MCMCglmm: correctly estimating phylogenetic heritability - R-SIG-mixed-models

Wed, Oct 3, 2012 4:07 AM #

Hi Iain,

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

is probably what you want to use. Presumably, you have multiple  
observations per species/population combination. In this case may want  
to interpret the residual variance as measurement error variance and  
exclude it from the denominator. Alternatively, you may interpret it  
as biological variation and include it. It depends on how you chose to  
interpret the residual variance and what you want the phylogentic  
heritability to refer to.  Note, that the fixed effects are also  
'removing' variance which may be phylogentic or not depending on the  
phylogenetic distribution of the predictors.

Cheers,

Jarrod


Quoting "Stott, Iain" <ims203 at exeter.ac.uk> on Fri, 28 Sep 2012  
15:31:49 +0000:

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



- - - - - - - - - - - -
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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Stott, Iain

Wed, Oct 17, 2012 8:37 AM #

Hi Jarrod,

Thanks for your help! I've gone with your suggestion and included the residual variance in the denominator: multiple observations per species/population combination are probably more closely associated with temporal changes in the environment so I'm more comfortable to interpret it as biological variation.

Heritability turns out to be vanishingly small. Could the DIC result be attributed partly to a skewness in the posterior for phylogeny ('animal')? Variance is small and the mean is estimated to be larger than the mode. The heritability postierior is also skewed and modal heritability is also smaller than the mean. We weren't expecting to see phylogenetic signal, so the heritability estimate helps explain the DIC result.

Do you have any ideas as to why (or how) phylogeny increases credible intervals on the mean? We've been bugged by the interpretation of this for ages.

Iain



- - - - - - - - - - - -
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/
- - - - - - - - - - - -

From: Jarrod Hadfield [j.hadfield at ed.ac.uk]
Sent: 03 October 2012 12:07
To: Stott, Iain
Cc: r-sig-mixed-models at r-project.org
Subject: Re: [R-sig-ME] MCMCglmm: correctly estimating phylogenetic heritability

Hi Iain,

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

is probably what you want to use. Presumably, you have multiple
observations per species/population combination. In this case may want
to interpret the residual variance as measurement error variance and
exclude it from the denominator. Alternatively, you may interpret it
as biological variation and include it. It depends on how you chose to
interpret the residual variance and what you want the phylogentic
heritability to refer to.  Note, that the fixed effects are also
'removing' variance which may be phylogentic or not depending on the
phylogenetic distribution of the predictors.

Cheers,

Jarrod


Quoting "Stott, Iain" <ims203 at exeter.ac.uk> on Fri, 28 Sep 2012
15:31:49 +0000:

> 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
>
>
>
> - - - - - - - - - - - -
> 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/
> - - - - - - - - - - - -
>
>
> _______________________________________________
> R-sig-mixed-models at r-project.org mailing list
> https://stat.ethz.ch/mailman/listinfo/r-sig-mixed-models
>
>



--
The University of Edinburgh is a charitable body, registered in
Scotland, with registration number SC005336.