rm(list = ls())

library(metafor)
library(ape)
library(Matrix)


metarep<-read.csv('ReproductionMarch.csv',na.strings="NA") ##

str(metarep)

#checking outliers
#metarep<-metarep [-c( 71), ]        ##keep outliers
#metarep<-metarep [-c(25, 57, 71), ] 

# Importing modified tree, transfrom to .tre file and Contstructing tree matrix

library(ape)
treeRep<-read.tree(file="phylipReproOrgOct.phy")
write.tree(treeRep, file="MyNewickRep.tre")

treeRepmod<-read.tree(file="MyNewickRep.tre")

treeRepmod
plot(treeRepmod, cex=1)
is.binary.tree(treeRepmod)


#importing modified tree from mesquite
RepTree<-read.tree(file="MyNewickRepOct.tre.phy")
write.tree(RepTree, file="RepTreeM.tre")

RepTreeM<-read.tree(file="RepTreeM.tre")

RepTreeM
plot(RepTreeM)
is.binary.tree(RepTreeM)


###CREATING CORRELATION MATRIX###

# getting a phylogenetic correlation matrix ready
CorMatrix<-vcv(compute.brlen(RepTreeM),corr=T)
CorMatrix

# the same
CorMatrix1<-vcv(corBrownian(1,compute.brlen(RepTreeM)),corr=T)
CorMatrix1

# expanding the matrix to match the dataframe
# animal = Spp

CorExt<-as.matrix(CorMatrix[match(metarep$Animal,rownames(CorMatrix)),match(metarep$Animal, colnames(CorMatrix))])
CorExt

# create square matrix matching N of ES, filled with zeros
V <- matrix(0,nrow = dim(metarep)[1],ncol = dim(metarep)[1])
rownames(V) <- metarep$ES_ID
colnames(V) <- metarep$ES_ID


# find start and end coordinates for the subsets
shared_coord <- which(metarep$Share_Control%in%metarep$Share_Control[duplicated(metarep$Share_Control)]==TRUE)
shared_coord


# matrix of combinations of coordinates for each experiment with shared control
combinations <- do.call("rbind", tapply(shared_coord, metarep[shared_coord,"Share_Control"], function(x) t(combn(x,2))))
combinations

# calculate covariance values between Hd values at the positions in shared_list and place them on the matrix

for (i in 1:dim(combinations)[1]){
  p1 <- combinations[i,1]
  p2 <- combinations[i,2]
  p1_p2_cov <- 1/metarep[p1,"n2Control"] + (metarep[p1,"hedges_g"]*metarep[p2,"hedges_g"]) / (2*(metarep[p1,"n1Infect"]+metarep[p1,"n2Control"]))
  V[p1,p2] <- p1_p2_cov
  V[p2,p1] <- p1_p2_cov
}

# add the diagonal - use df$Vg as matrix diagonal
diag(V) <-  metarep$Vg
V[35:52,35:52]


#*********************************************************************
#TESTING RANDOM MODELS, PHYLOGENY VS. NON-PYHOGENY MODEL, estimations
#**********************************************************************

# MODEL 1 - phylogenetic model
phyl<-rma.mv(yi=hedges_g,V=V,random = list (~ 1|IDstudy, ~1|Animal, ~1|focalID,  ~1|ES_ID), R=list(Animal=CorExt), data=metarep, method="REML")
summary(phyl)

# MODEL 2 - non-phylogenetic model
nonphyl<-rma.mv(yi=hedges_g,V=V,random = list (~ 1|IDstudy, ~1|focalID, ~1|ES_ID), data=metarep, method="REML")
summary(nonphyl) 


# ML MODEL 1 - phylogenetic model
phylML<-rma.mv(yi=hedges_g,V=V,random = list (~ 1|IDstudy, ~1|Animal, ~1|focalID,  ~1|ES_ID), R=list(Animal=CorExt), data=metarep, method="ML")
summary(phylML)

# ML MODEL 2 - non-phylogenetic model
nonphylML<-rma.mv(yi=hedges_g,V=V,random = list (~ 1|IDstudy, ~1|focalID, ~1|ES_ID), data=metarep, method="ML")
summary(nonphylML) 


#plot funnel
funnel(phyl)
funnel(nonphyl)


# MODEL 1, PHYLOGENY - for this we get H2 which equals to lambda

s2m <- sum(1/metarep$Vg) * (phyl$k-1) / (sum(1/metarep$Vg)^2 - sum((1/metarep$Vg)^2))
# This gives "Measurement variance" - formula 11 in Nakagawa et al. 2012
s2m # typical sampling error

# total variance
s2t<-sum(phyl$sigma2)+s2m
s2t

I2t<-sum(phyl$sigma2)/s2t
I2t*100 # 71.27437% - total heterogeneity

I2s<-phyl$sigma2[1]/s2t
I2s*100 # 51.5699% variance due to unique study ID

I2a<-phyl$sigma2[2]/s2t
I2a*100 #  1.625937e-07% due to phylogeny

I2g<-phyl$sigma2[3]/s2t
I2g*100 # 1.407842e-08% variance due to common focal individual (group same)

I2e<-phyl$sigma2[4]/s2t
I2e*100 #  19.70447% residual against sampling error (i.e. effect-size or observation-specific variance)

H2 <-phyl$sigma2[2]/sum(phyl$sigma2)
H2 # Pagel's lambda to describe phylogenetic signal (2.281237e-09)  - close to zero.


