I just tried this using the code below, and I can't see a trend. I calculated the mean tip value across the species in each simulation, and made a box plot over 10000 simulations. Although sim.char() doesn't do this, one can simply draw these numbers from a multivariate normal distribution - and so their expected mean is zero.
rr<-c(0.001, 0.01, 0.1, 1, 10, 100, 1000) phy<-birthdeath.tree(b=1, d=0, taxa.stop=20) allMeans<-matrix(nrow=10000, ncol=length(rr)) for(i in 1:length(rr)) { mm<-rr[i] ss<-sim.char(phy, as.matrix(rr[i]), nsims=10000) allMeans[,i]<-apply(ss, 3, FUN=mean) } meanmeans<-apply(allMeans, 2, FUN=mean) cc<-as.numeric(allMeans) xx<-rep(rr, each=10000) plot(as.factor(xx), cc) On May 20, 2011, at 12:32 PM, Dean Adams wrote: > Hi all, > > I'm observing a curious pattern in continuous trait data simulated on a > phylogeny that I cannot explain. I thought I'd throw it out to the group for > ideas. My apologies if this was addressed in an earlier thread. > > I'm exploring four different R functions for simulating continuous data under > Brownian Motion: 'rTraitCont' in Ape, 'sim.char' in Geiger, > 'transformPhylo.sim' from MotMot, and 'fastBM' from Liam Revell's > PhyTools-beta. For these simulations I generate a tree (in this case a > perfectly-balanced tree) and simulate 100 data sets on the same phylogeny > using a particular initial BM rate parameter (sigma). For each simulation, I > calculate the mean & variance of the simulated tips data, and then summarize > these across 100 simulations to understand some general properties of the 4 > data-generating functions. I'm using a wide range of initial sigmas to see > how things fall out (sigma = 0.0001, 0.001. 0.01 ... 1000). > > At sigma = 1.0, the mean of the variance in tips data across simulations is > similar for all 4 methods. And as expected, as sigma increases or decreases, > the mean variation among tips values also increases or decreases. For each > sigma value, mean levels of variation are also similar for 3 of the 4 > methods: with rTraitCont having much larger relative levels of variation as > sigma >>1 , and much smaller relative levels of variation as sigma << 1. (I > suspect this might be due to a scaling difference in the functions: sim.char, > fastBM, and transformPhylo.sim all use ~sqrt(sigma*branchlengths) when > generating random normal data, but I'm not certain what rTraitCont uses.) > > However, the most curious finding is that for all methods, as sigma > increases, so too does the mean trait value across the tips (and the converse > occurs as sigma decreases). This observation is curious to me, as one should > not see a predictable shift in the mean under Brownian motion. I thought > this might be due to simulating too few data sets and taking the mean of the > mean, but the pattern remained when 10,000 simulated data sets were generated > (though obviously, the effect was smaller, with mean values closer to zero). > I then repeated the simulations for different numbers of taxa (N=16, 32, 64, > 128) and the pattern was still present. So I think this observation is > robust. > > Presently, I am at a loss to explain this observation, though I have a > nagging suspicion that I'm missing something obvious. For instance, it may be > related to the Central limit theorem, as increasing the number of simulated > data sets decreased the magnitude of the mean effect across them. But that > doesn't fully explain why the mean deviation from zero increases > systematically with an increasing rate parameter (sigma). > > Any thoughts on this would be greatly appreciated. > > Best, > > Dean > > -- > Dr. Dean C. Adams > Associate Professor > Department of Ecology, Evolution, and Organismal Biology > Department of Statistics > Iowa State University > Ames, Iowa > 50011 > www.public.iastate.edu/~dcadams/ > phone: 515-294-3834 > > _______________________________________________ > R-sig-phylo mailing list > R-sig-phylo@r-project.org > https://stat.ethz.ch/mailman/listinfo/r-sig-phylo Luke Harmon Assistant Professor Biological Sciences University of Idaho 208-885-0346 lu...@uidaho.edu [[alternative HTML version deleted]] _______________________________________________ R-sig-phylo mailing list R-sig-phylo@r-project.org https://stat.ethz.ch/mailman/listinfo/r-sig-phylo