---
title: 'D. galeata & Fish Kairomones -part II: adaptive potential-'
author: "Verena Tams"
date: "July 2018"
output: html_document
---

In this second part of the analysis I test for the adaptive potential (response ~ treatment * pop + (treatment|pop/clone) +(1|round)). I use a linear mixed effect model and test wether a random intercept or random slope model is appropriate.

I define a significant interaction of presence of predator and genotype origin ('EnvironmentxPopulation') as an indication for the possible presence of local adaptation for a predator environment.

For hypothesis testing (significant 'Environment x Population' interaction) I use the function Anova(model, type=2). This test performs a Wald Chi-Square-Test with the underlying null hypothesis that there is no significant interaction between the two explanatory variables.

```{r SetWd}
#setwd()
```

```{r LoadData, warning=FALSE}
#load data
FKn15<- read.table("./Input/FKmaster.txt", header = T)
FKn15.no0<- FKn15[ which(FKn15$AFR > 5), ]
rates<- read.table("./Input/surv_repro_relfit.txt", header = T)
FKn15.no_na<- subset(FKn15, !is.na(length))
FKn15.no0$Indiv <- factor(1:nrow(FKn15.no0)) 
#load libraries (package)
library(lme4)
library(ordinal)
library(MASS)
library(car)
library(RVAideMemoire)
```

###Age at First Reproduction (AFR)
```{r ModelAFR}
#random slope & intercept model
AFR.model.gammap <- glmer(AFR ~ treatment * pop + (1|pop/clone), family=Gamma(link="log"), data=FKn15.no0)
AFR.model.gammap2 <- glmer(AFR ~ treatment *pop + (treatment|pop/clone), family=Gamma(link="log"), data=FKn15.no0)
anova(AFR.model.gammap, AFR.model.gammap2) #slope? ***

#random slope & intercept model plus random factor 'round'
AFR.model.gammap3 <- glmer(AFR ~ treatment *pop + (treatment|pop/clone) + (1|round), family=Gamma(link="log"), data=FKn15.no0)
AFR.null.gammap3_1 <- glmer(AFR ~ treatment + pop + (treatment|pop/clone) + (1|round), family=Gamma(link="log"), data=FKn15.no0) 
anova(AFR.null.gammap3_1, AFR.model.gammap3) #TxP? n.s. no interaction
AFR.null.gammap3_2 <- glmer(AFR ~ treatment + (treatment|pop/clone) + (1|round), family=Gamma(link="log"), data=FKn15.no0) 
anova(AFR.null.gammap3_2, AFR.model.gammap3) 
anova(AFR.model.gammap2, AFR.model.gammap3) #round? n.s.
Anova(AFR.model.gammap3, type=2)#TxP? n.s., T**
```

###Total Number of Broods (broods)
```{r ModelBroods}
# fit the model
FKn15.no0$broodsF <- factor(FKn15.no0$broods, levels = sort(unique(FKn15.no0$broods)), ordered=TRUE)

#random slope & intercept model
broods.model.clmmp <- clmm(broodsF ~ treatment * pop + (1|pop/clone), data=FKn15.no0, link="probit")
broods.model.clmmp2 <- clmm(broodsF ~ treatment*pop + (treatment|pop/clone), data=FKn15.no0, link="probit")
anova(broods.model.clmmp, broods.model.clmmp2) #slope? ***

#random slope & intercept model plus random factor 'round'
broods.model.clmmp3 <- clmm(broodsF ~ treatment*pop + (treatment|pop/clone) +(1|round), data=FKn15.no0, link="probit")
broods.null.clmmp3_1 <- clmm(broodsF ~ treatment+pop + (treatment|pop/clone) +(1|round), data=FKn15.no0, link="probit")
anova(broods.null.clmmp3_1, broods.model.clmmp3) #TxP? n.s
broods.null.clmmp3_2 <- clmm(broodsF ~ treatment + (treatment|pop/clone) +(1|round), data=FKn15.no0, link="probit")
anova(broods.null.clmmp3_2, broods.model.clmmp3) #TxP? n.s.
anova(broods.model.clmmp2, broods.model.clmmp3) #round? n.s.
Anova.clmm(broods.model.clmmp3)
```

