Does MCMCglmm heritability correspond to lambda estimates?

mcmcglmm_lambda.R

# load required packages

require(phytools)
require(geiger)
require(MCMCglmm)

data(bird.families) 

# CASE 1: very high lambda

set.seed(1982)
phylo.effect<- fastBM(bird.families)

phylosig(bird.families, phylo.effect, method='lambda')

test.data <- data.frame(phenotype=phylo.effect, taxon=names(phylo.effect))

Ainv <- inverseA(bird.families)$Ainv

prior<-list(R=list(V=1, nu=0.002), G=list(G1=list(V=1, nu=0.002)))

model1<-MCMCglmm(phenotype~1, random=~taxon, ginverse=list(taxon=Ainv),
data=test.data, prior=prior, verbose=FALSE)

herit.1<-model1$VCV[,"taxon"]/(model1$VCV[,"taxon"]+model1$VCV[,"units"])

hist(herit.1)

posterior.mode(herit.1)

# CASE 2: very high lambda

set.seed(1982)
no.phylo.effect<- setNames(rnorm(length(bird.families$tip.label)), bird.families$tip.label)

phylosig(bird.families, no.phylo.effect, method='lambda')

test.data.2<-data.frame(phenotype=no.phylo.effect, taxon=names(no.phylo.effect))

Ainv<-inverseA(bird.families)$Ainv

model2<-MCMCglmm(phenotype~1, random=~taxon, ginverse=list(taxon=Ainv),
data=test.data.2, prior=prior, verbose=FALSE)

herit.2<-model2$VCV[,"taxon"]/(model2$VCV[,"taxon"]+model2$VCV[,"units"])

hist(herit.2)

posterior.mode(herit.2)

# CASE 3: intermediate lambda

set.seed(1982)
intermediate.phylo.effect<- fastBM(transform(bird.families, 'lambda', lambda=0.3))

phylosig(bird.families, intermediate.phylo.effect, method='lambda') # actually estimates to be 0.5

test.data.3 <- data.frame(phenotype=intermediate.phylo.effect, taxon=names(intermediate.phylo.effect))

Ainv <- inverseA(bird.families)$Ainv

model3<-MCMCglmm(phenotype~1, random=~taxon, ginverse=list(taxon=Ainv),
data=test.data.3, prior=prior, verbose=FALSE)

herit.3<-model3$VCV[,"taxon"]/(model3$VCV[,"taxon"]+model3$VCV[,"units"])

hist(herit.3)

posterior.mode(herit.3)