I'll second Brian's self-citation. O'Meara et al. 2006 is I think one of the best introductions to the phylogenetic covariance matrix, and I often direct students to it.
Brian's point about the relationship between observed and expected covariance is illustrated here in a brief note I wrote up for students this spring: https://github.com/andrew-hipp/PCM-2018/blob/master/R-tutorials/2018-PCM-covarianceMatrixRuminations.ipynb It might be helpful, or it might not. I hope so! Take care, Andrew On Sat, Aug 25, 2018 at 1:33 PM, Brian O'Meara <omeara.br...@gmail.com> wrote: > Hi, Agus. The variance-covariance matrix comes from the tree and the > evolutionary model, not the data. Each entry between taxa A and B in the > VCV is how much covariance I should expect between data for taxa A and B > simulated up that tree using that model. I don't want to be *that guy*, but > O'Meara et al. (2006) > https://onlinelibrary.wiley.com/doi/10.1111/j.0014-3820.2006.tb01171.x has > a fairly accessible explanation of this (largely b/c I was just learning > about VCVs when working on that paper). Hansen and Martins (1996) > https://onlinelibrary.wiley.com/doi/10.1111/j.1558-5646.1996.tb03914.x > have > a much more detailed description of how you get these covariance matrices > from microevolutionary processes. > > Typically, ape::vcv() is how you get a variance covariance for a phylogeny, > assuming Brownian motion and no measurement error. It just basically takes > the history two taxa share to create the covariance (or variance, if the > two taxa are the same taxon). A different approach, which seems to be what > you're doing, would be to simulate up a tree many times, and then for each > pair of taxa (including the pair of a taxon with itself, the diagonal of > the VCV), calculate the covariance. These approaches should get the same > results, though the shared history on the tree approach is faster. > > Best, > Brian > > > _______________________________________________________________________ > Brian O'Meara, http://www.brianomeara.info, especially Calendar > <http://brianomeara.info/calendars/omeara/>, CV > <http://brianomeara.info/cv/>, and Feedback > <http://brianomeara.info/teaching/feedback/> > > Associate Professor, Dept. of Ecology & Evolutionary Biology, UT Knoxville > Associate Head, Dept. of Ecology & Evolutionary Biology, UT Knoxville > > > > On Sat, Aug 25, 2018 at 1:16 PM Agus Camacho <agus.cama...@gmail.com> > wrote: > > > Dear list users, > > > > I am trying to make an easy R demonstration to teach the > > variance-covariance matrix to students. However, After consulting the > > internet and books, I found myself facing three difficulties to > understand > > the math and code behind this important matrix. As this list is answered > by > > several authors of books of phylocomp methods, thought this might make an > > useful general discussion. > > > > Here we go, > > > > 1) I dont know how to generate a phyloVCV matrix in R (Liams kindly > > described some options here > > < > > http://blog.phytools.org/2013/12/three-different-ways-to- > calculate-among.html > > > > > but I cannot tell for sure what is X made of. It would seem a dataframe > of > > some variables measured across species. But then, I get errors when I > > write: > > > > tree <- pbtree(n = 10, scale = 1) > > tree$tip.label <- sprintf("sp%s",seq(1:n)) > > x <- fastBM(tree) > > y <- fastBM(tree) > > X=data.frame(x,y) > > rownames(X)=tree$tip.label > > ## Revell (2009) > > A<-matrix(1,nrow(X),1)%*%apply(X,2,fastAnc,tree=tree)[1,] > > V1<-t(X-A)%*%solve(vcv(tree))%*%(X-A)/(nrow(X)-1) > > ## Butler et al. (2000) > > Z<-solve(t(chol(vcv(tree))))%*%(X-A) > > V2<-t(Z)%*%Z/(nrow(X)-1) > > > > ## pics > > Y<-apply(X,2,pic,phy=tree) > > V3<-t(Y)%*%Y/nrow(Y) > > > > 2) The phyloVCV matrix has n x n coordinates defined by the n species, > and > > it represents covariances among observations made across the n species, > > right?. Still, I do no know whether these covariances are calculated over > > a) X vs Y values for each pair of species coordinates in the matrix, > across > > the n species, or b) directly over the vector of n residuals of Y, after > > correlating Y vs X, across all pairs of species coordinates. I think it > may > > be a) because, by definition, variance cannot be calculated for a single > > value. I am not sure though, since it seems the whole point of PGLS is to > > control phylosignal within the residuals of a regression procedure, prior > > to actually making it. > > > > 3) If I create two perfeclty correlated variables with independent > > observations and calculate a covariance or correlation matrix for them, I > > do not get a diagonal matrix, with zeros at the off diagonals (ex. here > > < > > https://www.dropbox.com/s/y8g3tkzk509pz58/vcvexamplewithrandomvariables. > xlsx?dl=0 > > >), > > why expect then a diagonal matrix for the case of independence among the > > observations? > > > > Thanks in advance and sorry if I missed anything obvious here! > > Agus > > Dr. Agustín Camacho Guerrero. Universidade de São Paulo. > > http://www.agustincamacho.com > > Laboratório de Comportamento e Fisiologia Evolutiva, Departamento de > > Fisiologia, > > Instituto de Biociências, USP.Rua do Matão, trav. 14, nº 321, Cidade > > Universitária, > > São Paulo - SP, CEP: 05508-090, Brasil. > > > > [[alternative HTML version deleted]] > > > > _______________________________________________ > > R-sig-phylo mailing list - R-sig-phylo@r-project.org > > https://stat.ethz.ch/mailman/listinfo/r-sig-phylo > > Searchable archive at > > http://www.mail-archive.com/r-sig-phylo@r-project.org/ > > > > [[alternative HTML version deleted]] > > _______________________________________________ > R-sig-phylo mailing list - R-sig-phylo@r-project.org > https://stat.ethz.ch/mailman/listinfo/r-sig-phylo > Searchable archive at http://www.mail-archive.com/r- > sig-ph...@r-project.org/ > -- Andrew Hipp, PhD Senior Scientist in Plant Systematics and Herbarium Curator, The Morton Arboretum Lecturer, Committee on Evolutionary Biology, University of Chicago The Morton Arboretum 4100 Illinois Route 53 / Lisle IL 60532-1293 / USA +1 630 725 2094 Lab: http://systematics.mortonarb.org/lab Hebarium data: http://vplants.org U of Chicago, CEB: http://evbio.uchicago.edu/ Phenology of the East Woods: http://systematics.mortonarb.org/phenology [[alternative HTML version deleted]] _______________________________________________ R-sig-phylo mailing list - R-sig-phylo@r-project.org https://stat.ethz.ch/mailman/listinfo/r-sig-phylo Searchable archive at http://www.mail-archive.com/r-sig-phylo@r-project.org/
