Rafael and Liam -- > > So far as I know, there is currently no way to explicitly take into account > sampling error in computing principal components while also accounting for > the phylogeny. However, it is relatively straightforward to compute scores > for individuals from a PCA conducted on species means. > > This would look as follows (in which Xm is a matrix containing values for > species for each trait, and Xi is a matrix with the same number of columns > but containing values for individuals): > > pca<-phyl.pca(tree,Xm) > Si<-Xi%*%pca$Evec > > Then, if you have a separate vector containing species ID as a factor, you > could compute means and variances for each component by species.
There are methods (not all implemented in R) for taking into account the within-species phenotypic covariation among individuals and also the evolutionary covariances between species (on a phylogeny). These include the method of Ives, Midford, and Garland (2007) and my own method (2008). The former assumes you know the within-species covariance matrix, the latter estimates it from the sampled individuals for each species. Both of these assume that the true within-species phenotypic covariance matrices are the same for all species. For my method, you can use Liam's package Rphylip to call my program Contrast if you also have PHYLIP installed. Once you infer these covariance matrices, those are the relevant sufficient statistics (if the distributions are multivariate normal). The PCA axes for either covariance matrix can then be computed from those, or the canonical variates axes, which are the principal components of the between-species covariation relative to the within-species covariation. You don't need to use the PCA machinery until after you estimate these two covariance matrices. Joe ---- Joe Felsenstein j...@gs.washington.edu Department of Genome Sciences and Department of Biology, University of Washington, Box 355065, Seattle, WA 98195-5065 USA _______________________________________________ R-sig-phylo mailing list - Remail@example.com https://stat.ethz.ch/mailman/listinfo/r-sig-phylo Searchable archive at http://firstname.lastname@example.org/