`"ape"`

(Paradis et al 2004)

`"MCMCglmm"`

(Hadfield, 2010a)

**Meta-analysis data** (`"data_effect.txt"`

), Data frame containing the effect sizes

**Phylogeny** (`"phylo.nex"`

), Phylogeny file (NEXUS file)

Let's use the same phylogeny as in the OPM section 11.1. We have an effect size in Fisher's z-transformation of correlation coefficient per species along with corresponding sample sizes (e.g. correlations between male coloration and reproductive success):

library(ape) library(MCMCglmm) phylo<-read.nexus("phylo.nex") data<-read.table("data_effect.txt",header=TRUE) head(data)

## Zr N phylo ## 1 0.28918 13 sp_1 ## 2 0.02416 40 sp_2 ## 3 0.19514 39 sp_3 ## 4 0.09831 40 sp_4 ## 5 0.13780 66 sp_5 ## 6 0.13711 41 sp_6

In recent versions of MCMCglmm, this command might fail and require that you install and load the library "orthopolynom". As you may have noticed the syntax is pretty much the same as in the OPM section 11.1, including the sameinv.phylo <- inverseA(phylo, nodes = "ALL", scale = TRUE)prior <- list(G = list(G1 = list(V = 1, nu = 0.02)), R = list(V = 1, nu = 0.02)) model_effect <- MCMCglmm(Zr ~ 1, random = ~phylo, family = "gaussian", mev = 1/(data$N - 3), ginverse = list(phylo = inv.phylo$Ainv), prior = prior, data = data, nitt = 5e+06, burnin = 1000, thin = 500)

summary(model_effect)

## ## Iterations = 1001:4999501 ## Thinning interval = 500 ## Sample size = 9998 ## ## DIC: -320.3 ## ## G-structure: ~animal ## ## post.mean l-95% CI u-95% CI eff.samp ## animal 0.00902 0.00175 0.0193 10423 ## ## R-structure: ~units ## ## post.mean l-95% CI u-95% CI eff.samp ## units 0.00608 0.00167 0.0111 9998 ## ## Location effects: Zr ~ 1 ## ## post.mean l-95% CI u-95% CI eff.samp pMCMC ## (Intercept) 0.1589 0.0601 0.2538 9147 0.0038 ** ## --- ## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

The meta-analytic mean is and is significantly larger than zero. In meta-analysis, it is common to plot what is called a funnel plot where effect sizes are plotted with the inverse of the squared root of sampling error variance, called `precision' (Fig. 11.2). As you see, effect sizes funnel down around the meta-analytic mean. This is what we exactly expect because effect sizes with low precisions (low sample sizes) should have larger sampling errors. Here, we do not go any further with phylogenetic meta-analysis. But to follow up on this topic, you may want to see recent examples of phylogenetic meta-regression models using MCMCglmm in Horváthová et al (2012) and Prokop et al (2012). Other important issues in meta-analysis include statistical heterogeneity and publication bias (for further information, see Koricheva et al, 2013; Nakagawa and Santos, 2012).