite (Intercept) 7.200e-06 0.002683
## CagingSite (Intercept) 0.000e+00 0.000000
## OriginSite (Intercept) 5.874e-05 0.007664
## Residual 5.797e-04 0.024077
## Number of obs: 229, groups:
## CageSiteID:CagingSite, 24; CagingSite, 4; OriginSite, 4
##
## Fixed effects:
## Estimate Std. Error t value
## (Intercept) 0.006413 0.015112 0.424
## TransplantContamLC -0.001616 0.005570 -0.290
## OriginContamLC -0.012745 0.009497 -1.342
## InjectionPBS 0.002997 0.005378 0.557
## SizeEnd 0.003617 0.001348 2.684
## TransplantContamLC:OriginContamLC 0.015062 0.006761 2.228
## TransplantContamLC:InjectionPBS -0.011911 0.006389 -1.864
## OriginContamLC:InjectionPBS 0.004340 0.006409 0.677
##
## Correlation of Fixed Effects:
## (Intr) TrnCLC OrgCLC InjPBS SizEnd TCLC:O TCLC:I
## TrnsplntCLC -0.204
## OrignCntmLC -0.327 0.207
## InjectinPBS -0.171 0.324 0.188
## SizeEnd -0.892 0.025 0.018 -0.001
## TrnCLC:OCLC 0.073 -0.588 -0.350 -0.020 0.039
## TrnCLC:IPBS 0.089 -0.554 -0.011 -0.583 0.012 0.033
## OrgCLC:IPBS 0.095 0.002 -0.312 -0.551 0.000 -0.004 -0.004
## optimizer (nloptwrap) convergence code: 0 (OK)
## boundary (singular) fit: see ?isSingular6.7.5 Refining the model
mod3 <-
lme4::lmer(
NLRatio.p ~ (TransplantContam + OriginContam) ^ 2 + (TransplantContam + Injection) ^ 2 + SizeEnd +
(1 | CagingSite / CageSiteID) + (1| OriginSite),
data = dat2,
na.action = na.exclude
)
car::Anova(mod3, type = "3")## Analysis of Deviance Table (Type III Wald chisquare tests)
##
## Response: NLRatio.p
## Chisq Df Pr(>Chisq)
## (Intercept) 0.1401 1 0.708140
## TransplantContam 0.0832 1 0.772984
## OriginContam 1.3888 1 0.238601
## Injection 1.2517 1 0.263235
## SizeEnd 7.1261 1 0.007597 **
## TransplantContam:OriginContam 4.8805 1 0.027162 *
## TransplantContam:Injection 3.4859 1 0.061893 .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1summary(mod3)## Linear mixed model fit by REML ['lmerMod']
## Formula: NLRatio.p ~ (TransplantContam + OriginContam)^2 + (TransplantContam +
## Injection)^2 + SizeEnd + (1 | CagingSite/CageSiteID) + (1 |
## OriginSite)
## Data: dat2
##
## REML criterion at convergence: -990.6
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -2.49767 -0.71902 -0.08241 0.62687 2.58596
##
## Random effects:
## Groups Name Variance Std.Dev.
## CageSiteID:CagingSite (Intercept) 8.585e-06 0.002930
## CagingSite (Intercept) 0.000e+00 0.000000
## OriginSite (Intercept) 5.974e-05 0.007729
## Residual 5.772e-04 0.024026
## Number of obs: 229, groups:
## CageSiteID:CagingSite, 24; CagingSite, 4; OriginSite, 4
##
## Fixed effects:
## Estimate Std. Error t value
## (Intercept) 0.005638 0.015062 0.374
## TransplantContamLC -0.001616 0.005601 -0.288
## OriginContamLC -0.010722 0.009098 -1.178
## InjectionPBS 0.005011 0.004479 1.119
## SizeEnd 0.003597 0.001347 2.669
## TransplantContamLC:OriginContamLC 0.015060 0.006817 2.209
## TransplantContamLC:InjectionPBS -0.011904 0.006376 -1.867
##
## Correlation of Fixed Effects:
## (Intr) TrnCLC OrgCLC InjPBS SizEnd TCLC:O
## TrnsplntCLC -0.206
## OrignCntmLC -0.317 0.220
## InjectinPBS -0.143 0.387 0.020
## SizeEnd -0.894 0.025 0.019 -0.001
## TrnCLC:OCLC 0.074 -0.590 -0.370 -0.026 0.039
## TrnCLC:IPBS 0.090 -0.550 -0.013 -0.702 0.012 0.033
## optimizer (nloptwrap) convergence code: 0 (OK)
## boundary (singular) fit: see ?isSingular6.7.6 Refining the model
mod4 <-
lme4::lmer(
NLRatio.p ~ (TransplantContam + OriginContam) ^ 2 + Injection + SizeEnd +
(1 | CagingSite / CageSiteID) + (1| OriginSite),
data = dat2,
na.action = na.exclude
)
car::Anova(mod4, type = "3")## Analysis of Deviance Table (Type III Wald chisquare tests)
##
## Response: NLRatio.p
## Chisq Df Pr(>Chisq)
## (Intercept) 0.2773 1 0.598502
## TransplantContam 2.5359 1 0.111286
## OriginContam 1.4604 1 0.226867
## Injection 0.0717 1 0.788917
## SizeEnd 7.2706 1 0.007009 **
## TransplantContam:OriginContam 5.2920 1 0.021424 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1summary(mod4)## Linear mixed model fit by REML ['lmerMod']
## Formula: NLRatio.p ~ (TransplantContam + OriginContam)^2 + Injection +
## SizeEnd + (1 | CagingSite/CageSiteID) + (1 | OriginSite)
## Data: dat2
##
## REML criterion at convergence: -995.4
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -2.36244 -0.75384 -0.03035 0.63291 2.44956
##
## Random effects:
## Groups Name Variance Std.Dev.
## CageSiteID:CagingSite (Intercept) 6.332e-06 0.002516
## CagingSite (Intercept) 0.000e+00 0.000000
## OriginSite (Intercept) 5.984e-05 0.007736
## Residual 5.853e-04 0.024194
## Number of obs: 229, groups:
## CageSiteID:CagingSite, 24; CagingSite, 4; OriginSite, 4
##
## Fixed effects:
## Estimate Std. Error t value
## (Intercept) 0.0079284 0.0150571 0.527
## TransplantContamLC -0.0073654 0.0046252 -1.592
## OriginContamLC -0.0109687 0.0090765 -1.208
## InjectionPBS -0.0008599 0.0032118 -0.268
## SizeEnd 0.0036515 0.0013542 2.696
## TransplantContamLC:OriginContamLC 0.0155111 0.0067427 2.300
##
## Correlation of Fixed Effects:
## (Intr) TrnCLC OrgCLC InjPBS SizEnd
## TrnsplntCLC -0.186
## OrignCntmLC -0.315 0.252
## InjectinPBS -0.113 0.001 0.015
## SizeEnd -0.900 0.038 0.020 0.010
## TrnCLC:OCLC 0.070 -0.683 -0.367 -0.004 0.039
## optimizer (nloptwrap) convergence code: 0 (OK)
## boundary (singular) fit: see ?isSingular6.7.7 Refining the model
mod5 <-
lme4::lmer(
NLRatio.p ~ (TransplantContam + OriginContam) ^ 2 + SizeEnd +
(1 | CagingSite / CageSiteID) + (1| OriginSite),
data = dat2,
na.action = na.exclude
)
car::Anova(mod5, type = "3")## Analysis of Deviance Table (Type III Wald chisquare tests)
##
## Response: NLRatio.p
## Chisq Df Pr(>Chisq)
## (Intercept) 0.2548 1 0.613743
## TransplantContam 2.5332 1 0.111473
## OriginContam 1.4435 1 0.229574
## SizeEnd 7.2813 1 0.006967 **
## TransplantContam:OriginContam 5.2818 1 0.021550 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1summary(mod5)## Linear mixed model fit by REML ['lmerMod']
## Formula: NLRatio.p ~ (TransplantContam + OriginContam)^2 + SizeEnd + (1 |
## CagingSite/CageSiteID) + (1 | OriginSite)
## Data: dat2
##
## REML criterion at convergence: -1005
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -2.38697 -0.74246 -0.04835 0.65242 2.43644
##
## Random effects:
## Groups Name Variance Std.Dev.
## CageSiteID:CagingSite (Intercept) 6.626e-06 0.002574
## CagingSite (Intercept) 0.000e+00 0.000000
## OriginSite (Intercept) 6.021e-05 0.007760
## Residual 5.826e-04 0.024138
## Number of obs: 229, groups:
## CageSiteID:CagingSite, 24; CagingSite, 4; OriginSite, 4
##
## Fixed effects:
## Estimate Std. Error t value
## (Intercept) 0.007545 0.014947 0.505
## TransplantContamLC -0.007363 0.004626 -1.592
## OriginContamLC -0.010929 0.009096 -1.201
## SizeEnd 0.003648 0.001352 2.698
## TransplantContamLC:OriginContamLC 0.015498 0.006743 2.298
##
## Correlation of Fixed Effects:
## (Intr) TrnCLC OrgCLC SizEnd
## TrnsplntCLC -0.187
## OrignCntmLC -0.317 0.251
## SizeEnd -0.904 0.038 0.019
## TrnCLC:OCLC 0.070 -0.684 -0.366 0.039
## optimizer (nloptwrap) convergence code: 0 (OK)
## boundary (singular) fit: see ?isSingularmodNLRatio.p <- mod5
RmodNLRatio.p <- MuMIn::r.squaredGLMM(modNLRatio.p )Here, the interactions between fish origin and the transplant site are significant. Also, the bigger the fish, the higher the NL ratio and hence the immune inflammatory response.
# check the relationships between th NlRatio and fish size
plot(NLRatio.p ~ SizeEnd, data = dat2)
abline(a = 0.007545 , b = 0.003648 , col = "red")
Now that we have identified the best model, add sex as covariate to check whether results are sensitive NB: sample size is reduced when adding sex variable within the model, for this reason the sex effect on results is checked on the final model
6.7.8 Test for the sex effect
dat2 = dat2[is.na(dat2$Sex) == F, ]
modSex <-
lme4::lmer(
NLRatio.p ~ (TransplantContam + OriginContam) ^ 2 + SizeEnd + Sex +
(1 | CagingSite / CageSiteID) + (1| OriginSite),
data = dat2,
na.action = na.exclude
)
car::Anova(modSex, type = "3")## Analysis of Deviance Table (Type III Wald chisquare tests)
##
## Response: NLRatio.p
## Chisq Df Pr(>Chisq)
## (Intercept) 0.2193 1 0.639579
## TransplantContam 2.3167 1 0.127989
## OriginContam 1.4037 1 0.236111
## SizeEnd 7.7020 1 0.005516 **
## Sex 0.4454 1 0.504542
## TransplantContam:OriginContam 4.9488 1 0.026109 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1summary(modSex)## Linear mixed model fit by REML ['lmerMod']
## Formula: NLRatio.p ~ (TransplantContam + OriginContam)^2 + SizeEnd + Sex +
## (1 | CagingSite/CageSiteID) + (1 | OriginSite)
## Data: dat2
##
## REML criterion at convergence: -990.4
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -2.33274 -0.75679 -0.06933 0.65173 2.47006
##
## Random effects:
## Groups Name Variance Std.Dev.
## CageSiteID:CagingSite (Intercept) 5.147e-06 0.002269
## CagingSite (Intercept) 0.000e+00 0.000000
## OriginSite (Intercept) 5.835e-05 0.007639
## Residual 5.877e-04 0.024242
## Number of obs: 228, groups:
## CageSiteID:CagingSite, 24; CagingSite, 4; OriginSite, 4
##
## Fixed effects:
## Estimate Std. Error t value
## (Intercept) 0.006994 0.014934 0.468
## TransplantContamLC -0.007028 0.004617 -1.522
## OriginContamLC -0.010650 0.008989 -1.185
## SizeEnd 0.003779 0.001362 2.775
## SexM -0.002234 0.003347 -0.667
## TransplantContamLC:OriginContamLC 0.014984 0.006735 2.225
##
## Correlation of Fixed Effects:
## (Intr) TrnCLC OrgCLC SizEnd SexM
## TrnsplntCLC -0.187
## OrignCntmLC -0.314 0.253
## SizeEnd -0.904 0.050 0.023
## SexM 0.020 -0.109 -0.024 -0.105
## TrnCLC:OCLC 0.071 -0.684 -0.371 0.028 0.086
## optimizer (nloptwrap) convergence code: 0 (OK)
## boundary (singular) fit: see ?isSingularAdding the sex as covariate does no change the significance of the interactions, also sex effect is non-significant. The mod5 is thus the best model.
6.7.9 Posthoc test (pairwise t-test)
The interactions between fish origin and the transplant site are significant. Hence, perform posthoc test (pairwise t-test) according to significant interactions.
pairwise.t.test(dat2$NLRatio.p, dat2$CxO2, p.adjust.method = "fdr")##
## Pairwise comparisons using t tests with pooled SD
##
## data: dat2$NLRatio.p and dat2$CxO2
##
## HC_HC HC_LC LC_HC
## HC_LC 0.074 - -
## LC_HC 0.219 0.529 -
## LC_LC 0.402 0.351 0.531
##
## P value adjustment method: fdrHere fish from LC sites, have a marginally lower NL ratio than fish from HC site when transplanted in HC site. However, the posthoc are mostly non-significant.
Also,because interaction between the contamination in origin and transplant site of fish is significant We test for parallel response between replicate populations.
6.7.10 Test for parallel responses between replicate populations (from the same origin)
6.7.10.1 For Populations from High contamination sites (AUSCOR and RIOU)
dat3 <- dat2[which(dat2$OriginSite %in% c("AUSCOR", "RIOU")),]
## build the null model
mod.null <-
glm(NLRatio.p ~ TransplantContam + OriginSite,
data = dat3)
## build the model with the site of origin in interaction with the level of contam in transplant sites
mod.par <-
glm(NLRatio.p ~ TransplantContam * OriginSite,
data = dat3)
anova(mod.null, mod.par, test = "LRT")## Analysis of Deviance Table
##
## Model 1: NLRatio.p ~ TransplantContam + OriginSite
## Model 2: NLRatio.p ~ TransplantContam * OriginSite
## Resid. Df Resid. Dev Df Deviance Pr(>Chi)
## 1 119 0.065380
## 2 118 0.065355 1 2.5656e-05 0.8296coef(mod.par)## (Intercept) TransplantContamLC
## 0.032098642 -0.008723136
## OriginSiteRIOU TransplantContamLC:OriginSiteRIOU
## 0.023609057 0.001839351summary(mod.par)##
## Call:
## glm(formula = NLRatio.p ~ TransplantContam * OriginSite, data = dat3)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -0.055708 -0.021626 0.000688 0.017677 0.058384
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.032099 0.004448 7.217 5.57e-11 ***
## TransplantContamLC -0.008723 0.006235 -1.399 0.164438
## OriginSiteRIOU 0.023609 0.006006 3.931 0.000143 ***
## TransplantContamLC:OriginSiteRIOU 0.001839 0.008546 0.215 0.829961
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for gaussian family taken to be 0.0005538531)
##
## Null deviance: 0.085831 on 121 degrees of freedom
## Residual deviance: 0.065355 on 118 degrees of freedom
## AIC: -562.68
##
## Number of Fisher Scoring iterations: 2The null model and the model including the site of origin in interaction with the level of contaminant in transplant sites are not significantly different, we hence cannot reject the null hypothesis: the slopes of HC populations are parallel.
6.7.10.2 For Populations from Low contamination sites (ARIMAS and CELFIG)
# We test for parallel response between replicate LC populations (ARIMAS and CELFIG)
dat4 <- dat2[which(dat2$OriginSite %in% c("ARIMAS", "CELFIG")),]
## build the null model
mod.null <-
glm(NLRatio.p ~ TransplantContam + OriginSite,
data = dat4)
## build the model with the site of origin in interaction with the level of contam in transplant sites
mod.par <-
glm(NLRatio.p ~ TransplantContam * OriginSite,
data = dat4)
anova(mod.null, mod.par, test = "LRT")## Analysis of Deviance Table
##
## Model 1: NLRatio.p ~ TransplantContam + OriginSite
## Model 2: NLRatio.p ~ TransplantContam * OriginSite
## Resid. Df Resid. Dev Df Deviance Pr(>Chi)
## 1 103 0.067919
## 2 102 0.067880 1 3.8896e-05 0.809coef(mod.par)## (Intercept) TransplantContamLC
## 0.035659899 0.008085113
## OriginSiteCELFIG TransplantContamLC:OriginSiteCELFIG
## -0.005996004 -0.002423457summary(mod.par)##
## Call:
## glm(formula = NLRatio.p ~ TransplantContam * OriginSite, data = dat4)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -0.043745 -0.017240 -0.002768 0.012915 0.057600
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.035660 0.004965 7.183 1.15e-10 ***
## TransplantContamLC 0.008085 0.007021 1.152 0.252
## OriginSiteCELFIG -0.005996 0.007088 -0.846 0.400
## TransplantContamLC:OriginSiteCELFIG -0.002423 0.010024 -0.242 0.809
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for gaussian family taken to be 0.0006654894)
##
## Null deviance: 0.070555 on 105 degrees of freedom
## Residual deviance: 0.067880 on 102 degrees of freedom
## AIC: -468.65
##
## Number of Fisher Scoring iterations: 2The null model and the model including the site of origin in interaction with the level of contaminant in transplant sites are not significantly different, we hence cannot reject the null hypothesis: the slopes of LC populations are parallel.
6.7.11 Visualize
The plot reported below correspond to the figure 2C from the manuscript
NLratioPlot1()
6.8 Available energy - Index (sum of lipids, proteins and carbohydrates)
6.8.1 Check the data
dat2 = dat1[is.na(dat1$AvailableEnerJ) == F, ]
hist(log(dat2$AvailableEnerJ + 1))
6.8.2 Visualize
par(mfrow=c(2,3))
boxplot(log(dat2$AvailableEnerJ + 1) ~ OriginContam, data = dat2)
boxplot(log(dat2$AvailableEnerJ + 1) ~ TransplantContam, data = dat2)
boxplot(log(dat2$AvailableEnerJ + 1) ~ Injection, data = dat2)
boxplot(log(dat2$AvailableEnerJ + 1) ~ TransplantContam * Injection, data = dat2)
boxplot(log(dat2$AvailableEnerJ + 1) ~ TransplantContam * OriginContam, data = dat2)
boxplot(log(dat2$AvailableEnerJ + 1) ~ TransplantContam * OriginContam * Injection, data = dat2)
6.8.3 Build the full model
modfull <-
lme4::lmer(
log(dat2$AvailableEnerJ + 1) ~ (TransplantContam + OriginContam + Injection) ^ 3 + SizeEnd +
(1 | CagingSite / CageSiteID) + (1| OriginSite),
data = dat2,
na.action = na.exclude
)
car::Anova(modfull, type = "3")## Analysis of Deviance Table (Type III Wald chisquare tests)
##
## Response: log(dat2$AvailableEnerJ + 1)
## Chisq Df Pr(>Chisq)
## (Intercept) 1877.0660 1 < 2e-16 ***
## TransplantContam 0.8135 1 0.36709
## OriginContam 0.1111 1 0.73890
## Injection 0.0048 1 0.94484
## SizeEnd 0.2945 1 0.58737
## TransplantContam:OriginContam 5.6046 1 0.01791 *
## TransplantContam:Injection 1.2846 1 0.25705
## OriginContam:Injection 0.0026 1 0.95910
## TransplantContam:OriginContam:Injection 0.3734 1 0.54115
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1summary(modfull)## Linear mixed model fit by REML ['lmerMod']
## Formula: log(dat2$AvailableEnerJ + 1) ~ (TransplantContam + OriginContam +
## Injection)^3 + SizeEnd + (1 | CagingSite/CageSiteID) + (1 |
## OriginSite)
## Data: dat2
##
## REML criterion at convergence: 140.9
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -3.1265 -0.5752 -0.0303 0.7151 3.1968
##
## Random effects:
## Groups Name Variance Std.Dev.
## CageSiteID:CagingSite (Intercept) 6.604e-11 8.127e-06
## CagingSite (Intercept) 4.647e-03 6.817e-02
## OriginSite (Intercept) 8.682e-03 9.318e-02
## Residual 9.059e-02 3.010e-01
## Number of obs: 243, groups:
## CageSiteID:CagingSite, 24; CagingSite, 4; OriginSite, 4
##
## Fixed effects:
## Estimate Std. Error t value
## (Intercept) 8.294203 0.191441 43.325
## TransplantContamLC 0.092137 0.102154 0.902
## OriginContamLC -0.040483 0.121459 -0.333
## InjectionPBS -0.005424 0.078395 -0.069
## SizeEnd 0.008824 0.016261 0.543
## TransplantContamLC:OriginContamLC -0.253471 0.107067 -2.367
## TransplantContamLC:InjectionPBS 0.122759 0.108310 1.133
## OriginContamLC:InjectionPBS 0.005768 0.112469 0.051
## TransplantContamLC:OriginContamLC:InjectionPBS -0.094713 0.154994 -0.611
##
## Correlation of Fixed Effects:
## (Intr) TrnCLC OrgCLC InjPBS SizEnd TrCLC:OCLC TCLC:I OCLC:I
## TrnsplntCLC -0.311
## OrignCntmLC -0.348 0.245
## InjectinPBS -0.213 0.377 0.317
## SizeEnd -0.858 0.044 0.036 0.013
## TrnCLC:OCLC 0.135 -0.527 -0.465 -0.359 0.015
## TrnCLC:IPBS 0.143 -0.521 -0.229 -0.724 0.003 0.497
## OrgCLC:IPBS 0.145 -0.263 -0.442 -0.697 -0.006 0.501 0.504
## TCLC:OCLC:I -0.097 0.364 0.320 0.506 -0.005 -0.690 -0.699 -0.726
## optimizer (nloptwrap) convergence code: 0 (OK)
## boundary (singular) fit: see ?isSingular6.8.4 Refining the model
mod2 <-
lme4::lmer(
log(dat2$AvailableEnerJ + 1) ~ (TransplantContam + OriginContam + Injection) ^ 2 + SizeEnd +
(1 | CagingSite / CageSiteID) + (1| OriginSite),
data = dat2,
na.action = na.exclude
)
car::Anova(mod2, type = "3")## Analysis of Deviance Table (Type III Wald chisquare tests)
##
## Response: log(dat2$AvailableEnerJ + 1)
## Chisq Df Pr(>Chisq)
## (Intercept) 1895.3183 1 < 2.2e-16 ***
## TransplantContam 1.4584 1 0.2271831
## OriginContam 0.0212 1 0.8843552
## Injection 0.0775 1 0.7806793
## SizeEnd 0.2929 1 0.5883630
## TransplantContam:OriginContam 14.8819 1 0.0001145 ***
## TransplantContam:Injection 0.9777 1 0.3227703
## OriginContam:Injection 0.3257 1 0.5682284
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1summary(mod2)## Linear mixed model fit by REML ['lmerMod']
## Formula: log(dat2$AvailableEnerJ + 1) ~ (TransplantContam + OriginContam +
## Injection)^2 + SizeEnd + (1 | CagingSite/CageSiteID) + (1 |
## OriginSite)
## Data: dat2
##
## REML criterion at convergence: 139.4
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -3.1704 -0.5721 -0.0226 0.7025 3.2394
##
## Random effects:
## Groups Name Variance Std.Dev.
## CageSiteID:CagingSite (Intercept) 0.000000 0.00000
## CagingSite (Intercept) 0.004647 0.06817
## OriginSite (Intercept) 0.008634 0.09292
## Residual 0.090348 0.30058
## Number of obs: 243, groups:
## CageSiteID:CagingSite, 24; CagingSite, 4; OriginSite, 4
##
## Fixed effects:
## Estimate Std. Error t value
## (Intercept) 8.282686 0.190252 43.535
## TransplantContamLC 0.114845 0.095098 1.208
## OriginContamLC -0.016697 0.114795 -0.145
## InjectionPBS 0.018805 0.067539 0.278
## SizeEnd 0.008788 0.016237 0.541
## TransplantContamLC:OriginContamLC -0.298608 0.077406 -3.858
## TransplantContamLC:InjectionPBS 0.076508 0.077376 0.989
## OriginContamLC:InjectionPBS -0.044103 0.077283 -0.571
##
## Correlation of Fixed Effects:
## (Intr) TrnCLC OrgCLC InjPBS SizEnd TCLC:O TCLC:I
## TrnsplntCLC -0.298
## OrignCntmLC -0.336 0.146
## InjectinPBS -0.191 0.241 0.190
## SizeEnd -0.862 0.050 0.040 0.019
## TrnCLC:OCLC 0.094 -0.409 -0.356 -0.017 0.016
## TrnCLC:IPBS 0.105 -0.400 -0.008 -0.600 -0.001 0.029
## OrgCLC:IPBS 0.109 0.002 -0.322 -0.556 -0.014 0.001 -0.005
## optimizer (nloptwrap) convergence code: 0 (OK)
## boundary (singular) fit: see ?isSingular6.8.5 Refining the model
mod3 <-
lme4::lmer(
log(dat2$AvailableEnerJ + 1) ~ (TransplantContam + OriginContam) ^ 2 + Injection + SizeEnd +
(1 | CagingSite / CageSiteID) + (1| OriginSite),
data = dat2,
na.action = na.exclude
)
car::Anova(mod3, type = "3")## Analysis of Deviance Table (Type III Wald chisquare tests)
##
## Response: log(dat2$AvailableEnerJ + 1)
## Chisq Df Pr(>Chisq)
## (Intercept) 1941.0315 1 < 2.2e-16 ***
## TransplantContam 3.0309 1 0.08169 .
## OriginContam 0.1145 1 0.73503
## Injection 0.9462 1 0.33070
## SizeEnd 0.2887 1 0.59106
## TransplantContam:OriginContam 15.1597 1 9.879e-05 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1summary(mod3)## Linear mixed model fit by REML ['lmerMod']
## Formula: log(dat2$AvailableEnerJ + 1) ~ (TransplantContam + OriginContam)^2 +
## Injection + SizeEnd + (1 | CagingSite/CageSiteID) + (1 | OriginSite)
## Data: dat2
##
## REML criterion at convergence: 134.1
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -3.2055 -0.6493 -0.0609 0.6893 3.3458
##
## Random effects:
## Groups Name Variance Std.Dev.
## CageSiteID:CagingSite (Intercept) 1.076e-08 0.0001037
## CagingSite (Intercept) 4.724e-03 0.0687319
## OriginSite (Intercept) 8.570e-03 0.0925770
## Residual 9.007e-02 0.3001240
## Number of obs: 243, groups:
## CageSiteID:CagingSite, 24; CagingSite, 4; OriginSite, 4
##
## Fixed effects:
## Estimate Std. Error t value
## (Intercept) 8.274302 0.187808 44.057
## TransplantContamLC 0.152433 0.087558 1.741
## OriginContamLC -0.036669 0.108346 -0.338
## InjectionPBS 0.037525 0.038578 0.973
## SizeEnd 0.008708 0.016208 0.537
## TransplantContamLC:OriginContamLC -0.300800 0.077256 -3.894
##
## Correlation of Fixed Effects:
## (Intr) TrnCLC OrgCLC InjPBS SizEnd
## TrnsplntCLC -0.283
## OrignCntmLC -0.320 0.164
## InjectinPBS -0.117 0.001 0.010
## SizeEnd -0.871 0.053 0.037 0.019
## TrnCLC:OCLC 0.092 -0.431 -0.376 0.003 0.0166.8.6 Refining the model
mod4 <-
lme4::lmer(
log(dat2$AvailableEnerJ + 1) ~ (TransplantContam + OriginContam) ^ 2 +
(1 | CagingSite / CageSiteID) + (1| OriginSite),
data = dat2,
na.action = na.exclude
)
car::Anova(mod4, type = "3")## Analysis of Deviance Table (Type III Wald chisquare tests)
##
## Response: log(dat2$AvailableEnerJ + 1)
## Chisq Df Pr(>Chisq)
## (Intercept) 7672.7861 1 < 2.2e-16 ***
## TransplantContam 2.9297 1 0.08697 .
## OriginContam 0.1164 1 0.73292
## TransplantContam:OriginContam 15.3300 1 9.027e-05 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1summary(mod4)## Linear mixed model fit by REML ['lmerMod']
## Formula: log(dat2$AvailableEnerJ + 1) ~ (TransplantContam + OriginContam)^2 +
## (1 | CagingSite/CageSiteID) + (1 | OriginSite)
## Data: dat2
##
## REML criterion at convergence: 124.2
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -3.0982 -0.6056 -0.0182 0.6854 3.3961
##
## Random effects:
## Groups Name Variance Std.Dev.
## CageSiteID:CagingSite (Intercept) 1.186e-09 3.444e-05
## CagingSite (Intercept) 4.786e-03 6.918e-02
## OriginSite (Intercept) 1.047e-02 1.023e-01
## Residual 8.965e-02 2.994e-01
## Number of obs: 243, groups:
## CageSiteID:CagingSite, 24; CagingSite, 4; OriginSite, 4
##
## Fixed effects:
## Estimate Std. Error t value
## (Intercept) 8.38025 0.09567 87.594
## TransplantContamLC 0.15013 0.08771 1.712
## OriginContamLC -0.03980 0.11663 -0.341
## TransplantContamLC:OriginContamLC -0.30173 0.07706 -3.915
##
## Correlation of Fixed Effects:
## (Intr) TrnCLC OrgCLC
## TrnsplntCLC -0.467
## OrignCntmLC -0.606 0.149
## TrnCLC:OCLC 0.207 -0.430 -0.349modAvailableEnerJ <- mod4
RmodAvailableEnerJ <- MuMIn::r.squaredGLMM(modAvailableEnerJ)Here, the interactions between fish origin and the transplant site are significant.
Now that we have identified the best model, add sex as covariate to check whether results are sensitive NB: sample size is reduced when adding sex variable within the model, for this reason the sex effect on results is checked on the final model
6.8.7 Test for the sex effect
dat2 = dat2[is.na(dat2$Sex) == F, ]
modSex <-
lme4::lmer(
log(dat2$AvailableEnerJ + 1) ~ (TransplantContam + OriginContam) ^ 2 + Sex +
(1 | CagingSite / CageSiteID) + (1| OriginSite),
data = dat2,
na.action = na.exclude
)
car::Anova(modSex, type = "3")## Analysis of Deviance Table (Type III Wald chisquare tests)
##
## Response: log(dat2$AvailableEnerJ + 1)
## Chisq Df Pr(>Chisq)
## (Intercept) 7513.2256 1 < 2.2e-16 ***
## TransplantContam 2.8305 1 0.0924909 .
## OriginContam 0.1612 1 0.6880167
## Sex 0.2442 1 0.6211753
## TransplantContam:OriginContam 14.7641 1 0.0001218 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1summary(modSex)## Linear mixed model fit by REML ['lmerMod']
## Formula: log(dat2$AvailableEnerJ + 1) ~ (TransplantContam + OriginContam)^2 +
## Sex + (1 | CagingSite/CageSiteID) + (1 | OriginSite)
## Data: dat2
##
## REML criterion at convergence: 126.8
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -3.1252 -0.5996 -0.0031 0.6878 3.3782
##
## Random effects:
## Groups Name Variance Std.Dev.
## CageSiteID:CagingSite (Intercept) 5.742e-11 7.577e-06
## CagingSite (Intercept) 5.320e-03 7.294e-02
## OriginSite (Intercept) 9.999e-03 1.000e-01
## Residual 8.942e-02 2.990e-01
## Number of obs: 242, groups:
## CageSiteID:CagingSite, 24; CagingSite, 4; OriginSite, 4
##
## Fixed effects:
## Estimate Std. Error t value
## (Intercept) 8.38668 0.09676 86.679
## TransplantContamLC 0.15276 0.09080 1.682
## OriginContamLC -0.04607 0.11472 -0.402
## SexM -0.01974 0.03994 -0.494
## TransplantContamLC:OriginContamLC -0.29793 0.07754 -3.842
##
## Correlation of Fixed Effects:
## (Intr) TrnCLC OrgCLC SexM
## TrnsplntCLC -0.468
## OrignCntmLC -0.584 0.148
## SexM -0.138 -0.055 -0.024
## TrnCLC:OCLC 0.189 -0.418 -0.357 0.101
## optimizer (nloptwrap) convergence code: 0 (OK)
## boundary (singular) fit: see ?isSingularAdding the sex as covariate does no change the significance of the interactions, also sex effect is non-significant. The mod5 is thus the best model.
