Hi All, Just a follow up on this. I was thinking about what Liam suggested, and I think it's a different test to what I suggested, but maybe I'm wrong.
In particular, Liam's using squared contrasts in y, so that's asking whether the absolute size of changes in y depends on x at the ancestral node. I might have missed something here, but that sounds very similar in principle to Freckleton's test of whether the variance of trait differences is unrelated to their absolute values [1], except that the latter looks for correlations between the absolute value of differences in x versus x at the ancestral node. It might be useful to consult that paper [1] to get some more ideas for how to interpret those kinds of results. However, I think that this test is not quite the same as asking whether the rate of evolution of y depends on x. For example, it's possible you could (correctly) see a relationship with Liam's test even if there was no relationship between the rate of evolution of y and x - as long as larger ancestral x's produce higher variance in y, then Liam's test will reveal a relationship. But the direction of the effect of x on the rate of y could still be completely randomly assigned among datapoints (that information disappears when squaring the y's). Not sure if I'm just confused here. Any thoughts? Rob On 16 March 2013 09:30, john d <[email protected]> wrote: > Thank you all for your ideas. I'll probably explore further Liam's method. > > sincerely, > > john > > On Tue, Mar 12, 2013 at 5:33 PM, Liam J. Revell <[email protected]> > wrote: > > I did a little further exploration of this proposed "method" - the > results & > > discussion are here: > > http://blog.phytools.org/2013/03/investigating-whether-rate-of-one.html > > > > Maybe this will be of some help in deciding the best approach to go > forward > > with. > > > > > > 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 6:03 PM, 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]] _______________________________________________ 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]/
