The functions ‘gls.ci’ and ‘gls.pi’ compute the confidence and prediction intervals of a bivariate generalized least-squares model. When the covariance among data points is based on the phylogenetic covariance, these functions compute the confidence and prediction intervals of the phylogenetic regression (pGLS).
Reference: Smaers JB & Rohlf FJ. Testing species’ deviations from allometric predictions using the phylogenetic regression. Evolution. 70 (5): 1145-1149.
Below a case study to exemplify the use of these functions.
Prepare the analysis
require(phytools); require(geiger); require(nlme); require(evomap) data<-primateData tree<-primateTree data<-log(data) tree<-treedata(tree,data,sort=T,warnings=T)$phy data<-as.data.frame(treedata(tree,data,sort=T,warnings=T)$data)
Run a phylogenetic regression of brain size to body size
pGLS<-gls(Brain~Body,data,correlation=corBrownian(phy=tree)) summary(pGLS) plot(Brain~Body,data=data,pch=19,cex=2,cex.lab=1) abline(pGLS)
Compute and plot the pGLS confidence intervals
pGLS_ci<-gls.ci(data$Brain,data$Body,vcv(tree)) lines(pGLS_ci$CI.plot$X,pGLS_ci$CI.plot$Lower2.5,lty=2) lines(pGLS_ci$CI.plot$X,pGLS_ci$CI.plot$Upper2.5,lty=2)
Compute and plot the pGLS prediction intervals
pGLS_pi<-gls.pi(data$Brain,data$Body,vcv(tree),1) lines(pGLS_pi$PI.plot$X,pGLS_pi$PI.plot$Lower2.5,lty=3) lines(pGLS_pi$PI.plot$X,pGLS_pi$PI.plot$Upper2.5,lty=3)
The above procedures can be extrapolated to incorporating various models of evolution by adjusting the variance-covariance matrix of the tree according to relevant model parameters (e.g. the lambda parameter).
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