# MODEL 2 - Non-phylo

# total variance
s2t<-sum(nonphyl$sigma2)+s2m
I2t<-sum(nonphyl$sigma2)/s2t
I2t*100 # 71.27437 % - total heterogeneity

I2s<-nonphyl$sigma2[1]/s2t
I2s*100 #   51.5699  % variance due to study

I2g<-nonphyl$sigma2[2]/s2t
I2g*100 # 3.162523e-08 variance due to common focal individual (group same)

I2e<-nonphyl$sigma2[3]/s2t
I2e*100 # 19.70447 %  residuals against sampling error (or effect-size-specific or observation-specific variance)


par(mfrow=c(1,1))

#FORESTPLOTS
#phylplot

forest(phyl, slab=paste(metarep$author, metarep$year, sep=","))
text(4,-7, "Hedges g [+/- 95% CI]", pos=2)

#forestplot nonphyl

par(mar=c(4,0,4,0))

forest0<-forest(nonphyl, slab=paste(metarep$Author, metarep$year),ilab=cbind(metarep$n1Infect, metarep$n2Control), ilab.xpos=c(16, 14), cex=0.8, ylim=c(-1, 90), order=order(metarep$Author), xlab="Hedges' g [+/- 95% CI]", mlab="")

### set font expansion factor (as in forest() above) and use bold italic
### font and save original settings in object 'op'

op <- par(cex=0.8, font=4)

### switch to bold font
par(font=2)

text(c(-19,14,16), 85, c("Authors & Year", "Nt", "Nc"))
text(24, 85, "Hedges' g", pos=2)
text(22, 84, "[+/- 95% CI]", pos=1, cex=0.9)

### set par back to the original settings

par(op)


##_________________________
#TRIM AND FILL
##__________________________

trimRep<-trimfill(phyl)

#---------------------------------------------------------------------
#Model 1 (Table S3) - "life-history stage" -- age and sex combined.
#---------------------------------------------------------------------
par(mfrow=c(1,1))

Repagesex<-rma.mv(yi=hedges_g,V=V,mods= ~factor(agesex) -1, random = list (~ 1|IDstudy, ~1|focalID, ~1|ES_ID), data=metarep, method="REML")
summary(Repagesex)

predictRepmain<-predict(Repagesex, newmods=rbind(c(1,0,0), c(0,1,0), c(0,0,1)), intercept=FALSE, digit=3)
predictRepmain


Repagesex1<-rma.mv(yi=hedges_g,V=V,mods= ~factor(agesex), random = list (~ 1|IDstudy, ~1|focalID, ~1|ES_ID), data=metarep, method="REML")
summary(Repagesex1)


#get all contrasts
predictRep<-predict(Repagesex1, newmods=rbind(c(1,0), c(0,1), c(-1,1)), intercept=FALSE, digit=4)
predictRep

predictRepC<-predict(Repagesex1, newmods=rbind(c(-1,1)), intercept=FALSE, digit=4)
predictRepC


#Forest plot of Survagesex, also showing contrast between female and male

op <- par(cex=0.8, font=2)

#trying contrasts - tweaking
forest (x=c(Repagesex$b, Repagesex1$b[2], Repagesex1$b[3], predictRepC$pred),sei=c(Repagesex$se, Repagesex1$se[2], Repagesex1$se[3], predictRepC$se), ci.lb=c(Repagesex$ci.lb, Repagesex1$ci.lb[2], Repagesex1$ci.lb[3], predictRepC$ci.lb), ci.ub=c(Repagesex$ci.ub, Repagesex1$ci.ub[2], Repagesex1$ci.ub[3], predictRepC$ci.ub), xlab="Hedges' g [+/- 95% CI]", slab=c("Male","Female","Juvenile", "Contrast (fem-male)", "Contrast (juv-male)", "Contrast (juv-fem)"),xlim=c(-5, 5), alim=c(-3.5,3.5),psize=2,cex=0.9, ylim=c(0,9))


text(c(-4.3), 6.7, c("Life-history stage"), cex=1.1)
text(4, 6.4, "Hedges' g [+/- 95% CI]", pos=3, cex=1.1)

### set par back to the original settings

par(op)


# get PHYLOGENETIC model too
Repagesexp<-rma.mv(yi=hedges_g,V=V,mods= ~factor(agesex) -1, random = list (~ 1|IDstudy, ~1|Animal, ~1|focalID,  ~1|ES_ID), R=list(Animal=CorExt), data=metarep, method="REML")
summary(Repagesexp)

predictRepmainp<-predict(Repagesexp, newmods=rbind(c(1,0,0), c(0,1,0), c(0,0,1)), intercept=FALSE, digit=3)
predictRepmainp


