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-phylo@r-project.org/
