Hi All, I have simpler, probably worse, and possibly useless suggestion. You could borrow from the rates of molecular evolution literature to do this. We often want to answer exactly these kinds of question, where the dependent variable is the rate of evolution, rather than range size. So, assuming you can estimate rates of range size evolution on the branches of your tree using some model, you could use a sister pairs or independent contrasts approach.
The simplest approach is sister pairs - just pick as many sister pairs as you can from your tree. Then for each sister pair, calculate the difference in the rate of range size evolution, and also the difference in each of your other traits (e.g. body size). You can then fit linear models on suitably transformed and standardised data. We wrote a review of how this applies to rates of molecular evolution, as well as some other approaches which might be helpful: Watching the clock: Studying variation in rates of molecular evolution between species http://www.sciencedirect.com/science/article/pii/S0169534710001461 The only slightly awkward aspect of this is that your rate estimates are calculated along a lineage, but your trait estimates are from extant organisms. This can be fixed too, using a method from this paper: Calculating independent contrasts for the comparative study of substitution rates http://www.sciencedirect.com/science/article/pii/S0022519307006522 However, it turns out that in practice it doesn't make much difference at all for rates of molecular evolution. Cheers, Rob On 12 March 2013 19:49, Sébastien Lavergne < [email protected]> wrote: > 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, 10241035. > > 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, 637643. > Venditti, C. and Pagel, M. (2008), MODEL MISSPECIFICATION NOT THE > NODE-DENSITY ARTIFACT. Evolution, 62: 2125212 > > > 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 > > ------------------------------------------------------------------------- > > > 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 > > >> > > >> _______________________________________________ > > >> R-sig-phylo mailing list - [email protected] > > >> https://stat.ethz.ch/mailman/listinfo/r-sig-phylo > > >> Searchable archive at > > >> http://www.mail-archive.com/[email protected]/ > > >> > > > > > > [[alternative HTML version deleted]] > > > > > > _______________________________________________ > > > R-sig-phylo mailing list - [email protected] > > > https://stat.ethz.ch/mailman/listinfo/r-sig-phylo > > > Searchable archive at > http://www.mail-archive.com/[email protected]/ > > > > > > > _______________________________________________ > > R-sig-phylo mailing list - [email protected] > > https://stat.ethz.ch/mailman/listinfo/r-sig-phylo > > Searchable archive at > http://www.mail-archive.com/[email protected]/ > > _______________________________________________ > R-sig-phylo mailing list - [email protected] > https://stat.ethz.ch/mailman/listinfo/r-sig-phylo > Searchable archive at > http://www.mail-archive.com/[email protected]/ > -- Rob Lanfear Research Fellow, Ecology, Evolution, and Genetics, Research School of Biology, Australian National University phone: +61 (0)2 6125 3611 www.robertlanfear.com [[alternative HTML version deleted]]
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