6.8.8 Posthoc test (pairwise t-test)
The interactions between fish origin and the transplant site are significant. Hence, perform posthoc test (pairwise t-test) according to significant interactions.
pairwise.t.test(log(dat2$AvailableEnerJ + 1), dat2$CxO2, p.adjust.method = "fdr")##
## Pairwise comparisons using t tests with pooled SD
##
## data: log(dat2$AvailableEnerJ + 1) and dat2$CxO2
##
## HC_HC HC_LC LC_HC
## HC_LC 0.3430 - -
## LC_HC 0.0150 0.0012 -
## LC_LC 0.0012 0.0150 1.3e-08
##
## P value adjustment method: fdrHere the available energy increases in LC fish when transplanted in HC sites. Similarly, the available energy increases in HC fish when transplanted in LC sites, suggesting that local condition within each study site could have driven the plastic responses rather than the level of contamination.
Also,because interaction between the contamination in origin and transplant site of fish is significant We test for parallel response between replicate populations.
6.8.9 Test for parallel responses between replicate populations (from the same origin)
6.8.9.1 For Populations from High contamination sites (AUSCOR and RIOU)
dat3 <- dat2[which(dat2$OriginSite %in% c("AUSCOR", "RIOU")),]
## build the null model
mod.null <-
glm(log(dat3$AvailableEnerJ + 1) ~ TransplantContam + OriginSite,
data = dat3)
## build the model with the site of origin in interaction with the level of contam in transplant sites
mod.par <-
glm(log(dat3$AvailableEnerJ + 1) ~ TransplantContam * OriginSite,
data = dat3)
anova(mod.null, mod.par, test = "LRT")## Analysis of Deviance Table
##
## Model 1: log(dat3$AvailableEnerJ + 1) ~ TransplantContam + OriginSite
## Model 2: log(dat3$AvailableEnerJ + 1) ~ TransplantContam * OriginSite
## Resid. Df Resid. Dev Df Deviance Pr(>Chi)
## 1 121 14.959
## 2 120 14.684 1 0.27469 0.1341coef(mod.par)## (Intercept) TransplantContamLC
## 8.2574774 0.2463168
## OriginSiteRIOU TransplantContamLC:OriginSiteRIOU
## 0.2419375 -0.1888528summary(mod.par)##
## Call:
## glm(formula = log(dat3$AvailableEnerJ + 1) ~ TransplantContam *
## OriginSite, data = dat3)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -0.94707 -0.21939 0.00947 0.22058 1.01919
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 8.25748 0.06732 122.657 < 2e-16 ***
## TransplantContamLC 0.24632 0.09078 2.713 0.00764 **
## OriginSiteRIOU 0.24194 0.09141 2.647 0.00922 **
## TransplantContamLC:OriginSiteRIOU -0.18885 0.12605 -1.498 0.13670
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for gaussian family taken to be 0.1223704)
##
## Null deviance: 16.204 on 123 degrees of freedom
## Residual deviance: 14.684 on 120 degrees of freedom
## AIC: 97.344
##
## Number of Fisher Scoring iterations: 2The null model and the model including the site of origin in interaction with the level of contaminant in transplant sites are not significantly different, we hence cannot reject the null hypothesis: the slopes of HC populations are parallel.
6.8.9.2 For Populations from Low contamination sites (ARIMAS and CELFIG)
# We test for parallel response between replicate LC populations (ARIMAS and CELFIG)
dat4 <- dat2[which(dat2$OriginSite %in% c("ARIMAS", "CELFIG")),]
## build the null model
mod.null <-
glm(log(dat4$AvailableEnerJ + 1) ~ TransplantContam + OriginSite,
data = dat4)
## build the model with the site of origin in interaction with the level of contam in transplant sites
mod.par <-
glm(log(dat4$AvailableEnerJ + 1) ~ TransplantContam * OriginSite,
data = dat4)
anova(mod.null, mod.par, test = "LRT")## Analysis of Deviance Table
##
## Model 1: log(dat4$AvailableEnerJ + 1) ~ TransplantContam + OriginSite
## Model 2: log(dat4$AvailableEnerJ + 1) ~ TransplantContam * OriginSite
## Resid. Df Resid. Dev Df Deviance Pr(>Chi)
## 1 115 6.5419
## 2 114 6.2558 1 0.28616 0.0224 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1coef(mod.par)## (Intercept) TransplantContamLC
## 8.34886418 -0.04548398
## OriginSiteCELFIG TransplantContamLC:OriginSiteCELFIG
## -0.03205983 -0.19760377summary(mod.par)##
## Call:
## glm(formula = log(dat4$AvailableEnerJ + 1) ~ TransplantContam *
## OriginSite, data = dat4)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -0.61943 -0.13182 -0.00938 0.16106 0.66008
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 8.34886 0.04350 191.928 <2e-16 ***
## TransplantContamLC -0.04548 0.06006 -0.757 0.4504
## OriginSiteCELFIG -0.03206 0.06327 -0.507 0.6133
## TransplantContamLC:OriginSiteCELFIG -0.19760 0.08653 -2.284 0.0242 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for gaussian family taken to be 0.05487516)
##
## Null deviance: 7.7037 on 117 degrees of freedom
## Residual deviance: 6.2558 on 114 degrees of freedom
## AIC: -1.7178
##
## Number of Fisher Scoring iterations: 2The null model and the model including the site of origin in interaction with the level of contaminant in transplant sites are significantly different, we hence reject the null hypothesis. here, the slopes of LC populations are not parallel.
6.8.10 Visualize
AvailEnerPlot1()
6.9 Available energy - Lipids
6.9.1 Check the data
dat2 = dat1[is.na(dat1$AvailableEnerJ) == F, ]
# transform variable to approx. normality
dat2$MuscleLipid.p <-
bimixt::boxcox(dat2$MuscleLipid, car::powerTransform(dat2$MuscleLipid)$lambda)6.9.2 Visualize
par(mfrow=c(2,3))
boxplot(MuscleLipid.p ~ OriginContam, data = dat2)
boxplot(MuscleLipid.p ~ TransplantContam, data = dat2)
boxplot(MuscleLipid.p ~ Injection, data = dat2)
boxplot(MuscleLipid.p ~ TransplantContam * Injection, data = dat2)
boxplot(MuscleLipid.p ~ TransplantContam * OriginContam, data = dat2)
boxplot(MuscleLipid.p ~ TransplantContam * OriginContam * Injection, data = dat2)
6.9.3 Build the full model
modfull <-
lme4::lmer(
MuscleLipid.p ~ (TransplantContam + OriginContam + Injection) ^ 3 + SizeEnd +
(1 | CagingSite / CageSiteID) + (1| OriginSite),
data = dat2,
na.action = na.exclude
)
car::Anova(modfull, type = "3")## Analysis of Deviance Table (Type III Wald chisquare tests)
##
## Response: MuscleLipid.p
## Chisq Df Pr(>Chisq)
## (Intercept) 239.7471 1 < 2e-16 ***
## TransplantContam 0.8741 1 0.34983
## OriginContam 0.0301 1 0.86220
## Injection 0.1457 1 0.70266
## SizeEnd 0.5445 1 0.46058
## TransplantContam:OriginContam 4.7471 1 0.02935 *
## TransplantContam:Injection 2.1557 1 0.14204
## OriginContam:Injection 0.0222 1 0.88161
## TransplantContam:OriginContam:Injection 1.3112 1 0.25218
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1summary(modfull)## Linear mixed model fit by REML ['lmerMod']
## Formula: MuscleLipid.p ~ (TransplantContam + OriginContam + Injection)^3 +
## SizeEnd + (1 | CagingSite/CageSiteID) + (1 | OriginSite)
## Data: dat2
##
## REML criterion at convergence: 945.4
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -3.3883 -0.5605 0.0452 0.6799 3.0051
##
## Random effects:
## Groups Name Variance Std.Dev.
## CageSiteID:CagingSite (Intercept) 0.0000 0.0000
## CagingSite (Intercept) 0.1360 0.3688
## OriginSite (Intercept) 0.1395 0.3735
## Residual 2.8308 1.6825
## Number of obs: 243, groups:
## CageSiteID:CagingSite, 24; CagingSite, 4; OriginSite, 4
##
## Fixed effects:
## Estimate Std. Error t value
## (Intercept) 15.62969 1.00942 15.484
## TransplantContamLC 0.52629 0.56293 0.935
## OriginContamLC -0.09958 0.57370 -0.174
## InjectionPBS -0.16728 0.43822 -0.382
## SizeEnd 0.06477 0.08778 0.738
## TransplantContamLC:OriginContamLC -1.30400 0.59850 -2.179
## TransplantContamLC:InjectionPBS 0.88893 0.60544 1.468
## OriginContamLC:InjectionPBS 0.09364 0.62870 0.149
## TransplantContamLC:OriginContamLC:InjectionPBS -0.99210 0.86641 -1.145
##
## Correlation of Fixed Effects:
## (Intr) TrnCLC OrgCLC InjPBS SizEnd TrCLC:OCLC TCLC:I OCLC:I
## TrnsplntCLC -0.324
## OrignCntmLC -0.320 0.295
## InjectinPBS -0.224 0.383 0.375
## SizeEnd -0.879 0.044 0.041 0.012
## TrnCLC:OCLC 0.143 -0.535 -0.550 -0.359 0.015
## TrnCLC:IPBS 0.150 -0.528 -0.271 -0.724 0.005 0.497
## OrgCLC:IPBS 0.153 -0.267 -0.523 -0.697 -0.005 0.501 0.504
## TCLC:OCLC:I -0.102 0.369 0.379 0.506 -0.007 -0.690 -0.699 -0.726
## optimizer (nloptwrap) convergence code: 0 (OK)
## boundary (singular) fit: see ?isSingular6.9.4 Refining the model
mod2 <-
lme4::lmer(
MuscleLipid.p ~ (TransplantContam + OriginContam + Injection) ^ 2 + SizeEnd +
(1 | CagingSite / CageSiteID) + (1| OriginSite),
data = dat2,
na.action = na.exclude
)
car::Anova(mod2, type = "3")## Analysis of Deviance Table (Type III Wald chisquare tests)
##
## Response: MuscleLipid.p
## Chisq Df Pr(>Chisq)
## (Intercept) 238.8706 1 < 2.2e-16 ***
## TransplantContam 2.1314 1 0.1443
## OriginContam 0.0801 1 0.7772
## Injection 0.0523 1 0.8190
## SizeEnd 0.5432 1 0.4611
## TransplantContam:OriginContam 16.7946 1 4.165e-05 ***
## TransplantContam:Injection 0.8709 1 0.3507
## OriginContam:Injection 0.9810 1 0.3220
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1summary(mod2)## Linear mixed model fit by REML ['lmerMod']
## Formula: MuscleLipid.p ~ (TransplantContam + OriginContam + Injection)^2 +
## SizeEnd + (1 | CagingSite/CageSiteID) + (1 | OriginSite)
## Data: dat2
##
## REML criterion at convergence: 948.3
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -3.4605 -0.5650 0.0736 0.6661 3.0749
##
## Random effects:
## Groups Name Variance Std.Dev.
## CageSiteID:CagingSite (Intercept) 3.336e-09 5.776e-05
## CagingSite (Intercept) 1.360e-01 3.688e-01
## OriginSite (Intercept) 1.370e-01 3.702e-01
## Residual 2.835e+00 1.684e+00
## Number of obs: 243, groups:
## CageSiteID:CagingSite, 24; CagingSite, 4; OriginSite, 4
##
## Fixed effects:
## Estimate Std. Error t value
## (Intercept) 15.50634 1.00329 15.455
## TransplantContamLC 0.76417 0.52343 1.460
## OriginContamLC 0.14962 0.52872 0.283
## InjectionPBS 0.08655 0.37831 0.229
## SizeEnd 0.06466 0.08773 0.737
## TransplantContamLC:OriginContamLC -1.77675 0.43355 -4.098
## TransplantContamLC:InjectionPBS 0.40446 0.43341 0.933
## OriginContamLC:InjectionPBS -0.42876 0.43290 -0.990
##
## Correlation of Fixed Effects:
## (Intr) TrnCLC OrgCLC InjPBS SizEnd TCLC:O TCLC:I
## TrnsplntCLC -0.311
## OrignCntmLC -0.305 0.181
## InjectinPBS -0.201 0.245 0.231
## SizeEnd -0.884 0.050 0.047 0.018
## TrnCLC:OCLC 0.102 -0.416 -0.433 -0.017 0.014
## TrnCLC:IPBS 0.111 -0.407 -0.009 -0.600 0.001 0.029
## OrgCLC:IPBS 0.116 0.002 -0.391 -0.556 -0.015 0.001 -0.005
## optimizer (nloptwrap) convergence code: 0 (OK)
## boundary (singular) fit: see ?isSingular6.9.5 Refining the model
mod3 <-
lme4::lmer(
MuscleLipid.p ~ (TransplantContam + OriginContam) ^ 2 + Injection + SizeEnd +
(1 | CagingSite / CageSiteID) + (1| OriginSite),
data = dat2,
na.action = na.exclude
)
car::Anova(mod3, type = "3")## Analysis of Deviance Table (Type III Wald chisquare tests)
##
## Response: MuscleLipid.p
## Chisq Df Pr(>Chisq)
## (Intercept) 245.6390 1 < 2.2e-16 ***
## TransplantContam 4.0056 1 0.04535 *
## OriginContam 0.0104 1 0.91884
## Injection 0.1728 1 0.67762
## SizeEnd 0.5289 1 0.46707
## TransplantContam:OriginContam 17.0371 1 3.666e-05 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1summary(mod3)## Linear mixed model fit by REML ['lmerMod']
## Formula: MuscleLipid.p ~ (TransplantContam + OriginContam)^2 + Injection +
## SizeEnd + (1 | CagingSite/CageSiteID) + (1 | OriginSite)
## Data: dat2
##
## REML criterion at convergence: 950.4
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -3.4628 -0.5463 0.0406 0.6027 3.2011
##
## Random effects:
## Groups Name Variance Std.Dev.
## CageSiteID:CagingSite (Intercept) 3.042e-09 5.515e-05
## CagingSite (Intercept) 1.389e-01 3.727e-01
## OriginSite (Intercept) 1.356e-01 3.682e-01
## Residual 2.833e+00 1.683e+00
## Number of obs: 243, groups:
## CageSiteID:CagingSite, 24; CagingSite, 4; OriginSite, 4
##
## Fixed effects:
## Estimate Std. Error t value
## (Intercept) 15.51410 0.98987 15.673
## TransplantContamLC 0.96279 0.48106 2.001
## OriginContamLC -0.04942 0.48497 -0.102
## InjectionPBS 0.08993 0.21634 0.416
## SizeEnd 0.06374 0.08764 0.727
## TransplantContamLC:OriginContamLC -1.78812 0.43321 -4.128
##
## Correlation of Fixed Effects:
## (Intr) TrnCLC OrgCLC InjPBS SizEnd
## TrnsplntCLC -0.296
## OrignCntmLC -0.284 0.209
## InjectinPBS -0.124 0.001 0.013
## SizeEnd -0.894 0.055 0.045 0.018
## TrnCLC:OCLC 0.100 -0.440 -0.471 0.003 0.014
## optimizer (nloptwrap) convergence code: 0 (OK)
## boundary (singular) fit: see ?isSingular6.9.6 Refining the model
mod4 <-
lme4::lmer(
MuscleLipid.p ~ (TransplantContam + OriginContam) ^ 2 +
(1 | CagingSite / CageSiteID) + (1| OriginSite),
data = dat2,
na.action = na.exclude
)
car::Anova(mod4, type = "3")## Analysis of Deviance Table (Type III Wald chisquare tests)
##
## Response: MuscleLipid.p
## Chisq Df Pr(>Chisq)
## (Intercept) 1213.6699 1 < 2.2e-16 ***
## TransplantContam 3.8681 1 0.04921 *
## OriginContam 0.0155 1 0.90078
## TransplantContam:OriginContam 17.2823 1 3.222e-05 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1summary(mod4)## Linear mixed model fit by REML ['lmerMod']
## Formula:
## MuscleLipid.p ~ (TransplantContam + OriginContam)^2 + (1 | CagingSite/CageSiteID) +
## (1 | OriginSite)
## Data: dat2
##
## REML criterion at convergence: 946.8
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -3.5072 -0.5768 0.0792 0.6150 3.2119
##
## Random effects:
## Groups Name Variance Std.Dev.
## CageSiteID:CagingSite (Intercept) 0.0000 0.0000
## CagingSite (Intercept) 0.1401 0.3743
## OriginSite (Intercept) 0.1966 0.4435
## Residual 2.8104 1.6764
## Number of obs: 243, groups:
## CageSiteID:CagingSite, 24; CagingSite, 4; OriginSite, 4
##
## Fixed effects:
## Estimate Std. Error t value
## (Intercept) 16.19882 0.46498 34.838
## TransplantContamLC 0.94566 0.48082 1.967
## OriginContamLC -0.06771 0.54309 -0.125
## TransplantContamLC:OriginContamLC -1.79370 0.43147 -4.157
##
## Correlation of Fixed Effects:
## (Intr) TrnCLC OrgCLC
## TrnsplntCLC -0.527
## OrignCntmLC -0.579 0.183
## TrnCLC:OCLC 0.239 -0.439 -0.420
## optimizer (nloptwrap) convergence code: 0 (OK)
## boundary (singular) fit: see ?isSingularmodLipids <- mod4
RmodLipids <- MuMIn::r.squaredGLMM(modLipids)Now that we have identified the best model, add sex as covariate to check whether results are sensitive NB: sample size is reduced when adding sex variable within the model, for this reason the sex effect on results is checked on the final model
6.9.7 Test for the sex effect
dat2 = dat2[is.na(dat2$Sex) == F, ]
modSex <-
lme4::lmer(
MuscleLipid.p ~ (TransplantContam + OriginContam) ^ 2 + Sex +
(1 | CagingSite / CageSiteID) + (1| OriginSite),
data = dat2,
na.action = na.exclude
)
car::Anova(modSex, type = "3")## Analysis of Deviance Table (Type III Wald chisquare tests)
##
## Response: MuscleLipid.p
## Chisq Df Pr(>Chisq)
## (Intercept) 1189.1135 1 < 2.2e-16 ***
## TransplantContam 3.7936 1 0.05145 .
## OriginContam 0.0291 1 0.86448
## Sex 0.2211 1 0.63820
## TransplantContam:OriginContam 16.7933 1 4.168e-05 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1summary(modSex)## Linear mixed model fit by REML ['lmerMod']
## Formula: MuscleLipid.p ~ (TransplantContam + OriginContam)^2 + Sex + (1 |
## CagingSite/CageSiteID) + (1 | OriginSite)
## Data: dat2
##
## REML criterion at convergence: 943.7
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -3.4675 -0.5731 0.0823 0.6265 3.1854
##
## Random effects:
## Groups Name Variance Std.Dev.
## CageSiteID:CagingSite (Intercept) 0.0000 0.0000
## CagingSite (Intercept) 0.1505 0.3879
## OriginSite (Intercept) 0.1855 0.4307
## Residual 2.8175 1.6786
## Number of obs: 242, groups:
## CageSiteID:CagingSite, 24; CagingSite, 4; OriginSite, 4
##
## Fixed effects:
## Estimate Std. Error t value
## (Intercept) 16.23357 0.47076 34.484
## TransplantContamLC 0.95939 0.49257 1.948
## OriginContamLC -0.09114 0.53398 -0.171
## SexM -0.10539 0.22414 -0.470
## TransplantContamLC:OriginContamLC -1.78346 0.43521 -4.098
##
## Correlation of Fixed Effects:
## (Intr) TrnCLC OrgCLC SexM
## TrnsplntCLC -0.522
## OrignCntmLC -0.555 0.184
## SexM -0.160 -0.057 -0.029
## TrnCLC:OCLC 0.218 -0.432 -0.431 0.101
## optimizer (nloptwrap) convergence code: 0 (OK)
## boundary (singular) fit: see ?isSingularThe sex effect is non-significant. The mod4 is thus the best model. Here, the interactions between fish origin and the transplant site are significant, confirming the pattern observed for the integrative measure of available energy previously observed.
6.10 Available energy - Proteins
6.10.1 Check the data
dat2 = dat1[is.na(dat1$AvailableEnerJ) == F, ]
hist(dat2$MuscleProtein)
6.10.2 Visualize
par(mfrow=c(2,3))
boxplot(MuscleProtein ~ OriginContam, data = dat2)
boxplot(MuscleProtein ~ TransplantContam, data = dat2)
boxplot(MuscleProtein ~ Injection, data = dat2)
boxplot(MuscleProtein ~ TransplantContam * Injection, data = dat2)
boxplot(MuscleProtein ~ TransplantContam * OriginContam, data = dat2)
boxplot(MuscleProtein ~ TransplantContam * OriginContam * Injection, data = dat2)
6.10.3 Build the full model
modfull <-
lme4::lmer(
MuscleProtein ~ (TransplantContam + OriginContam + Injection) ^ 3 + SizeEnd +
(1 | CagingSite / CageSiteID) + (1| OriginSite),
data = dat2,
na.action = na.exclude
)
car::Anova(modfull, type = "3")## Analysis of Deviance Table (Type III Wald chisquare tests)
##
## Response: MuscleProtein
## Chisq Df Pr(>Chisq)
## (Intercept) 72.3614 1 < 2e-16 ***
## TransplantContam 0.0505 1 0.82225
## OriginContam 0.5392 1 0.46276
## Injection 0.1729 1 0.67756
## SizeEnd 0.0200 1 0.88757
## TransplantContam:OriginContam 1.1311 1 0.28754
## TransplantContam:Injection 1.0491 1 0.30571
## OriginContam:Injection 0.1112 1 0.73880
## TransplantContam:OriginContam:Injection 2.9188 1 0.08755 .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1summary(modfull)## Linear mixed model fit by REML ['lmerMod']
## Formula: MuscleProtein ~ (TransplantContam + OriginContam + Injection)^3 +
## SizeEnd + (1 | CagingSite/CageSiteID) + (1 | OriginSite)
## Data: dat2
##
## REML criterion at convergence: 3336.7
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -2.60471 -0.62743 0.01437 0.59565 2.93523
##
## Random effects:
## Groups Name Variance Std.Dev.
## CageSiteID:CagingSite (Intercept) 1.963e-09 4.430e-05
## CagingSite (Intercept) 0.000e+00 0.000e+00
## OriginSite (Intercept) 1.171e+04 1.082e+02
## Residual 7.769e+04 2.787e+02
## Number of obs: 243, groups:
## CageSiteID:CagingSite, 24; CagingSite, 4; OriginSite, 4
##
## Fixed effects:
## Estimate Std. Error t value
## (Intercept) 1526.254 179.421 8.507
## TransplantContamLC 15.825 70.440 0.225
## OriginContamLC -95.483 130.032 -0.734
## InjectionPBS 30.187 72.600 0.416
## SizeEnd -2.159 15.273 -0.141
## TransplantContamLC:OriginContamLC -105.421 99.123 -1.064
## TransplantContamLC:InjectionPBS -102.738 100.304 -1.024
## OriginContamLC:InjectionPBS 34.730 104.155 0.333
## TransplantContamLC:OriginContamLC:InjectionPBS 245.234 143.540 1.708
##
## Correlation of Fixed Effects:
## (Intr) TrnCLC OrgCLC InjPBS SizEnd TrCLC:OCLC TCLC:I OCLC:I
## TrnsplntCLC -0.255
## OrignCntmLC -0.388 0.285
## InjectinPBS -0.211 0.507 0.275
## SizeEnd -0.859 0.058 0.030 0.015
## TrnCLC:OCLC 0.131 -0.707 -0.402 -0.360 0.017
## TrnCLC:IPBS 0.141 -0.699 -0.198 -0.724 0.003 0.497
## OrgCLC:IPBS 0.144 -0.353 -0.383 -0.697 -0.006 0.501 0.505
## TCLC:OCLC:I -0.096 0.488 0.277 0.506 -0.005 -0.690 -0.699 -0.726
## optimizer (nloptwrap) convergence code: 0 (OK)
## boundary (singular) fit: see ?isSingular6.10.4 Refining the model
mod2 <-
lme4::lmer(
MuscleProtein ~ (TransplantContam + OriginContam + Injection) ^ 2 + SizeEnd +
(1 | CagingSite / CageSiteID) + (1| OriginSite),
data = dat2,
na.action = na.exclude
)
car::Anova(mod2, type = "3")## Analysis of Deviance Table (Type III Wald chisquare tests)
##
## Response: MuscleProtein
## Chisq Df Pr(>Chisq)
## (Intercept) 75.1757 1 < 2e-16 ***
## TransplantContam 0.4846 1 0.48633
## OriginContam 1.5581 1 0.21195
## Injection 0.2680 1 0.60469
## SizeEnd 0.0182 1 0.89255
## TransplantContam:OriginContam 0.0252 1 0.87389
## TransplantContam:Injection 0.0558 1 0.81328
## OriginContam:Injection 5.1861 1 0.02277 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1summary(mod2)## Linear mixed model fit by REML ['lmerMod']
## Formula: MuscleProtein ~ (TransplantContam + OriginContam + Injection)^2 +
## SizeEnd + (1 | CagingSite/CageSiteID) + (1 | OriginSite)
## Data: dat2
##
## REML criterion at convergence: 3351.4
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -2.69191 -0.66757 0.03888 0.63366 3.03282
##
## Random effects:
## Groups Name Variance Std.Dev.
## CageSiteID:CagingSite (Intercept) 0.000e+00 0.000e+00
## CagingSite (Intercept) 1.930e-11 4.393e-06
## OriginSite (Intercept) 1.190e+04 1.091e+02
## Residual 7.832e+04 2.799e+02
## Number of obs: 243, groups:
## CageSiteID:CagingSite, 24; CagingSite, 4; OriginSite, 4
##
## Fixed effects:
## Estimate Std. Error t value
## (Intercept) 1556.133 179.477 8.670
## TransplantContamLC -42.962 61.714 -0.696
## OriginContamLC -157.057 125.824 -1.248
## InjectionPBS -32.552 62.882 -0.518
## SizeEnd -2.072 15.339 -0.135
## TransplantContamLC:OriginContamLC 11.433 72.029 0.159
## TransplantContamLC:InjectionPBS 17.016 72.040 0.236
## OriginContamLC:InjectionPBS 163.859 71.953 2.277
##
## Correlation of Fixed Effects:
## (Intr) TrnCLC OrgCLC InjPBS SizEnd TCLC:O TCLC:I
## TrnsplntCLC -0.239
## OrignCntmLC -0.378 0.178
## InjectinPBS -0.189 0.345 0.162
## SizeEnd -0.863 0.069 0.033 0.020
## TrnCLC:OCLC 0.090 -0.586 -0.302 -0.017 0.019
## TrnCLC:IPBS 0.104 -0.573 -0.006 -0.600 -0.001 0.029
## OrgCLC:IPBS 0.108 0.002 -0.274 -0.556 -0.014 0.001 -0.005
## optimizer (nloptwrap) convergence code: 0 (OK)
## boundary (singular) fit: see ?isSingular6.10.5 Refining the model
mod3 <-
lme4::lmer(
MuscleProtein ~ (Injection + OriginContam) ^ 2 + TransplantContam + SizeEnd +
(1 | CagingSite / CageSiteID) + (1| OriginSite),
data = dat2,
na.action = na.exclude
)
car::Anova(mod3, type = "3")## Analysis of Deviance Table (Type III Wald chisquare tests)
##
## Response: MuscleProtein
## Chisq Df Pr(>Chisq)
## (Intercept) 76.3940 1 < 2e-16 ***
## Injection 0.2228 1 0.63692
## OriginContam 1.5859 1 0.20792
## TransplantContam 0.6546 1 0.41846
## SizeEnd 0.0200 1 0.88740
## Injection:OriginContam 5.2335 1 0.02216 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1summary(mod3)## Linear mixed model fit by REML ['lmerMod']
## Formula: MuscleProtein ~ (Injection + OriginContam)^2 + TransplantContam +
## SizeEnd + (1 | CagingSite/CageSiteID) + (1 | OriginSite)
## Data: dat2
##
## REML criterion at convergence: 3372.3
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -2.7069 -0.6835 0.0192 0.6125 3.0499
##
## Random effects:
## Groups Name Variance Std.Dev.
## CageSiteID:CagingSite (Intercept) 0 0.0
## CagingSite (Intercept) 0 0.0
## OriginSite (Intercept) 11926 109.2
## Residual 77683 278.7
## Number of obs: 243, groups:
## CageSiteID:CagingSite, 24; CagingSite, 4; OriginSite, 4
##
## Fixed effects:
## Estimate Std. Error t value
## (Intercept) 1549.863 177.322 8.740
## InjectionPBS -23.641 50.086 -0.472
## OriginContamLC -151.109 119.993 -1.259
## TransplantContamLC -29.267 36.173 -0.809
## SizeEnd -2.163 15.278 -0.142
## InjectionPBS:OriginContamLC 163.928 71.657 2.288
##
## Correlation of Fixed Effects:
## (Intr) InjPBS OrgCLC TrnCLC SizEnd
## InjectinPBS -0.160
## OrignCntmLC -0.373 0.206
## TrnsplntCLC -0.223 0.003 0.003
## SizeEnd -0.872 0.024 0.040 0.136
## InjPBS:OCLC 0.109 -0.699 -0.285 0.000 -0.014
## optimizer (nloptwrap) convergence code: 0 (OK)
## boundary (singular) fit: see ?isSingular6.10.6 Refining the model
mod4 <-
lme4::lmer(
MuscleProtein ~ (Injection + OriginContam) ^ 2 +
(1 | CagingSite / CageSiteID) + (1| OriginSite),
data = dat2,
na.action = na.exclude
)
car::Anova(mod4, type = "3")## Analysis of Deviance Table (Type III Wald chisquare tests)
##
## Response: MuscleProtein
## Chisq Df Pr(>Chisq)
## (Intercept) 339.6044 1 < 2e-16 ***
## Injection 0.2213 1 0.63809
## OriginContam 1.6859 1 0.19415
## Injection:OriginContam 5.2605 1 0.02181 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1summary(mod4)## Linear mixed model fit by REML ['lmerMod']
## Formula:
## MuscleProtein ~ (Injection + OriginContam)^2 + (1 | CagingSite/CageSiteID) +
## (1 | OriginSite)
## Data: dat2
##
## REML criterion at convergence: 3389.2
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -2.75840 -0.65962 -0.01681 0.57098 3.10906
##
## Random effects:
## Groups Name Variance Std.Dev.
## CageSiteID:CagingSite (Intercept) 0 0
## CagingSite (Intercept) 0 0
## OriginSite (Intercept) 11026 105
## Residual 77287 278
## Number of obs: 243, groups:
## CageSiteID:CagingSite, 24; CagingSite, 4; OriginSite, 4
##
## Fixed effects:
## Estimate Std. Error t value
## (Intercept) 1513.01 82.10 18.428
## InjectionPBS -23.49 49.94 -0.470
## OriginContamLC -150.65 116.02 -1.298
## InjectionPBS:OriginContamLC 163.91 71.47 2.294
##
## Correlation of Fixed Effects:
## (Intr) InjPBS OrgCLC
## InjectinPBS -0.299
## OrignCntmLC -0.708 0.212
## InjPBS:OCLC 0.209 -0.699 -0.294
## optimizer (nloptwrap) convergence code: 0 (OK)
## boundary (singular) fit: see ?isSingularmodProtein <- mod4
RmodProtein <- MuMIn::r.squaredGLMM(modProtein)Now that we have identified the best model, add sex as covariate to check whether results are sensitive NB: sample size is reduced when adding sex variable within the model, for this reason the sex effect on results is checked on the final model
6.10.7 Test for the sex effect
dat2 = dat2[is.na(dat2$Sex) == F, ]
modSex <-
lme4::lmer(
MuscleProtein ~ (Injection + OriginContam) ^ 2 + Sex +
(1 | CagingSite / CageSiteID) + (1| OriginSite),
data = dat2,
na.action = na.exclude
)
car::Anova(modSex, type = "3")## Analysis of Deviance Table (Type III Wald chisquare tests)
##
## Response: MuscleProtein
## Chisq Df Pr(>Chisq)
## (Intercept) 338.1336 1 < 2e-16 ***
## Injection 0.2654 1 0.60641
## OriginContam 2.0614 1 0.15107
## Sex 0.3682 1 0.54396
## Injection:OriginContam 6.3645 1 0.01164 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1summary(modSex)## Linear mixed model fit by REML ['lmerMod']
## Formula:
## MuscleProtein ~ (Injection + OriginContam)^2 + Sex + (1 | CagingSite/CageSiteID) +
## (1 | OriginSite)
## Data: dat2
##
## REML criterion at convergence: 3356.6
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -2.76403 -0.63054 0.02422 0.60396 2.65019
##
## Random effects:
## Groups Name Variance Std.Dev.
## CageSiteID:CagingSite (Intercept) 0 0.0
## CagingSite (Intercept) 0 0.0
## OriginSite (Intercept) 10824 104.0
## Residual 74589 273.1
## Number of obs: 242, groups:
## CageSiteID:CagingSite, 24; CagingSite, 4; OriginSite, 4
##
## Fixed effects:
## Estimate Std. Error t value
## (Intercept) 1522.81 82.81 18.388
## InjectionPBS -25.33 49.16 -0.515
## OriginContamLC -164.92 114.87 -1.436
## SexM -22.09 36.40 -0.607
## InjectionPBS:OriginContamLC 177.47 70.35 2.523
##
## Correlation of Fixed Effects:
## (Intr) InjPBS OrgCLC SexM
## InjectinPBS -0.303
## OrignCntmLC -0.695 0.210
## SexM -0.195 0.062 0.010
## InjPBS:OCLC 0.202 -0.696 -0.293 0.010
## optimizer (nloptwrap) convergence code: 0 (OK)
## boundary (singular) fit: see ?isSingularThe sex effect is non-significant. The mod4 is thus the best model. Here, the interactions between fish origin and the immune challenge are significant, with LC fish site having a decreasing level of proteins in their muscle when immune challenged. On the contrary HC fish have a constant level of proteins, whatever the injection (control saline solution or antigen mixture).