Repagesex1p<-rma.mv(yi=hedges_g,V=V,mods= ~factor(agesex), random = list (~ 1|IDstudy, ~1|Animal, ~1|focalID,  ~1|ES_ID), R=list(Animal=CorExt), data=metarep, method="REML")
summary(Repagesex1p)


#get all contrasts
predictRepp<-predict(Repagesex1p, newmods=rbind(c(1,0), c(0,1), c(-1,1)), intercept=FALSE, digit=4)
predictRepp

predictRepCp<-predict(Repagesex1p, newmods=rbind(c(-1,1)), intercept=FALSE, digit=4)
predictRepCp



#..............................
# Model 2 - Treatment agent details (Table S4) -- Replicating Bacteria or virus vs. Other elicitor (e.g. LPS, implant, heat
#-killed, PHA), implant
#..............................

RepIA<-rma.mv(yi=hedges_g,V=V,mods= ~factor(infectionAgent)-1, random = list (~ 1|IDstudy, ~1|focalID, ~1|ES_ID),data=metarep, method="REML")
summary(RepIA)


predictRepIA<-predict(RepIA, newmods=rbind(c(1,0), c(0,1)), digit=4)
predictRepIA

RepIA1<-rma.mv(yi=hedges_g,V=V,mods= ~factor(infectionAgent), random = list (~ 1|IDstudy, ~1|focalID, ~1|ES_ID), data=metarep, method="REML")
summary(RepIA1)

predictRepIA1<-predict(RepIA1, newmods=rbind(c(0,1)), intercept=FALSE)
predictRepIA1



#forest plot

op <- par(cex=0.8, font=2)

## alternative forest plot
forest(x=c(RepIA$b,RepIA1$b[2]),sei=c(RepIA$se,RepIA1$se[2]), ci.lb=c(RepIA$ci.lb,RepIA1$ci.lb[2]), 
  ci.ub=c(RepIA$ci.ub,RepIA1$ci.ub[2]), xlab="Hedges' g [+/- 95% CI]", slab=c("Non-replic. agent","Replic. agent","Contrast (Replic. - Non-replic.)"),xlim=c(-4, 4), ylim=c(0.5, 5.6), alim=c(-3.5,3.5),psize=2,cex=1.0)


text(c(-3.4), 3.4, c("Treatment agent"), cex=1.1)
text(3.2, 3.3, "Hedges' g [+/- 95% CI]", pos=3, cex=1.1)

### set par back to the original settings

par(op)



#PHYLOGENETIC model too
RepIAp<-rma.mv(yi=hedges_g,V=V,mods= ~factor(infectionAgent)-1, random = list (~ 1|IDstudy, ~1|Animal, ~1|focalID,  ~1|ES_ID), R=list(Animal=CorExt),data=metarep, method="REML")
summary(RepIAp)


predictRepIAp<-predict(RepIAp, newmods=rbind(c(1,0), c(0,1)), digit=4)
predictRepIAp

RepIA1p<-rma.mv(yi=hedges_g,V=V,mods= ~factor(infectionAgent), random = list (~ 1|IDstudy, ~1|Animal, ~1|focalID,  ~1|ES_ID), R=list(Animal=CorExt), data=metarep, method="REML")
summary(RepIA1p)



#..............................
# Model 3 (Table S5) - Vertebrate and invertebrate
#..............................

RepInvertvert<-rma.mv(yi=hedges_g,V=V,mods= ~factor(invertvert)-1, random = list(~ 1 | IDstudy, ~1|focalID, ~1|ES_ID ), data=metarep, method="REML")
summary(RepInvertvert)

predictInvertrep<-predict(RepInvertvert, newmods=rbind(c(1,0), c(0,1)), intercept=FALSE)
predictInvertrep

RepInvertvert1<-rma.mv(yi=hedges_g,V=V,mods= ~factor(invertvert), random = list (~ 1 | IDstudy, ~1|focalID, ~1|ES_ID ), data=metarep, method="REML")
summary(RepInvertvert1)

predictInvertrep1<-predict(RepInvertvert1, newmods=rbind(c(0,1)), intercept=FALSE)
predictInvertrep1


#forest plot

op <- par(cex=0.8, font=2)

## alternative forest plot
forest(x=c(RepInvertvert$b,RepInvertvert1$b[2]),sei=c(RepInvertvert$se,RepInvertvert1$se[2]), ci.lb=c(RepInvertvert$ci.lb,RepInvertvert1$ci.lb[2]), 
  ci.ub=c(RepInvertvert$ci.ub,RepInvertvert1$ci.ub[2]), xlab="Hedges' g", slab=c("Invertebrates","Vertebrates","Contrast (Vert-Invert)"),xlim=c(-4, 4), ylim=c(0.5, 5.6), alim=c(-3.5,3.5),psize=2,cex=1.0)


text(c(-3.1), 3.4, c("Animal kingdom group"), cex=1.1)
text(3.2, 3.3, "Hedges' g [+/- 95% CI]", pos=3, cex=1.1)

### set par back to the original settings

par(op)



#....................................................................
##MODEL 4 - FULL MODEL WITH ALL MODERATORS (MAIN EFFECT MODEL) (Table S6a) - because of insufficient data we did not test the interaction here (not data in each cell)
#.....................................................................

