Hi there,
My one-euro contribution.
Another approach can be the following one:
-you rescale the branch lenghts of your tree while keeping its topology
constant based on the pairwise (triangular) matrix of range size
differences (or range overlaps, whatever metric you choose). This tree
rescaling can be done with the optim.phylo function written by Liam.
-you get (relative) species level rates of evolution by computing
tips-to-root distances. Then you can use this rate as your new dependent
variable.
You can find an example of this approach there:
Cooper & Purvis (2009) What factors shape rates of phenotypic evolution?
A comparative study of cranial morphology of four mammalian clades.
Journal of Evolutionary Biology, 22, 1024–1035.
One drawback of this approach is apparently that these rates estimates
can tend to be higher for species that are separated from the root by a
greater number of node (with a curvilinear relationship), but you can
either test or correct for this bias. A simple linear relationship
between species rates and node density is, however, (sometimes) taken as
an evidence for punctual evolution.
More references here:
Venditti C, Meade A & Pagel M (2006) Detecting the Node-Density
Artifact in Phylogeny Reconstruction. Systematic Biology, 55, 637–643.
Venditti, C. and Pagel, M. (2008), MODEL MISSPECIFICATION NOT THE
NODE-DENSITY ARTIFACT. Evolution, 62: 2125–212
Cheers
Seb
--
-------------------------------------------------------------------------
Sébastien Lavergne
Laboratoire d'Ecologie Alpine, UMR-CNRS 5553
Université Joseph Fourier
BP 53, 38041 Grenoble Cedex 9, France
tel +33 (0)4 76 63 54 50
http://seb.lavergne.free.fr/
http://www-leca.ujf-grenoble.fr/membres/lavergne.htm
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On Mon, 2013-03-11 at 18:03 -0400, Liam J. Revell wrote:
> Hi John & Matt.
>
> What about the admittedly ad hoc approach of computing the correlation
> between the states at ancestral nodes for x & the squared contrasts for
> corresponding nodes for y? Then you can generate a null distribution for
> the test statistic (say, a Pearson or Spearman rank correlation) by
> simulation. This seems to give reasonable type I error when the null is
> correct, and when I simulate under the alternative (i.e., the rate of
> Brownian evolution along a branch depends on the state at the
> originating node) it sometimes is significant.
>
> Here's a function that does what I've described (I think - please check
> it carefully!). It needs phytools and all dependencies.
>
> ratebystate<-function(tree,x,y,nsim=100,method=c("pearson","spearman")){
> method<-method[1]
> if(!is.binary.tree(tree)) tree<-multi2di(tree)
> V<-phyl.vcv(cbind(x,y),vcv(tree),lambda=1)$R
> a<-fastAnc(tree,x)
> b<-pic(y,tree)[names(a)]^2
> r<-cor(a,b,method=method)
> beta<-setNames(lm(b~a)$coefficients[2],NULL)
> foo<-function(tree,V){
> XY<-sim.corrs(tree,V)
> a<-fastAnc(tree,XY[,1])
> b<-pic(XY[,2],tree)[names(a)]^2
> r<-cor(a,b,method=method)
> return(r)
> }
> r.null<-c(r,replicate(nsim-1,foo(tree,V)))
> P<-mean(abs(r.null)>=abs(r))
> return(list(beta=beta,r=r,P=P,method=method))
> }
>
> Perhaps this is a good idea. I don't know. All the best, Liam
>
> Liam J. Revell, Assistant Professor of Biology
> University of Massachusetts Boston
> web: http://faculty.umb.edu/liam.revell/
> email: [email protected]
> blog: http://blog.phytools.org
>
> On 3/11/2013 4:03 PM, Matt Pennell wrote:
> > John,
> >
> > This is a tricky question. If your independent variables were discrete, you
> > could use a stochastic character mapping approach to map "state regimes"
> > onto your tree and ask whether the regimes had different rates using a
> > model selection approach. (This could be done with the R packages phytools
> > or ouwie, depending on what models of trait evolution you are interested in
> > investigating).
> >
> > However, since your independent variables are continuous, there is no
> > equivalent of the stochastic mapping approach to answer this question. As
> > far as I am aware, no model-based framework exists to address your question
> > (sorry that to be a downer). One could conceivably derive such a model
> > following Rich Fitzjohn's approach in QuaSSE (Sys Bio 2010) but instead of
> > the rate of speciation/extinction depending on the state of the continuous
> > variable, let the rate of a second variable be a function of the state of
> > the first. But this would certainly be a lot of effort to accomplish.
> >
> > I agree with you as I do not think getting rates from standardized
> > independent contrasts (sensu Garland 1992) will really allow you to get at
> > your question.
> >
> > the TL;DR version is that no such method exists (at least to my knowledge)
> > but this would definitely be a useful innovation.
> >
> > hope this was at least somewhat helpful.
> >
> > cheers,
> > matt
> >
> >
> >
> >
> > On Mon, Mar 11, 2013 at 12:50 PM, john d <[email protected]> wrote:
> >
> >> Dear colleagues,
> >>
> >> I got a philosophical/methodological/practical question.
> >>
> >> I have a continuous dependent variable (e.g. range size) and a few
> >> "independent" variables (e.g. body mass, encephalization ratio), and I
> >> want to test how the rate of evolution of the dependent variable is
> >> affected by the independent variables. The PCMs that I'm familiar with
> >> cannot be used to answer this question, because they usually try to
> >> predict the dependent variable based on the independent variables
> >> (e.g. PGLM) instead of looking at the rates of evolution. The whole
> >> thing gets tricky if one decides to deal with the rates of evolution
> >> of the indepentent variables as well (or not).
> >>
> >> I guess one possibility would be to use standardized independent
> >> contrasts (as in Garland 1992) for the estimation of rates. But I'm
> >> not sure how to try to predict the *rate* of evolution of range size
> >> from the values of the "independent" variables (and not their own
> >> rates, which is what I guess I'd get if I transformed all variables
> >> into standardized contrasts).
> >>
> >> Any thoughts?
> >>
> >> John
> >>
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> >>
> >
> > [[alternative HTML version deleted]]
> >
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>
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