pairwise.t.test(dat2$MuscleProtein, dat2$O2xI, p.adjust.method = "fdr")##
## Pairwise comparisons using t tests with pooled SD
##
## data: dat2$MuscleProtein and dat2$O2xI
##
## HC_AMIX HC_PBS LC_AMIX
## HC_PBS 0.8066 - -
## LC_AMIX 0.0057 0.0111 -
## LC_PBS 0.8066 0.8066 0.0098
##
## P value adjustment method: fdr6.11 Available energy - Carbohydrates
6.11.1 Check the data
dat2 = dat1[is.na(dat1$AvailableEnerJ) == F, ]
hist(log(dat2$MuscleCarbohydrate))
6.11.2 Visualize
par(mfrow=c(2,3))
boxplot(log(dat2$MuscleCarbohydrate) ~ OriginContam, data = dat2)
boxplot(log(dat2$MuscleCarbohydrate) ~ TransplantContam, data = dat2)
boxplot(log(dat2$MuscleCarbohydrate) ~ Injection, data = dat2)
boxplot(log(dat2$MuscleCarbohydrate) ~ TransplantContam * Injection, data = dat2)
boxplot(log(dat2$MuscleCarbohydrate) ~ TransplantContam * OriginContam, data = dat2)
boxplot(log(dat2$MuscleCarbohydrate) ~ TransplantContam * OriginContam * Injection, data = dat2)
6.11.3 Build the full model
modfull <-
lme4::lmer(
log(dat2$MuscleCarbohydrate) ~ (TransplantContam + OriginContam + Injection) ^ 3 + SizeEnd +
(1 | CagingSite / CageSiteID) + (1| OriginSite),
data = dat2,
na.action = na.exclude
)
car::Anova(modfull, type = "3")## Analysis of Deviance Table (Type III Wald chisquare tests)
##
## Response: log(dat2$MuscleCarbohydrate)
## Chisq Df Pr(>Chisq)
## (Intercept) 367.1817 1 < 2e-16 ***
## TransplantContam 0.5896 1 0.44259
## OriginContam 4.3332 1 0.03738 *
## Injection 0.5074 1 0.47625
## SizeEnd 0.3274 1 0.56717
## TransplantContam:OriginContam 6.0797 1 0.01367 *
## TransplantContam:Injection 0.0196 1 0.88857
## OriginContam:Injection 1.7999 1 0.17973
## TransplantContam:OriginContam:Injection 0.1076 1 0.74287
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1summary(modfull)## Linear mixed model fit by REML ['lmerMod']
## Formula: log(dat2$MuscleCarbohydrate) ~ (TransplantContam + OriginContam +
## Injection)^3 + SizeEnd + (1 | CagingSite/CageSiteID) + (1 |
## OriginSite)
## Data: dat2
##
## REML criterion at convergence: 119.6
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -2.5702 -0.6259 0.1120 0.6593 2.5329
##
## Random effects:
## Groups Name Variance Std.Dev.
## CageSiteID:CagingSite (Intercept) 0.0002886 0.01699
## CagingSite (Intercept) 0.0179209 0.13387
## OriginSite (Intercept) 0.0000000 0.00000
## Residual 0.0824606 0.28716
## Number of obs: 243, groups:
## CageSiteID:CagingSite, 24; CagingSite, 4; OriginSite, 4
##
## Fixed effects:
## Estimate Std. Error t value
## (Intercept) 3.186285 0.166282 19.162
## TransplantContamLC 0.117167 0.152594 0.768
## OriginContamLC 0.156032 0.074957 2.082
## InjectionPBS 0.053292 0.074811 0.712
## SizeEnd 0.007105 0.012416 0.572
## TransplantContamLC:OriginContamLC -0.254236 0.103109 -2.466
## TransplantContamLC:InjectionPBS 0.014481 0.103351 0.140
## OriginContamLC:InjectionPBS -0.143983 0.107322 -1.342
## TransplantContamLC:OriginContamLC:InjectionPBS 0.048517 0.147890 0.328
##
## Correlation of Fixed Effects:
## (Intr) TrnCLC OrgCLC InjPBS SizEnd TrCLC:OCLC TCLC:I OCLC:I
## TrnsplntCLC -0.483
## OrignCntmLC -0.259 0.246
## InjectinPBS -0.226 0.241 0.490
## SizeEnd -0.758 0.025 0.044 0.006
## TrnCLC:OCLC 0.152 -0.340 -0.725 -0.356 0.015
## TrnCLC:IPBS 0.149 -0.333 -0.354 -0.724 0.015 0.493
## OrgCLC:IPBS 0.156 -0.168 -0.683 -0.697 -0.002 0.497 0.505
## TCLC:OCLC:I -0.101 0.232 0.495 0.506 -0.014 -0.684 -0.699 -0.726
## optimizer (nloptwrap) convergence code: 0 (OK)
## boundary (singular) fit: see ?isSingular6.11.4 Refining the model
mod2 <-
lme4::lmer(
log(dat2$MuscleCarbohydrate) ~ (TransplantContam + OriginContam + Injection) ^ 2 + SizeEnd +
(1 | CagingSite / CageSiteID) + (1| OriginSite),
data = dat2,
na.action = na.exclude
)
car::Anova(mod2, type = "3")## Analysis of Deviance Table (Type III Wald chisquare tests)
##
## Response: log(dat2$MuscleCarbohydrate)
## Chisq Df Pr(>Chisq)
## (Intercept) 372.6047 1 < 2.2e-16 ***
## TransplantContam 0.5049 1 0.477360
## OriginContam 4.8750 1 0.027249 *
## Injection 0.4016 1 0.526289
## SizeEnd 0.3325 1 0.564180
## TransplantContam:OriginContam 9.4054 1 0.002163 **
## TransplantContam:Injection 0.2694 1 0.603704
## OriginContam:Injection 2.5818 1 0.108098
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1summary(mod2)## Linear mixed model fit by REML ['lmerMod']
## Formula: log(dat2$MuscleCarbohydrate) ~ (TransplantContam + OriginContam +
## Injection)^2 + SizeEnd + (1 | CagingSite/CageSiteID) + (1 |
## OriginSite)
## Data: dat2
##
## REML criterion at convergence: 117.7
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -2.5977 -0.6287 0.1023 0.6809 2.5155
##
## Random effects:
## Groups Name Variance Std.Dev.
## CageSiteID:CagingSite (Intercept) 0.0003481 0.01866
## CagingSite (Intercept) 0.0179094 0.13383
## OriginSite (Intercept) 0.0000000 0.00000
## Residual 0.0821005 0.28653
## Number of obs: 243, groups:
## CageSiteID:CagingSite, 24; CagingSite, 4; OriginSite, 4
##
## Fixed effects:
## Estimate Std. Error t value
## (Intercept) 3.191944 0.165360 19.303
## TransplantContamLC 0.105441 0.148393 0.711
## OriginContamLC 0.143834 0.065144 2.208
## InjectionPBS 0.040809 0.064399 0.634
## SizeEnd 0.007155 0.012408 0.577
## TransplantContamLC:OriginContamLC -0.231120 0.075361 -3.067
## TransplantContamLC:InjectionPBS 0.038293 0.073770 0.519
## OriginContamLC:InjectionPBS -0.118397 0.073685 -1.607
##
## Correlation of Fixed Effects:
## (Intr) TrnCLC OrgCLC InjPBS SizEnd TCLC:O TCLC:I
## TrnsplntCLC -0.475
## OrignCntmLC -0.241 0.156
## InjectinPBS -0.203 0.147 0.319
## SizeEnd -0.763 0.029 0.059 0.015
## TrnCLC:OCLC 0.115 -0.255 -0.610 -0.016 0.007
## TrnCLC:IPBS 0.110 -0.244 -0.013 -0.600 0.006 0.029
## OrgCLC:IPBS 0.120 0.001 -0.540 -0.556 -0.018 0.001 -0.005
## optimizer (nloptwrap) convergence code: 0 (OK)
## boundary (singular) fit: see ?isSingular6.11.5 Refining the model
mod3 <-
lme4::lmer(
log(dat2$MuscleCarbohydrate) ~ (TransplantContam + OriginContam) ^ 2 + Injection + SizeEnd +
(1 | CagingSite / CageSiteID) + (1| OriginSite),
data = dat2,
na.action = na.exclude
)
car::Anova(mod3, type = "3")## Analysis of Deviance Table (Type III Wald chisquare tests)
##
## Response: log(dat2$MuscleCarbohydrate)
## Chisq Df Pr(>Chisq)
## (Intercept) 386.4042 1 < 2.2e-16 ***
## TransplantContam 0.7383 1 0.390203
## OriginContam 2.5671 1 0.109107
## Injection 0.0070 1 0.933181
## SizeEnd 0.2962 1 0.586268
## TransplantContam:OriginContam 9.4985 1 0.002056 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1summary(mod3)## Linear mixed model fit by REML ['lmerMod']
## Formula: log(dat2$MuscleCarbohydrate) ~ (TransplantContam + OriginContam)^2 +
## Injection + SizeEnd + (1 | CagingSite/CageSiteID) + (1 | OriginSite)
## Data: dat2
##
## REML criterion at convergence: 113.8
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -2.7435 -0.5677 0.0726 0.6620 2.4868
##
## Random effects:
## Groups Name Variance Std.Dev.
## CageSiteID:CagingSite (Intercept) 0.0003136 0.01771
## CagingSite (Intercept) 0.0181006 0.13454
## OriginSite (Intercept) 0.0000000 0.00000
## Residual 0.0824140 0.28708
## Number of obs: 243, groups:
## CageSiteID:CagingSite, 24; CagingSite, 4; OriginSite, 4
##
## Fixed effects:
## Estimate Std. Error t value
## (Intercept) 3.214453 0.163526 19.657
## TransplantContamLC 0.124211 0.144558 0.859
## OriginContamLC 0.087790 0.054793 1.602
## InjectionPBS 0.003094 0.036907 0.084
## SizeEnd 0.006758 0.012417 0.544
## TransplantContamLC:OriginContamLC -0.232115 0.075314 -3.082
##
## Correlation of Fixed Effects:
## (Intr) TrnCLC OrgCLC InjPBS SizEnd
## TrnsplntCLC -0.469
## OrignCntmLC -0.210 0.186
## InjectinPBS -0.123 0.000 0.019
## SizeEnd -0.771 0.032 0.059 0.016
## TrnCLC:OCLC 0.113 -0.255 -0.724 0.003 0.007
## optimizer (nloptwrap) convergence code: 0 (OK)
## boundary (singular) fit: see ?isSingular6.11.6 Refining the model
mod4 <-
lme4::lmer(
log(dat2$MuscleCarbohydrate) ~ (TransplantContam + OriginContam) ^ 2 +
(1 | CagingSite / CageSiteID) + (1| OriginSite),
data = dat2,
na.action = na.exclude
)
car::Anova(mod4, type = "3")## Analysis of Deviance Table (Type III Wald chisquare tests)
##
## Response: log(dat2$MuscleCarbohydrate)
## Chisq Df Pr(>Chisq)
## (Intercept) 1043.8093 1 < 2.2e-16 ***
## TransplantContam 0.7218 1 0.395558
## OriginContam 2.5004 1 0.113818
## TransplantContam:OriginContam 9.6379 1 0.001906 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1summary(mod4)## Linear mixed model fit by REML ['lmerMod']
## Formula: log(dat2$MuscleCarbohydrate) ~ (TransplantContam + OriginContam)^2 +
## (1 | CagingSite/CageSiteID) + (1 | OriginSite)
## Data: dat2
##
## REML criterion at convergence: 102.4
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -2.74057 -0.58246 0.07299 0.69077 2.51534
##
## Random effects:
## Groups Name Variance Std.Dev.
## CageSiteID:CagingSite (Intercept) 0.000265 0.01628
## CagingSite (Intercept) 0.017795 0.13340
## OriginSite (Intercept) 0.000000 0.00000
## Residual 0.081869 0.28613
## Number of obs: 243, groups:
## CageSiteID:CagingSite, 24; CagingSite, 4; OriginSite, 4
##
## Fixed effects:
## Estimate Std. Error t value
## (Intercept) 3.28444 0.10166 32.308
## TransplantContamLC 0.12175 0.14330 0.850
## OriginContamLC 0.08596 0.05436 1.581
## TransplantContamLC:OriginContamLC -0.23238 0.07485 -3.104
##
## Correlation of Fixed Effects:
## (Intr) TrnCLC OrgCLC
## TrnsplntCLC -0.709
## OrignCntmLC -0.261 0.185
## TrnCLC:OCLC 0.189 -0.256 -0.726
## optimizer (nloptwrap) convergence code: 0 (OK)
## boundary (singular) fit: see ?isSingularmodCarboh <- mod4
RmodCarboh <- MuMIn::r.squaredGLMM(modCarboh)Now that we have identified the best model, add sex as covariate to check whether results are sensitive NB: sample size is reduced when adding sex variable within the model, for this reason the sex effect on results is checked on the final model
6.11.7 Test for the sex effect
dat2 = dat2[is.na(dat2$Sex) == F, ]
modSex <-
lme4::lmer(
log(dat2$MuscleCarbohydrate) ~ (TransplantContam + OriginContam) ^ 2 + Sex +
(1 | CagingSite / CageSiteID) + (1| OriginSite),
data = dat2,
na.action = na.exclude
)
car::Anova(modSex, type = "3")## Analysis of Deviance Table (Type III Wald chisquare tests)
##
## Response: log(dat2$MuscleCarbohydrate)
## Chisq Df Pr(>Chisq)
## (Intercept) 1013.2175 1 < 2.2e-16 ***
## TransplantContam 0.7518 1 0.385901
## OriginContam 2.4458 1 0.117843
## Sex 0.5670 1 0.451469
## TransplantContam:OriginContam 9.7814 1 0.001763 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1summary(modSex)## Linear mixed model fit by REML ['lmerMod']
## Formula: log(dat2$MuscleCarbohydrate) ~ (TransplantContam + OriginContam)^2 +
## Sex + (1 | CagingSite/CageSiteID) + (1 | OriginSite)
## Data: dat2
##
## REML criterion at convergence: 106.9
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -2.75737 -0.57667 0.03485 0.66901 2.49046
##
## Random effects:
## Groups Name Variance Std.Dev.
## CageSiteID:CagingSite (Intercept) 0.0001979 0.01407
## CagingSite (Intercept) 0.0182223 0.13499
## OriginSite (Intercept) 0.0000000 0.00000
## Residual 0.0823006 0.28688
## Number of obs: 242, groups:
## CageSiteID:CagingSite, 24; CagingSite, 4; OriginSite, 4
##
## Fixed effects:
## Estimate Std. Error t value
## (Intercept) 3.29392 0.10348 31.831
## TransplantContamLC 0.12559 0.14484 0.867
## OriginContamLC 0.08535 0.05458 1.564
## SexM -0.02888 0.03835 -0.753
## TransplantContamLC:OriginContamLC -0.23545 0.07528 -3.128
##
## Correlation of Fixed Effects:
## (Intr) TrnCLC OrgCLC SexM
## TrnsplntCLC -0.699
## OrignCntmLC -0.248 0.183
## SexM -0.124 -0.034 -0.049
## TrnCLC:OCLC 0.172 -0.254 -0.728 0.101
## optimizer (nloptwrap) convergence code: 0 (OK)
## boundary (singular) fit: see ?isSingularThe sex effect is non-significant. The mod4 is thus the best model. Here, the interactions between fish origin and the transplant site are significant, confirming the pattern observed for the integrative measure of available energy previously observed.
6.12 Daily mass changes
6.12.1 Check the data
dat2 = dat1[is.na(dat1$DailyMassChange) == F, ]
# transform variable to approx. normality
dat2$DailyMassChange.p <-
bimixt::boxcox(dat2$DailyMassChange + 3,
car::powerTransform(dat2$DailyMassChange + 3)$lambda)
hist(dat2$DailyMassChange.p)
6.12.2 Visualize
par(mfrow=c(2,3))
boxplot(DailyMassChange.p ~ OriginContam, data = dat2)
boxplot(DailyMassChange.p ~ TransplantContam, data = dat2)
boxplot(DailyMassChange.p ~ Injection, data = dat2)
boxplot(DailyMassChange.p ~ TransplantContam * Injection, data = dat2)
boxplot(DailyMassChange.p ~ TransplantContam * OriginContam, data = dat2)
boxplot(DailyMassChange.p ~ TransplantContam * OriginContam * Injection, data = dat2)
6.12.3 Build the full model
modfull <-
lme4::lmer(
DailyMassChange.p ~ (TransplantContam + OriginContam + Injection) ^ 3 + SizeEnd +
(1 | CagingSite / CageSiteID) + (1| OriginSite),
data = dat2,
na.action = na.exclude
)
car::Anova(modfull, type = "3")## Analysis of Deviance Table (Type III Wald chisquare tests)
##
## Response: DailyMassChange.p
## Chisq Df Pr(>Chisq)
## (Intercept) 15.8885 1 6.719e-05 ***
## TransplantContam 0.1775 1 0.673520
## OriginContam 1.7041 1 0.191755
## Injection 0.5038 1 0.477828
## SizeEnd 2.7096 1 0.099745 .
## TransplantContam:OriginContam 7.6762 1 0.005596 **
## TransplantContam:Injection 0.3860 1 0.534387
## OriginContam:Injection 1.4633 1 0.226406
## TransplantContam:OriginContam:Injection 0.8882 1 0.345957
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1summary(modfull)## Linear mixed model fit by REML ['lmerMod']
## Formula: DailyMassChange.p ~ (TransplantContam + OriginContam + Injection)^3 +
## SizeEnd + (1 | CagingSite/CageSiteID) + (1 | OriginSite)
## Data: dat2
##
## REML criterion at convergence: 93.9
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -4.4412 -0.5700 0.0571 0.5996 3.1697
##
## Random effects:
## Groups Name Variance Std.Dev.
## CageSiteID:CagingSite (Intercept) 0.003799 0.06164
## CagingSite (Intercept) 0.059924 0.24479
## OriginSite (Intercept) 0.005396 0.07346
## Residual 0.070161 0.26488
## Number of obs: 248, groups:
## CageSiteID:CagingSite, 24; CagingSite, 4; OriginSite, 4
##
## Fixed effects:
## Estimate Std. Error t value
## (Intercept) 0.94405 0.23684 3.986
## TransplantContamLC 0.10781 0.25587 0.421
## OriginContamLC 0.13745 0.10529 1.305
## InjectionPBS 0.04748 0.06690 0.710
## SizeEnd 0.02351 0.01428 1.646
## TransplantContamLC:OriginContamLC -0.29247 0.10556 -2.771
## TransplantContamLC:InjectionPBS -0.05833 0.09387 -0.621
## OriginContamLC:InjectionPBS -0.11757 0.09719 -1.210
## TransplantContamLC:OriginContamLC:InjectionPBS 0.12739 0.13517 0.942
##
## Correlation of Fixed Effects:
## (Intr) TrnCLC OrgCLC InjPBS SizEnd TrCLC:OCLC TCLC:I OCLC:I
## TrnsplntCLC -0.549
## OrignCntmLC -0.239 0.103
## InjectinPBS -0.143 0.124 0.302
## SizeEnd -0.607 0.014 0.033 0.014
## TrnCLC:OCLC 0.101 -0.205 -0.510 -0.301 0.016
## TrnCLC:IPBS 0.095 -0.177 -0.215 -0.712 0.001 0.430
## OrgCLC:IPBS 0.097 -0.086 -0.429 -0.688 -0.008 0.428 0.490
## TCLC:OCLC:I -0.065 0.123 0.308 0.495 -0.002 -0.602 -0.694 -0.7196.12.4 Refining the model
mod2 <-
lme4::lmer(
DailyMassChange.p ~ (TransplantContam + OriginContam + Injection) ^ 2 + SizeEnd +
(1 | CagingSite / CageSiteID) + (1| OriginSite),
data = dat2,
na.action = na.exclude
)
car::Anova(mod2, type = "3")## Analysis of Deviance Table (Type III Wald chisquare tests)
##
## Response: DailyMassChange.p
## Chisq Df Pr(>Chisq)
## (Intercept) 16.4593 1 4.971e-05 ***
## TransplantContam 0.0945 1 0.758506
## OriginContam 1.1422 1 0.285195
## Injection 0.0787 1 0.779052
## SizeEnd 2.7144 1 0.099448 .
## TransplantContam:OriginContam 7.5825 1 0.005894 **
## TransplantContam:Injection 0.0022 1 0.962993
## OriginContam:Injection 0.5876 1 0.443337
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1summary(mod2)## Linear mixed model fit by REML ['lmerMod']
## Formula: DailyMassChange.p ~ (TransplantContam + OriginContam + Injection)^2 +
## SizeEnd + (1 | CagingSite/CageSiteID) + (1 | OriginSite)
## Data: dat2
##
## REML criterion at convergence: 92.7
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -4.5140 -0.5651 0.0643 0.5870 3.1142
##
## Random effects:
## Groups Name Variance Std.Dev.
## CageSiteID:CagingSite (Intercept) 0.003851 0.06206
## CagingSite (Intercept) 0.059988 0.24492
## OriginSite (Intercept) 0.005354 0.07317
## Residual 0.070103 0.26477
## Number of obs: 248, groups:
## CageSiteID:CagingSite, 24; CagingSite, 4; OriginSite, 4
##
## Fixed effects:
## Estimate Std. Error t value
## (Intercept) 0.958781 0.236327 4.057
## TransplantContamLC 0.078117 0.254084 0.307
## OriginContamLC 0.106900 0.100026 1.069
## InjectionPBS 0.016304 0.058113 0.281
## SizeEnd 0.023513 0.014271 1.648
## TransplantContamLC:OriginContamLC -0.232617 0.084476 -2.754
## TransplantContamLC:InjectionPBS 0.003133 0.067528 0.046
## OriginContamLC:InjectionPBS -0.051771 0.067535 -0.767
##
## Correlation of Fixed Effects:
## (Intr) TrnCLC OrgCLC InjPBS SizEnd TCLC:O TCLC:I
## TrnsplntCLC -0.546
## OrignCntmLC -0.231 0.070
## InjectinPBS -0.127 0.074 0.182
## SizeEnd -0.608 0.015 0.035 0.017
## TrnCLC:OCLC 0.078 -0.165 -0.429 -0.005 0.018
## TrnCLC:IPBS 0.069 -0.128 -0.001 -0.590 0.000 0.021
## OrgCLC:IPBS 0.073 0.004 -0.314 -0.551 -0.014 -0.009 -0.0186.12.5 Refining the model
mod3 <-
lme4::lmer(
DailyMassChange.p ~ (TransplantContam + OriginContam) ^ 2 + Injection + SizeEnd +
(1 | CagingSite / CageSiteID) + (1| OriginSite),
data = dat2,
na.action = na.exclude
)
car::Anova(mod3, type = "3")## Analysis of Deviance Table (Type III Wald chisquare tests)
##
## Response: DailyMassChange.p
## Chisq Df Pr(>Chisq)
## (Intercept) 17.0593 1 3.623e-05 ***
## TransplantContam 0.1008 1 0.75085
## OriginContam 0.7564 1 0.38446
## Injection 0.0443 1 0.83334
## SizeEnd 2.7067 1 0.09992 .
## TransplantContam:OriginContam 7.7238 1 0.00545 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1summary(mod3)## Linear mixed model fit by REML ['lmerMod']
## Formula: DailyMassChange.p ~ (TransplantContam + OriginContam)^2 + Injection +
## SizeEnd + (1 | CagingSite/CageSiteID) + (1 | OriginSite)
## Data: dat2
##
## REML criterion at convergence: 86.2
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -4.5818 -0.5506 0.0588 0.6014 3.1688
##
## Random effects:
## Groups Name Variance Std.Dev.
## CageSiteID:CagingSite (Intercept) 0.003751 0.06124
## CagingSite (Intercept) 0.060026 0.24500
## OriginSite (Intercept) 0.005448 0.07381
## Residual 0.069723 0.26405
## Number of obs: 248, groups:
## CageSiteID:CagingSite, 24; CagingSite, 4; OriginSite, 4
##
## Fixed effects:
## Estimate Std. Error t value
## (Intercept) 0.970727 0.235026 4.130
## TransplantContamLC 0.080002 0.251963 0.318
## OriginContamLC 0.082800 0.095204 0.870
## InjectionPBS -0.007081 0.033652 -0.210
## SizeEnd 0.023431 0.014242 1.645
## TransplantContamLC:OriginContamLC -0.233196 0.083908 -2.779
##
## Correlation of Fixed Effects:
## (Intr) TrnCLC OrgCLC InjPBS SizEnd
## TrnsplntCLC -0.545
## OrignCntmLC -0.220 0.073
## InjectinPBS -0.078 -0.002 0.008
## SizeEnd -0.609 0.015 0.032 0.016
## TrnCLC:OCLC 0.077 -0.163 -0.451 0.005 0.0186.12.6 Refining the model
mod4 <-
lme4::lmer(
DailyMassChange.p ~ (TransplantContam + OriginContam) ^ 2 + SizeEnd +
(1 | CagingSite / CageSiteID) + (1| OriginSite),
data = dat2,
na.action = na.exclude
)
car::Anova(mod4, type = "3")## Analysis of Deviance Table (Type III Wald chisquare tests)
##
## Response: DailyMassChange.p
## Chisq Df Pr(>Chisq)
## (Intercept) 17.0349 1 3.67e-05 ***
## TransplantContam 0.1006 1 0.751141
## OriginContam 0.7581 1 0.383911
## SizeEnd 2.7346 1 0.098194 .
## TransplantContam:OriginContam 7.7194 1 0.005463 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1summary(mod4)## Linear mixed model fit by REML ['lmerMod']
## Formula: DailyMassChange.p ~ (TransplantContam + OriginContam)^2 + SizeEnd +
## (1 | CagingSite/CageSiteID) + (1 | OriginSite)
## Data: dat2
##
## REML criterion at convergence: 81.2
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -4.6078 -0.5608 0.0519 0.5984 3.1870
##
## Random effects:
## Groups Name Variance Std.Dev.
## CageSiteID:CagingSite (Intercept) 0.003781 0.06149
## CagingSite (Intercept) 0.060029 0.24501
## OriginSite (Intercept) 0.005469 0.07395
## Residual 0.069423 0.26348
## Number of obs: 248, groups:
## CageSiteID:CagingSite, 24; CagingSite, 4; OriginSite, 4
##
## Fixed effects:
## Estimate Std. Error t value
## (Intercept) 0.96658 0.23419 4.127
## TransplantContamLC 0.07991 0.25197 0.317
## OriginContamLC 0.08299 0.09531 0.871
## SizeEnd 0.02351 0.01422 1.654
## TransplantContamLC:OriginContamLC -0.23314 0.08391 -2.778
##
## Correlation of Fixed Effects:
## (Intr) TrnCLC OrgCLC SizEnd
## TrnsplntCLC -0.547
## OrignCntmLC -0.220 0.073
## SizeEnd -0.609 0.015 0.032
## TrnCLC:OCLC 0.078 -0.163 -0.450 0.0186.12.7 Refining the model
mod5 <-
lme4::lmer(
DailyMassChange.p ~ (TransplantContam + OriginContam) ^ 2 +
(1 | CagingSite / CageSiteID) + (1| OriginSite),
data = dat2,
na.action = na.exclude
)
car::Anova(mod5, type = "3")## Analysis of Deviance Table (Type III Wald chisquare tests)
##
## Response: DailyMassChange.p
## Chisq Df Pr(>Chisq)
## (Intercept) 46.0496 1 1.153e-11 ***
## TransplantContam 0.0872 1 0.76776
## OriginContam 0.5827 1 0.44526
## TransplantContam:OriginContam 4.9114 1 0.02668 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1summary(mod5)## Linear mixed model fit by REML ['lmerMod']
## Formula: DailyMassChange.p ~ (TransplantContam + OriginContam)^2 + (1 |
## CagingSite/CageSiteID) + (1 | OriginSite)
## Data: dat2
##
## REML criterion at convergence: 107.2
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -4.4880 -0.5227 0.0623 0.5611 3.1177
##
## Random effects:
## Groups Name Variance Std.Dev.
## CageSiteID:CagingSite (Intercept) 0.006937 0.08329
## CagingSite (Intercept) 0.057970 0.24077
## OriginSite (Intercept) 0.000000 0.00000
## Residual 0.077979 0.27925
## Number of obs: 252, groups:
## CageSiteID:CagingSite, 24; CagingSite, 4; OriginSite, 4
##
## Fixed effects:
## Estimate Std. Error t value
## (Intercept) 1.20243 0.17719 6.786
## TransplantContamLC 0.07397 0.25048 0.295
## OriginContamLC 0.05348 0.07005 0.763
## TransplantContamLC:OriginContamLC -0.21739 0.09809 -2.216
##
## Correlation of Fixed Effects:
## (Intr) TrnCLC OrgCLC
## TrnsplntCLC -0.707
## OrignCntmLC -0.194 0.138
## TrnCLC:OCLC 0.139 -0.194 -0.714
## optimizer (nloptwrap) convergence code: 0 (OK)
## boundary (singular) fit: see ?isSingularmodDMC <- mod5
RmodDMC <- MuMIn::r.squaredGLMM(modDMC)Here, the interactions between fish origin and the transplant site are significant.