#Non-phylogenetic model
RepFull<-rma.mv(yi=hedges_g,V=V, mods= ~  factor(agesex)+factor(infectionAgent), random = list(~ 1 | IDstudy, ~1|focalID, ~1|ES_ID ), data=metarep, method="REML")
summary(RepFull)

funnelMeta<-funnel(RepFull)


#Phylogenetic model (Table S6b)
RepPhylFull<-rma.mv(yi=hedges_g,V=V, mods= ~ factor(agesex)+factor(infectionAgent), random = list (~ 1|IDstudy, ~1|Animal,~1|focalID, ~1|ES_ID), R=list(Animal=CorExt), data=metarep, method="REML")
summary(RepPhylFull)

funnelMeta<-funnel(RepPhylFull)

# ML for AIC..........................................
#Non-phylogenetic model
RepFullML<-rma.mv(yi=hedges_g,V=V, mods= ~  factor(agesex)+factor(infectionAgent), random = list(~ 1 | IDstudy, ~1|focalID, ~1|ES_ID ), data=metarep, method="ML")
summary(RepFullML)


#Phylogenetic model (Table S8b)
RepPhylFullML<-rma.mv(yi=hedges_g,V=V, mods= ~ factor(agesex) +factor(infectionAgent), random = list (~ 1|IDstudy, ~1|Animal,~1|focalID, ~1|ES_ID), R=list(Animal=CorExt), data=metarep, method="ML")
summary(RepPhylFullML)


#............................................................
#FOREST PLOT NON-PHYL FULL MODEL NO INTERACTIONS

#Non-phylogenetic model
RepFullC<-rma.mv(yi=hedges_g,V=V, mods= ~  factor(agesex)+factor(infectionAgent)-1, random = list(~ 1 | IDstudy, ~1|focalID, ~1|ES_ID ), data=metarep, method="REML")
summary(RepFullC)

predContr<-predict(RepFullC, newmods=rbind(c(0, -1, 1, 0)))
predContr

op <- par(cex=0.8, font=2)

#plot WITHOUT THE INTERCEPT
forest(x=c(RepFull$b[2], RepFull$b[3], predContr$pred, RepFull$b[4]),sei=c(RepFull$se[2], RepFull$se[3],
      predContr$se, RepFull$se[4]), ci.lb=c(RepFull$ci.lb[2], RepFull$ci.lb[3], predContr$ci.lb,RepFull$ci.lb[4]),
      ci.ub=c(RepFull$ci.ub[2],RepFull$ci.ub[3], predContr$ci.ub, RepFull$ci.ub[4]),xlab="Hedges' g", 
      slab=c("male-fem","juv-fem","juv-male", "" ),font=1, xlim=c(-7, 7),
       ylim=c(-0.2, 7), alim=c(-3.5,3.5),psize=1.5,cex=1.0)

addpoly(nonphyl, row=0, cex=1.0, mlab="Meta-analytic mean", font=4)

text(c(-6.0), 4.7, c("Life-history stage"), cex=1.0)
text(c(-6.0), 1.0, c("Treatment agent"), cex=1.0)
text(c(-4.2), 1.0, c("(repl-nonrepl)"), font=1, cex=1.0)
text(c(-6.2), 5.3, c("Moderator"), cex=1.1)
text(5.5, 5.1, "Hedges' g [+/- 95% CI]", pos=3, cex=1.2)
abline(h=0.4, lwd=1, col="black", lty=3)
title(outer=FALSE, main="REPRODUCTION FULL DATA", line=-7.2)

### set par back to the original settings
par(op)


library(bbmle)
AICtab(RepPhylFullML, RepFullML, RepFullinvertML) #Because the model is better without invertvert, we proceed to work with main effects that do not include that


#Calculate I2 for SurvFullmain and SurvFullPhylmain (Table S7)
#------------------------------------
# SurvFullPhyl - get H2 which equals to lambda

s2m <- sum(1/metarep$Vg) * (RepPhylFull$k-1) / (sum(1/metarep$Vg)^2 - sum((1/metarep$Vg)^2))
s2m # typical sampling error

