Hi Liam, I think you're right, and I'm wrong.
I included the reference below, which I left out of the last email. Rob [1] Freckleton, R.P. (2000) Phylogenetic tests of ecological and evolutionary hypotheses: checking for phylogenetic independence. Funct. Ecol. 14, 129134 On 16 March 2013 11:01, Liam J. Revell <[email protected]> wrote: > Hi Rob - > > Regarding your comment: "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." > > Perhaps I'm missing something, but this is exactly what we are looking for > - that is, an effect of x on the instantaneous variance of the Brownian > process of evolution in y (i.e., the "rate of evolution" in y, sensu > O'Meara et al. 2006 and other refs). > > > All the best, Liam > > Liam J. Revell, Assistant Professor of Biology > University of Massachusetts Boston > web: > http://faculty.umb.edu/liam.**revell/<http://faculty.umb.edu/liam.revell/> > email: [email protected] > blog: http://blog.phytools.org > > On 3/15/2013 7:15 PM, Rob Lanfear wrote: > >> 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] >> <mailto:[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] >> <mailto:[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<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/<http://faculty.umb.edu/liam.revell/> >> > email: [email protected] <mailto:[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/<http://faculty.umb.edu/liam.revell/> >> >> email: [email protected] <mailto:[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] >> <mailto:[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] >> <mailto:R-sig-phylo@r-project.**org <[email protected]>> >> >> >>>> >> https://stat.ethz.ch/mailman/**listinfo/r-sig-phylo<https://stat.ethz.ch/mailman/listinfo/r-sig-phylo> >> >>>> Searchable archive at >> >>>> >> http://www.mail-archive.com/r-**[email protected]/<http://www.mail-archive.com/[email protected]/> >> >>>> >> >>> >> >>> [[alternative HTML version deleted]] >> >>> >> >>> ______________________________**_________________ >> >>> R-sig-phylo mailing list - [email protected] >> <mailto:R-sig-phylo@r-project.**org <[email protected]>> >> >> >>> >> https://stat.ethz.ch/mailman/**listinfo/r-sig-phylo<https://stat.ethz.ch/mailman/listinfo/r-sig-phylo> >> >>> Searchable archive at >> >>> >> http://www.mail-archive.com/r-**[email protected]/<http://www.mail-archive.com/[email protected]/> >> >>> >> >> >> >> ______________________________**_________________ >> >> R-sig-phylo mailing list - [email protected] >> <mailto:R-sig-phylo@r-project.**org <[email protected]>> >> >> >> >> https://stat.ethz.ch/mailman/**listinfo/r-sig-phylo<https://stat.ethz.ch/mailman/listinfo/r-sig-phylo> >> >> Searchable archive at >> >> >> http://www.mail-archive.com/r-**[email protected]/<http://www.mail-archive.com/[email protected]/> >> >> >> > >> >> ______________________________**_________________ >> R-sig-phylo mailing list - [email protected] >> <mailto:R-sig-phylo@r-project.**org <[email protected]>> >> >> >> https://stat.ethz.ch/mailman/**listinfo/r-sig-phylo<https://stat.ethz.ch/mailman/listinfo/r-sig-phylo> >> Searchable archive at >> >> http://www.mail-archive.com/r-**[email protected]/<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 <http://www.robertlanfear.com> >> >> > -- 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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