Now that we have identified the best model, add sex as covariate to check whether results are sensitive NB: sample size is reduced when adding sex variable within the model, for this reason the sex effect on results is checked on the final model
6.12.8 Test for the sex effect
dat2 = dat2[is.na(dat2$Sex) == F, ]
modSex <-
lme4::lmer(
DailyMassChange.p ~ (TransplantContam + OriginContam) ^ 2 + Sex +
(1 | CagingSite / CageSiteID) + (1| OriginSite),
data = dat2,
na.action = na.exclude
)
car::Anova(modSex, type = "3")## Analysis of Deviance Table (Type III Wald chisquare tests)
##
## Response: DailyMassChange.p
## Chisq Df Pr(>Chisq)
## (Intercept) 46.4776 1 9.267e-12 ***
## TransplantContam 0.0955 1 0.757281
## OriginContam 2.6068 1 0.106406
## Sex 0.5753 1 0.448174
## TransplantContam:OriginContam 8.9250 1 0.002813 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1summary(modSex)## Linear mixed model fit by REML ['lmerMod']
## Formula: DailyMassChange.p ~ (TransplantContam + OriginContam)^2 + Sex +
## (1 | CagingSite/CageSiteID) + (1 | OriginSite)
## Data: dat2
##
## REML criterion at convergence: 62.7
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -4.8836 -0.5478 0.0778 0.5956 3.4584
##
## Random effects:
## Groups Name Variance Std.Dev.
## CageSiteID:CagingSite (Intercept) 5.185e-03 7.201e-02
## CagingSite (Intercept) 5.904e-02 2.430e-01
## OriginSite (Intercept) 8.010e-12 2.830e-06
## Residual 6.446e-02 2.539e-01
## Number of obs: 247, groups:
## CageSiteID:CagingSite, 24; CagingSite, 4; OriginSite, 4
##
## Fixed effects:
## Estimate Std. Error t value
## (Intercept) 1.21094 0.17762 6.817
## TransplantContamLC 0.07746 0.25064 0.309
## OriginContamLC 0.10133 0.06276 1.615
## SexM -0.02610 0.03441 -0.758
## TransplantContamLC:OriginContamLC -0.26263 0.08791 -2.987
##
## Correlation of Fixed Effects:
## (Intr) TrnCLC OrgCLC SexM
## TrnsplntCLC -0.705
## OrignCntmLC -0.168 0.122
## SexM -0.064 -0.018 -0.045
## TrnCLC:OCLC 0.117 -0.172 -0.716 0.081
## optimizer (nloptwrap) convergence code: 0 (OK)
## boundary (singular) fit: see ?isSingularAdding the sex as covariate does no change the significance of the interactions, also sex effect is non-significant. The mod5 is thus the best model.
6.12.9 Posthoc test (pairwise t-test)
The interactions between fish origin and the transplant site are significant. Hence, perform posthoc test (pairwise t-test) according to significant interactions.
pairwise.t.test(dat2$DailyMassChange.p, dat2$CxO2, p.adjust.method = "fdr")##
## Pairwise comparisons using t tests with pooled SD
##
## data: dat2$DailyMassChange.p and dat2$CxO2
##
## HC_HC HC_LC LC_HC
## HC_LC 0.378 - -
## LC_HC 0.382 0.851 -
## LC_LC 0.132 0.014 0.014
##
## P value adjustment method: fdrHere the posthoc are non significant, except between the HC and LC fish when exposed to LC sites, likely because responses were very different depending on the population considered (see non-parallel plastic responses below). Also,because interaction between the contamination in origin and transplant site of fish is significant We test for parallel response between replicate populations.
6.12.10 Test for parallel responses between replicate populations (from the same origin)
6.12.10.1 For Populations from High contamination sites (AUSCOR and RIOU)
dat3 <- dat2[which(dat2$OriginSite %in% c("AUSCOR", "RIOU")),]
## build the null model
mod.null <-
glm(DailyMassChange.p ~ TransplantContam + OriginSite,
data = dat3)
## build the model with the site of origin in interaction with the level of contam in transplant sites
mod.par <-
glm(DailyMassChange.p ~ TransplantContam * OriginSite,
data = dat3)
anova(mod.null, mod.par, test = "LRT")## Analysis of Deviance Table
##
## Model 1: DailyMassChange.p ~ TransplantContam + OriginSite
## Model 2: DailyMassChange.p ~ TransplantContam * OriginSite
## Resid. Df Resid. Dev Df Deviance Pr(>Chi)
## 1 125 6.4448
## 2 124 5.0924 1 1.3524 9.546e-09 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1coef(mod.par)## (Intercept) TransplantContamLC
## 0.9855391 0.2785145
## OriginSiteRIOU TransplantContamLC:OriginSiteRIOU
## 0.4367652 -0.4118958summary(mod.par)##
## Call:
## glm(formula = DailyMassChange.p ~ TransplantContam * OriginSite,
## data = dat3)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -0.52373 -0.12763 0.00892 0.13518 0.59893
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.98554 0.03763 26.189 < 2e-16 ***
## TransplantContamLC 0.27851 0.05158 5.400 3.27e-07 ***
## OriginSiteRIOU 0.43677 0.05122 8.526 4.38e-14 ***
## TransplantContamLC:OriginSiteRIOU -0.41190 0.07178 -5.739 6.91e-08 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for gaussian family taken to be 0.04106755)
##
## Null deviance: 8.1850 on 127 degrees of freedom
## Residual deviance: 5.0924 on 124 degrees of freedom
## AIC: -39.46
##
## Number of Fisher Scoring iterations: 2The null model and the model including the site of origin in interaction with the level of contaminant in transplant sites are significantly different, we hence reject the null hypothesis, here the slopes of HC populations are not parallel.
6.12.10.2 For Populations from Low contamination sites (ARIMAS and CELFIG)
# We test for parallel response between replicate LC populations (ARIMAS and CELFIG)
dat4 <- dat2[which(dat2$OriginSite %in% c("ARIMAS", "CELFIG")),]
## build the null model
mod.null <-
glm(DailyMassChange.p ~ TransplantContam + OriginSite,
data = dat4)
## build the model with the site of origin in interaction with the level of contam in transplant sites
mod.par <-
glm(DailyMassChange.p ~ TransplantContam * OriginSite,
data = dat4)
anova(mod.null, mod.par, test = "LRT")## Analysis of Deviance Table
##
## Model 1: DailyMassChange.p ~ TransplantContam + OriginSite
## Model 2: DailyMassChange.p ~ TransplantContam * OriginSite
## Resid. Df Resid. Dev Df Deviance Pr(>Chi)
## 1 116 13.396
## 2 115 11.297 1 2.0997 3.778e-06 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1coef(mod.par)## (Intercept) TransplantContamLC
## 1.02261170 0.08832977
## OriginSiteCELFIG TransplantContamLC:OriginSiteCELFIG
## 0.54826564 -0.53245772summary(mod.par)##
## Call:
## glm(formula = DailyMassChange.p ~ TransplantContam * OriginSite,
## data = dat4)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -1.19383 -0.18877 0.00355 0.18266 0.91144
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1.02261 0.05820 17.570 < 2e-16 ***
## TransplantContamLC 0.08833 0.08036 1.099 0.274
## OriginSiteCELFIG 0.54827 0.08382 6.541 1.76e-09 ***
## TransplantContamLC:OriginSiteCELFIG -0.53246 0.11517 -4.623 9.95e-06 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for gaussian family taken to be 0.09823347)
##
## Null deviance: 16.343 on 118 degrees of freedom
## Residual deviance: 11.297 on 115 degrees of freedom
## AIC: 67.51
##
## Number of Fisher Scoring iterations: 2The null model and the model including the site of origin in interaction with the level of contaminant in transplant sites are significantly different, we hence reject the null hypothesis, here the slopes of LC populations are not parallel.
6.12.11 Visualize
DMCPlot1()
6.13 HSI
6.13.1 Check the data
dat2 = dat1[is.na(dat1$HSI) == F, ]
# transform variable to approx. normality
dat2$HSI.p <- bimixt::boxcox(dat2$HSI, car::powerTransform(dat2$HSI)$lambda)
hist(dat2$HSI.p)
6.13.2 Visualize
par(mfrow=c(2,3))
boxplot(HSI.p ~ OriginContam, data = dat2)
boxplot(HSI.p ~ TransplantContam, data = dat2)
boxplot(HSI.p ~ Injection, data = dat2)
boxplot(HSI.p ~ TransplantContam * Injection, data = dat2)
boxplot(HSI.p ~ TransplantContam * OriginContam, data = dat2)
boxplot(HSI.p ~ TransplantContam * OriginContam * Injection, data = dat2)
6.13.3 Build the full model
modfull <-
lme4::lmer(
HSI.p ~ (TransplantContam + OriginContam + Injection) ^ 3 + SizeEnd +
(1 | CagingSite / CageSiteID) + (1| OriginSite),
data = dat2,
na.action = na.exclude
)
car::Anova(modfull, type = "3")## Analysis of Deviance Table (Type III Wald chisquare tests)
##
## Response: HSI.p
## Chisq Df Pr(>Chisq)
## (Intercept) 0.1222 1 0.72664
## TransplantContam 0.0241 1 0.87661
## OriginContam 0.0383 1 0.84479
## Injection 0.1593 1 0.68984
## SizeEnd 5.0481 1 0.02465 *
## TransplantContam:OriginContam 1.9608 1 0.16143
## TransplantContam:Injection 0.0554 1 0.81391
## OriginContam:Injection 0.0203 1 0.88683
## TransplantContam:OriginContam:Injection 0.1900 1 0.66290
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1summary(modfull)## Linear mixed model fit by REML ['lmerMod']
## Formula: HSI.p ~ (TransplantContam + OriginContam + Injection)^3 + SizeEnd +
## (1 | CagingSite/CageSiteID) + (1 | OriginSite)
## Data: dat2
##
## REML criterion at convergence: 240.2
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -3.5377 -0.4674 0.0100 0.4845 4.0412
##
## Random effects:
## Groups Name Variance Std.Dev.
## CageSiteID:CagingSite (Intercept) 0.01483 0.1218
## CagingSite (Intercept) 0.04700 0.2168
## OriginSite (Intercept) 0.05889 0.2427
## Residual 0.12635 0.3555
## Number of obs: 247, groups:
## CageSiteID:CagingSite, 24; CagingSite, 4; OriginSite, 4
##
## Fixed effects:
## Estimate Std. Error t value
## (Intercept) 0.11082 0.31699 0.350
## TransplantContamLC 0.03793 0.24427 0.155
## OriginContamLC 0.05252 0.26825 0.196
## InjectionPBS 0.03585 0.08982 0.399
## SizeEnd -0.04535 0.02018 -2.247
## TransplantContamLC:OriginContamLC -0.22386 0.15987 -1.400
## TransplantContamLC:InjectionPBS 0.02967 0.12607 0.235
## OriginContamLC:InjectionPBS 0.01865 0.13105 0.142
## TransplantContamLC:OriginContamLC:InjectionPBS -0.07929 0.18189 -0.436
##
## Correlation of Fixed Effects:
## (Intr) TrnCLC OrgCLC InjPBS SizEnd TrCLC:OCLC TCLC:I OCLC:I
## TrnsplntCLC -0.399
## OrignCntmLC -0.432 0.097
## InjectinPBS -0.144 0.175 0.159
## SizeEnd -0.640 0.021 0.018 0.015
## TrnCLC:OCLC 0.116 -0.323 -0.304 -0.266 0.014
## TrnCLC:IPBS 0.097 -0.249 -0.113 -0.712 -0.002 0.381
## OrgCLC:IPBS 0.098 -0.120 -0.229 -0.685 -0.009 0.384 0.488
## TCLC:OCLC:I -0.067 0.173 0.165 0.494 0.001 -0.537 -0.693 -0.7206.13.4 Refining the model
mod2 <-
lme4::lmer(
HSI.p ~ (TransplantContam + OriginContam + Injection) ^ 2 + SizeEnd +
(1 | CagingSite / CageSiteID) + (1| OriginSite),
data = dat2,
na.action = na.exclude
)
car::Anova(mod2, type = "3")## Analysis of Deviance Table (Type III Wald chisquare tests)
##
## Response: HSI.p
## Chisq Df Pr(>Chisq)
## (Intercept) 0.1042 1 0.74686
## TransplantContam 0.0548 1 0.81493
## OriginContam 0.0738 1 0.78590
## Injection 0.5004 1 0.47933
## SizeEnd 5.0740 1 0.02429 *
## TransplantContam:OriginContam 3.7542 1 0.05267 .
## TransplantContam:Injection 0.0085 1 0.92639
## OriginContam:Injection 0.0615 1 0.80419
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1summary(mod2)## Linear mixed model fit by REML ['lmerMod']
## Formula: HSI.p ~ (TransplantContam + OriginContam + Injection)^2 + SizeEnd +
## (1 | CagingSite/CageSiteID) + (1 | OriginSite)
## Data: dat2
##
## REML criterion at convergence: 238.9
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -3.5179 -0.4467 0.0328 0.4906 4.0196
##
## Random effects:
## Groups Name Variance Std.Dev.
## CageSiteID:CagingSite (Intercept) 0.01489 0.1220
## CagingSite (Intercept) 0.04696 0.2167
## OriginSite (Intercept) 0.05887 0.2426
## Residual 0.12588 0.3548
## Number of obs: 247, groups:
## CageSiteID:CagingSite, 24; CagingSite, 4; OriginSite, 4
##
## Fixed effects:
## Estimate Std. Error t value
## (Intercept) 0.102002 0.316004 0.323
## TransplantContamLC 0.056299 0.240521 0.234
## OriginContamLC 0.071857 0.264532 0.272
## InjectionPBS 0.055155 0.077970 0.707
## SizeEnd -0.045386 0.020149 -2.253
## TransplantContamLC:OriginContamLC -0.261344 0.134881 -1.938
## TransplantContamLC:InjectionPBS -0.008382 0.090722 -0.092
## OriginContamLC:InjectionPBS -0.022495 0.090734 -0.248
##
## Correlation of Fixed Effects:
## (Intr) TrnCLC OrgCLC InjPBS SizEnd TCLC:O TCLC:I
## TrnsplntCLC -0.394
## OrignCntmLC -0.428 0.071
## InjectinPBS -0.128 0.104 0.091
## SizeEnd -0.641 0.021 0.018 0.017
## TrnCLC:OCLC 0.095 -0.278 -0.259 -0.002 0.017
## TrnCLC:IPBS 0.070 -0.182 0.002 -0.591 -0.002 0.014
## OrgCLC:IPBS 0.072 0.007 -0.161 -0.547 -0.012 -0.005 -0.0226.13.5 Refining the model
mod3 <-
lme4::lmer(
HSI.p ~ (TransplantContam + OriginContam) ^ 2 + Injection + SizeEnd +
(1 | CagingSite / CageSiteID) + (1| OriginSite),
data = dat2,
na.action = na.exclude
)
car::Anova(mod3, type = "3")## Analysis of Deviance Table (Type III Wald chisquare tests)
##
## Response: HSI.p
## Chisq Df Pr(>Chisq)
## (Intercept) 0.1246 1 0.72405
## TransplantContam 0.0491 1 0.82462
## OriginContam 0.0552 1 0.81426
## Injection 0.7845 1 0.37577
## SizeEnd 5.1540 1 0.02319 *
## TransplantContam:OriginContam 3.7545 1 0.05267 .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1summary(mod3)## Linear mixed model fit by REML ['lmerMod']
## Formula: HSI.p ~ (TransplantContam + OriginContam)^2 + Injection + SizeEnd +
## (1 | CagingSite/CageSiteID) + (1 | OriginSite)
## Data: dat2
##
## REML criterion at convergence: 233
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -3.5095 -0.4566 0.0265 0.5062 4.0599
##
## Random effects:
## Groups Name Variance Std.Dev.
## CageSiteID:CagingSite (Intercept) 0.01502 0.1226
## CagingSite (Intercept) 0.04697 0.2167
## OriginSite (Intercept) 0.05890 0.2427
## Residual 0.12478 0.3532
## Number of obs: 247, groups:
## CageSiteID:CagingSite, 24; CagingSite, 4; OriginSite, 4
##
## Fixed effects:
## Estimate Std. Error t value
## (Intercept) 0.11081 0.31385 0.353
## TransplantContamLC 0.05241 0.23652 0.222
## OriginContamLC 0.06135 0.26115 0.235
## InjectionPBS 0.03997 0.04513 0.886
## SizeEnd -0.04555 0.02006 -2.270
## TransplantContamLC:OriginContamLC -0.26144 0.13492 -1.938
##
## Correlation of Fixed Effects:
## (Intr) TrnCLC OrgCLC InjPBS SizEnd
## TrnsplntCLC -0.391
## OrignCntmLC -0.425 0.074
## InjectinPBS -0.079 -0.003 0.002
## SizeEnd -0.642 0.021 0.016 0.016
## TrnCLC:OCLC 0.095 -0.280 -0.263 0.007 0.0176.13.6 Refining the model
mod4 <-
lme4::lmer(
HSI.p ~ TransplantContam + Injection + OriginContam + SizeEnd +
(1 | CagingSite / CageSiteID) + (1| OriginSite),
data = dat2,
na.action = na.exclude
)
car::Anova(mod4, type = "3")## Analysis of Deviance Table (Type III Wald chisquare tests)
##
## Response: HSI.p
## Chisq Df Pr(>Chisq)
## (Intercept) 0.3260 1 0.56801
## TransplantContam 0.1166 1 0.73275
## Injection 0.7948 1 0.37264
## OriginContam 0.0793 1 0.77825
## SizeEnd 5.1853 1 0.02278 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1summary(mod4)## Linear mixed model fit by REML ['lmerMod']
## Formula: HSI.p ~ TransplantContam + Injection + OriginContam + SizeEnd +
## (1 | CagingSite/CageSiteID) + (1 | OriginSite)
## Data: dat2
##
## REML criterion at convergence: 234.4
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -3.5314 -0.4699 0.0166 0.4858 3.9932
##
## Random effects:
## Groups Name Variance Std.Dev.
## CageSiteID:CagingSite (Intercept) 0.01893 0.1376
## CagingSite (Intercept) 0.04553 0.2134
## OriginSite (Intercept) 0.05804 0.2409
## Residual 0.12490 0.3534
## Number of obs: 247, groups:
## CageSiteID:CagingSite, 24; CagingSite, 4; OriginSite, 4
##
## Fixed effects:
## Estimate Std. Error t value
## (Intercept) 0.17794 0.31163 0.571
## TransplantContamLC -0.07694 0.22532 -0.341
## InjectionPBS 0.04026 0.04515 0.892
## OriginContamLC -0.07083 0.25154 -0.282
## SizeEnd -0.04577 0.02010 -2.277
##
## Correlation of Fixed Effects:
## (Intr) TrnCLC InjPBS OrgCLC
## TrnsplntCLC -0.379
## InjectinPBS -0.080 -0.001
## OrignCntmLC -0.417 0.000 0.004
## SizeEnd -0.650 0.027 0.016 0.0216.13.7 Refining the model
mod5 <-
lme4::lmer(
HSI.p ~ SizeEnd +
(1 | CagingSite / CageSiteID) + (1| OriginSite),
data = dat2,
na.action = na.exclude
)
performance::check_model(mod5)
car::Anova(mod5, type = "3")## Analysis of Deviance Table (Type III Wald chisquare tests)
##
## Response: HSI.p
## Chisq Df Pr(>Chisq)
## (Intercept) 0.1886 1 0.66411
## SizeEnd 4.7807 1 0.02878 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1summary(mod5)## Linear mixed model fit by REML ['lmerMod']
## Formula: HSI.p ~ SizeEnd + (1 | CagingSite/CageSiteID) + (1 | OriginSite)
## Data: dat2
##
## REML criterion at convergence: 228.5
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -3.5897 -0.4568 0.0296 0.4640 4.0940
##
## Random effects:
## Groups Name Variance Std.Dev.
## CageSiteID:CagingSite (Intercept) 0.01891 0.1375
## CagingSite (Intercept) 0.02755 0.1660
## OriginSite (Intercept) 0.03462 0.1861
## Residual 0.12481 0.3533
## Number of obs: 247, groups:
## CageSiteID:CagingSite, 24; CagingSite, 4; OriginSite, 4
##
## Fixed effects:
## Estimate Std. Error t value
## (Intercept) 0.10156 0.23389 0.434
## SizeEnd -0.04355 0.01992 -2.186
##
## Correlation of Fixed Effects:
## (Intr)
## SizeEnd -0.832modHSI <- mod5
RmodHSI <- MuMIn::r.squaredGLMM(modHSI)The treatments has no effect on HSI but the HSI is higher in bigger fish Represent the relation between fish size and HSI
plot(HSI.p ~ SizeEnd, data = dat2)
abline(b = -0.04355, a = 0.10156, col = "red")
Now that we have identified the best model, add sex as covariate to check whether results are sensitive NB: sample size is reduced when adding sex variable within the model, for this reason the sex effect on results is checked on the final model
6.13.8 Test for the sex effect
dat2 = dat2[is.na(dat2$Sex) == F, ]
modSex <-
lme4::lmer(
HSI.p ~ SizeEnd + Sex +
(1 | CagingSite / CageSiteID) + (1| OriginSite),
data = dat2,
na.action = na.exclude
)
car::Anova(modSex, type = "3")## Analysis of Deviance Table (Type III Wald chisquare tests)
##
## Response: HSI.p
## Chisq Df Pr(>Chisq)
## (Intercept) 0.1307 1 0.71769
## SizeEnd 3.8317 1 0.05029 .
## Sex 1.6701 1 0.19624
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1summary(modSex)## Linear mixed model fit by REML ['lmerMod']
## Formula: HSI.p ~ SizeEnd + Sex + (1 | CagingSite/CageSiteID) + (1 | OriginSite)
## Data: dat2
##
## REML criterion at convergence: 231.1
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -3.6703 -0.4511 0.0584 0.5046 4.2012
##
## Random effects:
## Groups Name Variance Std.Dev.
## CageSiteID:CagingSite (Intercept) 0.01821 0.1349
## CagingSite (Intercept) 0.02858 0.1691
## OriginSite (Intercept) 0.03231 0.1798
## Residual 0.12472 0.3532
## Number of obs: 247, groups:
## CageSiteID:CagingSite, 24; CagingSite, 4; OriginSite, 4
##
## Fixed effects:
## Estimate Std. Error t value
## (Intercept) 0.08426 0.23304 0.362
## SizeEnd -0.03932 0.02009 -1.957
## SexM -0.06291 0.04868 -1.292
##
## Correlation of Fixed Effects:
## (Intr) SizEnd
## SizeEnd -0.831
## SexM 0.040 -0.143The sex effect is non-significant. The mod5 is thus the best model. Here, there is no interaction, and hence no posthoc test nor parallelism test to conduct
6.14 GSI
6.14.1 Check the data
dat2 = dat1[is.na(dat1$GSI) == F, ]
dat2 = dat2[is.na(dat2$Sex) == F, ]
# transform variable to approx. normality
dat2$GSI.p <- bimixt::boxcox(dat2$GSI, car::powerTransform(dat2$GSI)$lambda)
hist(dat2$GSI.p)
6.14.2 Visualize
par(mfrow=c(2,3))
boxplot(GSI.p ~ OriginContam, data = dat2)
boxplot(GSI.p ~ TransplantContam, data = dat2)
boxplot(GSI.p ~ Injection, data = dat2)
boxplot(GSI.p ~ TransplantContam * Injection, data = dat2)
boxplot(GSI.p ~ TransplantContam * OriginContam, data = dat2)
boxplot(GSI.p ~ TransplantContam * OriginContam * Injection, data = dat2)
6.14.3 Build the full model
modfull <-
lme4::lmer(
GSI.p ~ (TransplantContam + OriginContam + Injection) ^ 3 + SizeEnd + Sex +
(1 | CagingSite / CageSiteID) + (1| OriginSite),
data = dat2,
na.action = na.exclude
)
car::Anova(modfull, type = "3")## Analysis of Deviance Table (Type III Wald chisquare tests)
##
## Response: GSI.p
## Chisq Df Pr(>Chisq)
## (Intercept) 4.9342 1 0.02633 *
## TransplantContam 0.4563 1 0.49936
## OriginContam 0.9120 1 0.33960
## Injection 0.7498 1 0.38654
## SizeEnd 0.1893 1 0.66350
## Sex 630.9592 1 < 2e-16 ***
## TransplantContam:OriginContam 1.3168 1 0.25117
## TransplantContam:Injection 0.5318 1 0.46585
## OriginContam:Injection 0.3518 1 0.55307
## TransplantContam:OriginContam:Injection 0.0025 1 0.96048
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1summary(modfull)## Linear mixed model fit by REML ['lmerMod']
## Formula: GSI.p ~ (TransplantContam + OriginContam + Injection)^3 + SizeEnd +
## Sex + (1 | CagingSite/CageSiteID) + (1 | OriginSite)
## Data: dat2
##
## REML criterion at convergence: 289.3
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -3.6652 -0.3581 0.0312 0.5165 3.8586
##
## Random effects:
## Groups Name Variance Std.Dev.
## CageSiteID:CagingSite (Intercept) 6.498e-09 8.061e-05
## CagingSite (Intercept) 0.000e+00 0.000e+00
## OriginSite (Intercept) 4.845e-02 2.201e-01
## Residual 1.678e-01 4.096e-01
## Number of obs: 244, groups:
## CageSiteID:CagingSite, 24; CagingSite, 4; OriginSite, 4
##
## Fixed effects:
## Estimate Std. Error t value
## (Intercept) 0.63484 0.28580 2.221
## TransplantContamLC -0.06934 0.10265 -0.676
## OriginContamLC -0.23282 0.24380 -0.955
## InjectionPBS -0.09019 0.10416 -0.866
## SizeEnd 0.01003 0.02304 0.435
## SexM -1.39931 0.05571 -25.119
## TransplantContamLC:OriginContamLC 0.16830 0.14667 1.148
## TransplantContamLC:InjectionPBS 0.10648 0.14601 0.729
## OriginContamLC:InjectionPBS 0.09070 0.15290 0.593
## TransplantContamLC:OriginContamLC:InjectionPBS -0.01050 0.21188 -0.050
##
## Correlation of Fixed Effects:
## (Intr) TrnCLC OrgCLC InjPBS SizEnd SexM TrCLC:OCLC TCLC:I OCLC:I
## TrnsplntCLC -0.215
## OrignCntmLC -0.438 0.217
## InjectinPBS -0.177 0.495 0.208
## SizeEnd -0.797 0.055 0.022 0.003
## SexM 0.047 -0.132 -0.045 -0.029 -0.133
## TrnCLC:OCLC 0.113 -0.706 -0.310 -0.348 0.004 0.150
## TrnCLC:IPBS 0.119 -0.699 -0.151 -0.715 0.002 0.084 0.495
## OrgCLC:IPBS 0.127 -0.348 -0.295 -0.684 -0.016 0.100 0.498 0.494
## TCLC:OCLC:I -0.089 0.489 0.215 0.494 0.012 -0.111 -0.692 -0.693 -0.725
## optimizer (nloptwrap) convergence code: 0 (OK)
## boundary (singular) fit: see ?isSingular6.14.4 Refining the model
mod2 <-
lme4::lmer(
GSI.p ~ (TransplantContam + OriginContam + Injection) ^ 2 + SizeEnd + Sex +
(1 | CagingSite / CageSiteID) + (1| OriginSite),
data = dat2,
na.action = na.exclude
)
car::Anova(mod2, type = "3")## Analysis of Deviance Table (Type III Wald chisquare tests)
##
## Response: GSI.p
## Chisq Df Pr(>Chisq)
## (Intercept) 4.9720 1 0.02576 *
## TransplantContam 0.5600 1 0.45425
## OriginContam 0.9356 1 0.33341
## Injection 0.9407 1 0.33211
## SizeEnd 0.1898 1 0.66308
## Sex 641.8109 1 < 2e-16 ***
## TransplantContam:OriginContam 2.3911 1 0.12203
## TransplantContam:Injection 0.9342 1 0.33377
## OriginContam:Injection 0.6577 1 0.41736
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1summary(mod2)## Linear mixed model fit by REML ['lmerMod']
## Formula: GSI.p ~ (TransplantContam + OriginContam + Injection)^2 + SizeEnd +
## Sex + (1 | CagingSite/CageSiteID) + (1 | OriginSite)
## Data: dat2
##
## REML criterion at convergence: 288
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -3.6703 -0.3597 0.0321 0.5143 3.8634
##
## Random effects:
## Groups Name Variance Std.Dev.
## CageSiteID:CagingSite (Intercept) 1.248e-10 1.117e-05
## CagingSite (Intercept) 0.000e+00 0.000e+00
## OriginSite (Intercept) 4.844e-02 2.201e-01
## Residual 1.671e-01 4.087e-01
## Number of obs: 244, groups:
## CageSiteID:CagingSite, 24; CagingSite, 4; OriginSite, 4
##
## Fixed effects:
## Estimate Std. Error t value
## (Intercept) 0.63378 0.28423 2.230
## TransplantContamLC -0.06686 0.08934 -0.748
## OriginContamLC -0.23023 0.23802 -0.967
## InjectionPBS -0.08764 0.09036 -0.970
## SizeEnd 0.01002 0.02299 0.436
## SexM -1.39960 0.05525 -25.334
## TransplantContamLC:OriginContamLC 0.16327 0.10559 1.546
## TransplantContamLC:InjectionPBS 0.10146 0.10497 0.967
## OriginContamLC:InjectionPBS 0.08520 0.10505 0.811
##
## Correlation of Fixed Effects:
## (Intr) TrnCLC OrgCLC InjPBS SizEnd SexM TCLC:O TCLC:I
## TrnsplntCLC -0.197
## OrignCntmLC -0.431 0.131
## InjectinPBS -0.153 0.334 0.120
## SizeEnd -0.799 0.056 0.020 -0.003
## SexM 0.037 -0.090 -0.022 0.030 -0.133
## TrnCLC:OCLC 0.071 -0.583 -0.228 -0.009 0.017 0.102
## TrnCLC:IPBS 0.079 -0.573 -0.003 -0.594 0.015 0.010 0.028
## OrgCLC:IPBS 0.091 0.012 -0.208 -0.543 -0.011 0.028 -0.008 -0.019
## optimizer (nloptwrap) convergence code: 0 (OK)
## boundary (singular) fit: see ?isSingular6.14.5 Refining the model
mod3 <-
lme4::lmer(
GSI.p ~ TransplantContam + OriginContam + Injection + SizeEnd + Sex +
(1 | CagingSite / CageSiteID) + (1| OriginSite),
data = dat2,
na.action = na.exclude
)
car::Anova(mod3, type = "3")## Analysis of Deviance Table (Type III Wald chisquare tests)
##
## Response: GSI.p
## Chisq Df Pr(>Chisq)
## (Intercept) 3.9463 1 0.04698 *
## TransplantContam 1.2417 1 0.26514
## OriginContam 0.2125 1 0.64483
## Injection 0.0094 1 0.92281
## SizeEnd 0.1580 1 0.69104
## Sex 654.4211 1 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1summary(mod3)## Linear mixed model fit by REML ['lmerMod']
## Formula: GSI.p ~ TransplantContam + OriginContam + Injection + SizeEnd +
## Sex + (1 | CagingSite/CageSiteID) + (1 | OriginSite)
## Data: dat2
##
## REML criterion at convergence: 283.9
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -3.7392 -0.4029 0.0402 0.4865 3.8015