# total variance
s2t<-sum(RepPhylFull$sigma2)+s2m
s2t

I2t<-sum(RepPhylFull$sigma2)/s2t
I2t*100 # total heterogeneity 

I2s<-RepPhylFull$sigma2[1]/s2t
I2s*100 # variance due to unique study

I2a<-RepPhylFull$sigma2[2]/s2t
I2a*100 # due to phylogeny

I2f<-RepPhylFull$sigma2[3]/s2t
I2f*100 # variance due to common focal individual


I2e<-RepPhylFull$sigma2[4]/s2t
I2e*100 # residuals against sampling error

H2 <-RepPhylFull$sigma2[2]/sum(RepPhylFull$sigma2)
H2 # lamdba - close to zero


# SurvFullmain non-phylo
# total variance

# total variance
s2t<-sum(RepFull$sigma2)+s2m
I2t<-sum(RepFull$sigma2)/s2t
I2t*100 #  total heterogeneity

I2s<-RepFull$sigma2[1]/s2t
I2s*100 #  variance due to study

I2f<-RepFull$sigma2[2]/s2t
I2f*100 # 0 variance due to focal individual

I2e<-RepFull$sigma2[3]/s2t
I2e*100 #  residuals against sampling error (or effect-size-specific//observation-specific variance)


# Calculate R2
#--------------------------------

#Non-phylogenetic model
full<-rma.mv(yi=hedges_g,V=V, mods= ~ factor(agesex)+factor(infectionAgent), random = list(~ 1 | IDstudy, ~1|focalID, ~1|ES_ID ), data=metarep, method="REML")
summary(full)

null<-rma.mv(yi=hedges_g,V=V, random = list(~ 1 | IDstudy, ~1|focalID, ~1|ES_ID ), data=metarep, method="REML")
summary(null)


R2m<-(sum(null$sigma2)-sum(full$sigma2))/sum(null$sigma2)
100*R2m #  % accounted for (marginal) - by fixed effects

R2c<-(sum(null$sigma2)-full$sigma2[3])/sum(null$sigma2)
100*R2c # % accounted for (conditional) - by fixed and random effects

sum(null$sigma2)
sum(full$sigma2)


table(metarep$matingStatus, metarep$infectionAgent)
table(metarep$matingStatus2, metarep$agesex)


#....................................................................
##MODEL 5 - FULL MODEL WITH ALL MODERATORS incl. INVERTVERT (MAIN EFFECT MODEL) (Table S8)
#.....................................................................

#Non-phylogenetic model
RepFullinvert<-rma.mv(yi=hedges_g,V=V, mods= ~  factor(agesex)+factor(infectionAgent)+factor(invertvert), random = list(~ 1 | IDstudy, ~1|focalID, ~1|ES_ID ), data=metarep, method="REML")
summary(RepFullinvert)

RepFullinvertML<-rma.mv(yi=hedges_g,V=V, mods= ~  factor(agesex)+factor(infectionAgent)+factor(invertvert), random = list(~ 1 | IDstudy, ~1|focalID, ~1|ES_ID ), data=metarep, method="REML")
summary(RepFullinvertML)



#***************************************************************************************
#........................................................................................
##CHECKING FUNNEL ASSUMETRY AND EGGER'S REGRESSION WITH MCMCglmm - META-ANALYTIC MODEL
#........................................................................................
#***************************************************************************************


prior<-list(R=list(V=1,nu=0),G=list(G1=list(V=1, nu=1, alpha.mu=0, alpha.V=1000), G2=list(V=1, nu=1, alpha.mu=0, alpha.V=1000), G3=list(V=1,fix=1))) # put a very small #number for R (nu=1*10^-7) because the initial parameter-expanded V=1, nu=0 didn't run - asked for a stronger prior)

prior1<-list(R=list(V=1,nu=0.002),G=list(G1=list(V=1, nu=1, alpha.mu=0, alpha.V=1000),G2=list(V=1, nu=1, alpha.mu=0, alpha.V=1000), G3=list(V=1,fix=1))) # parameter expanded prior #(close to non-informative, also parameter-expanded prior; USE THIS, PRODUCES BEST GRAPHS)


prior2<-list(R=list(V=1,nu=0.002),G=list(G1=list(V=1, nu=0.002),G2=list(V=1, nu=1, alpha.mu=0, alpha.V=1000), G3=list(V=1,fix=1))) 
#inverse-Gamma prior. slightly informative


#playing around with some other priors...

prior3<-list(R=list(V=1,nu=0.002),G=list(G1=list(V=1, nu=1, alpha.mu=0.002, alpha.V=1000),G2=list(V=1, nu=1, alpha.mu=0, alpha.V=1000), G3=list(V=1,fix=1))) 

prior4<- list(R=list(V=1,nu=0.0000001),G=list(G1=list(V=1, nu=0),G2=list(V=1, nu=1, alpha.mu=0, alpha.V=1000), G3=list(V=1,fix=1))) 

prior5<- list(R=list(V=1,nu=0.0000001),G=list(G1=list(V=1, nu=0.02),G2=list(V=1, nu=1, alpha.mu=0, alpha.V=1000), G3=list(V=1,fix=1))) 


#*********************************************
#EGGERS prediction meta-analytic model
#*********************************************
library(MCMCglmm)

