[R-sig-ME] MCMCglmm: correctly estimating phylogenetic heritability

[Stott, Iain]

Dear all,

I am working with MCMCglmm models that include a phylogenetic component. The aim of the study is to estimate the influence of phylogeny on certain aspects of demography in plant populations.

The models are constructed as follows: 
Univariate response
One fixed factor (categorical, four levels)
Two nested random grouping factors (Population nested within Species)
Phylogenetic scaling of random effects (using a 'phylo' object and the 'animal' argument)
Default uninformative priors for fixed effects (mu=0, sigma^2=10^10)
Uninformative priors for random effects and residuals (V=1, nu=0.001)
Parameter expansion for random effects priors (I had some problems with chains sticking at 0)

DIC from models with phylogeny vs. without phylogeny are very similar, hence there are two separate sets of rival models. The only discernable effect that phylogeny has is to increase the credible intervals on the fixed effect posteriors.

Estimating a heritability factor (i.e. something akin to Pagel's lambda) could clear up how important phylogeny actually is. Hadfield & Nakagawa (2010) in J. Evol. Biol. state that this can be found using:

var(phylo)/(var(phylo)+var(residual)) .

Fitted variance for phylogeny is very small compared to species, population and residuals which could explain some of the strange results we're getting: phylogeny may be statistically important, but have a very small effect. BUT, the variance attributed to phylogeny seems to be partitioned primarily into Species in non-phylogenetic models (which makes sense). SO, is the above correct or should we actually be using something like:

var(phylo)/(var(phylo)+var(residual)+var(random effects)) ?


Hope someone can shed some light,

Iain 



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Dr. Iain Stott
Centre for Ecology and Conservation
University of Exeter, Cornwall Campus
Tremough, Treliever Road
Penryn, Cornwall, TR10 9EZ, UK.
Tel (office): 01326 371852
http://biosciences.exeter.ac.uk/staff/postgradresearch/iainstott/
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