##
## Random effects:
## Groups Name Variance Std.Dev.
## CageSiteID:CagingSite (Intercept) 0.0006149 0.0248
## CagingSite (Intercept) 0.0000000 0.0000
## OriginSite (Intercept) 0.0491028 0.2216
## Residual 0.1672205 0.4089
## Number of obs: 244, groups:
## CageSiteID:CagingSite, 24; CagingSite, 4; OriginSite, 4
##
## Fixed effects:
## Estimate Std. Error t value
## (Intercept) 0.561239 0.282524 1.987
## TransplantContamLC 0.060024 0.053866 1.114
## OriginContamLC -0.105105 0.228015 -0.461
## InjectionPBS 0.005104 0.052679 0.097
## SizeEnd 0.009155 0.023035 0.397
## SexM -1.409437 0.055096 -25.582
##
## Correlation of Fixed Effects:
## (Intr) TrnCLC OrgCLC InjPBS SizEnd
## TrnsplntCLC -0.192
## OrignCntmLC -0.422 -0.001
## InjectinPBS -0.096 -0.012 0.007
## SizeEnd -0.807 0.123 0.023 -0.002
## SexM 0.028 -0.044 0.007 0.087 -0.137
## optimizer (nloptwrap) convergence code: 0 (OK)
## boundary (singular) fit: see ?isSingular6.14.6 Refining the model
mod4 <-
lme4::lmer(
GSI.p ~ Sex +
(1 | CagingSite / CageSiteID) + (1| OriginSite),
data = dat2,
na.action = na.exclude
)
performance::check_model(mod4)
car::Anova(mod4, type = "3")## Analysis of Deviance Table (Type III Wald chisquare tests)
##
## Response: GSI.p
## Chisq Df Pr(>Chisq)
## (Intercept) 37.318 1 1.004e-09 ***
## Sex 673.900 1 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1summary(mod4)## Linear mixed model fit by REML ['lmerMod']
## Formula: GSI.p ~ Sex + (1 | CagingSite/CageSiteID) + (1 | OriginSite)
## Data: dat2
##
## REML criterion at convergence: 270.5
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -3.8345 -0.3850 0.0610 0.5162 3.7582
##
## Random effects:
## Groups Name Variance Std.Dev.
## CageSiteID:CagingSite (Intercept) 0.0006987 0.02643
## CagingSite (Intercept) 0.0000000 0.00000
## OriginSite (Intercept) 0.0380456 0.19505
## Residual 0.1658745 0.40728
## Number of obs: 244, groups:
## CageSiteID:CagingSite, 24; CagingSite, 4; OriginSite, 4
##
## Fixed effects:
## Estimate Std. Error t value
## (Intercept) 0.63031 0.10318 6.109
## SexM -1.40539 0.05414 -25.960
##
## Correlation of Fixed Effects:
## (Intr)
## SexM -0.200
## optimizer (nloptwrap) convergence code: 0 (OK)
## boundary (singular) fit: see ?isSingularmodGSI <- mod4
RmodGSI <- MuMIn::r.squaredGLMM(modGSI)The treatments has no effect on GSI but the GSI is higher in females. Represent the relation between fish sex and GSI
boxplot(GSI.p ~ Sex, data = dat2)
Here, there is no interaction, and hence no posthoc test nor parallelism test to conduct
6.15 Summary of the best models for traits excepted gene expression (Table 3 from the manuscript)
The following table report the results of the best models tested above, this table correspond to the Table 3 in the manuscript. Excepted for the survival (GLM), the table report the marginal and conditional Rsquared (R2m and R2c respectively).| Estimate | Std. Error | t or z value | df | Chisq | p.value | |
|---|---|---|---|---|---|---|
| Survival | n = 268 | ||||||
| Intercept | -19.6 | 1350 | -0.0144 | NA | NA | NA |
| Transplant (LC) | 16.1 | 1350 | 0.0119 | 1 | 2.68 | 0.102 |
| Origin (LC) | 18.3 | 1350 | 0.0135 | 1 | 22 | <0.0001 |
| Transplant (LC): Origin (LC) | -17.9 | 1350 | -0.0132 | 1 | 6.59 | <0.05 |
| Bioaccumulation | n = 248 | R2m = 0.0498 | R2c = 0.385 | ||||||
| Intercept | 0.00786 | 0.957 | 0.00821 | 1 | 0.0000675 | 0.993 |
| Transplant (LC) | 0.358 | 1.35 | 0.264 | 1 | 0.0699 | 0.791 |
| Origin (LC) | 0.499 | 0.352 | 1.42 | 1 | 2.01 | 0.156 |
| Imm. challenge (PBS) | 0.18 | 0.325 | 0.554 | 1 | 0.306 | 0.58 |
| Transplant (LC): Origin (LC) | -1.09 | 0.491 | -2.22 | 1 | 4.91 | <0.05 |
| Transplant (LC): imm. Challenge (PBS) | -0.972 | 0.452 | -2.15 | 1 | 4.62 | <0.05 |
| Oxidative stress index | n = 166 | R2m = 0.0629 | R2c = 0.258 | ||||||
| Intercept | 3.54 | 0.355 | 9.97 | 1 | 99.4 | <0.0001 |
| Size | -0.101 | 0.0333 | -3.03 | 1 | 9.21 | <0.01 |
| Oxidative damage | n = 179 | R2m = 0.0837 | R2c = 0.34 | ||||||
| Intercept | 2.07 | 0.246 | 8.41 | 1 | 70.7 | <0.0001 |
| Size | -0.0838 | 0.0227 | -3.7 | 1 | 13.7 | <0.01 |
| Antioxidant capacity | n = 169 | R2m = 0.0502 | R2c = 0.0661 | ||||||
| Intercept | 11.3 | 0.163 | 69.5 | 1 | 4830 | <0.0001 |
| Origin (LC) | -0.558 | 0.236 | -2.36 | 1 | 5.59 | <0.05 |
| Local immune response | n = 249 | R2m = 0.409 | R2c = 0.492 | ||||||
| Intercept | 26.2 | 2.43 | 10.8 | 1 | 117 | <0.0001 |
| Imm. challenge (PBS) | -23.4 | 1.66 | -14.1 | 1 | 199 | <0.0001 |
| NL inflammatory immune response | n = 229 | R2m = 0.0714 | R2c = 0.167 | ||||||
| Intercept | 0.00754 | 0.0149 | 0.505 | 1 | 0.255 | 0.614 |
| Transplant (LC) | -0.00736 | 0.00463 | -1.59 | 1 | 2.53 | 0.111 |
| Origin (LC) | -0.0109 | 0.0091 | -1.2 | 1 | 1.44 | 0.23 |
| Size | 0.00365 | 0.00135 | 2.7 | 1 | 7.28 | <0.01 |
| Transplant (LC): Origin (LC) | 0.0155 | 0.00674 | 2.3 | 1 | 5.28 | <0.05 |
| Available energy | n = 243 | R2m = 0.13 | R2c = 0.256 | ||||||
| Intercept | 8.38 | 0.0957 | 87.6 | 1 | 7670 | <0.0001 |
| Transplant (LC) | 0.15 | 0.0877 | 1.71 | 1 | 2.93 | 0.087 |
| Origin (LC) | -0.0398 | 0.117 | -0.341 | 1 | 0.116 | 0.733 |
| Transplant (LC): Origin (LC) | -0.302 | 0.0771 | -3.92 | 1 | 15.3 | <0.0001 |
| Daily mass change | n = 252 | R2m = 0.028 | R2c = 0.47 | ||||||
| Intercept | 1.2 | 0.177 | 6.79 | 1 | 46 | <0.0001 |
| Transplant (LC) | 0.074 | 0.25 | 0.295 | 1 | 0.0872 | 0.768 |
| Origin (LC) | 0.0535 | 0.0701 | 0.763 | 1 | 0.583 | 0.445 |
| Transplant (LC): Origin (LC) | -0.217 | 0.0981 | -2.22 | 1 | 4.91 | <0.05 |
| HSI | n = 247 | R2m = 0.0211 | R2c = 0.407 | ||||||
| Intercept | 0.102 | 0.234 | 0.434 | 1 | 0.189 | 0.664 |
| Size | -0.0436 | 0.0199 | -2.19 | 1 | 4.78 | <0.05 |
| GSI | n = 244 | R2m = 0.696 | R2c = 0.753 | ||||||
| Intercept | 0.63 | 0.103 | 6.11 | 1 | 37.3 | <0.0001 |
| Sex (M) | -1.41 | 0.0541 | -26 | 1 | 674 | <0.0001 |
6.16 Genes expression
The summary of the results of the best models selected below is reported in Table 4 from the manuscript and is also available in the section “Summary of the best models for gene expression (Table 4 from the manuscript)”
6.16.1 Mtl
6.16.1.1 Check the data
dat2 = dat1[is.na(dat1$DeltaCtMtl) == F, ]
# transform variable to approx. normality
dat2$DeltaCtMtl.p <-
bimixt::boxcox(dat2$DeltaCtMtl, car::powerTransform(dat2$DeltaCtMtl)$lambda)
hist(dat2$DeltaCtMtl.p)
6.16.1.2 Visualize
par(mfrow=c(2,3))
boxplot(DeltaCtMtl.p ~ OriginContam, data = dat2)
boxplot(DeltaCtMtl.p ~ TransplantContam, data = dat2)
boxplot(DeltaCtMtl.p ~ Injection, data = dat2)
boxplot(DeltaCtMtl.p ~ TransplantContam * Injection, data = dat2)
boxplot(DeltaCtMtl.p ~ TransplantContam * OriginContam, data = dat2)
boxplot(DeltaCtMtl.p ~ TransplantContam * OriginContam * Injection, data = dat2)
6.16.1.3 Build the full model
modfull <-
lme4::lmer(
DeltaCtMtl.p ~ (TransplantContam + OriginContam + Injection) ^ 3 + SizeEnd +
(1 | CagingSite / CageSiteID) + (1| OriginSite),
data = dat2,
na.action = na.exclude
)
car::Anova(modfull, type = "3")## Analysis of Deviance Table (Type III Wald chisquare tests)
##
## Response: DeltaCtMtl.p
## Chisq Df Pr(>Chisq)
## (Intercept) 10.2927 1 0.001336 **
## TransplantContam 0.2395 1 0.624548
## OriginContam 6.7105 1 0.009585 **
## Injection 1.2214 1 0.269086
## SizeEnd 1.3946 1 0.237623
## TransplantContam:OriginContam 0.1196 1 0.729470
## TransplantContam:Injection 0.3075 1 0.579197
## OriginContam:Injection 3.4508 1 0.063221 .
## TransplantContam:OriginContam:Injection 1.0149 1 0.313739
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1summary(modfull)## Linear mixed model fit by REML ['lmerMod']
## Formula: DeltaCtMtl.p ~ (TransplantContam + OriginContam + Injection)^3 +
## SizeEnd + (1 | CagingSite/CageSiteID) + (1 | OriginSite)
## Data: dat2
##
## REML criterion at convergence: 738.2
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -2.4967 -0.5453 0.0038 0.5515 3.3103
##
## Random effects:
## Groups Name Variance Std.Dev.
## CageSiteID:CagingSite (Intercept) 0.03839 0.1959
## CagingSite (Intercept) 0.00000 0.0000
## OriginSite (Intercept) 0.07785 0.2790
## Residual 1.10408 1.0508
## Number of obs: 246, groups:
## CageSiteID:CagingSite, 24; CagingSite, 4; OriginSite, 4
##
## Fixed effects:
## Estimate Std. Error t value
## (Intercept) 2.03364 0.63388 3.208
## TransplantContamLC -0.13847 0.28294 -0.489
## OriginContamLC -1.03660 0.40016 -2.590
## InjectionPBS -0.29320 0.26530 -1.105
## SizeEnd -0.06670 0.05648 -1.181
## TransplantContamLC:OriginContamLC 0.13920 0.40250 0.346
## TransplantContamLC:InjectionPBS 0.20641 0.37221 0.555
## OriginContamLC:InjectionPBS 0.71604 0.38546 1.858
## TransplantContamLC:OriginContamLC:InjectionPBS -0.54224 0.53825 -1.007
##
## Correlation of Fixed Effects:
## (Intr) TrnCLC OrgCLC InjPBS SizEnd TrCLC:OCLC TCLC:I OCLC:I
## TrnsplntCLC -0.267
## OrignCntmLC -0.341 0.355
## InjectinPBS -0.211 0.446 0.316
## SizeEnd -0.896 0.049 0.033 0.013
## TrnCLC:OCLC 0.132 -0.700 -0.509 -0.313 0.028
## TrnCLC:IPBS 0.138 -0.636 -0.224 -0.712 0.004 0.447
## OrgCLC:IPBS 0.144 -0.307 -0.448 -0.688 -0.008 0.445 0.490
## TCLC:OCLC:I -0.091 0.439 0.320 0.493 -0.008 -0.628 -0.692 -0.716
## optimizer (nloptwrap) convergence code: 0 (OK)
## boundary (singular) fit: see ?isSingular6.16.1.4 Refining the model
mod2 <-
lme4::lmer(
DeltaCtMtl.p ~ (TransplantContam + OriginContam + Injection) ^ 2 + SizeEnd +
(1 | CagingSite / CageSiteID) + (1| OriginSite),
data = dat2,
na.action = na.exclude
)
car::Anova(mod2, type = "3")## Analysis of Deviance Table (Type III Wald chisquare tests)
##
## Response: DeltaCtMtl.p
## Chisq Df Pr(>Chisq)
## (Intercept) 9.7828 1 0.001762 **
## TransplantContam 0.0026 1 0.959182
## OriginContam 5.7677 1 0.016323 *
## Injection 0.4896 1 0.484121
## SizeEnd 1.4036 1 0.236114
## TransplantContam:OriginContam 0.1378 1 0.710449
## TransplantContam:Injection 0.0394 1 0.842634
## OriginContam:Injection 2.6489 1 0.103624
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1summary(mod2)## Linear mixed model fit by REML ['lmerMod']
## Formula: DeltaCtMtl.p ~ (TransplantContam + OriginContam + Injection)^2 +
## SizeEnd + (1 | CagingSite/CageSiteID) + (1 | OriginSite)
## Data: dat2
##
## REML criterion at convergence: 739.8
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -2.5664 -0.5191 -0.0122 0.5910 3.3659
##
## Random effects:
## Groups Name Variance Std.Dev.
## CageSiteID:CagingSite (Intercept) 0.03628 0.1905
## CagingSite (Intercept) 0.00000 0.0000
## OriginSite (Intercept) 0.07756 0.2785
## Residual 1.10544 1.0514
## Number of obs: 246, groups:
## CageSiteID:CagingSite, 24; CagingSite, 4; OriginSite, 4
##
## Fixed effects:
## Estimate Std. Error t value
## (Intercept) 1.97302 0.63081 3.128
## TransplantContamLC -0.01294 0.25290 -0.051
## OriginContamLC -0.90740 0.37783 -2.402
## InjectionPBS -0.16163 0.23101 -0.700
## SizeEnd -0.06690 0.05647 -1.185
## TransplantContamLC:OriginContamLC -0.11545 0.31098 -0.371
## TransplantContamLC:InjectionPBS -0.05341 0.26902 -0.199
## OriginContamLC:InjectionPBS 0.43825 0.26927 1.628
##
## Correlation of Fixed Effects:
## (Intr) TrnCLC OrgCLC InjPBS SizEnd TCLC:O TCLC:I
## TrnsplntCLC -0.253
## OrignCntmLC -0.330 0.250
## InjectinPBS -0.192 0.296 0.192
## SizeEnd -0.901 0.058 0.038 0.019
## TrnCLC:OCLC 0.096 -0.605 -0.416 -0.005 0.029
## TrnCLC:IPBS 0.105 -0.514 -0.004 -0.592 -0.002 0.022
## OrgCLC:IPBS 0.114 0.012 -0.332 -0.552 -0.019 -0.009 -0.009
## optimizer (nloptwrap) convergence code: 0 (OK)
## boundary (singular) fit: see ?isSingular6.16.1.5 Refining the model
mod3 <-
lme4::lmer(
DeltaCtMtl.p ~ TransplantContam + OriginContam + Injection + SizeEnd +
(1 | CagingSite / CageSiteID) + (1| OriginSite),
data = dat2,
na.action = na.exclude
)
car::Anova(mod3, type = "3")## Analysis of Deviance Table (Type III Wald chisquare tests)
##
## Response: DeltaCtMtl.p
## Chisq Df Pr(>Chisq)
## (Intercept) 9.2349 1 0.002374 **
## TransplantContam 0.3748 1 0.540388
## OriginContam 5.6894 1 0.017068 *
## Injection 0.0229 1 0.879776
## SizeEnd 1.2851 1 0.256945
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1summary(mod3)## Linear mixed model fit by REML ['lmerMod']
## Formula: DeltaCtMtl.p ~ TransplantContam + OriginContam + Injection +
## SizeEnd + (1 | CagingSite/CageSiteID) + (1 | OriginSite)
## Data: dat2
##
## REML criterion at convergence: 740.5
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -2.6909 -0.5467 -0.0089 0.5865 3.2568
##
## Random effects:
## Groups Name Variance Std.Dev.
## CageSiteID:CagingSite (Intercept) 0.03112 0.1764
## CagingSite (Intercept) 0.00000 0.0000
## OriginSite (Intercept) 0.07763 0.2786
## Residual 1.10777 1.0525
## Number of obs: 246, groups:
## CageSiteID:CagingSite, 24; CagingSite, 4; OriginSite, 4
##
## Fixed effects:
## Estimate Std. Error t value
## (Intercept) 1.88316 0.61968 3.039
## TransplantContamLC -0.09415 0.15378 -0.612
## OriginContamLC -0.75883 0.31814 -2.385
## InjectionPBS 0.02036 0.13462 0.151
## SizeEnd -0.06396 0.05642 -1.134
##
## Correlation of Fixed Effects:
## (Intr) TrnCLC OrgCLC InjPBS
## TrnsplntCLC -0.236
## OrignCntmLC -0.303 0.003
## InjectinPBS -0.116 -0.007 0.012
## SizeEnd -0.918 0.123 0.052 0.013
## optimizer (nloptwrap) convergence code: 0 (OK)
## boundary (singular) fit: see ?isSingular6.16.1.6 Refining the model
mod4 <-
lme4::lmer(
DeltaCtMtl.p ~ OriginContam +
(1 | CagingSite / CageSiteID) + (1| OriginSite),
data = dat2,
na.action = na.exclude
)
car::Anova(mod4, type = "3")## Analysis of Deviance Table (Type III Wald chisquare tests)
##
## Response: DeltaCtMtl.p
## Chisq Df Pr(>Chisq)
## (Intercept) 29.5067 1 5.572e-08 ***
## OriginContam 5.4731 1 0.01931 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1summary(mod4)## Linear mixed model fit by REML ['lmerMod']
## Formula: DeltaCtMtl.p ~ OriginContam + (1 | CagingSite/CageSiteID) + (1 |
## OriginSite)
## Data: dat2
##
## REML criterion at convergence: 734
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -2.6964 -0.5456 0.0223 0.5869 3.2087
##
## Random effects:
## Groups Name Variance Std.Dev.
## CageSiteID:CagingSite (Intercept) 2.107e-02 1.451e-01
## CagingSite (Intercept) 1.535e-10 1.239e-05
## OriginSite (Intercept) 7.854e-02 2.802e-01
## Residual 1.108e+00 1.052e+00
## Number of obs: 246, groups:
## CageSiteID:CagingSite, 24; CagingSite, 4; OriginSite, 4
##
## Fixed effects:
## Estimate Std. Error t value
## (Intercept) 1.2111 0.2229 5.432
## OriginContamLC -0.7403 0.3164 -2.339
##
## Correlation of Fixed Effects:
## (Intr)
## OrignCntmLC -0.705
## optimizer (nloptwrap) convergence code: 0 (OK)
## boundary (singular) fit: see ?isSingularMtl expression is significantly different according to fish origin. More specifically, HC fish have higher Mtl expression than LC fish.
Now that we have identified the best model, add sex as covariate to check whether results are sensitive NB: sample size is reduced when adding sex variable within the model, for this reason the sex effect on results is checked on the final model
6.16.1.7 Test for the sex effect
dat2 = dat2[is.na(dat2$Sex) == F, ]
modSex <-
lme4::lmer(
DeltaCtMtl.p ~ OriginContam + Sex +
(1 | CagingSite / CageSiteID) + (1| OriginSite),
data = dat2,
na.action = na.exclude
)
performance::check_model(modSex)
car::Anova(modSex, type = "3")## Analysis of Deviance Table (Type III Wald chisquare tests)
##
## Response: DeltaCtMtl.p
## Chisq Df Pr(>Chisq)
## (Intercept) 31.3296 1 2.177e-08 ***
## OriginContam 5.1233 1 0.02361 *
## Sex 4.2371 1 0.03955 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1summary(modSex)## Linear mixed model fit by REML ['lmerMod']
## Formula: DeltaCtMtl.p ~ OriginContam + Sex + (1 | CagingSite/CageSiteID) +
## (1 | OriginSite)
## Data: dat2
##
## REML criterion at convergence: 728.9
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -2.8237 -0.5927 0.0607 0.6000 3.3720
##
## Random effects:
## Groups Name Variance Std.Dev.
## CageSiteID:CagingSite (Intercept) 2.007e-02 1.417e-01
## CagingSite (Intercept) 2.039e-10 1.428e-05
## OriginSite (Intercept) 8.545e-02 2.923e-01
## Residual 1.093e+00 1.045e+00
## Number of obs: 245, groups:
## CageSiteID:CagingSite, 24; CagingSite, 4; OriginSite, 4
##
## Fixed effects:
## Estimate Std. Error t value
## (Intercept) 1.3248 0.2367 5.597
## OriginContamLC -0.7395 0.3267 -2.263
## SexM -0.2866 0.1392 -2.058
##
## Correlation of Fixed Effects:
## (Intr) OrgCLC
## OrignCntmLC -0.688
## SexM -0.234 0.013
## optimizer (nloptwrap) convergence code: 0 (OK)
## boundary (singular) fit: see ?isSingularmodMtl <- modSex
RmodMtl <- MuMIn::r.squaredGLMM(modMtl)The sex effect is significant. The modSex is thus the best model. Here, there is no interaction, and hence no posthoc test nor parallelism test to conduct
boxplot(DeltaCtMtl.p ~ OriginContam, data = dat2)
boxplot(DeltaCtMtl.p ~ Sex, data = dat2)
# compute mean and Se for LC and HC groups
meanVal <-
data.frame(
mean = c(mean(dat2$DeltaCtMtl.p[which(dat2$OriginContam == "LC")]),
mean(dat2$DeltaCtMtl.p[which(dat2$OriginContam == "HC")])),
Se = c(
sd(dat2$DeltaCtMtl.p[which(dat2$OriginContam == "LC")]) / sqrt(length(dat2$DeltaCtMtl.p[which(dat2$OriginContam == "LC")])),
sd(dat2$DeltaCtMtl.p[which(dat2$OriginContam == "HC")]) / sqrt(length(dat2$DeltaCtMtl.p[which(dat2$OriginContam == "HC")]))
),
row.names = c("LC", "HC"),
n = c(length(dat2$DeltaCtMtl.p[which(dat2$OriginContam == "LC")]),
length(dat2$DeltaCtMtl.p[which(dat2$OriginContam == "HC")]))
)
kableExtra::kable_classic(
kableExtra::kbl(meanVal),
bootstrap_options = c("striped", "hover", "condensed", "responsive"),
full_width = F,
html_font = "arial",
font_size = 10
)| mean | Se | n | |
|---|---|---|---|
| LC | 0.4778226 | 0.0925794 | 117 |
| HC | 1.2116222 | 0.1011425 | 128 |
6.16.2 Cat
6.16.2.1 Check the data
dat2 = dat1[is.na(dat1$DeltaCtCat) == F, ]
# transform variable to approx. normality
dat2$DeltaCtCat.p <-
bimixt::boxcox(dat2$DeltaCtCat, car::powerTransform(dat2$DeltaCtCat)$lambda)
hist(dat2$DeltaCtCat.p)
6.16.2.2 Visualize
par(mfrow=c(2,3))
boxplot(DeltaCtCat.p ~ OriginContam, data = dat2)
boxplot(DeltaCtCat.p ~ TransplantContam, data = dat2)
boxplot(DeltaCtCat.p ~ Injection, data = dat2)
boxplot(DeltaCtCat.p ~ TransplantContam * Injection, data = dat2)
boxplot(DeltaCtCat.p ~ TransplantContam * OriginContam, data = dat2)
boxplot(DeltaCtCat.p ~ TransplantContam * OriginContam * Injection, data = dat2)
6.16.2.3 Build the full model
modfull <-
lme4::lmer(
DeltaCtCat.p ~ (TransplantContam + OriginContam + Injection) ^ 3 + SizeEnd +
(1 | CagingSite / CageSiteID) + (1| OriginSite),
data = dat2,
na.action = na.exclude
)
car::Anova(modfull, type = "3")## Analysis of Deviance Table (Type III Wald chisquare tests)
##
## Response: DeltaCtCat.p
## Chisq Df Pr(>Chisq)
## (Intercept) 126.6869 1 < 2.2e-16 ***
## TransplantContam 0.1362 1 0.712039
## OriginContam 0.5148 1 0.473082
## Injection 3.3333 1 0.067889 .
## SizeEnd 7.2135 1 0.007236 **
## TransplantContam:OriginContam 3.9098 1 0.048005 *
## TransplantContam:Injection 0.0240 1 0.876997
## OriginContam:Injection 1.3774 1 0.240550
## TransplantContam:OriginContam:Injection 0.9025 1 0.342112
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1summary(modfull)## Linear mixed model fit by REML ['lmerMod']
## Formula: DeltaCtCat.p ~ (TransplantContam + OriginContam + Injection)^3 +
## SizeEnd + (1 | CagingSite/CageSiteID) + (1 | OriginSite)
## Data: dat2
##
## REML criterion at convergence: 144.8
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -2.46127 -0.65109 0.00029 0.65431 2.80017
##
## Random effects:
## Groups Name Variance Std.Dev.
## CageSiteID:CagingSite (Intercept) 0.0001937 0.01392
## CagingSite (Intercept) 0.0053361 0.07305
## OriginSite (Intercept) 0.0745272 0.27300
## Residual 0.0899628 0.29994
## Number of obs: 246, groups:
## CageSiteID:CagingSite, 24; CagingSite, 4; OriginSite, 4
##
## Fixed effects:
## Estimate Std. Error t value
## (Intercept) -3.01890 0.26821 -11.256
## TransplantContamLC 0.03849 0.10429 0.369
## OriginContamLC -0.20325 0.28328 -0.717
## InjectionPBS 0.13817 0.07568 1.826
## SizeEnd 0.04571 0.01702 2.686
## TransplantContamLC:OriginContamLC -0.20956 0.10598 -1.977
## TransplantContamLC:InjectionPBS -0.01643 0.10617 -0.155
## OriginContamLC:InjectionPBS -0.12905 0.10996 -1.174
## TransplantContamLC:OriginContamLC:InjectionPBS 0.14586 0.15353 0.950
##
## Correlation of Fixed Effects:
## (Intr) TrnCLC OrgCLC InjPBS SizEnd TrCLC:OCLC TCLC:I OCLC:I
## TrnsplntCLC -0.218
## OrignCntmLC -0.536 0.094
## InjectinPBS -0.142 0.346 0.127
## SizeEnd -0.638 0.038 0.014 0.012
## TrnCLC:OCLC 0.077 -0.499 -0.190 -0.340 0.032
## TrnCLC:IPBS 0.094 -0.492 -0.091 -0.713 0.003 0.485
## OrgCLC:IPBS 0.096 -0.238 -0.181 -0.688 -0.005 0.483 0.490
## TCLC:OCLC:I -0.061 0.340 0.129 0.493 -0.009 -0.681 -0.691 -0.7166.16.2.4 Refining the model
mod2 <-
lme4::lmer(
DeltaCtCat.p ~ (TransplantContam + OriginContam + Injection) ^ 2 + SizeEnd +
(1 | CagingSite / CageSiteID) + (1| OriginSite),
data = dat2,
na.action = na.exclude
)
car::Anova(mod2, type = "3")## Analysis of Deviance Table (Type III Wald chisquare tests)
##
## Response: DeltaCtCat.p
## Chisq Df Pr(>Chisq)
## (Intercept) 125.8848 1 < 2.2e-16 ***
## TransplantContam 0.0025 1 0.960361
## OriginContam 0.7176 1 0.396928
## Injection 2.4353 1 0.118634
## SizeEnd 7.2547 1 0.007072 **
## TransplantContam:OriginContam 3.2785 1 0.070194 .
## TransplantContam:Injection 0.4832 1 0.486969
## OriginContam:Injection 0.4998 1 0.479585
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1summary(mod2)## Linear mixed model fit by REML ['lmerMod']
## Formula: DeltaCtCat.p ~ (TransplantContam + OriginContam + Injection)^2 +
## SizeEnd + (1 | CagingSite/CageSiteID) + (1 | OriginSite)
## Data: dat2
##
## REML criterion at convergence: 143.8
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -2.41117 -0.62645 -0.00176 0.63321 2.86447
##
## Random effects:
## Groups Name Variance Std.Dev.
## CageSiteID:CagingSite (Intercept) 0.0002758 0.01661
## CagingSite (Intercept) 0.0053064 0.07284
## OriginSite (Intercept) 0.0745138 0.27297
## Residual 0.0898674 0.29978
## Number of obs: 246, groups:
## CageSiteID:CagingSite, 24; CagingSite, 4; OriginSite, 4
##
## Fixed effects:
## Estimate Std. Error t value
## (Intercept) -3.003235 0.267672 -11.220
## TransplantContamLC 0.004873 0.098038 0.050
## OriginContamLC -0.237975 0.280922 -0.847
## InjectionPBS 0.102721 0.065825 1.561
## SizeEnd 0.045826 0.017014 2.693
## TransplantContamLC:OriginContamLC -0.141069 0.077910 -1.811
## TransplantContamLC:InjectionPBS 0.053295 0.076668 0.695
## OriginContamLC:InjectionPBS -0.054245 0.076729 -0.707
##
## Correlation of Fixed Effects:
## (Intr) TrnCLC OrgCLC InjPBS SizEnd TCLC:O TCLC:I
## TrnsplntCLC -0.211
## OrignCntmLC -0.533 0.054
## InjectinPBS -0.129 0.218 0.074
## SizeEnd -0.639 0.043 0.015 0.018
## TrnCLC:OCLC 0.049 -0.390 -0.140 -0.007 0.035
## TrnCLC:IPBS 0.072 -0.379 -0.002 -0.592 -0.004 0.026
## OrgCLC:IPBS 0.075 0.008 -0.127 -0.552 -0.016 -0.010 -0.0096.16.2.5 Refining the model
mod3 <-
lme4::lmer(
DeltaCtCat.p ~ TransplantContam + OriginContam + Injection + SizeEnd +
(1 | CagingSite / CageSiteID) + (1| OriginSite),
data = dat2,
na.action = na.exclude
)
car::Anova(mod3, type = "3")## Analysis of Deviance Table (Type III Wald chisquare tests)
##
## Response: DeltaCtCat.p
## Chisq Df Pr(>Chisq)
## (Intercept) 126.0929 1 < 2.2e-16 ***
## TransplantContam 0.2040 1 0.651486
## OriginContam 1.4996 1 0.220734
## Injection 7.4079 1 0.006494 **
## SizeEnd 7.4541 1 0.006329 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1summary(mod3)## Linear mixed model fit by REML ['lmerMod']
## Formula: DeltaCtCat.p ~ TransplantContam + OriginContam + Injection +
## SizeEnd + (1 | CagingSite/CageSiteID) + (1 | OriginSite)
## Data: dat2
##
## REML criterion at convergence: 138.2
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -2.52701 -0.68507 -0.06431 0.63540 2.78093
##
## Random effects:
## Groups Name Variance Std.Dev.
## CageSiteID:CagingSite (Intercept) 0.001279 0.03576
## CagingSite (Intercept) 0.005106 0.07145
## OriginSite (Intercept) 0.073363 0.27086
## Residual 0.089638 0.29940
## Number of obs: 246, groups:
## CageSiteID:CagingSite, 24; CagingSite, 4; OriginSite, 4
##
## Fixed effects:
## Estimate Std. Error t value
## (Intercept) -2.97561 0.26499 -11.229
## TransplantContamLC -0.03728 0.08254 -0.452
## OriginContamLC -0.33552 0.27399 -1.225
## InjectionPBS 0.10420 0.03828 2.722
## SizeEnd 0.04647 0.01702 2.730
##
## Correlation of Fixed Effects:
## (Intr) TrnCLC OrgCLC InjPBS
## TrnsplntCLC -0.198
## OrignCntmLC -0.528 0.001
## InjectinPBS -0.077 -0.004 0.004
## SizeEnd -0.647 0.066 0.018 0.0126.16.2.6 Refining the model
mod4 <-
lme4::lmer(
DeltaCtCat.p ~ Injection + SizeEnd +
(1 | CagingSite / CageSiteID) + (1| OriginSite),
data = dat2,
na.action = na.exclude
)
car::Anova(mod4, type = "3")## Analysis of Deviance Table (Type III Wald chisquare tests)
##
## Response: DeltaCtCat.p
## Chisq Df Pr(>Chisq)
## (Intercept) 199.6151 1 < 2.2e-16 ***
## Injection 7.4260 1 0.006429 **
## SizeEnd 7.5935 1 0.005858 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1summary(mod4)## Linear mixed model fit by REML ['lmerMod']
## Formula: DeltaCtCat.p ~ Injection + SizeEnd + (1 | CagingSite/CageSiteID) +
## (1 | OriginSite)
## Data: dat2
##
## REML criterion at convergence: 135.7
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -2.57273 -0.65230 -0.03892 0.63278 2.82713
##
## Random effects:
## Groups Name Variance Std.Dev.
## CageSiteID:CagingSite (Intercept) 0.001260 0.03550
## CagingSite (Intercept) 0.002643 0.05141
## OriginSite (Intercept) 0.085284 0.29204
## Residual 0.089642 0.29940
## Number of obs: 246, groups:
## CageSiteID:CagingSite, 24; CagingSite, 4; OriginSite, 4
##
## Fixed effects:
## Estimate Std. Error t value
## (Intercept) -3.16488 0.22401 -14.129
## InjectionPBS 0.10433 0.03828 2.725
## SizeEnd 0.04676 0.01697 2.756
##
## Correlation of Fixed Effects:
## (Intr) InjPBS
## InjectinPBS -0.090
## SizeEnd -0.740 0.012Cat expression is significantly different according to immune challenge. More specifically, HC fish have higher Cat expression than LC fish. Also, bigger fish have higher expression of Cat.