AinvG <- solve(V)
AnivG <- as(AinvG,"dgCMatrix")

metaMC<-MCMCglmm(hedges_g ~ 1, random = ~IDstudy+focalID+ES_ID, data=metarep, verbose=T,nitt=13000*50,thin=50, burnin=3000*50, prior=prior1, pr=T, ginverse=list(ES_ID = AnivG))
summary(metaMC)

plot(metaMC$Sol[,1]) # fixed effeinversects - just intercept (first row is the intercept). 
plot(metaMC$VCV) # random effects (i.e. the posterior distribution for the variance component [unit is the residual effect])

autocorr(metaMC$VCV)


#EGGERS
Prediction<-predict(metaMC, marginal=~ES_ID) ##predicted values for subset effect size ID to explore bias between effect sizes

Precision<-sqrt(1/metarep$Vg)
MR<-metarep$hedges_g-Prediction
zMR<-MR*Precision
# Egger's regression
Egger<-lm(zMR~Precision)
summary(Egger) ##the intercept is not signficant - no evidence of funnel asymetry, which supports the general trend of the graph


#do trim and fill on residuals
res.model<-rma(yi=MR, vi=Vg, data=metarep)
trimMOrph<-trimfill(res.model)
summary(trimMOrph)

L0.TF<-trimfill(res.model, estimator="L0")
summary(L0.TF)

R0.TF<-trimfill(res.model, estimator="R0")
summary(R0.TF)

par(mfrow=c(1,2))
funnel(L0.TF)
funnel(R0.TF)

#PHYLOGENETIC MODEL FOR Eggers and TRIM AND FILL

names(metarep)[7]<-"animal" # change name of "Animal" column to "animal" to be compatible with MCMCglmm

#expand prior to include Animal
prior1<-list(R=list(V=1,nu=0.002),G=list(G1=list(V=1, nu=1, alpha.mu=0, alpha.V=1000),G2=list(V=1, nu=1, alpha.mu=0, alpha.V=1000),G3=list(V=1, nu=1, alpha.mu=0, alpha.V=1000), G4=list(V=1,fix=1))) # parameter expanded prior #(close to non-informative, also parameter-expanded prior; USE THIS, PRODUCES BEST GRAPHS AND GOOD OUTCOME)


metaMCp<-MCMCglmm(hedges_g ~ 1, random = ~IDstudy+animal+ focalID+ES_ID, data=metarep, pedigree = RepTreeM, verbose=T,nitt=13000*50,thin=50, burnin=3000*50, prior=prior1, pr=T, ginverse=list(ES_ID = AnivG))
summary(metaMCp)

#Eggers phylo model
Predictionp<-predict(metaMCp, marginal=~ES_ID) ##predicted values for subset effect size ID to explore bias between effect sizes

Precisionp<-sqrt(1/metarep$Vg)
MRp<-metarep$hedges_g-Predictionp
zMRp<-MRp*Precisionp
# Egger's regression
Eggerp<-lm(zMRp~Precisionp)
summary(Eggerp) ##the intercept is not signficant - no evidence of funnel asymetry, which supports the general trend of the graph

#do trim and fill on residuals non-phylo model
res.modelp<-rma(yi=MRp, vi=Vg, data=metarep)
trimMOrphp<-trimfill(res.modelp)
summary(trimMOrphp)

L0.TFp<-trimfill(res.modelp, estimator="L0")
summary(L0.TFp)

R0.TFp<-trimfill(res.modelp, estimator="R0")
summary(R0.TFp)

par(mfrow=c(2,2))
funnel(L0.TF, main="Non-phylogenetic, estimate L0", xlab="Hedges g (residuals)", ylab="SE", pch=16, cex=0.8)
funnel(R0.TF, main="Non-phylogenetic, estimate R0", xlab="Hedges g (residuals)", ylab="SE", pch=16, cex=0.8)
funnel(L0.TFp, main="Phylogenetic, estimate L0", xlab="Hedges g (residuals)", ylab="SE", pch=16, cex=0.8)
funnel(R0.TFp, main="Phylogenetic, estimate R0", xlab="Hedges g (residuals)", ylab="SE", pch=16, cex=0.5)


#Gelman-Rubin stats
metaMC1<-MCMCglmm(hedges_g ~ 1, random= ~ IDstudy+focalID+ES_ID, data=metarep, verbose=T,nitt=13000*50,thin=50, burnin=3000*50, prior=prior1, pr=T, ginverse=list(ES_ID = AnivG))
summary(metaMC1)

metaMC2<-MCMCglmm(hedges_g ~ 1, random= ~ IDstudy+focalID+ES_ID, data=metarep, verbose=T,nitt=13000*50,thin=50, burnin=3000*50, prior=prior1, pr=T, ginverse=list(ES_ID = AnivG))
summary(metaMC2)


### Gelman-Rubin diagnostic
gelman.diag(list(metaMC$Sol[,1],metaMC1$Sol[,1],metaMC2$Sol[,1]))
gelman.diag(list(metaMC$VCV[,c(1,2,4)],metaMC1$VCV[,c(1,2,4)],metaMC2$VCV[,c(1,2,4)]))
gelman.diag(list(metaMC$Deviance,metaMC1$Deviance,metaMC2$Deviance))
# All of these are 1 EXACTLY (OR CLOSE TO), indicating very good convergence between runs