###Total Number of Offspring (offspring)
```{r ModelOff}
#random slope & intercept model
offspring.model.glmmp <- glmer(offspring ~ treatment * pop + (1|pop/clone), data=FKn15.no0, family =poisson())
offspring.model.glmmp2 <- glmer(offspring ~ treatment * pop + (treatment|pop/clone), data=FKn15.no0, family = poisson())
anova(offspring.model.glmmp, offspring.model.glmmp2) #slope? ***

#random slope & intercept model plus random factor 'round'
offspring.model.glmmp3 <- glmer(offspring ~ treatment * pop + (treatment|pop/clone) +(1|round), data=FKn15.no0, family = poisson())
offspring.null.glmmp3_1 <- glmer(offspring ~ treatment + pop + (treatment|pop/clone)+(1|round), data=FKn15.no0, family = poisson())
anova(offspring.null.glmmp3_1,offspring.model.glmmp3) # TxP? n.s.
offspring.null.glmmp3_2 <- glmer(offspring ~ treatment + (treatment|pop/clone)+(1|round), data=FKn15.no0, family = poisson())
anova(offspring.null.glmmp3_2,offspring.model.glmmp3)
anova(offspring.model.glmmp2,offspring.model.glmmp3) #round? n.s.
Anova(offspring.model.glmmp3, type=2)#TxP? n.s., P**
```

###Total Number of Offspring of First Brood (brood1)
```{r ModelBrood1}
#random slope & intercept model
brood1.model.glmmp <- glmer(brood1 ~ treatment *pop + (1 |pop/clone), data=FKn15.no0, family=Gamma(link="log"))
brood1.model.glmmp2 <- glmer(brood1 ~ treatment * pop + (treatment|pop/clone), family=Gamma(link="log"), data=FKn15.no0)
anova(brood1.model.glmmp, brood1.model.glmmp2) #slope? ***

#random slope & intercept model plus random factor 'round'
brood1.model.glmmp3 <- glmer(brood1 ~ treatment * pop + (treatment|pop/clone) +(1|round), family=Gamma(link="log"), data=FKn15.no0)
brood1.null.glmmp3_1 <- glmer(brood1 ~ treatment + pop + (treatment|pop/clone) +(1|round), family=Gamma(link="log"), data=FKn15.no0)
anova(brood1.null.glmmp3_1, brood1.model.glmmp3) #TxP? n.s.
brood1.null.glmmp3_2 <- glmer(brood1 ~ treatment + (treatment|pop/clone) +(1|round), family=Gamma(link="log"), data=FKn15.no0)
anova(brood1.null.glmmp3_2, brood1.model.glmmp3) 
anova(brood1.model.glmmp2, brood1.model.glmmp3) #round? n.s.
Anova(brood1.model.glmmp3, type=2)#TxP? n.s., P**
```

###Survival (surv)
```{r ModelSurv}
#random slope & intercept model
surv.model.glmmp <- glmer(survived_t14 ~ treatment * pop + (1|pop/clone), data=FKn15, family = binomial(link = "logit"))
surv.model.glmmp2 <-glmer(survived_t14 ~ treatment *pop + (treatment|pop/clone), data=FKn15, family = binomial(link = "logit"))
anova(surv.model.glmmp, surv.model.glmmp2) #slope? n.s. 

#random intercept model plus random factor 'round'
surv.model.glmmp3 <- glmer(survived_t14 ~ treatment * pop + (1|pop/clone) + (1|round), data=FKn15, family = binomial(link = "logit"))
surv.null.glmmp3_1 <- glmer(survived_t14 ~ treatment +pop + (1 |pop/clone) + (1|round), data=FKn15, family = binomial(link = "logit"))
anova(surv.null.glmmp3_1,surv.model.glmmp3) #TxP? n.s.
surv.null.glmmp3_2 <- glmer(survived_t14 ~ treatment + (1 |pop/clone) + (1|round), data=FKn15, family = binomial(link = "logit"))
anova(surv.null.glmmp3_2,surv.model.glmmp3) 
anova(surv.model.glmmp,surv.model.glmmp3) #round? n.s.
Anova(surv.model.glmmp3, type=2)#TxP? n.s.
```

###relative fitness within each population (relnest)
```{r ModelRelnest}
#random slope & intercept model
relnest.model.glmmp <- glmer(relfit.nested ~ treatment * pop + (1|pop/clone), data=rates, family = Gamma(link="log"))
relnest.model.glmmp2 <- glmer(relfit.nested ~ treatment *pop + (treatment |pop/clone), data=rates, family = Gamma(link="log"))
anova(relnest.model.glmmp, relnest.model.glmmp2) #slope? ***

#random slope & intercept model plus random factor 'round'
relnest.model.glmmp3 <- glmer(relfit.nested ~ treatment *pop + (treatment |pop/clone) +(1|round), data=rates, family = Gamma(link="log"))
relnest.null.glmmp3_1 <- glmer(relfit.nested ~ treatment +pop + (treatment |pop/clone) +(1|round), data=rates, family = Gamma(link="log"))
anova(relnest.null.glmmp3_1, relnest.model.glmmp3) #TxP? n.s.
relnest.null.glmmp3_2 <- glmer(relfit.nested ~ treatment + (treatment |pop/clone)+(1|round), data=rates, family = Gamma(link="log"))
anova(relnest.null.glmmp3_2, relnest.model.glmmp3) 
anova(relnest.model.glmmp2,relnest.model.glmmp3) #round? n.s.
Anova(relnest.model.glmmp3, type=2)#TxP? n.s., P*
```