plot(DeltaCtCat.p ~ SizeEnd, data = dat2)
abline(a = -3.16488, b = 0.04676 , col = "red")
Now that we have identified the best model, add sex as covariate to check whether results are sensitive NB: sample size is reduced when adding sex variable within the model, for this reason the sex effect on results is checked on the final model
6.16.2.7 Test for the sex effect
dat2 = dat2[is.na(dat2$Sex) == F, ]
modSex <-
lme4::lmer(
DeltaCtCat.p ~ Injection + SizeEnd + Sex +
(1 | CagingSite / CageSiteID) + (1| OriginSite),
data = dat2,
na.action = na.exclude
)
performance::check_model(modSex)
car::Anova(modSex, type = "3")## Analysis of Deviance Table (Type III Wald chisquare tests)
##
## Response: DeltaCtCat.p
## Chisq Df Pr(>Chisq)
## (Intercept) 205.8893 1 < 2.2e-16 ***
## Injection 7.0398 1 0.007972 **
## SizeEnd 9.3052 1 0.002285 **
## Sex 5.8286 1 0.015767 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1summary(modSex)## Linear mixed model fit by REML ['lmerMod']
## Formula:
## DeltaCtCat.p ~ Injection + SizeEnd + Sex + (1 | CagingSite/CageSiteID) +
## (1 | OriginSite)
## Data: dat2
##
## REML criterion at convergence: 133.1
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -2.75224 -0.65983 -0.02391 0.65897 2.88861
##
## Random effects:
## Groups Name Variance Std.Dev.
## CageSiteID:CagingSite (Intercept) 0.000310 0.01761
## CagingSite (Intercept) 0.003288 0.05734
## OriginSite (Intercept) 0.082352 0.28697
## Residual 0.088084 0.29679
## Number of obs: 245, groups:
## CageSiteID:CagingSite, 24; CagingSite, 4; OriginSite, 4
##
## Fixed effects:
## Estimate Std. Error t value
## (Intercept) -3.17559 0.22131 -14.349
## InjectionPBS 0.10112 0.03811 2.653
## SizeEnd 0.05157 0.01690 3.050
## SexM -0.09578 0.03967 -2.414
##
## Correlation of Fixed Effects:
## (Intr) InjPBS SizEnd
## InjectinPBS -0.088
## SizeEnd -0.737 0.003
## SexM 0.012 0.074 -0.117modCat<- modSex
RmodCat <- MuMIn::r.squaredGLMM(modCat)The sex effect is significant. The modSex is thus the best model. Here, there is no interaction, and hence no posthoc test nor parallelism test to conduct
boxplot(DeltaCtCat.p ~ OriginContam, data = dat2)
boxplot(DeltaCtCat.p ~ Sex, data = dat2)
# compute mean and Se for LC and HC groups
meanVal <-
data.frame(
mean = c(mean(dat2$DeltaCtCat.p[which(dat2$Injection == "PBS")]),
mean(dat2$DeltaCtCat.p[which(dat2$Injection == "AMIX")])),
Se = c(
sd(dat2$DeltaCtCat.p[which(dat2$Injection == "PBS")]) / sqrt(length(dat2$DeltaCtCat.p[which(dat2$Injection == "PBS")])),
sd(dat2$DeltaCtCat.p[which(dat2$Injection == "AMIX")]) / sqrt(length(dat2$DeltaCtCat.p[which(dat2$Injection == "AMIX")]))
),
row.names = c("PBS", "AMIX"),
n = c(length(dat2$DeltaCtCat.p[which(dat2$Injection == "PBS")]),
length(dat2$DeltaCtCat.p[which(dat2$Injection == "AMIX")]))
)
kableExtra::kable_classic(
kableExtra::kbl(meanVal),
bootstrap_options = c("striped", "hover", "condensed", "responsive"),
full_width = F,
html_font = "arial",
font_size = 10
)| mean | Se | n | |
|---|---|---|---|
| PBS | -2.589656 | 0.0414297 | 116 |
| AMIX | -2.702629 | 0.0358039 | 129 |
6.16.3 GPX
6.16.3.1 Check the data
dat2 = dat1[is.na(dat1$DeltaCtGpx) == F, ]
# transform variable to approx. normality
dat2$DeltaCtGpx.p <-
bimixt::boxcox(dat2$DeltaCtGpx, car::powerTransform(dat2$DeltaCtMtl)$lambda)
hist(dat2$DeltaCtGpx.p)
6.16.3.2 Visualize
par(mfrow=c(2,3))
boxplot(DeltaCtGpx.p ~ OriginContam, data = dat2)
boxplot(DeltaCtGpx.p ~ TransplantContam, data = dat2)
boxplot(DeltaCtGpx.p ~ Injection, data = dat2)
boxplot(DeltaCtGpx.p ~ TransplantContam * Injection, data = dat2)
boxplot(DeltaCtGpx.p ~ TransplantContam * OriginContam, data = dat2)
boxplot(DeltaCtGpx.p ~ TransplantContam * OriginContam * Injection, data = dat2)
6.16.3.3 Build the full model
modfull <-
lme4::lmer(
DeltaCtGpx.p ~ (TransplantContam + OriginContam + Injection) ^ 3 + SizeEnd +
(1 | CagingSite / CageSiteID) + (1| OriginSite),
data = dat2,
na.action = na.exclude
)
car::Anova(modfull, type = "3")## Analysis of Deviance Table (Type III Wald chisquare tests)
##
## Response: DeltaCtGpx.p
## Chisq Df Pr(>Chisq)
## (Intercept) 20.8492 1 4.969e-06 ***
## TransplantContam 0.7396 1 0.3898
## OriginContam 1.3179 1 0.2510
## Injection 0.0458 1 0.8306
## SizeEnd 1.6136 1 0.2040
## TransplantContam:OriginContam 0.2413 1 0.6233
## TransplantContam:Injection 0.1609 1 0.6883
## OriginContam:Injection 0.2995 1 0.5842
## TransplantContam:OriginContam:Injection 0.7050 1 0.4011
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1summary(modfull)## Linear mixed model fit by REML ['lmerMod']
## Formula: DeltaCtGpx.p ~ (TransplantContam + OriginContam + Injection)^3 +
## SizeEnd + (1 | CagingSite/CageSiteID) + (1 | OriginSite)
## Data: dat2
##
## REML criterion at convergence: 467.7
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -3.3815 -0.5235 0.1590 0.6273 2.6625
##
## Random effects:
## Groups Name Variance Std.Dev.
## CageSiteID:CagingSite (Intercept) 0.007445 0.08629
## CagingSite (Intercept) 0.000000 0.00000
## OriginSite (Intercept) 0.029427 0.17154
## Residual 0.355216 0.59600
## Number of obs: 246, groups:
## CageSiteID:CagingSite, 24; CagingSite, 4; OriginSite, 4
##
## Fixed effects:
## Estimate Std. Error t value
## (Intercept) -1.65475 0.36240 -4.566
## TransplantContamLC 0.13352 0.15526 0.860
## OriginContamLC -0.26738 0.23291 -1.148
## InjectionPBS 0.03219 0.15044 0.214
## SizeEnd 0.04084 0.03215 1.270
## TransplantContamLC:OriginContamLC -0.10854 0.22097 -0.491
## TransplantContamLC:InjectionPBS 0.08466 0.21105 0.401
## OriginContamLC:InjectionPBS 0.11962 0.21859 0.547
## TransplantContamLC:OriginContamLC:InjectionPBS -0.25629 0.30522 -0.840
##
## Correlation of Fixed Effects:
## (Intr) TrnCLC OrgCLC InjPBS SizEnd TrCLC:OCLC TCLC:I OCLC:I
## TrnsplntCLC -0.258
## OrignCntmLC -0.346 0.334
## InjectinPBS -0.209 0.462 0.308
## SizeEnd -0.892 0.049 0.032 0.013
## TrnCLC:OCLC 0.124 -0.699 -0.480 -0.324 0.029
## TrnCLC:IPBS 0.137 -0.657 -0.219 -0.713 0.004 0.462
## OrgCLC:IPBS 0.143 -0.318 -0.437 -0.688 -0.007 0.460 0.490
## TCLC:OCLC:I -0.090 0.454 0.312 0.493 -0.008 -0.649 -0.691 -0.716
## optimizer (nloptwrap) convergence code: 0 (OK)
## boundary (singular) fit: see ?isSingular6.16.3.4 Refining the model
mod2 <-
lme4::lmer(
DeltaCtGpx.p ~ (TransplantContam + OriginContam + Injection) ^ 2 + SizeEnd +
(1 | CagingSite / CageSiteID) + (1| OriginSite),
data = dat2,
na.action = na.exclude
)
car::Anova(mod2, type = "3")## Analysis of Deviance Table (Type III Wald chisquare tests)
##
## Response: DeltaCtGpx.p
## Chisq Df Pr(>Chisq)
## (Intercept) 21.7743 1 3.067e-06 ***
## TransplantContam 1.9614 1 0.1614
## OriginContam 0.8686 1 0.3513
## Injection 0.5214 1 0.4703
## SizeEnd 1.6117 1 0.2043
## TransplantContam:OriginContam 1.8803 1 0.1703
## TransplantContam:Injection 0.0626 1 0.8024
## OriginContam:Injection 0.0059 1 0.9387
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1summary(mod2)## Linear mixed model fit by REML ['lmerMod']
## Formula: DeltaCtGpx.p ~ (TransplantContam + OriginContam + Injection)^2 +
## SizeEnd + (1 | CagingSite/CageSiteID) + (1 | OriginSite)
## Data: dat2
##
## REML criterion at convergence: 467.8
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -3.4450 -0.5319 0.1816 0.6129 2.6032
##
## Random effects:
## Groups Name Variance Std.Dev.
## CageSiteID:CagingSite (Intercept) 0.006866 0.08286
## CagingSite (Intercept) 0.000000 0.00000
## OriginSite (Intercept) 0.029659 0.17222
## Residual 0.355130 0.59593
## Number of obs: 246, groups:
## CageSiteID:CagingSite, 24; CagingSite, 4; OriginSite, 4
##
## Fixed effects:
## Estimate Std. Error t value
## (Intercept) -1.68401 0.36089 -4.666
## TransplantContamLC 0.19272 0.13761 1.400
## OriginContamLC -0.20628 0.22133 -0.932
## InjectionPBS 0.09452 0.13090 0.722
## SizeEnd 0.04081 0.03215 1.270
## TransplantContamLC:OriginContamLC -0.22885 0.16689 -1.371
## TransplantContamLC:InjectionPBS -0.03815 0.15244 -0.250
## OriginContamLC:InjectionPBS -0.01174 0.15258 -0.077
##
## Correlation of Fixed Effects:
## (Intr) TrnCLC OrgCLC InjPBS SizEnd TCLC:O TCLC:I
## TrnsplntCLC -0.244
## OrignCntmLC -0.336 0.225
## InjectinPBS -0.190 0.308 0.186
## SizeEnd -0.897 0.060 0.037 0.019
## TrnCLC:OCLC 0.086 -0.596 -0.381 -0.006 0.031
## TrnCLC:IPBS 0.103 -0.536 -0.004 -0.592 -0.002 0.024
## OrgCLC:IPBS 0.112 0.012 -0.322 -0.552 -0.019 -0.009 -0.009
## optimizer (nloptwrap) convergence code: 0 (OK)
## boundary (singular) fit: see ?isSingular6.16.3.5 Refining the model
mod3 <-
lme4::lmer(
DeltaCtGpx.p ~ TransplantContam + OriginContam + Injection + SizeEnd +
(1 | CagingSite / CageSiteID) + (1| OriginSite),
data = dat2,
na.action = na.exclude
)
car::Anova(mod3, type = "3")## Analysis of Deviance Table (Type III Wald chisquare tests)
##
## Response: DeltaCtGpx.p
## Chisq Df Pr(>Chisq)
## (Intercept) 20.9880 1 4.622e-06 ***
## TransplantContam 0.5733 1 0.44894
## OriginContam 2.8518 1 0.09127 .
## Injection 0.8497 1 0.35665
## SizeEnd 1.7297 1 0.18845
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1summary(mod3)## Linear mixed model fit by REML ['lmerMod']
## Formula: DeltaCtGpx.p ~ TransplantContam + OriginContam + Injection +
## SizeEnd + (1 | CagingSite/CageSiteID) + (1 | OriginSite)
## Data: dat2
##
## REML criterion at convergence: 464.1
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -3.5478 -0.4710 0.1555 0.6057 2.5766
##
## Random effects:
## Groups Name Variance Std.Dev.
## CageSiteID:CagingSite (Intercept) 0.008683 0.09318
## CagingSite (Intercept) 0.000000 0.00000
## OriginSite (Intercept) 0.030534 0.17474
## Residual 0.352196 0.59346
## Number of obs: 246, groups:
## CageSiteID:CagingSite, 24; CagingSite, 4; OriginSite, 4
##
## Fixed effects:
## Estimate Std. Error t value
## (Intercept) -1.63029 0.35586 -4.581
## TransplantContamLC 0.06476 0.08553 0.757
## OriginContamLC -0.32844 0.19449 -1.689
## InjectionPBS 0.06996 0.07590 0.922
## SizeEnd 0.04221 0.03209 1.315
##
## Correlation of Fixed Effects:
## (Intr) TrnCLC OrgCLC InjPBS
## TrnsplntCLC -0.232
## OrignCntmLC -0.315 0.003
## InjectinPBS -0.114 -0.007 0.011
## SizeEnd -0.909 0.125 0.048 0.013
## optimizer (nloptwrap) convergence code: 0 (OK)
## boundary (singular) fit: see ?isSingular6.16.3.6 Refining the model
mod4 <-
lme4::lmer(
DeltaCtGpx.p ~ OriginContam +
(1 | CagingSite / CageSiteID) + (1| OriginSite),
data = dat2,
na.action = na.exclude
)
car::Anova(mod4, type = "3")## Analysis of Deviance Table (Type III Wald chisquare tests)
##
## Response: DeltaCtGpx.p
## Chisq Df Pr(>Chisq)
## (Intercept) 149.6900 1 <2e-16 ***
## OriginContam 6.5657 1 0.0104 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1summary(mod4)## Linear mixed model fit by REML ['lmerMod']
## Formula: DeltaCtGpx.p ~ OriginContam + (1 | CagingSite/CageSiteID) + (1 |
## OriginSite)
## Data: dat2
##
## REML criterion at convergence: 455.2
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -3.4423 -0.5022 0.1522 0.6138 2.7332
##
## Random effects:
## Groups Name Variance Std.Dev.
## CageSiteID:CagingSite (Intercept) 0.009036 0.09506
## CagingSite (Intercept) 0.000000 0.00000
## OriginSite (Intercept) 0.010510 0.10252
## Residual 0.353388 0.59446
## Number of obs: 246, groups:
## CageSiteID:CagingSite, 24; CagingSite, 4; OriginSite, 4
##
## Fixed effects:
## Estimate Std. Error t value
## (Intercept) -1.1464 0.0937 -12.235
## OriginContamLC -0.3418 0.1334 -2.562
##
## Correlation of Fixed Effects:
## (Intr)
## OrignCntmLC -0.702
## optimizer (nloptwrap) convergence code: 0 (OK)
## boundary (singular) fit: see ?isSingularGpx expression is significantly different according to fish origin. More specifically, HC fish have higher Gpx expression than LC fish.
Now that we have identified the best model, add sex as covariate to check whether results are sensitive NB: sample size is reduced when adding sex variable within the model, for this reason the sex effect on results is checked on the final model
6.16.3.7 Test for the sex effect
dat2 = dat2[is.na(dat2$Sex) == F, ]
modSex <-
lme4::lmer(
DeltaCtGpx.p ~ OriginContam + Sex +
(1 | CagingSite / CageSiteID) + (1| OriginSite),
data = dat2,
na.action = na.exclude
)
performance::check_model(modSex)
car::Anova(modSex, type = "3")## Analysis of Deviance Table (Type III Wald chisquare tests)
##
## Response: DeltaCtGpx.p
## Chisq Df Pr(>Chisq)
## (Intercept) 112.5356 1 < 2e-16 ***
## OriginContam 6.4537 1 0.01107 *
## Sex 5.2931 1 0.02141 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1summary(modSex)## Linear mixed model fit by REML ['lmerMod']
## Formula: DeltaCtGpx.p ~ OriginContam + Sex + (1 | CagingSite/CageSiteID) +
## (1 | OriginSite)
## Data: dat2
##
## REML criterion at convergence: 452.3
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -3.3444 -0.4585 0.1213 0.5956 2.5866
##
## Random effects:
## Groups Name Variance Std.Dev.
## CageSiteID:CagingSite (Intercept) 5.543e-03 7.445e-02
## CagingSite (Intercept) 4.261e-11 6.527e-06
## OriginSite (Intercept) 1.214e-02 1.102e-01
## Residual 3.508e-01 5.923e-01
## Number of obs: 245, groups:
## CageSiteID:CagingSite, 24; CagingSite, 4; OriginSite, 4
##
## Fixed effects:
## Estimate Std. Error t value
## (Intercept) -1.07457 0.10130 -10.608
## OriginContamLC -0.34854 0.13720 -2.540
## SexM -0.18119 0.07875 -2.301
##
## Correlation of Fixed Effects:
## (Intr) OrgCLC
## OrignCntmLC -0.673
## SexM -0.309 0.017
## optimizer (nloptwrap) convergence code: 0 (OK)
## boundary (singular) fit: see ?isSingularmodGpx <- modSex
RmodGpx <- MuMIn::r.squaredGLMM(modGpx)The sex effect is significant. The modSex is thus the best model. Here, there is no interaction, and hence no posthoc test nor parallelism test to conduct
boxplot(DeltaCtGpx.p ~ OriginContam, data = dat2)
boxplot(DeltaCtGpx.p ~ Sex, data = dat2)
# compute mean and Se for LC and HC groups
meanVal <-
data.frame(
mean = c(mean(dat2$DeltaCtGpx.p[which(dat2$OriginContam == "LC")]),
mean(dat2$DeltaCtGpx.p[which(dat2$OriginContam == "HC")])),
Se = c(
sd(dat2$DeltaCtGpx.p[which(dat2$OriginContam == "LC")]) / sqrt(length(dat2$DeltaCtGpx.p[which(dat2$OriginContam == "LC")])),
sd(dat2$DeltaCtGpx.p[which(dat2$OriginContam == "HC")]) / sqrt(length(dat2$DeltaCtGpx.p[which(dat2$OriginContam == "HC")]))
),
row.names = c("LC", "HC"),
n = c(length(dat2$DeltaCtGpx.p[which(dat2$OriginContam == "LC")]),
length(dat2$DeltaCtGpx.p[which(dat2$OriginContam == "HC")]))
)
kableExtra::kable_classic(
kableExtra::kbl(meanVal),
bootstrap_options = c("striped", "hover", "condensed", "responsive"),
full_width = F,
html_font = "arial",
font_size = 10
)| mean | Se | n | |
|---|---|---|---|
| LC | -1.490080 | 0.0533207 | 117 |
| HC | -1.149969 | 0.0560095 | 128 |
6.16.4 Casp3
6.16.4.1 Check the data
dat2 = dat1[is.na(dat1$DeltaCtCasp3) == F, ]
# transform variable to approx. normality
dat2$DeltaCtCasp3.p <-
bimixt::boxcox(dat2$DeltaCtCasp3, car::powerTransform(dat2$DeltaCtMtl)$lambda)
hist(dat2$DeltaCtCasp3.p)
6.16.4.2 Visualize
par(mfrow=c(2,3))
boxplot(DeltaCtCasp3.p ~ OriginContam, data = dat2)
boxplot(DeltaCtCasp3.p ~ TransplantContam, data = dat2)
boxplot(DeltaCtCasp3.p ~ Injection, data = dat2)
boxplot(DeltaCtCasp3.p ~ TransplantContam * Injection, data = dat2)
boxplot(DeltaCtCasp3.p ~ TransplantContam * OriginContam, data = dat2)
boxplot(DeltaCtCasp3.p ~ TransplantContam * OriginContam * Injection, data = dat2)
6.16.4.3 Build the full model
modfull <-
lme4::lmer(
DeltaCtCasp3.p ~ (TransplantContam + OriginContam + Injection) ^ 3 + SizeEnd +
(1 | CagingSite / CageSiteID) + (1| OriginSite),
data = dat2,
na.action = na.exclude
)
car::Anova(modfull, type = "3")## Analysis of Deviance Table (Type III Wald chisquare tests)
##
## Response: DeltaCtCasp3.p
## Chisq Df Pr(>Chisq)
## (Intercept) 209.1082 1 < 2.2e-16 ***
## TransplantContam 0.0021 1 0.963343
## OriginContam 10.4111 1 0.001253 **
## Injection 0.2313 1 0.630533
## SizeEnd 43.1668 1 5.027e-11 ***
## TransplantContam:OriginContam 0.0000 1 0.999188
## TransplantContam:Injection 0.4093 1 0.522341
## OriginContam:Injection 1.7747 1 0.182800
## TransplantContam:OriginContam:Injection 0.0092 1 0.923781
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1summary(modfull)## Linear mixed model fit by REML ['lmerMod']
## Formula: DeltaCtCasp3.p ~ (TransplantContam + OriginContam + Injection)^3 +
## SizeEnd + (1 | CagingSite/CageSiteID) + (1 | OriginSite)
## Data: dat2
##
## REML criterion at convergence: 548.2
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -2.18169 -0.63883 -0.09077 0.59191 2.29276
##
## Random effects:
## Groups Name Variance Std.Dev.
## CageSiteID:CagingSite (Intercept) 0.001552 0.03939
## CagingSite (Intercept) 0.000000 0.00000
## OriginSite (Intercept) 0.001942 0.04407
## Residual 0.511377 0.71511
## Number of obs: 246, groups:
## CageSiteID:CagingSite, 24; CagingSite, 4; OriginSite, 4
##
## Fixed effects:
## Estimate Std. Error t value
## (Intercept) -5.0390380 0.3484674 -14.461
## TransplantContamLC 0.0081695 0.1777545 0.046
## OriginContamLC -0.5997254 0.1858674 -3.227
## InjectionPBS -0.0867806 0.1804259 -0.481
## SizeEnd 0.2100963 0.0319774 6.570
## TransplantContamLC:OriginContamLC -0.0002577 0.2531360 -0.001
## TransplantContamLC:InjectionPBS -0.1619011 0.2530731 -0.640
## OriginContamLC:InjectionPBS 0.3492433 0.2621585 1.332
## TransplantContamLC:OriginContamLC:InjectionPBS -0.0350206 0.3660468 -0.096
##
## Correlation of Fixed Effects:
## (Intr) TrnCLC OrgCLC InjPBS SizEnd TrCLC:OCLC TCLC:I OCLC:I
## TrnsplntCLC -0.300
## OrignCntmLC -0.303 0.479
## InjectinPBS -0.258 0.484 0.463
## SizeEnd -0.929 0.049 0.048 0.013
## TrnCLC:OCLC 0.156 -0.699 -0.690 -0.339 0.025
## TrnCLC:IPBS 0.165 -0.688 -0.329 -0.713 0.011 0.484
## OrgCLC:IPBS 0.179 -0.333 -0.657 -0.688 -0.010 0.482 0.490
## TCLC:OCLC:I -0.111 0.476 0.470 0.493 -0.011 -0.680 -0.691 -0.716
## optimizer (nloptwrap) convergence code: 0 (OK)
## boundary (singular) fit: see ?isSingular6.16.4.4 Refining the model
mod2 <-
lme4::lmer(
DeltaCtCasp3.p ~ (TransplantContam + OriginContam + Injection) ^ 2 + SizeEnd +
(1 | CagingSite / CageSiteID) + (1| OriginSite),
data = dat2,
na.action = na.exclude
)
car::Anova(mod2, type = "3")## Analysis of Deviance Table (Type III Wald chisquare tests)
##
## Response: DeltaCtCasp3.p
## Chisq Df Pr(>Chisq)
## (Intercept) 211.8814 1 < 2.2e-16 ***
## TransplantContam 0.0109 1 0.9170049
## OriginContam 12.9746 1 0.0003158 ***
## Injection 0.2494 1 0.6175203
## SizeEnd 43.0676 1 5.288e-11 ***
## TransplantContam:OriginContam 0.0082 1 0.9278250
## TransplantContam:Injection 0.9595 1 0.3273181
## OriginContam:Injection 3.2908 1 0.0696711 .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1summary(mod2)## Linear mixed model fit by REML ['lmerMod']
## Formula: DeltaCtCasp3.p ~ (TransplantContam + OriginContam + Injection)^2 +
## SizeEnd + (1 | CagingSite/CageSiteID) + (1 | OriginSite)
## Data: dat2
##
## REML criterion at convergence: 548.1
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -2.19213 -0.63792 -0.09036 0.59237 2.28990
##
## Random effects:
## Groups Name Variance Std.Dev.
## CageSiteID:CagingSite (Intercept) 0.001766 0.04203
## CagingSite (Intercept) 0.000000 0.00000
## OriginSite (Intercept) 0.002009 0.04482
## Residual 0.509045 0.71347
## Number of obs: 246, groups:
## CageSiteID:CagingSite, 24; CagingSite, 4; OriginSite, 4
##
## Fixed effects:
## Estimate Std. Error t value
## (Intercept) -5.04030 0.34627 -14.556
## TransplantContamLC 0.01628 0.15623 0.104
## OriginContamLC -0.59139 0.16418 -3.602
## InjectionPBS -0.07823 0.15665 -0.499
## SizeEnd 0.20981 0.03197 6.563
## TransplantContamLC:OriginContamLC -0.01681 0.18557 -0.091
## TransplantContamLC:InjectionPBS -0.17869 0.18242 -0.980
## OriginContamLC:InjectionPBS 0.33126 0.18261 1.814
##
## Correlation of Fixed Effects:
## (Intr) TrnCLC OrgCLC InjPBS SizEnd TCLC:O TCLC:I
## TrnsplntCLC -0.283
## OrignCntmLC -0.286 0.330
## InjectinPBS -0.235 0.325 0.300
## SizeEnd -0.936 0.062 0.060 0.021
## TrnCLC:OCLC 0.110 -0.583 -0.572 -0.006 0.023
## TrnCLC:IPBS 0.123 -0.565 -0.006 -0.592 0.004 0.026
## OrgCLC:IPBS 0.144 0.012 -0.519 -0.552 -0.026 -0.010 -0.009
## optimizer (nloptwrap) convergence code: 0 (OK)
## boundary (singular) fit: see ?isSingular6.16.4.5 Refining the model
mod3 <-
lme4::lmer(
DeltaCtCasp3.p ~ TransplantContam + (OriginContam + Injection)^2 + SizeEnd +
(1 | CagingSite / CageSiteID) + (1| OriginSite),
data = dat2,
na.action = na.exclude
)
car::Anova(mod3, type = "3")## Analysis of Deviance Table (Type III Wald chisquare tests)
##
## Response: DeltaCtCasp3.p
## Chisq Df Pr(>Chisq)
## (Intercept) 211.6011 1 < 2.2e-16 ***
## TransplantContam 0.6898 1 0.40622
## OriginContam 19.4837 1 1.015e-05 ***
## Injection 1.7977 1 0.17999
## SizeEnd 42.4736 1 7.164e-11 ***
## OriginContam:Injection 3.2660 1 0.07073 .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1summary(mod3)## Linear mixed model fit by REML ['lmerMod']
## Formula: DeltaCtCasp3.p ~ TransplantContam + (OriginContam + Injection)^2 +
## SizeEnd + (1 | CagingSite/CageSiteID) + (1 | OriginSite)
## Data: dat2
##
## REML criterion at convergence: 545.9
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -2.1546 -0.6130 -0.1134 0.5822 2.2985
##
## Random effects:
## Groups Name Variance Std.Dev.
## CageSiteID:CagingSite (Intercept) 0.000000 0.00000
## CagingSite (Intercept) 0.000000 0.00000
## OriginSite (Intercept) 0.002616 0.05114
## Residual 0.508083 0.71280
## Number of obs: 246, groups:
## CageSiteID:CagingSite, 24; CagingSite, 4; OriginSite, 4
##
## Fixed effects:
## Estimate Std. Error t value
## (Intercept) -4.98732 0.34285 -14.547
## TransplantContamLC -0.07621 0.09176 -0.831
## OriginContamLC -0.59881 0.13566 -4.414
## InjectionPBS -0.16913 0.12614 -1.341
## SizeEnd 0.20914 0.03209 6.517
## OriginContamLC:InjectionPBS 0.32963 0.18240 1.807
##
## Correlation of Fixed Effects:
## (Intr) TrnCLC OrgCLC InjPBS SizEnd
## TrnsplntCLC -0.258
## OrignCntmLC -0.277 0.002
## InjectinPBS -0.204 -0.007 0.453
## SizeEnd -0.952 0.132 0.089 0.029
## OrgCLC:IPBS 0.147 0.003 -0.634 -0.692 -0.026
## optimizer (nloptwrap) convergence code: 0 (OK)
## boundary (singular) fit: see ?isSingular6.16.4.6 Refining the model
mod4 <-
lme4::lmer(
DeltaCtCasp3.p ~ TransplantContam + OriginContam + Injection + SizeEnd +
(1 | CagingSite / CageSiteID) + (1| OriginSite),
data = dat2,
na.action = na.exclude
)
car::Anova(mod4, type = "3")## Analysis of Deviance Table (Type III Wald chisquare tests)
##
## Response: DeltaCtCasp3.p
## Chisq Df Pr(>Chisq)
## (Intercept) 220.7014 1 < 2.2e-16 ***
## TransplantContam 0.6933 1 0.4050
## OriginContam 17.4701 1 2.919e-05 ***
## Injection 0.0156 1 0.9005
## SizeEnd 42.3555 1 7.610e-11 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1summary(mod4)## Linear mixed model fit by REML ['lmerMod']
## Formula: DeltaCtCasp3.p ~ TransplantContam + OriginContam + Injection +
## SizeEnd + (1 | CagingSite/CageSiteID) + (1 | OriginSite)
## Data: dat2
##
## REML criterion at convergence: 547.6
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -2.2414 -0.6378 -0.1475 0.6448 2.3176
##
## Random effects:
## Groups Name Variance Std.Dev.
## CageSiteID:CagingSite (Intercept) 0.000000 0.00000
## CagingSite (Intercept) 0.000000 0.00000
## OriginSite (Intercept) 0.002793 0.05285
## Residual 0.512812 0.71611
## Number of obs: 246, groups:
## CageSiteID:CagingSite, 24; CagingSite, 4; OriginSite, 4
##
## Fixed effects:
## Estimate Std. Error t value
## (Intercept) -5.07491 0.34161 -14.856
## TransplantContamLC -0.07676 0.09218 -0.833
## OriginContamLC -0.44336 0.10607 -4.180
## InjectionPBS -0.01144 0.09152 -0.125
## SizeEnd 0.21029 0.03231 6.508
##
## Correlation of Fixed Effects:
## (Intr) TrnCLC OrgCLC InjPBS
## TrnsplntCLC -0.260
## OrignCntmLC -0.241 0.004
## InjectinPBS -0.143 -0.008 0.025
## SizeEnd -0.959 0.133 0.093 0.015
## optimizer (nloptwrap) convergence code: 0 (OK)
## boundary (singular) fit: see ?isSingular6.16.4.7 Refining the model
mod5 <-
lme4::lmer(
DeltaCtCasp3.p ~ OriginContam + SizeEnd +
(1 | CagingSite / CageSiteID) + (1| OriginSite),
data = dat2,
na.action = na.exclude
)
performance::check_model(mod5)
car::Anova(mod5, type = "3")## Analysis of Deviance Table (Type III Wald chisquare tests)
##
## Response: DeltaCtCasp3.p
## Chisq Df Pr(>Chisq)
## (Intercept) 270.215 1 < 2.2e-16 ***
## OriginContam 20.109 1 7.314e-06 ***
## SizeEnd 48.992 1 2.570e-12 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1summary(mod5)## Linear mixed model fit by REML ['lmerMod']
## Formula:
## DeltaCtCasp3.p ~ OriginContam + SizeEnd + (1 | CagingSite/CageSiteID) +
## (1 | OriginSite)
## Data: dat2
##
## REML criterion at convergence: 542.4
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -2.2329 -0.6460 -0.1196 0.6673 2.3653
##
## Random effects:
## Groups Name Variance Std.Dev.
## CageSiteID:CagingSite (Intercept) 0.000000 0.0000
## CagingSite (Intercept) 0.000000 0.0000
## OriginSite (Intercept) 0.001289 0.0359
## Residual 0.510566 0.7145
## Number of obs: 246, groups:
## CageSiteID:CagingSite, 24; CagingSite, 4; OriginSite, 4
##
## Fixed effects:
## Estimate Std. Error t value
## (Intercept) -5.19004 0.31573 -16.438
## OriginContamLC -0.44163 0.09848 -4.484
## SizeEnd 0.21743 0.03106 6.999
##
## Correlation of Fixed Effects:
## (Intr) OrgCLC
## OrignCntmLC -0.245
## SizeEnd -0.976 0.098
## optimizer (nloptwrap) convergence code: 0 (OK)
## boundary (singular) fit: see ?isSingularmodCasp3 <- mod5
RmodCasp3 <- MuMIn::r.squaredGLMM(modCasp3)Casp3 expression is significantly different according to fish origin. More specifically, HC fish have higher Casp3 expression than LC fish. Also, the bigger the fish, the higher the level of Casp3 expression.