#################################################
# GETTING ready for MCMCglmm - metaregression
#################################################

metarep2<-with(metarep,data.frame(hedges_g,Vg,Share_Control,agesex, invertvert, infectionAgent,matingStatus,matingStatus1, matingStatus2, IDstudy,focalID, Animal, ES_ID,n1Infect,n2Control))

summary(metarep2)

Sub<-which(complete.cases(metarep2)==T)
metarep2<-metarep2[Sub,]
str(metarep2)

# preparing for V2

# create square matrix matching N of ES, filled with zeros
V2 <- matrix(0,nrow = dim(metarep2)[1],ncol = dim(metarep2)[1])
rownames(V2) <- metarep2$ES_ID
colnames(V2) <- metarep2$ES_ID

# find start and end coordinates for the subsets
shared_coord <- which(metarep2$Share_Control%in%metarep2$Share_Control[duplicated(metarep2$Share_Control)]==TRUE)
shared_coord


# matrix of combinations of coordinates for each experiment with shared control
combinations <- do.call("rbind", tapply(shared_coord, metarep2[shared_coord,"Share_Control"], function(x) t(combn(x,2))))
combinations

for (i in 1:dim(combinations)[1]){
  p1 <- combinations[i,1]
  p2 <- combinations[i,2]
  p1_p2_cov <- 1/metarep2[p1,"n2Control"] + (metarep2[p1,"Vg"]*metarep2[p2,"Vg"]) / (2*(metarep2[p1,"n1Infect"]+metarep2[p1,"n2Control"]))
  V2[p1,p2] <- p1_p2_cov
  V2[p2,p1] <- p1_p2_cov
}

diag(V2) <-  metarep2$Vg

V2[35:52,35:52]

#preparations finished

# getting V ready for MCMCglmm - meta-regression
AinvG1 <- solve(V2)
AnivG1 <- as(AinvG1,"dgCMatrix")


library(MCMCglmm)

metaMCfull<-MCMCglmm(hedges_g ~ factor(agesex)+factor(infectionAgent), random= ~ IDstudy+focalID+ES_ID, data=metarep2, verbose=T,nitt=13000*50,thin=50, burnin=3000*50, prior=prior1, pr=T, ginverse=list(ES_ID = AnivG1))
summary(metaMCfull)

#Eggers prediction
Prediction1<-predict(metaMCfull, marginal=~ES_ID) ##predicted values for subset effect size ID to explore bias between effect sizes

Precision1<-sqrt(1/metarep2$Vg)
MR1<-metarep2$hedges_g-Prediction1
zMR1<-MR1*Precision1
# Egger's regression
Egger1<-lm(zMR1~Precision1)
summary(Egger1) ##the intercept is not signficant - no evidence of funnel asymetry, which support the general trend of the graph


#RE-RUNNING FOR GELMAN-RUBIN STATISTICS
metaMCfull1<-MCMCglmm(hedges_g ~ agesex + infectionAgent, random= ~ IDstudy+focalID+ES_ID, data=metarep2, verbose=T,nitt=13000*50,thin=50, burnin=3000*50, prior=prior1, pr=T, ginverse=list(ES_ID = AnivG1))
summary(metaMCfull1)

metaMCfull2<-MCMCglmm(hedges_g ~ agesex + infectionAgent, random= ~ IDstudy+focalID+ES_ID, data=metarep2, verbose=T,nitt=13000*50,thin=50, burnin=3000*50, prior=prior1, pr=T, ginverse=list(ES_ID = AnivG1))
summary(metaMCfull2)


### Gelman-Rubin diagnostic
gelman.diag(list(metaMCfull$Sol[,1],metaMCfull1$Sol[,1],metaMCfull2$Sol[,1]))
gelman.diag(list(metaMCfull$VCV[,c(1,2,4)],metaMCfull1$VCV[,c(1,2,4)],metaMCfull2$VCV[,c(1,2,4)]))
gelman.diag(list(metaMCfull$Deviance,metaMCfull1$Deviance,metaMCfull2$Deviance))
# All of these are 1 EXACTLY (OR LOSE TO), indicating very good convergence between runs


#************************
#R^2 from MCMCglmm
#************************
mFixed <- mean(metaMCfull$Sol[,2]) * metaMCfull$X[, 2] + mean(metaMCfull$Sol[, 3]) * metaMCfull$X[, 3] + mean(metaMCfull$Sol[ ,4]) * metaMCfull$X[, 4]

#Calculation of the variance of the fitted values
mVarF<- var(mFixed)
mVarF

#MCMCglmm -marginal 
mVarF/(mVarF+sum(apply(metaMCfull$VCV,2,mean)[-3]))  