###relative fitness among all populations (relclone)
```{r ModelRelclone}
#random slope & intercept model
relclone.model.glmmp <- glmer(relfit.clone ~ treatment * pop + (1|pop/clone), data=rates, family = Gamma(link="log"))
relclone.model.glmmp2 <- glmer(relfit.clone ~ treatment *pop + (treatment |pop/clone), data=rates, family = Gamma(link="log"))
anova(relclone.model.glmmp, relclone.model.glmmp2) #slope? ***

#random slope & intercept model plus random factor 'round'
relclone.model.glmmp3 <- glmer(relfit.clone ~ treatment *pop + (treatment |pop/clone) +(1|round), data=rates, family = Gamma(link="log"))
relclone.null.glmmp3_1 <- glmer(relfit.clone ~ treatment +pop + (treatment |pop/clone) +(1|round), data=rates, family = Gamma(link="log"))
anova(relclone.null.glmmp3_1, relclone.model.glmmp3) #TxP? n.s.
relclone.null.glmmp3_2 <- glmer(relfit.clone ~ treatment + (treatment |pop/clone) +(1|round), data=rates, family = Gamma(link="log"))
anova(relclone.null.glmmp3_2, relclone.model.glmmp3) 
anova(relclone.model.glmmp2, relclone.model.glmmp3) #round? ***
Anova(relclone.model.glmmp3, type=2)#TxP? n.s., P**
```

###Somatic Growth rate (SGR)
```{r ModelSGR}
#random slope & intercept model
SGR.model.glmmp <- lmer(SGR ~ treatment * pop + (1|pop/clone), data=FKn15,REML=FALSE)
SGR.model.glmmp2 <- lmer(SGR ~ treatment*pop + (treatment|pop/clone), data=FKn15, REML=FALSE)
anova(SGR.model.glmmp, SGR.model.glmmp2) #slope? ***

#random slope & intercept model plus random factor 'round'
SGR.model.glmmp3 <- lmer(SGR ~ treatment*pop + (treatment|pop/clone) +(1|round), data=FKn15, REML=FALSE)
SGR.null.glmmp3_1 <- lmer(SGR ~ treatment + pop+ (treatment |pop/clone)+(1|round), data=FKn15, REML=FALSE)
anova(SGR.null.glmmp3_1, SGR.model.glmmp3) #TxP? n.s.
SGR.null.glmmp3_2 <- lmer(SGR ~ treatment + (treatment |pop/clone)+(1|round), data=FKn15, REML=FALSE)
anova(SGR.null.glmmp3_2, SGR.model.glmmp3) 
anova(SGR.model.glmmp2, SGR.model.glmmp3) #round? n.s.
Anova(SGR.model.glmmp3, type=2)#TxP? n.s.
```

#### Body length (size)
```{r ModelSize}
#random slope & intercept model
length.model.glmm <- glmer(length ~ treatment * pop + (1 |pop/clone), data=FKn15.no_na, family = Gamma(link="log")) 
length.model.glmm2 <- glmer(length ~ treatment *pop + (treatment|pop/clone), data=FKn15.no_na, family = Gamma(link="log"))
anova(length.model.glmm, length.model.glmm2) #slope? ***

#random slope & intercept model plus random factor 'round'
length.model.glmm3<- glmer(length ~ treatment *pop + (treatment|pop/clone) +(1|round), data=FKn15.no_na, family = Gamma(link="log"))
length.null.glmm3_1 <- glmer(length ~ treatment + pop + (treatment |pop/clone) +(1|round), data=FKn15.no_na, family = Gamma(link="log"))
anova(length.null.glmm3_1, length.model.glmm3) #TxP? n.s.
length.null.glmm3_2 <- glmer(length ~ treatment + (treatment |pop/clone) +(1|round), data=FKn15.no_na, family = Gamma(link="log"))
anova(length.null.glmm3_2, length.model.glmm3) 
anova(length.model.glmm2, length.model.glmm3) #round? n.s.
Anova(length.model.glmm3, type=2)#TxP? n.s.
```