The Phylogenetic Ornstein-Uhlenbeck Mixed Model

The Phylogenetic Ornstein-Uhlenbeck Mixed Model (POUMM) allows to estimate the phylogenetic heritability of continuous traits, to test hypotheses of neutral evolution versus stabilizing selection, to quantify the strength of stabilizing selection, to estimate measurement error and to make predictions about the evolution of a phenotype and phenotypic variation in a population. The package implements combined maximum likelihood and Bayesian inference of the univariate Phylogenetic Ornstein-Uhlenbeck Mixed Model, fast parallel likelihood calculation, maximum likelihood inference of the genotypic values at the tips, functions for summarizing and plotting traces and posterior samples, functions for simulation of a univariate continuous trait evolution model along a phylogenetic tree. So far, the package has been used for estimating the heritability of quantitative traits in macroevolutionary and epidemiological studies, see e.g. Bertels et al. (2017) and Mitov and Stadler (2018) . The algorithm for parallel POUMM likelihood calculation has been published in Mitov and Stadler (2019) .

The Phylogenetic Ornstein-Uhlenbeck Mixed Model (POUMM) allows to estimate the phylogenetic heritability of a continuous trait, to test hypotheses of neutral evolution versus stabilizing selection, to quantify the strength of stabilizing selection, to estimate measurement error and to make predictions about the evolution of a phenotype and phenotypic variation in a population. The POUMM package provides an easy and efficient way to perform this variety of analyses on large macro-evolutionary or epidemic trees. It implements a fast-likelihood calculation algorithm enabling MCMC-sampling with millions of iterations within minutes on contemporary multiple core processors. The package provides functions for configuring the fit of the model and a number of standard generic functions such as logLik, plot, summary, allowing a visual and a statistical assessment of the goodness of fit. This is an important step before using the model fit to answer relevant biological questions.

Using the R-package

Here is a quick example on how to use the package on a simulated tree and data:

N <- 500 
 
# phylogeny
tr <- ape::rtree(N)
 
# for the example, simulate trait values on the tree according to a POUMM model.
z <- rVNodesGivenTreePOUMM(
  tree = tr,   
  z0 = 0,      # fixed value at the root
  alpha = 2,   # selection strength of the OU process
  theta = 3,   # long term mean of the OU process
  sigma = 1,   # unit-time standard deviation of the OU process
  sigmae = 1   # standard deviation of the non-heritable component
)[1:N]         # only the values at the N tips will be available in reality
 
# A combined ML and MCMC fit of the model with default parameter settings.
fit <- POUMM(z, tr)
 
plot(fit)
summary(fit)
AIC(fit)
BIC(fit)
coef(fit)
logLik(fit)
fitted(fit)
plot(resid(fit))
abline(h=0)
 
# fit PMM to the same data and do a likelihood ratio test
fitPMM <- POUMM(z, tr)
lmtest::lrtest(fitPMM, fit)

For an introduction to the model parameters and the package, read the User guide. More advanced topics, such as parametrizations and interpretations of the model fit are covered in the other package vignettes and in the package help-pages, e.g. ?POUMM, ?specifyPOUMM, ?summary.POUMM, ?plot.POUMM.