plot(DeltaCtCasp3.p ~ SizeEnd, data = dat2)
abline(a = -5.19004, b = 0.21743, col = "red")
Now that we have identified the best model, add sex as covariate to check whether results are sensitive NB: sample size is reduced when adding sex variable within the model, for this reason the sex effect on results is checked on the final model
6.16.4.8 Test for the sex effect
dat2 = dat2[is.na(dat2$Sex) == F, ]
modSex <-
lme4::lmer(
DeltaCtCasp3.p ~ OriginContam + SizeEnd + Sex +
(1 | CagingSite / CageSiteID) + (1| OriginSite),
data = dat2,
na.action = na.exclude
)
car::Anova(modSex, type = "3")## Analysis of Deviance Table (Type III Wald chisquare tests)
##
## Response: DeltaCtCasp3.p
## Chisq Df Pr(>Chisq)
## (Intercept) 251.6319 1 < 2.2e-16 ***
## OriginContam 17.5314 1 2.826e-05 ***
## SizeEnd 44.7003 1 2.296e-11 ***
## Sex 0.0736 1 0.7862
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1summary(modSex)## Linear mixed model fit by REML ['lmerMod']
## Formula:
## DeltaCtCasp3.p ~ OriginContam + SizeEnd + Sex + (1 | CagingSite/CageSiteID) +
## (1 | OriginSite)
## Data: dat2
##
## REML criterion at convergence: 544
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -2.2358 -0.6397 -0.1252 0.6708 2.3654
##
## Random effects:
## Groups Name Variance Std.Dev.
## CageSiteID:CagingSite (Intercept) 0.00000 0.0000
## CagingSite (Intercept) 0.00000 0.0000
## OriginSite (Intercept) 0.00255 0.0505
## Residual 0.51416 0.7170
## Number of obs: 245, groups:
## CageSiteID:CagingSite, 24; CagingSite, 4; OriginSite, 4
##
## Fixed effects:
## Estimate Std. Error t value
## (Intercept) -5.16841 0.32582 -15.863
## OriginContamLC -0.44057 0.10522 -4.187
## SizeEnd 0.21420 0.03204 6.686
## SexM 0.02565 0.09455 0.271
##
## Correlation of Fixed Effects:
## (Intr) OrgCLC SizEnd
## OrignCntmLC -0.250
## SizeEnd -0.968 0.095
## SexM -0.051 0.021 -0.066
## optimizer (nloptwrap) convergence code: 0 (OK)
## boundary (singular) fit: see ?isSingularThe sex effect is not significant. The mod5 is thus the best model. Here, there is no interaction, and hence no posthoc test nor parallelism test to conduct
boxplot(DeltaCtCasp3.p ~ OriginContam, data = dat2)
# compute mean and Se for LC and HC groups
meanVal <-
data.frame(
mean = c(mean(dat2$DeltaCtCasp3.p[which(dat2$OriginContam == "LC")]),
mean(dat2$DeltaCtCasp3.p[which(dat2$OriginContam == "HC")])),
Se = c(
sd(dat2$DeltaCtCasp3.p[which(dat2$OriginContam == "LC")]) / sqrt(length(dat2$DeltaCtCasp3.p[which(dat2$OriginContam == "LC")])),
sd(dat2$DeltaCtCasp3.p[which(dat2$OriginContam == "HC")]) / sqrt(length(dat2$DeltaCtCasp3.p[which(dat2$OriginContam == "HC")]))
),
row.names = c("LC", "HC"),
n = c(length(dat2$DeltaCtCasp3.p[which(dat2$OriginContam == "LC")]),
length(dat2$DeltaCtCasp3.p[which(dat2$OriginContam == "HC")]))
)
kableExtra::kable_classic(
kableExtra::kbl(meanVal),
bootstrap_options = c("striped", "hover", "condensed", "responsive"),
full_width = F,
html_font = "arial",
font_size = 10
)| mean | Se | n | |
|---|---|---|---|
| LC | -3.542152 | 0.0677479 | 117 |
| HC | -3.030752 | 0.0741425 | 128 |
6.16.5 Pcx
6.16.5.1 Check the data
dat2 = dat1[is.na(dat1$DeltaCtPcx) == F, ]
# transform variable to approx. normality
dat2$DeltaCtPcx.p <-
bimixt::boxcox(dat2$DeltaCtPcx, car::powerTransform(dat2$DeltaCtMtl)$lambda)
hist(dat2$DeltaCtPcx.p)
6.16.5.2 Visualize
par(mfrow=c(2,3))
boxplot(DeltaCtPcx.p ~ OriginContam, data = dat2)
boxplot(DeltaCtPcx.p ~ TransplantContam, data = dat2)
boxplot(DeltaCtPcx.p ~ Injection, data = dat2)
boxplot(DeltaCtPcx.p ~ TransplantContam * Injection, data = dat2)
boxplot(DeltaCtPcx.p ~ TransplantContam * OriginContam, data = dat2)
boxplot(DeltaCtPcx.p ~ TransplantContam * OriginContam * Injection, data = dat2)
6.16.5.3 Build the full model
modfull <-
lme4::lmer(
DeltaCtPcx.p ~ (TransplantContam + OriginContam + Injection) ^ 3 + SizeEnd +
(1 | CagingSite / CageSiteID) + (1| OriginSite),
data = dat2,
na.action = na.exclude
)
car::Anova(modfull, type = "3")## Analysis of Deviance Table (Type III Wald chisquare tests)
##
## Response: DeltaCtPcx.p
## Chisq Df Pr(>Chisq)
## (Intercept) 107.6861 1 <2e-16 ***
## TransplantContam 0.0189 1 0.8905
## OriginContam 0.0681 1 0.7941
## Injection 2.2942 1 0.1299
## SizeEnd 1.4059 1 0.2357
## TransplantContam:OriginContam 0.6035 1 0.4372
## TransplantContam:Injection 0.3826 1 0.5362
## OriginContam:Injection 0.5533 1 0.4570
## TransplantContam:OriginContam:Injection 0.0928 1 0.7606
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1summary(modfull)## Linear mixed model fit by REML ['lmerMod']
## Formula: DeltaCtPcx.p ~ (TransplantContam + OriginContam + Injection)^3 +
## SizeEnd + (1 | CagingSite/CageSiteID) + (1 | OriginSite)
## Data: dat2
##
## REML criterion at convergence: 267.4
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -2.5255 -0.6242 0.0045 0.6279 3.6097
##
## Random effects:
## Groups Name Variance Std.Dev.
## CageSiteID:CagingSite (Intercept) 0.007666 0.08755
## CagingSite (Intercept) 0.000000 0.00000
## OriginSite (Intercept) 0.105554 0.32489
## Residual 0.151573 0.38932
## Number of obs: 240, groups:
## CageSiteID:CagingSite, 24; CagingSite, 4; OriginSite, 4
##
## Fixed effects:
## Estimate Std. Error t value
## (Intercept) -3.49927 0.33721 -10.377
## TransplantContamLC 0.01544 0.11217 0.138
## OriginContamLC -0.08953 0.34302 -0.261
## InjectionPBS 0.14892 0.09832 1.515
## SizeEnd 0.02767 0.02334 1.186
## TransplantContamLC:OriginContamLC -0.12166 0.15660 -0.777
## TransplantContamLC:InjectionPBS 0.08742 0.14132 0.619
## OriginContamLC:InjectionPBS -0.10626 0.14285 -0.744
## TransplantContamLC:OriginContamLC:InjectionPBS -0.06149 0.20181 -0.305
##
## Correlation of Fixed Effects:
## (Intr) TrnCLC OrgCLC InjPBS SizEnd TrCLC:OCLC TCLC:I OCLC:I
## TrnsplntCLC -0.225
## OrignCntmLC -0.518 0.155
## InjectinPBS -0.149 0.418 0.136
## SizeEnd -0.696 0.099 0.016 0.015
## TrnCLC:OCLC 0.116 -0.710 -0.225 -0.299 -0.006
## TrnCLC:IPBS 0.113 -0.622 -0.095 -0.696 -0.024 0.444
## OrgCLC:IPBS 0.101 -0.288 -0.194 -0.688 -0.008 0.424 0.479
## TCLC:OCLC:I -0.075 0.435 0.137 0.487 0.011 -0.611 -0.700 -0.708
## optimizer (nloptwrap) convergence code: 0 (OK)
## boundary (singular) fit: see ?isSingular6.16.5.4 Refining the model
mod2 <-
lme4::lmer(
DeltaCtPcx.p ~ (TransplantContam + OriginContam + Injection) ^ 2 + SizeEnd +
(1 | CagingSite / CageSiteID) + (1| OriginSite),
data = dat2,
na.action = na.exclude
)
car::Anova(mod2, type = "3")## Analysis of Deviance Table (Type III Wald chisquare tests)
##
## Response: DeltaCtPcx.p
## Chisq Df Pr(>Chisq)
## (Intercept) 109.0217 1 < 2e-16 ***
## TransplantContam 0.0903 1 0.76375
## OriginContam 0.0490 1 0.82480
## Injection 3.6415 1 0.05636 .
## SizeEnd 1.4181 1 0.23372
## TransplantContam:OriginContam 1.4858 1 0.22286
## TransplantContam:Injection 0.3234 1 0.56958
## OriginContam:Injection 1.8527 1 0.17347
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1summary(mod2)## Linear mixed model fit by REML ['lmerMod']
## Formula: DeltaCtPcx.p ~ (TransplantContam + OriginContam + Injection)^2 +
## SizeEnd + (1 | CagingSite/CageSiteID) + (1 | OriginSite)
## Data: dat2
##
## REML criterion at convergence: 266.1
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -2.5506 -0.6470 0.0109 0.6336 3.5963
##
## Random effects:
## Groups Name Variance Std.Dev.
## CageSiteID:CagingSite (Intercept) 7.646e-03 8.744e-02
## CagingSite (Intercept) 9.086e-11 9.532e-06
## OriginSite (Intercept) 1.055e-01 3.248e-01
## Residual 1.510e-01 3.885e-01
## Number of obs: 240, groups:
## CageSiteID:CagingSite, 24; CagingSite, 4; OriginSite, 4
##
## Fixed effects:
## Estimate Std. Error t value
## (Intercept) -3.50685 0.33586 -10.441
## TransplantContamLC 0.03030 0.10083 0.301
## OriginContamLC -0.07519 0.33964 -0.221
## InjectionPBS 0.16352 0.08569 1.908
## SizeEnd 0.02774 0.02329 1.191
## TransplantContamLC:OriginContamLC -0.15083 0.12374 -1.219
## TransplantContamLC:InjectionPBS 0.05727 0.10070 0.569
## OriginContamLC:InjectionPBS -0.13707 0.10070 -1.361
##
## Correlation of Fixed Effects:
## (Intr) TrnCLC OrgCLC InjPBS SizEnd TCLC:O TCLC:I
## TrnsplntCLC -0.214
## OrignCntmLC -0.514 0.107
## InjectinPBS -0.129 0.262 0.080
## SizeEnd -0.696 0.104 0.014 0.011
## TrnCLC:OCLC 0.089 -0.623 -0.180 -0.001 0.001
## TrnCLC:IPBS 0.085 -0.493 0.001 -0.569 -0.023 0.028
## OrgCLC:IPBS 0.068 0.032 -0.138 -0.557 0.000 -0.015 -0.033
## optimizer (nloptwrap) convergence code: 0 (OK)
## boundary (singular) fit: see ?isSingular6.16.5.5 Refining the model
mod3 <-
lme4::lmer(
DeltaCtPcx.p ~ TransplantContam + (OriginContam + Injection)^2 + SizeEnd +
(1 | CagingSite / CageSiteID) + (1| OriginSite),
data = dat2,
na.action = na.exclude
)
car::Anova(mod3, type = "3")## Analysis of Deviance Table (Type III Wald chisquare tests)
##
## Response: DeltaCtPcx.p
## Chisq Df Pr(>Chisq)
## (Intercept) 110.3238 1 < 2.2e-16 ***
## TransplantContam 0.0756 1 0.783360
## OriginContam 0.2075 1 0.648767
## Injection 7.4937 1 0.006191 **
## SizeEnd 1.4519 1 0.228225
## OriginContam:Injection 1.8522 1 0.173526
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1summary(mod3)## Linear mixed model fit by REML ['lmerMod']
## Formula: DeltaCtPcx.p ~ TransplantContam + (OriginContam + Injection)^2 +
## SizeEnd + (1 | CagingSite/CageSiteID) + (1 | OriginSite)
## Data: dat2
##
## REML criterion at convergence: 262.8
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -2.6471 -0.6634 0.0107 0.5713 3.5715
##
## Random effects:
## Groups Name Variance Std.Dev.
## CageSiteID:CagingSite (Intercept) 0.007977 0.08932
## CagingSite (Intercept) 0.000000 0.00000
## OriginSite (Intercept) 0.103693 0.32201
## Residual 0.150707 0.38821
## Number of obs: 240, groups:
## CageSiteID:CagingSite, 24; CagingSite, 4; OriginSite, 4
##
## Fixed effects:
## Estimate Std. Error t value
## (Intercept) -3.48672 0.33196 -10.504
## TransplantContamLC -0.01731 0.06297 -0.275
## OriginContamLC -0.15097 0.33145 -0.455
## InjectionPBS 0.19271 0.07040 2.737
## SizeEnd 0.02804 0.02327 1.205
## OriginContamLC:InjectionPBS -0.13685 0.10055 -1.361
##
## Correlation of Fixed Effects:
## (Intr) TrnCLC OrgCLC InjPBS SizEnd
## TrnsplntCLC -0.194
## OrignCntmLC -0.509 -0.004
## InjectinPBS -0.100 -0.018 0.104
## SizeEnd -0.702 0.150 0.015 -0.003
## OrgCLC:IPBS 0.073 0.011 -0.144 -0.700 -0.001
## optimizer (nloptwrap) convergence code: 0 (OK)
## boundary (singular) fit: see ?isSingular6.16.5.6 Refining the model
mod4 <-
lme4::lmer(
DeltaCtPcx.p ~ TransplantContam + OriginContam + Injection + SizeEnd +
(1 | CagingSite / CageSiteID) + (1| OriginSite),
data = dat2,
na.action = na.exclude
)
car::Anova(mod4, type = "3")## Analysis of Deviance Table (Type III Wald chisquare tests)
##
## Response: DeltaCtPcx.p
## Chisq Df Pr(>Chisq)
## (Intercept) 108.8221 1 <2e-16 ***
## TransplantContam 0.0672 1 0.7954
## OriginContam 0.4344 1 0.5099
## Injection 6.2241 1 0.0126 *
## SizeEnd 1.4435 1 0.2296
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1summary(mod4)## Linear mixed model fit by REML ['lmerMod']
## Formula: DeltaCtPcx.p ~ TransplantContam + OriginContam + Injection +
## SizeEnd + (1 | CagingSite/CageSiteID) + (1 | OriginSite)
## Data: dat2
##
## REML criterion at convergence: 261.9
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -2.5499 -0.6893 0.0111 0.6220 3.4685
##
## Random effects:
## Groups Name Variance Std.Dev.
## CageSiteID:CagingSite (Intercept) 0.008103 0.09002
## CagingSite (Intercept) 0.000000 0.00000
## OriginSite (Intercept) 0.103298 0.32140
## Residual 0.151211 0.38886
## Number of obs: 240, groups:
## CageSiteID:CagingSite, 24; CagingSite, 4; OriginSite, 4
##
## Fixed effects:
## Estimate Std. Error t value
## (Intercept) -3.45390 0.33109 -10.432
## TransplantContamLC -0.01639 0.06320 -0.259
## OriginContamLC -0.21581 0.32744 -0.659
## InjectionPBS 0.12562 0.05035 2.495
## SizeEnd 0.02800 0.02331 1.201
##
## Correlation of Fixed Effects:
## (Intr) TrnCLC OrgCLC InjPBS
## TrnsplntCLC -0.196
## OrignCntmLC -0.505 -0.002
## InjectinPBS -0.070 -0.015 0.005
## SizeEnd -0.705 0.150 0.015 -0.005
## optimizer (nloptwrap) convergence code: 0 (OK)
## boundary (singular) fit: see ?isSingular6.16.5.7 Refining the model
mod5 <-
lme4::lmer(
DeltaCtPcx.p ~ Injection +
(1 | CagingSite / CageSiteID) + (1| OriginSite),
data = dat2,
na.action = na.exclude
)
car::Anova(mod5, type = "3")## Analysis of Deviance Table (Type III Wald chisquare tests)
##
## Response: DeltaCtPcx.p
## Chisq Df Pr(>Chisq)
## (Intercept) 410.9888 1 < 2e-16 ***
## Injection 6.2643 1 0.01232 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1summary(mod5)## Linear mixed model fit by REML ['lmerMod']
## Formula: DeltaCtPcx.p ~ Injection + (1 | CagingSite/CageSiteID) + (1 |
## OriginSite)
## Data: dat2
##
## REML criterion at convergence: 254.3
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -2.4705 -0.6975 -0.0188 0.6402 3.4955
##
## Random effects:
## Groups Name Variance Std.Dev.
## CageSiteID:CagingSite (Intercept) 0.008078 0.08988
## CagingSite (Intercept) 0.000000 0.00000
## OriginSite (Intercept) 0.099706 0.31576
## Residual 0.150697 0.38820
## Number of obs: 240, groups:
## CageSiteID:CagingSite, 24; CagingSite, 4; OriginSite, 4
##
## Fixed effects:
## Estimate Std. Error t value
## (Intercept) -3.29796 0.16268 -20.273
## InjectionPBS 0.12580 0.05026 2.503
##
## Correlation of Fixed Effects:
## (Intr)
## InjectinPBS -0.146
## optimizer (nloptwrap) convergence code: 0 (OK)
## boundary (singular) fit: see ?isSingularPcx expression is significantly different according to the immune challenge. More specifically, immune challenged fish injected with the antigen mixture (AMIX) have a lower Pcx gene expression compare to the fish injected with the control saline solution (PBS).
Now that we have identified the best model, add sex as covariate to check whether results are sensitive NB: sample size is reduced when adding sex variable within the model, for this reason the sex effect on results is checked on the final model
6.16.5.8 Test for the sex effect
dat2 = dat2[is.na(dat2$Sex) == F, ]
modSex <-
lme4::lmer(
DeltaCtPcx.p ~ Injection + Sex +
(1 | CagingSite / CageSiteID) + (1| OriginSite),
data = dat2,
na.action = na.exclude
)
performance::check_model(modSex)
car::Anova(modSex, type = "3")## Analysis of Deviance Table (Type III Wald chisquare tests)
##
## Response: DeltaCtPcx.p
## Chisq Df Pr(>Chisq)
## (Intercept) 392.0753 1 < 2e-16 ***
## Injection 5.9462 1 0.01475 *
## Sex 4.9243 1 0.02648 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1summary(modSex)## Linear mixed model fit by REML ['lmerMod']
## Formula: DeltaCtPcx.p ~ Injection + Sex + (1 | CagingSite/CageSiteID) +
## (1 | OriginSite)
## Data: dat2
##
## REML criterion at convergence: 250.6
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -2.3234 -0.6714 -0.0291 0.7023 3.4292
##
## Random effects:
## Groups Name Variance Std.Dev.
## CageSiteID:CagingSite (Intercept) 0.004934 0.07024
## CagingSite (Intercept) 0.000000 0.00000
## OriginSite (Intercept) 0.100530 0.31706
## Residual 0.148851 0.38581
## Number of obs: 239, groups:
## CageSiteID:CagingSite, 24; CagingSite, 4; OriginSite, 4
##
## Fixed effects:
## Estimate Std. Error t value
## (Intercept) -3.25501 0.16439 -19.801
## InjectionPBS 0.12242 0.05021 2.438
## SexM -0.11662 0.05255 -2.219
##
## Correlation of Fixed Effects:
## (Intr) InjPBS
## InjectinPBS -0.156
## SexM -0.135 0.083
## optimizer (nloptwrap) convergence code: 0 (OK)
## boundary (singular) fit: see ?isSingularmodPcx <- modSex
RmodPcx <- MuMIn::r.squaredGLMM(modPcx)The sex effect is significant. The modSex is thus the best model. Here, there is no interaction, and hence no posthoc test nor parallelism test to conduct
boxplot(DeltaCtPcx.p ~ Injection, data = dat2)
# compute mean and Se for LC and HC groups
meanVal <-
data.frame(
mean = c(mean(dat2$DeltaCtPcx.p[which(dat2$Injection == "PBS")]),
mean(dat2$DeltaCtPcx.p[which(dat2$Injection == "AMIX")])),
Se = c(
sd(dat2$DeltaCtPcx.p[which(dat2$Injection == "PBS")]) / sqrt(length(dat2$DeltaCtPcx.p[which(dat2$Injection == "PBS")])),
sd(dat2$DeltaCtPcx.p[which(dat2$Injection == "AMIX")]) / sqrt(length(dat2$DeltaCtPcx.p[which(dat2$Injection == "AMIX")]))
),
row.names = c("PBS", "AMIX"),
n = c(length(dat2$DeltaCtPcx.p[which(dat2$Injection == "PBS")]),
length(dat2$DeltaCtPcx.p[which(dat2$Injection == "AMIX")]))
)
kableExtra::kable_classic(
kableExtra::kbl(meanVal),
bootstrap_options = c("striped", "hover", "condensed", "responsive"),
full_width = F,
html_font = "arial",
font_size = 10
)| mean | Se | n | |
|---|---|---|---|
| PBS | -3.171033 | 0.0463890 | 114 |
| AMIX | -3.307949 | 0.0419337 | 125 |
6.16.6 Pygl
6.16.6.1 Check the data
dat2 = dat1[is.na(dat1$DeltaCtPygl) == F, ]
# transform variable to approx. normality
dat2$DeltaCtPygl.p <-
bimixt::boxcox(dat2$DeltaCtPygl, car::powerTransform(dat2$DeltaCtMtl)$lambda)
hist(dat2$DeltaCtPygl.p)
6.16.6.2 Visualize
par(mfrow=c(2,3))
boxplot(DeltaCtPygl.p ~ OriginContam, data = dat2)
boxplot(DeltaCtPygl.p ~ TransplantContam, data = dat2)
boxplot(DeltaCtPygl.p ~ Injection, data = dat2)
boxplot(DeltaCtPygl.p ~ TransplantContam * Injection, data = dat2)
boxplot(DeltaCtPygl.p ~ TransplantContam * OriginContam, data = dat2)
boxplot(DeltaCtPygl.p ~ TransplantContam * OriginContam * Injection, data = dat2)
6.16.6.3 Build the full model
modfull <-
lme4::lmer(
DeltaCtPygl.p ~ (TransplantContam + OriginContam + Injection) ^ 3 + SizeEnd +
(1 | CagingSite / CageSiteID) + (1| OriginSite),
data = dat2,
na.action = na.exclude
)
car::Anova(modfull, type = "3")## Analysis of Deviance Table (Type III Wald chisquare tests)
##
## Response: DeltaCtPygl.p
## Chisq Df Pr(>Chisq)
## (Intercept) 124.1855 1 <2e-16 ***
## TransplantContam 1.2894 1 0.2562
## OriginContam 0.4564 1 0.4993
## Injection 1.5179 1 0.2179
## SizeEnd 1.2137 1 0.2706
## TransplantContam:OriginContam 0.3061 1 0.5801
## TransplantContam:Injection 0.8515 1 0.3561
## OriginContam:Injection 0.1938 1 0.6598
## TransplantContam:OriginContam:Injection 1.9743 1 0.1600
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1summary(modfull)## Linear mixed model fit by REML ['lmerMod']
## Formula: DeltaCtPygl.p ~ (TransplantContam + OriginContam + Injection)^3 +
## SizeEnd + (1 | CagingSite/CageSiteID) + (1 | OriginSite)
## Data: dat2
##
## REML criterion at convergence: 221.1
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -3.7762 -0.4925 0.0060 0.6019 2.7845
##
## Random effects:
## Groups Name Variance Std.Dev.
## CageSiteID:CagingSite (Intercept) 0.005033 0.07094
## CagingSite (Intercept) 0.000000 0.00000
## OriginSite (Intercept) 0.007040 0.08390
## Residual 0.134533 0.36679
## Number of obs: 226, groups:
## CageSiteID:CagingSite, 24; CagingSite, 4; OriginSite, 4
##
## Fixed effects:
## Estimate Std. Error t value
## (Intercept) -2.70225 0.24249 -11.144
## TransplantContamLC 0.12416 0.10934 1.136
## OriginContamLC -0.09012 0.13340 -0.676
## InjectionPBS 0.12528 0.10168 1.232
## SizeEnd 0.02411 0.02189 1.102
## TransplantContamLC:OriginContamLC -0.08167 0.14760 -0.553
## TransplantContamLC:InjectionPBS 0.13129 0.14228 0.923
## OriginContamLC:InjectionPBS 0.06204 0.14095 0.440
## TransplantContamLC:OriginContamLC:InjectionPBS -0.27621 0.19658 -1.405
##
## Correlation of Fixed Effects:
## (Intr) TrnCLC OrgCLC InjPBS SizEnd TrCLC:OCLC TCLC:I OCLC:I
## TrnsplntCLC -0.370
## OrignCntmLC -0.334 0.387
## InjectinPBS -0.240 0.430 0.346
## SizeEnd -0.920 0.177 0.060 0.056
## TrnCLC:OCLC 0.214 -0.729 -0.547 -0.315 -0.066
## TrnCLC:IPBS 0.201 -0.646 -0.249 -0.717 -0.072 0.474
## OrgCLC:IPBS 0.173 -0.310 -0.480 -0.721 -0.040 0.436 0.517
## TCLC:OCLC:I -0.140 0.467 0.346 0.518 0.047 -0.633 -0.723 -0.718
## optimizer (nloptwrap) convergence code: 0 (OK)
## boundary (singular) fit: see ?isSingular6.16.6.4 Refining the model
mod2 <-
lme4::lmer(
DeltaCtPygl.p ~ (TransplantContam + OriginContam + Injection) ^ 2 + SizeEnd +
(1 | CagingSite / CageSiteID) + (1| OriginSite),
data = dat2,
na.action = na.exclude
)
car::Anova(mod2, type = "3")## Analysis of Deviance Table (Type III Wald chisquare tests)
##
## Response: DeltaCtPygl.p
## Chisq Df Pr(>Chisq)
## (Intercept) 130.7321 1 < 2e-16 ***
## TransplantContam 4.0936 1 0.04305 *
## OriginContam 0.0409 1 0.83976
## Injection 5.2326 1 0.02217 *
## SizeEnd 1.3619 1 0.24321
## TransplantContam:OriginContam 3.4698 1 0.06250 .
## TransplantContam:Injection 0.0183 1 0.89242
## OriginContam:Injection 0.6638 1 0.41521
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1summary(mod2)## Linear mixed model fit by REML ['lmerMod']
## Formula: DeltaCtPygl.p ~ (TransplantContam + OriginContam + Injection)^2 +
## SizeEnd + (1 | CagingSite/CageSiteID) + (1 | OriginSite)
## Data: dat2
##
## REML criterion at convergence: 221.7
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -3.8555 -0.4702 0.0152 0.5567 2.6701