# MCMCglmm - conditional
(mVarF+sum(apply(metaMCfull$VCV,2,mean)[-3:-4]))/(mVarF+sum(apply(metaMCfull$VCV,2,mean)[-3]))



#SAME ANALYSIS BUT INCLUDING INVERTVERT
metaMCfulli<-MCMCglmm(hedges_g ~ agesex + infectionAgent+invertvert, random= ~ IDstudy+focalID+ES_ID, data=metarep2, verbose=T,nitt=13000*50,thin=50, burnin=3000*50, prior=prior1, pr=T, ginverse=list(ES_ID = AnivG1))
summary(metaMCfulli)

mFixedi <- mean(metaMCfulli$Sol[,2]) * metaMCfulli$X[, 2] + mean(metaMCfulli$Sol[, 3]) * metaMCfulli$X[, 3] + mean(metaMCfulli$Sol[ ,4]) * metaMCfulli$X[, 4] +mean(metaMCfulli$Sol[ ,5]) * metaMCfulli$X[, 5]

#Calculation of the variance of the fitted values
mVarFi<- var(mFixedi)
mVarFi

#MCMCglmm -marginal 
mVarFi/(mVarFi+sum(apply(metaMCfulli$VCV,2,mean)[-3]))  

# MCMCglmm - conditional
(mVarFi+sum(apply(metaMCfulli$VCV,2,mean)[-3:-4]))/(mVarFi+sum(apply(metaMCfulli$VCV,2,mean)[-3]))



#PLOTS

# plot funnel plot with precision on y-axis META-REGRESSION  FULL MAIN MODEL

par(mfrow=c(1,1))

par(mfrow=c(2,2))

funnel(nonphyl, main="Meta-analytic model Metafor original", xlab="Hedges' g", ylab="SE", pch=16, cex=0.8)

plot(metarep$hedges_g, Precision, xlab="Hedges' g", ylab="Precision (1/SE)", xlim=c(-7, 7), pch=16, cex=0.8)
abline(v=mean(metaMC$Sol[,1]),lwd=1, lty=1) # mcmc mean
abline(v=  -0.1315, col="red", lwd=1, lty=3) # metafor mean 
abline(v=0, col="black", lwd=1, lty=2) # metafor no effect
title(main="Meta-analytic model Metafor Precision")

#plot of residuals from MCMC
plot(MR, Precision, xlab="Hedges' g (residuals)", ylab="Precision (1/SE)", xlim=c(-7, 7), pch=16, cex=0.8)
abline(v=0,lwd=1, lty=2) #no effect
title(main="Meta-analytic model Reproduction (MCMC)")

#plot of residuals Meta-regression 
plot(MR1,Precision1, xlab="Hedges' g (residuals)", ylab="Precision (1/SE)" , xlim=c(-7, 7), pch=16, cex=0.8)
abline(v=0,lwd=1, lty=2) #no effect
title(main="Meta-regression model MCMC")


#*****************************************************************
#FOREST PLOT UNIVARIATE TESTS COMBINED
#*****************************************************************
op <- par(cex=0.8, font=2)

#trying contrasts - tweaking
forest (x=c(RepIA1$b[2], RepIA$b[2], RepIA$b[1],predictRepC$pred,Repagesex1$b[3], Repagesex1$b[2], Repagesex$b[3], 
  Repagesex$b[2],Repagesex$b[1]),sei=c(RepIA1$se[2], RepIA$se[2], RepIA$se[1],predictRepC$se,Repagesex1$se[3], Repagesex1$se[2], Repagesex$se[3], 
  Repagesex$se[2],Repagesex$se[1]), ci.lb=c(RepIA1$ci.lb[2], RepIA$ci.lb[2], RepIA$ci.lb[1],predictRepC$ci.lb,Repagesex1$ci.lb[3], Repagesex1$ci.lb[2], Repagesex$ci.lb[3],Repagesex$ci.lb[2],Repagesex$ci.lb[1]), 
  ci.ub=c(RepIA1$ci.ub[2], RepIA$ci.ub[2], RepIA$ci.ub[1],predictRepC$ci.ub,Repagesex1$ci.ub[3], Repagesex1$ci.ub[2], Repagesex$ci.ub[3],Repagesex$ci.ub[2],Repagesex$ci.ub[1]), 
  xlab="Hedges g",slab=c("Contrast (Replic. - Non-replic.)","Replic. agent", "Non-replic. agent","Contrast (juv-fem)", "Contrast (juv-male)" ,"Contrast (fem-male)" ,
        "Juvenile", "Female", "Male"),alim=c(-3.5,3.5),psize=2,cex=0.9, ylim=c(-1.5,13), rows=c(-1:1, 4:9))

### switch to bold font
par(font=4)

text(c(-3.0), 11.5, c("MODERATOR"), cex=1.2,font=2)
text(2.8, 11.2, "Hedges' g [+/- 95% CI]", pos=3, cex=1.2, font=2)
text(-2.9, 9.8, "Life-history stage", pos=3, cex=1.1)
text(-3.0, 1.8, "Treatment agent", pos=3, cex=1.1)
text(-3.2, 12.9, "(b)", pos=2, cex=1.5, font=2)

### set par back to the original settings

par(op)