Hi Shinichi, Thanks so much for the prompt and detailed response. I should've reread some of that literature before writing to the list-serv.
So, what I am gathering from your answer is that it is unnecessary to co-estimate lambda and transform the tree's branch lengths by it, since lambda is implicitly always co-estimated. Hence if var(phylo) is inferred to be very small in absolute value and/or very small in proportion to the total random effect + residual variance, then lambda would be very close to zero. In any case, I'll have to do some reading to understand why the branch length transformation using lambda (or kappa or delta for that matter) that is done in the ML context isn't necessary in the Bayesian context in MCMCglmm. Perhaps it's something related to a different parameterization that makes it more computationally tractable in ML, i.e. that optimizing lambda (to infer how much variance is accounted for by the phylogeny) is easier than optimizing var(phylo) while also optimizing var(residuals) and the other random effects. Maybe optimizing lambda isn't computationally easier, but simply a different way to achieve the same goal? Thanks again, Dan. Shinichi Nakagawa wrote: > Hi, Daniel > > lamda and H^2 are equivalent as we say in Hadfield and Nakagawa (2010) > or said also in Housworth et al (2004) > > Housworth E, Martins E, Lynch M (2004) The phylogenetic mixed model. > Am Nat 163(1):8496. > > lamda = var(phylo)/(var(phylo)+var(residuals)) > > A mathematical proof of this is in Hansen and Orzack 2005 > > Hansen TF, Orzack SH (2005) Assessing current adaptation and > phylogenetic inertia as explanations of trait evolution: the need for > controlled comparisons. Evolution 59(10):20632072 > > More general verison of H^2 or lamda is > > lamda = var(phylo)/(var(phylo)+var(all other random effects + > residuals)) (probably not including measurment errors) > > Best wishes, > > Shinichi > > On 24/07/2014, at 10:51 am, Daniel Fulop <dfulop....@gmail.com > <mailto:dfulop....@gmail.com>> wrote: > >> Dear R-sig-phylo list, >> >> I'm following up on a, seemingly unaddressed question from August >> 2013 about whether or not MCMCglmm co-estimates Pagel's lambda within >> a phylogenetic regression. Seraina's original message is copied at >> bottom. >> >> From what I can tell MCMCglmm doesn't co-estimate lambda, but perhaps >> I'm missing something. If it does, then I would like to know how to >> specify that lambda be co-estimated. >> >> I have a complicated model with random effects apart from accounting >> for phylogeny that is unable to be fit by lme(); I get an >> optimization error when trying to include corPagel(fixed=FALSE) >> within the lme() call, whether I specify the non-phylogenetic random >> effects by formula or with pdMat constructors. >> >> I'm analyzing plant growth of 10 species in 2 temperatures (control >> and cold) over a timeline, where I have several plants per species >> and daily measurements over 12 days; my model is (following lme4 >> formula syntax): >> >> plant_height ~ day * temp * species + (day | ID) >> >> My goal is to estimate/predict a growth rate for each species (while >> accounting for daily variation/noise in growth rate at the individual >> plant level => hence the day | ID random effect term) to then compare >> the growth rates in cold versus control temperatures for each species >> ...to then assess which species seems most cold tolerant as measured >> by growth rate difference (cold - control) and relative growth rate >> (cold / control). >> >> As an aside, I've fit the model without random effects but with >> corPagel(fixed=FALSE)in gls() and lambda is estimated as equal to >> zero or effectively so, depending on whether the starting value is 0 >> or not. Likewise, I've fit the full mixed model without the >> phylogeny with lme() and lmer() and then analyzed the phylogenetic >> signal of the residuals with phylosig() in phytools and again lambda >> is estimated as equal to 0. So, perhaps I shouldn't worry about >> fitting a phylogenetic regression in this particular case. >> >> However, I have similar data from this and other experiments and so >> it would be ideal to find a robust way of running a phylogenetic >> mixed model regression with co-estimation of lambda, i.e. a way that >> doesn't lead to an optimization error. Perhaps MCMCglmm offers that? >> >> Thanks in advance for any input you could provide as to MCMCglmm and >> phylogenetic signal! >> Cheers, >> Dan. >> >> -- >> Daniel Fulop, Ph.D. >> Postdoctoral Scholar >> Dept. Plant Biology, UC Davis >> Maloof Lab, Rm. 2220 >> Life Sciences Addition, One Shields Ave. >> Davis, CA 95616 >> >> Original message from Seraina Graber: >> >> Dear MCMCglmm users, >> I am running a simple model corrrecting for phylogenetic >> relationships using MCMCglmm. Now I am interested in the phylogenetic >> signal, the analogue to Pagels lambda. >> Now I have two questions: >> 1.) According to Hadfield and Nakagawa (2010) the analogue to lambda >> (Pagel) in the mixed model approach is >> var(phylo)/var(phylo)+var(residuals), however, in another >> conversation about pyhlogenetic signal in MCMCglmm I found that >> actually var(phylo)/var(phylo)+var(residuals)+var(random effects) is >> the right measurement for the phylogenetic signal. But isnt the >> var(phylo) and var(random effects) basically the same, cos actually >> the pyhlogeny is the random effect in such a model? so for me rather >> var(phylo)/var(phylo) + var(residuals) makes more sense. >> My model: >> MCMCglmm(Y ~ X random=~animal, data="" pedigree=phylotree, pr=F, >> saveX=F, pl=T), X and Y are two continuous variables. >> 2.) Comparing to the PGLS function in caper, there the >> variance-covariance matrix is adjusted for the strength of the >> phylogenetic signal (estimated lambda scales the off-diagonals of the >> phylogenetic vcv matrix). Is that somehow done in the MCMCglmm >> approach? if yes, how? >> For any help I am very grateful. >> Cheers, >> Sereina >> >> _______________________________________________ >> R-sig-phylo mailing list - R-sig-phylo@r-project.org >> <mailto:R-sig-phylo@r-project.org> >> https://stat.ethz.ch/mailman/listinfo/r-sig-phylo >> Searchable archive at >> http://www.mail-archive.com/r-sig-phylo@r-project.org/ > > ________________________________ > Shinichi Nakagawa, PhD > (Associate Professor of Behavioural Ecology) > Department of Zoology > University of Otago > 340 Great King Street > P. O. Box 56 > Dunedin, New Zealand > Tel: +64-3-479-5046 > Fax: +64-3-479-7584 > http://sparrow.otago.ac.nz/ > > > > > > -- Daniel Fulop, Ph.D. Postdoctoral Scholar Dept. Plant Biology, UC Davis Maloof Lab, Rm. 2220 Life Sciences Addition, One Shields Ave. Davis, CA 95616 [[alternative HTML version deleted]]
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