##
## Random effects:
## Groups Name Variance Std.Dev.
## CageSiteID:CagingSite (Intercept) 0.004984 0.07060
## CagingSite (Intercept) 0.000000 0.00000
## OriginSite (Intercept) 0.007048 0.08395
## Residual 0.135180 0.36767
## Number of obs: 226, groups:
## CageSiteID:CagingSite, 24; CagingSite, 4; OriginSite, 4
##
## Fixed effects:
## Estimate Std. Error t value
## (Intercept) -2.75029 0.24054 -11.434
## TransplantContamLC 0.19585 0.09680 2.023
## OriginContamLC -0.02533 0.12528 -0.202
## InjectionPBS 0.19937 0.08716 2.287
## SizeEnd 0.02557 0.02191 1.167
## TransplantContamLC:OriginContamLC -0.21294 0.11432 -1.863
## TransplantContamLC:InjectionPBS -0.01332 0.09847 -0.135
## OriginContamLC:InjectionPBS -0.08014 0.09836 -0.815
##
## Correlation of Fixed Effects:
## (Intr) TrnCLC OrgCLC InjPBS SizEnd TCLC:O TCLC:I
## TrnsplntCLC -0.348
## OrignCntmLC -0.307 0.272
## InjectinPBS -0.198 0.248 0.208
## SizeEnd -0.924 0.176 0.047 0.038
## TrnCLC:OCLC 0.163 -0.633 -0.451 0.021 -0.047
## TrnCLC:IPBS 0.145 -0.506 0.001 -0.579 -0.055 0.030
## OrgCLC:IPBS 0.104 0.041 -0.356 -0.587 -0.009 -0.035 -0.005
## optimizer (nloptwrap) convergence code: 0 (OK)
## boundary (singular) fit: see ?isSingular6.16.6.5 Refining the model
mod3 <-
lme4::lmer(
DeltaCtPygl.p ~ (TransplantContam + OriginContam)^2 + Injection + SizeEnd +
(1 | CagingSite / CageSiteID) + (1| OriginSite),
data = dat2,
na.action = na.exclude
)
car::Anova(mod3, type = "3")## Analysis of Deviance Table (Type III Wald chisquare tests)
##
## Response: DeltaCtPygl.p
## Chisq Df Pr(>Chisq)
## (Intercept) 133.3751 1 < 2.2e-16 ***
## TransplantContam 5.3113 1 0.021187 *
## OriginContam 0.2787 1 0.597543
## Injection 9.4640 1 0.002095 **
## SizeEnd 1.3406 1 0.246924
## TransplantContam:OriginContam 3.5640 1 0.059047 .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1summary(mod3)## Linear mixed model fit by REML ['lmerMod']
## Formula: DeltaCtPygl.p ~ (TransplantContam + OriginContam)^2 + Injection +
## SizeEnd + (1 | CagingSite/CageSiteID) + (1 | OriginSite)
## Data: dat2
##
## REML criterion at convergence: 216.8
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -3.8260 -0.4845 0.0207 0.5715 2.7511
##
## Random effects:
## Groups Name Variance Std.Dev.
## CageSiteID:CagingSite (Intercept) 0.005119 0.07155
## CagingSite (Intercept) 0.000000 0.00000
## OriginSite (Intercept) 0.006988 0.08360
## Residual 0.134274 0.36643
## Number of obs: 226, groups:
## CageSiteID:CagingSite, 24; CagingSite, 4; OriginSite, 4
##
## Fixed effects:
## Estimate Std. Error t value
## (Intercept) -2.72511 0.23596 -11.549
## TransplantContamLC 0.19237 0.08347 2.305
## OriginContamLC -0.06169 0.11686 -0.528
## InjectionPBS 0.15064 0.04897 3.076
## SizeEnd 0.02525 0.02181 1.158
## TransplantContamLC:OriginContamLC -0.21580 0.11431 -1.888
##
## Correlation of Fixed Effects:
## (Intr) TrnCLC OrgCLC InjPBS SizEnd
## TrnsplntCLC -0.329
## OrignCntmLC -0.294 0.357
## InjectinPBS -0.094 -0.044 -0.002
## SizeEnd -0.931 0.172 0.047 0.001
## TrnCLC:OCLC 0.166 -0.716 -0.498 0.031 -0.045
## optimizer (nloptwrap) convergence code: 0 (OK)
## boundary (singular) fit: see ?isSingular6.16.6.6 Refining the model
mod4 <-
lme4::lmer(
DeltaCtPygl.p ~ TransplantContam + OriginContam + Injection + SizeEnd +
(1 | CagingSite / CageSiteID) + (1| OriginSite),
data = dat2,
na.action = na.exclude
)
car::Anova(mod4, type = "3")## Analysis of Deviance Table (Type III Wald chisquare tests)
##
## Response: DeltaCtPygl.p
## Chisq Df Pr(>Chisq)
## (Intercept) 130.4728 1 < 2.2e-16 ***
## TransplantContam 1.7193 1 0.189788
## OriginContam 2.9271 1 0.087103 .
## Injection 9.7301 1 0.001813 **
## SizeEnd 1.2323 1 0.266962
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1summary(mod4)## Linear mixed model fit by REML ['lmerMod']
## Formula: DeltaCtPygl.p ~ TransplantContam + OriginContam + Injection +
## SizeEnd + (1 | CagingSite/CageSiteID) + (1 | OriginSite)
## Data: dat2
##
## REML criterion at convergence: 217.7
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -3.6998 -0.5206 0.0379 0.5447 2.6484
##
## Random effects:
## Groups Name Variance Std.Dev.
## CageSiteID:CagingSite (Intercept) 0.007478 0.08648
## CagingSite (Intercept) 0.000000 0.00000
## OriginSite (Intercept) 0.006357 0.07973
## Residual 0.134472 0.36670
## Number of obs: 226, groups:
## CageSiteID:CagingSite, 24; CagingSite, 4; OriginSite, 4
##
## Fixed effects:
## Estimate Std. Error t value
## (Intercept) -2.65959 0.23284 -11.422
## TransplantContamLC 0.08078 0.06161 1.311
## OriginContamLC -0.17138 0.10017 -1.711
## InjectionPBS 0.15283 0.04900 3.119
## SizeEnd 0.02420 0.02180 1.110
##
## Correlation of Fixed Effects:
## (Intr) TrnCLC OrgCLC InjPBS
## TrnsplntCLC -0.304
## OrignCntmLC -0.245 0.000
## InjectinPBS -0.101 -0.030 0.016
## SizeEnd -0.938 0.190 0.028 0.002
## optimizer (nloptwrap) convergence code: 0 (OK)
## boundary (singular) fit: see ?isSingular6.16.6.7 Refining the model
mod5 <-
lme4::lmer(
DeltaCtPygl.p ~ Injection +
(1 | CagingSite / CageSiteID) + (1| OriginSite),
data = dat2,
na.action = na.exclude
)
performance::check_model(mod5)
car::Anova(mod5, type = "3")## Analysis of Deviance Table (Type III Wald chisquare tests)
##
## Response: DeltaCtPygl.p
## Chisq Df Pr(>Chisq)
## (Intercept) 1087.830 1 < 2.2e-16 ***
## Injection 10.084 1 0.001496 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1summary(mod5)## Linear mixed model fit by REML ['lmerMod']
## Formula: DeltaCtPygl.p ~ Injection + (1 | CagingSite/CageSiteID) + (1 |
## OriginSite)
## Data: dat2
##
## REML criterion at convergence: 209.9
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -3.7510 -0.5203 0.0299 0.5532 2.5889
##
## Random effects:
## Groups Name Variance Std.Dev.
## CageSiteID:CagingSite (Intercept) 0.006913 0.08315
## CagingSite (Intercept) 0.000000 0.00000
## OriginSite (Intercept) 0.016728 0.12934
## Residual 0.134468 0.36670
## Number of obs: 226, groups:
## CageSiteID:CagingSite, 24; CagingSite, 4; OriginSite, 4
##
## Fixed effects:
## Estimate Std. Error t value
## (Intercept) -2.47089 0.07492 -32.982
## InjectionPBS 0.15549 0.04896 3.175
##
## Correlation of Fixed Effects:
## (Intr)
## InjectinPBS -0.309
## optimizer (nloptwrap) convergence code: 0 (OK)
## boundary (singular) fit: see ?isSingularmodPygl <- mod5
RmodPygl <- MuMIn::r.squaredGLMM(modPygl)Pygl expression is significantly different according to the immune challenge. More specifically, immune challenged fish injected with the antigen mixture (AMIX) have a lower Pygl gene expression compare to the fish injected with the control saline solution (PBS).
Now that we have identified the best model, add sex as covariate to check whether results are sensitive NB: sample size is reduced when adding sex variable within the model, for this reason the sex effect on results is checked on the final model
6.16.6.8 Test for the sex effect
dat2 = dat2[is.na(dat2$Sex) == F, ]
modSex <-
lme4::lmer(
DeltaCtPygl.p ~ Injection + Sex +
(1 | CagingSite / CageSiteID) + (1| OriginSite),
data = dat2,
na.action = na.exclude
)
car::Anova(modSex, type = "3")## Analysis of Deviance Table (Type III Wald chisquare tests)
##
## Response: DeltaCtPygl.p
## Chisq Df Pr(>Chisq)
## (Intercept) 978.8302 1 < 2.2e-16 ***
## Injection 9.7481 1 0.001795 **
## Sex 0.2304 1 0.631264
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1summary(modSex)## Linear mixed model fit by REML ['lmerMod']
## Formula: DeltaCtPygl.p ~ Injection + Sex + (1 | CagingSite/CageSiteID) +
## (1 | OriginSite)
## Data: dat2
##
## REML criterion at convergence: 213.8
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -3.6951 -0.5427 0.0298 0.5821 2.5559
##
## Random effects:
## Groups Name Variance Std.Dev.
## CageSiteID:CagingSite (Intercept) 0.00643 0.08019
## CagingSite (Intercept) 0.00000 0.00000
## OriginSite (Intercept) 0.01703 0.13050
## Residual 0.13576 0.36846
## Number of obs: 225, groups:
## CageSiteID:CagingSite, 24; CagingSite, 4; OriginSite, 4
##
## Fixed effects:
## Estimate Std. Error t value
## (Intercept) -2.46144 0.07867 -31.286
## InjectionPBS 0.15460 0.04952 3.122
## SexM -0.02499 0.05207 -0.480
##
## Correlation of Fixed Effects:
## (Intr) InjPBS
## InjectinPBS -0.323
## SexM -0.285 0.095
## optimizer (nloptwrap) convergence code: 0 (OK)
## boundary (singular) fit: see ?isSingularThe sex effect is not significant. The mod5 is thus the best model. Here, there is no interaction, and hence no posthoc test nor parallelism test to conduct
boxplot(DeltaCtPygl.p ~ Injection, data = dat2)
# compute mean and Se for LC and HC groups
meanVal <-
data.frame(
mean = c(mean(dat2$DeltaCtPygl.p[which(dat2$Injection == "PBS")]),
mean(dat2$DeltaCtPygl.p[which(dat2$Injection == "AMIX")])),
Se = c(
sd(dat2$DeltaCtPygl.p[which(dat2$Injection == "PBS")]) / sqrt(length(dat2$DeltaCtPygl.p[which(dat2$Injection == "PBS")])),
sd(dat2$DeltaCtPygl.p[which(dat2$Injection == "AMIX")]) / sqrt(length(dat2$DeltaCtPygl.p[which(dat2$Injection == "AMIX")]))
),
row.names = c("PBS", "AMIX"),
n = c(length(dat2$DeltaCtPygl.p[which(dat2$Injection == "PBS")]),
length(dat2$DeltaCtPygl.p[which(dat2$Injection == "AMIX")]))
)
kableExtra::kable_classic(
kableExtra::kbl(meanVal),
bootstrap_options = c("striped", "hover", "condensed", "responsive"),
full_width = F,
html_font = "arial",
font_size = 10
)| mean | Se | n | |
|---|---|---|---|
| PBS | -2.323065 | 0.0396051 | 107 |
| AMIX | -2.486398 | 0.0343619 | 118 |
6.16.7 CqActb (β-actin)
6.16.7.1 Check the data
dat2 = dat1[is.na(dat1$CqActb) == F, ]
# transform variable to approx. normality
dat2$CqActb.p <-
bimixt::boxcox(dat2$CqActb, car::powerTransform(dat2$DeltaCtMtl)$lambda)
hist(dat2$CqActb.p)
6.16.7.2 Visualize
par(mfrow=c(2,3))
boxplot(CqActb.p ~ OriginContam, data = dat2)
boxplot(CqActb.p ~ TransplantContam, data = dat2)
boxplot(CqActb.p ~ Injection, data = dat2)
boxplot(CqActb.p ~ TransplantContam * Injection, data = dat2)
boxplot(CqActb.p ~ TransplantContam * OriginContam, data = dat2)
boxplot(CqActb.p ~ TransplantContam * OriginContam * Injection, data = dat2)
6.16.7.3 Build the full model
modfull <-
lme4::lmer(
CqActb.p ~ (TransplantContam + OriginContam + Injection) ^ 3 + SizeEnd +
(1 | CagingSite / CageSiteID) + (1| OriginSite),
data = dat2,
na.action = na.exclude
)
car::Anova(modfull, type = "3")## Analysis of Deviance Table (Type III Wald chisquare tests)
##
## Response: CqActb.p
## Chisq Df Pr(>Chisq)
## (Intercept) 4800.4064 1 < 2e-16 ***
## TransplantContam 0.8446 1 0.35808
## OriginContam 1.6791 1 0.19504
## Injection 1.3007 1 0.25409
## SizeEnd 5.3729 1 0.02045 *
## TransplantContam:OriginContam 0.9971 1 0.31800
## TransplantContam:Injection 0.2766 1 0.59897
## OriginContam:Injection 0.7924 1 0.37337
## TransplantContam:OriginContam:Injection 0.1447 1 0.70368
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1summary(modfull)## Linear mixed model fit by REML ['lmerMod']
## Formula: CqActb.p ~ (TransplantContam + OriginContam + Injection)^3 +
## SizeEnd + (1 | CagingSite/CageSiteID) + (1 | OriginSite)
## Data: dat2
##
## REML criterion at convergence: -535
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -3.4702 -0.6521 0.0416 0.5684 2.5732
##
## Random effects:
## Groups Name Variance Std.Dev.
## CageSiteID:CagingSite (Intercept) 2.614e-05 5.112e-03
## CagingSite (Intercept) 4.127e-12 2.031e-06
## OriginSite (Intercept) 3.204e-03 5.661e-02
## Residual 5.145e-03 7.173e-02
## Number of obs: 246, groups:
## CageSiteID:CagingSite, 24; CagingSite, 4; OriginSite, 4
##
## Fixed effects:
## Estimate Std. Error t value
## (Intercept) 4.049539 0.058448 69.285
## TransplantContamLC -0.016481 0.017934 -0.919
## OriginContamLC -0.077057 0.059466 -1.296
## InjectionPBS -0.020642 0.018099 -1.140
## SizeEnd 0.009387 0.004050 2.318
## TransplantContamLC:OriginContamLC -0.025505 0.025541 -0.999
## TransplantContamLC:InjectionPBS 0.013351 0.025388 0.526
## OriginContamLC:InjectionPBS 0.023410 0.026298 0.890
## TransplantContamLC:OriginContamLC:InjectionPBS 0.013967 0.036720 0.380
##
## Correlation of Fixed Effects:
## (Intr) TrnCLC OrgCLC InjPBS SizEnd TrCLC:OCLC TCLC:I OCLC:I
## TrnsplntCLC -0.188
## OrignCntmLC -0.518 0.151
## InjectinPBS -0.155 0.481 0.145
## SizeEnd -0.696 0.051 0.015 0.011
## TrnCLC:OCLC 0.085 -0.699 -0.217 -0.337 0.033
## TrnCLC:IPBS 0.102 -0.684 -0.103 -0.713 0.004 0.481
## OrgCLC:IPBS 0.105 -0.331 -0.206 -0.688 -0.005 0.479 0.490
## TCLC:OCLC:I -0.066 0.473 0.147 0.493 -0.009 -0.676 -0.691 -0.716
## optimizer (nloptwrap) convergence code: 0 (OK)
## boundary (singular) fit: see ?isSingular6.16.7.4 Refining the model
mod2 <-
lme4::lmer(
CqActb.p ~ (TransplantContam + OriginContam + Injection) ^ 2 + SizeEnd +
(1 | CagingSite / CageSiteID) + (1| OriginSite),
data = dat2,
na.action = na.exclude
)
car::Anova(mod2, type = "3")## Analysis of Deviance Table (Type III Wald chisquare tests)
##
## Response: CqActb.p
## Chisq Df Pr(>Chisq)
## (Intercept) 4832.5358 1 < 2e-16 ***
## TransplantContam 1.5556 1 0.21232
## OriginContam 1.8664 1 0.17188
## Injection 2.3380 1 0.12625
## SizeEnd 5.3960 1 0.02018 *
## TransplantContam:OriginContam 1.0097 1 0.31497
## TransplantContam:Injection 1.1990 1 0.27351
## OriginContam:Injection 2.7838 1 0.09522 .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1summary(mod2)## Linear mixed model fit by REML ['lmerMod']
## Formula: CqActb.p ~ (TransplantContam + OriginContam + Injection)^2 +
## SizeEnd + (1 | CagingSite/CageSiteID) + (1 | OriginSite)
## Data: dat2
##
## REML criterion at convergence: -539.6
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -3.4962 -0.6592 0.0368 0.5907 2.6011
##
## Random effects:
## Groups Name Variance Std.Dev.
## CageSiteID:CagingSite (Intercept) 0.0000298 0.005459
## CagingSite (Intercept) 0.0000000 0.000000
## OriginSite (Intercept) 0.0032064 0.056625
## Residual 0.0051237 0.071580
## Number of obs: 246, groups:
## CageSiteID:CagingSite, 24; CagingSite, 4; OriginSite, 4
##
## Fixed effects:
## Estimate Std. Error t value
## (Intercept) 4.051127 0.058276 69.516
## TransplantContamLC -0.019717 0.015809 -1.247
## OriginContamLC -0.080383 0.058838 -1.366
## InjectionPBS -0.024034 0.015718 -1.529
## SizeEnd 0.009389 0.004042 2.323
## TransplantContamLC:OriginContamLC -0.018944 0.018852 -1.005
## TransplantContamLC:InjectionPBS 0.020043 0.018304 1.095
## OriginContamLC:InjectionPBS 0.030569 0.018322 1.668
##
## Correlation of Fixed Effects:
## (Intr) TrnCLC OrgCLC InjPBS SizEnd TCLC:O TCLC:I
## TrnsplntCLC -0.179
## OrignCntmLC -0.515 0.094
## InjectinPBS -0.141 0.323 0.084
## SizeEnd -0.697 0.062 0.017 0.018
## TrnCLC:OCLC 0.054 -0.584 -0.162 -0.006 0.036
## TrnCLC:IPBS 0.077 -0.560 -0.002 -0.592 -0.002 0.025
## OrgCLC:IPBS 0.083 0.012 -0.145 -0.552 -0.017 -0.010 -0.009
## optimizer (nloptwrap) convergence code: 0 (OK)
## boundary (singular) fit: see ?isSingular6.16.7.5 Refining the model
mod3 <-
lme4::lmer(
CqActb.p ~ TransplantContam + OriginContam + Injection + SizeEnd +
(1 | CagingSite / CageSiteID) + (1| OriginSite),
data = dat2,
na.action = na.exclude
)
car::Anova(mod3, type = "3")## Analysis of Deviance Table (Type III Wald chisquare tests)
##
## Response: CqActb.p
## Chisq Df Pr(>Chisq)
## (Intercept) 4897.3886 1 < 2e-16 ***
## TransplantContam 4.1955 1 0.04053 *
## OriginContam 1.7623 1 0.18434
## Injection 0.0097 1 0.92168
## SizeEnd 5.7249 1 0.01673 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1summary(mod3)## Linear mixed model fit by REML ['lmerMod']
## Formula: CqActb.p ~ TransplantContam + OriginContam + Injection + SizeEnd +
## (1 | CagingSite/CageSiteID) + (1 | OriginSite)
## Data: dat2
##
## REML criterion at convergence: -553
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -3.3786 -0.6177 -0.0041 0.6109 2.6272
##
## Random effects:
## Groups Name Variance Std.Dev.
## CageSiteID:CagingSite (Intercept) 1.954e-05 0.004421
## CagingSite (Intercept) 0.000e+00 0.000000
## OriginSite (Intercept) 3.162e-03 0.056233
## Residual 5.176e-03 0.071946
## Number of obs: 246, groups:
## CageSiteID:CagingSite, 24; CagingSite, 4; OriginSite, 4
##
## Fixed effects:
## Estimate Std. Error t value
## (Intercept) 4.0407558 0.0577405 69.981
## TransplantContamLC -0.0193609 0.0094523 -2.048
## OriginContamLC -0.0756946 0.0570200 -1.328
## InjectionPBS 0.0009043 0.0091975 0.098
## SizeEnd 0.0097049 0.0040561 2.393
##
## Correlation of Fixed Effects:
## (Intr) TrnCLC OrgCLC InjPBS
## TrnsplntCLC -0.178
## OrignCntmLC -0.508 0.001
## InjectinPBS -0.085 -0.007 0.005
## SizeEnd -0.707 0.137 0.021 0.012
## optimizer (nloptwrap) convergence code: 0 (OK)
## boundary (singular) fit: see ?isSingular6.16.7.6 Refining the model
mod4 <-
lme4::lmer(
CqActb.p ~ TransplantContam + SizeEnd +
(1 | CagingSite / CageSiteID) + (1| OriginSite),
data = dat2,
na.action = na.exclude
)
car::Anova(mod4, type = "3")## Analysis of Deviance Table (Type III Wald chisquare tests)
##
## Response: CqActb.p
## Chisq Df Pr(>Chisq)
## (Intercept) 6027.3927 1 < 2e-16 ***
## TransplantContam 4.2031 1 0.04035 *
## SizeEnd 5.6332 1 0.01762 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1summary(mod4)## Linear mixed model fit by REML ['lmerMod']
## Formula: CqActb.p ~ TransplantContam + SizeEnd + (1 | CagingSite/CageSiteID) +
## (1 | OriginSite)
## Data: dat2
##
## REML criterion at convergence: -562.7
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -3.3849 -0.6200 -0.0148 0.6192 2.6233
##
## Random effects:
## Groups Name Variance Std.Dev.
## CageSiteID:CagingSite (Intercept) 2.177e-05 0.004666
## CagingSite (Intercept) 0.000e+00 0.000000
## OriginSite (Intercept) 3.999e-03 0.063237
## Residual 5.153e-03 0.071785
## Number of obs: 246, groups:
## CageSiteID:CagingSite, 24; CagingSite, 4; OriginSite, 4
##
## Fixed effects:
## Estimate Std. Error t value
## (Intercept) 4.004158 0.051576 77.636
## TransplantContamLC -0.019377 0.009452 -2.050
## SizeEnd 0.009624 0.004055 2.373
##
## Correlation of Fixed Effects:
## (Intr) TrnCLC
## TrnsplntCLC -0.199
## SizeEnd -0.779 0.137
## optimizer (nloptwrap) convergence code: 0 (OK)
## boundary (singular) fit: see ?isSingularNow that we have identified the best model, add sex as covariate to check whether results are sensitive NB: sample size is reduced when adding sex variable within the model, for this reason the sex effect on results is checked on the final model
6.16.7.7 Test for the sex effect
dat2 = dat2[is.na(dat2$Sex) == F, ]
modSex <-
lme4::lmer(
CqActb.p ~ TransplantContam + SizeEnd + Sex +
(1 | CagingSite / CageSiteID) + (1| OriginSite),
data = dat2,
na.action = na.exclude
)
performance::check_model(modSex)
car::Anova(modSex, type = "3")## Analysis of Deviance Table (Type III Wald chisquare tests)
##
## Response: CqActb.p
## Chisq Df Pr(>Chisq)
## (Intercept) 6037.4561 1 < 2e-16 ***
## TransplantContam 3.8189 1 0.05068 .
## SizeEnd 6.0967 1 0.01354 *
## Sex 1.1895 1 0.27544
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1summary(modSex)## Linear mixed model fit by REML ['lmerMod']
## Formula:
## CqActb.p ~ TransplantContam + SizeEnd + Sex + (1 | CagingSite/CageSiteID) +
## (1 | OriginSite)
## Data: dat2
##
## REML criterion at convergence: -553
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -3.3943 -0.6446 0.0074 0.6235 2.6828
##
## Random effects:
## Groups Name Variance Std.Dev.
## CageSiteID:CagingSite (Intercept) 0.0000548 0.007403
## CagingSite (Intercept) 0.0000000 0.000000
## OriginSite (Intercept) 0.0039459 0.062816
## Residual 0.0051468 0.071741
## Number of obs: 245, groups:
## CageSiteID:CagingSite, 24; CagingSite, 4; OriginSite, 4
##
## Fixed effects:
## Estimate Std. Error t value
## (Intercept) 4.003488 0.051524 77.701
## TransplantContamLC -0.019078 0.009763 -1.954
## SizeEnd 0.010094 0.004088 2.469
## SexM -0.010466 0.009596 -1.091
##
## Correlation of Fixed Effects:
## (Intr) TrnCLC SizEnd
## TrnsplntCLC -0.199
## SizeEnd -0.778 0.136
## SexM 0.024 -0.041 -0.117
## optimizer (nloptwrap) convergence code: 0 (OK)
## boundary (singular) fit: see ?isSingularmodActb <- modSex
RmodActb <- MuMIn::r.squaredGLMM(modActb)The sex effect is significant. The modSex is thus the best model. Here, there is no interaction, and hence no posthoc test nor parallelism test to conduct
6.17 Summary of the best models for gene expression (Table 4 from the manuscript)
The following table report the results of the best models tested above, this table correspond to the Table 4 in the manuscript. The table report the marginal and conditional Rsquared (R2m and R2c respectively).| Estimate | Std. Error | t or z value | df | Chisq | p.value | ||
|---|---|---|---|---|---|---|---|
| Mtl - Metallothionein | n = 245 | R2m = 0.113 | R2c = 0.191 | |||||||
| Metal sequestration | Intercept | 1.32 | 0.237 | 5.6 | 1 | 31.3 | <0.0001 |
| Origin (LC) | -0.739 | 0.327 | -2.26 | 1 | 5.12 | <0.05 | |
| Sex (M) | -0.287 | 0.139 | -2.06 | 1 | 4.24 | <0.05 | |
| Cat - Catalase | n = 245 | R2m = 0.0582 | R2c = 0.523 | |||||||
| Antioxidant - Cat | Intercept | -3.18 | 0.221 | -14.3 | 1 | 206 | <0.0001 |
| Imm. challenge (PBS) | 0.101 | 0.0381 | 2.65 | 1 | 7.04 | <0.01 | |
| Size | 0.0516 | 0.0169 | 3.05 | 1 | 9.31 | <0.01 | |
| Sex (M) | -0.0958 | 0.0397 | -2.41 | 1 | 5.83 | <0.05 | |
| Gpx - Glutathione peroxidase | n = 245 | R2m = 0.0918 | R2c = 0.135 | |||||||
| Antioxidant - Gpx | Intercept | -1.07 | 0.101 | -10.6 | 1 | 113 | <0.0001 |
| Origin (LC) | -0.349 | 0.137 | -2.54 | 1 | 6.45 | <0.05 | |
| Sex (M) | -0.181 | 0.0788 | -2.3 | 1 | 5.29 | <0.05 | |
| Casp3 - Caspase 3 | n = 246 | R2m = 0.253 | R2c = 0.255 | |||||||
| Apoptosis effector | Intercept | -5.19 | 0.316 | -16.4 | 1 | 270 | <0.0001 |
| Origin (LC) | -0.442 | 0.0985 | -4.48 | 1 | 20.1 | <0.0001 | |
| Size | 0.217 | 0.0311 | 7 | 1 | 49 | <0.0001 | |
| Pcx - Pyruvate carboxylase | n = 239 | R2m = 0.0289 | R2c = 0.432 | |||||||
| Energy metabolism (oxaloacetate synthesis & gluconeogenesis) | Intercept | -3.26 | 0.164 | -19.8 | 1 | 392 | <0.0001 |
| Imm. challenge (PBS) | 0.122 | 0.0502 | 2.44 | 1 | 5.95 | <0.05 | |
| Sex (M) | -0.117 | 0.0526 | -2.22 | 1 | 4.92 | <0.05 | |
| Pygl - Glycogen phosphorylase | n = 226 | R2m = 0.0369 | R2c = 0.181 | |||||||
| Energy metabolism (glycogen breakdown to produce glucose) | Intercept | -2.47 | 0.0749 | -33 | 1 | 1090 | <0.0001 |
| Imm. challenge (PBS) | 0.155 | 0.049 | 3.18 | 1 | 10.1 | <0.01 | |
7 R session informations
sessionInfo()## R version 4.1.0 (2021-05-18)
## Platform: x86_64-w64-mingw32/x64 (64-bit)
## Running under: Windows 10 x64 (build 22621)
##
## Matrix products: default
##
## locale:
## [1] LC_COLLATE=French_France.1252 LC_CTYPE=French_France.1252
## [3] LC_MONETARY=French_France.1252 LC_NUMERIC=C
## [5] LC_TIME=French_France.1252
##
## attached base packages:
## [1] stats graphics grDevices utils datasets methods base
##
## loaded via a namespace (and not attached):
## [1] httr_1.4.3 tidyr_1.2.0 sass_0.4.0
## [4] jsonlite_1.7.2 viridisLite_0.4.0 splines_4.1.0
## [7] carData_3.0-4 bslib_0.3.1 datawizard_0.2.3
## [10] assertthat_0.2.1 stats4_4.1.0 highr_0.9
## [13] cellranger_1.1.0 yaml_2.2.1 bayestestR_0.11.5
## [16] ggrepel_0.9.1 pillar_1.7.0 lattice_0.20-44
## [19] glue_1.6.2 pROC_1.17.0.1 digest_0.6.27
## [22] rvest_1.0.3 minqa_1.2.4 colorspace_2.0-2
## [25] MuMIn_1.43.17 plyr_1.8.6 htmltools_0.5.2
## [28] Matrix_1.3-3 pkgconfig_2.0.3 haven_2.4.1
## [31] purrr_0.3.4 patchwork_1.1.1 scales_1.1.1
## [34] webshot_0.5.2 svglite_2.1.0.9000 openxlsx_4.2.4
## [37] rio_0.5.27 lme4_1.1-27 tibble_3.1.6
## [40] mgcv_1.8-35 generics_0.1.0 farver_2.1.0
## [43] car_3.0-10 ggplot2_3.3.5 bimixt_1.0
## [46] ellipsis_0.3.2 cli_3.2.0 magrittr_2.0.2
## [49] crayon_1.4.1 readxl_1.3.1 evaluate_0.15
## [52] fansi_0.5.0 nlme_3.1-152 MASS_7.3-54
## [55] forcats_0.5.1 xml2_1.3.2 foreign_0.8-81
## [58] tools_4.1.0 data.table_1.14.2 hms_1.1.0
## [61] lifecycle_1.0.1 see_0.6.9 stringr_1.4.0
## [64] munsell_0.5.0 zip_2.2.0 kableExtra_1.3.4.9000
## [67] compiler_4.1.0 jquerylib_0.1.4 systemfonts_1.0.4
## [70] rlang_1.0.2 grid_4.1.0 nloptr_1.2.2.2
## [73] rstudioapi_0.13 labeling_0.4.2 rmarkdown_2.14
## [76] boot_1.3-28 gtable_0.3.0 abind_1.4-5
## [79] DBI_1.1.1 curl_4.3.1 R6_2.5.0
## [82] knitr_1.39 dplyr_1.0.8 performance_0.8.0
## [85] fastmap_1.1.0 utf8_1.2.1 insight_0.16.0
## [88] stringi_1.6.1 Rcpp_1.0.7 vctrs_0.3.8
## [91] tidyselect_1.1.1 xfun_0.308 References
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Jacquin, L., Reader, S.M., Boniface, A., Mateluna, J., Patalas, I., Pérez-Jvostov, F., Hendry, A.P., 2016. Parallel and nonparallel behavioural evolution in response to parasitism and predation in Trinidadian guppies. J. Evol. Biol. 29, 1406–1422. https://doi.org/10.1111/jeb.12880.
Petitjean, Q., Jacquin, L., Riem, L., Pitout, M., Perrault, A., Cousseau, M., Laffaille, P., Jean, S., 2020a. Intraspecific variability of responses to combined metal contamination and immune challenge among wild fish populations. Environ. Pollut. 116042. https://doi.org/10.1016/j.envpol.2020.116042.
Petitjean, Q., Jean, S., Côte, J., Larcher, T., Angelier, F., Ribout, C., Perrault, A., Laffaille, P., Jacquin, L., 2020b. Direct and indirect effects of multiple environmental stressors on fish health in human-altered rivers. Sci. Total Environ. 742, 140657. https://doi.org/10.1016/j.scitotenv.2020.140657.