Hi Cody, I remember a similar discussion with Aaron some time ago. It seems difficult to interpret negative eigenvalues in the multivariate Ornstein-Uhlenbeck process, excepted maybe in some particular situations. Adaptation should result in positive values. Krzysztof Bartoszek writes a bit on it and possible interpretations in terms of character displacement or repulsion between traits (Bartoszek et al. 2012 - J. Theor. Biol.). Maybe Aaron have more idea on it? Julien
Date: Wed, 6 May 2015 10:10:10 -0400 Subject: Re: [R-sig-phylo] Off-diagonal elements in multivariate OU evolution From: [email protected] To: [email protected] CC: [email protected]; [email protected] Hi Julien and Aaron, Thank to you both for your suggestions. Julien, yes I think that is more what I am interested in, but I was (probably incorrectly) worried that an unconstrained sigma matrix might scoop up some of the signal that is actually due to an interaction in 'selection', and would therefore appear to be a good model. Do decomp="diagonal" and decomp="diagonalPositive" have different biological interpretations? What do negative values in the alpha matrix mean? __________________________________________________________________ Cody Dey [email protected] On Wed, May 6, 2015 at 9:51 AM, Julien Clavel <[email protected]> wrote: Hi Cody, Maybe in your case you are rather interested in testing whether there is significant interaction in the "selection" strength (i.e. you constrain the alpha matrix but not the sigma matrix) than testing for significant correlations between traits? e.g. mvOU(tree, data, model="OU1", param=list(decomp="diagonal")) vs. mvOU(tree, data, model="OU1", param=list(decomp="symmetricPositive")) Best, Julien > Date: Wed, 6 May 2015 08:41:04 -0400 > From: [email protected] > To: [email protected] > CC: [email protected] > Subject: Re: [R-sig-phylo] Off-diagonal elements in multivariate OU evolution > > Hi Aaron and Julien, > > Thanks for the responses. I will try different methods for computing the > log-likelihood and will report back on the list (they take a while to > run...). > > The traits are a continuous plumage ornamentation score for male and female > passerines. They way they are calculated is a bit complicated, but they > have approximately the same mean and variances, and both have a maximum > value of 100. > > A scatterplot fills in most of the space above the 1:1 line (i.e. males are > almost always more ornamented than females, but all other combinations are > possible albeit with different densities) and there is a correlation in the > raw data of R2 ~ 0.28 > > My goal is to test whether there are cross-sex genetic constraints that > limit the independent evolution of male and female ornamentation, and then > in other analyses look at sex-specific responses to different ecological > factors. It seems obvious to me that there is co-evolution of male and > female ornamentation given the correlation between the sexes (in the raw > data) and my knowledge of the system, but it would be nice to show this > statistically. > > Cody > > > > __________________________________________________________________ > > Cody Dey > [email protected] > > On Wed, May 6, 2015 at 7:00 AM, Aaron King <[email protected]> wrote: > > > Cody, > > > > Have you taken care to scale your data so that they have approximately the > > same means and variances? Sometimes numerical issues arise due to a > > mismatch of scales? What are your variables? If you plot one against the > > other, what do you see? > > > > Regarding the interpretations: a good deal depends on just what the > > variables are. The conclusion: significant off-diagonal elements -> > > coevolution is overly simplistic, but that is the general idea, yes. > > > > Aaron > > > > On Tue, May 5, 2015 at 5:17 PM, Cody Dey <[email protected]> wrote: > > > >> Hi all, > >> > >> I have a large dataset (~6000 species) including two traits of interest. I > >> am hoping to test whether the extant patterns are more consistent with > >> each > >> trait evolving independently under OU processes (with 1 regime per trait) > >> or if the traits have co-evolved in some manner (i.e. the traits influence > >> one another's optima). > >> > >> I have been trying to use mvMORPH and mvSLOUCH to fit two models (one of > >> independent evolution, and one of dependent evolution) using the code > >> below. My plan was then to compare AIC values from the two models. From > >> what I gather, the off-diagonal elements of the alpha and sigma matrix > >> determine whether there is co-evolution of the trait optima, and the > >> stochastic element of the OU processes, respectively. > >> > >> ##in mvMORPH > >> > >> independ.evolv<-mvOU(tree, data, model="OU1", > >> param=list(alpha="constraint", sigma="constraint")) > >> depend.evolv<-mvOU(tree, data, model="OU1", param=list(alpha=NULL, > >> sigma=NULL)) > >> > >> ##and a similar thing in mvSLOUCH > >> independ.evolv<-ouchModel(tree, data, regimes=NULL, Atype="Diagonal", > >> Syytype="Diagonal") > >> depend.evolv<-ouchModel(tree, data, regimes=NULL, > >> Atype="DecomposableReal", > >> Syytype="UpperTri") > >> > >> My questions are: > >> > >> 1. Is my interpretation of these models correct? Specifically I am > >> concerned about the interpretation of the alpha matrix. I am somewhat > >> confused as to how the off-diagonal alpha elements influence the OU > >> process > >> when I have specified 1 regime per trait. > >> > >> 2. I am frequently encountering errors during model fitting in mvMORPH of > >> the type"Error in loglik_mvmorph(dat, matEstim$V, matEstim$W, n, p, error > >> = > >> error, : the leading minor of order 5833 is not positive definite". I > >> gather this has to do with a problem in the matrix decomposition, but is > >> there a practical solution? I have tried some of the other 'decomp' > >> options but this does not seem to help. > >> > >> 3. I had a few emails with Krzysztof Bartoszek (author of mvSLOUCH) and he > >> suggested that such a large dataset would be problematic. Would this be an > >> issue for mvMORPH as well? If so, is there a generally acceptable > >> work-around for reducing the size of comparative data sets to accommodate > >> models like this? > >> > >> Many thanks in advance > >> > >> > >> ____________________________________________________________________________ > >> > >> Cody Dey > >> [email protected] > >> McMaster University > >> Department of Biology > >> > >> [[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]/ > >> > > > > > > > > -- > > Aaron A. King, Ph.D. > > Ecology & Evolutionary Biology > > Mathematics > > Center for the Study of Complex Systems > > University of Michigan > > GPG Public Key: 0x15780975 > > > > [[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]/ [[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]/
