A multiple variance Brownian motion framework for estimating variable rates and inferring ancestral states

Abstract

To understand the nature of the evolutionary process, it is of paramount importance that temporal patterns of change in biological traits are accurately documented. The paleontological record is, however, inherently incomplete, leaving researchers with only a limited set of observed taxonomic units (OTUs) to estimate broader patterns of biological change. In this context, phylogenetic comparative methods have been developed aiming to estimate patterns of phenotypic change through time based on a phylogenetic tree and a limited set of OTUs. Such methods typically employ mathematical models proposing how change is likely to have unfolded over time. The most commonly used model, Brownian motion (BM), assumes that average trait change is proportional to the square root of time and that the rate of evolution is stochastically constant across all branches. This, however, lies in contrast to the commonly agreed notion that many biological traits change at different rates along different branches of the tree of life. We present a method for inferring ancestral states that allows for different evolutionary rates along different branches of the phylogenetic tree. The goal is to include the effects of variation in rates of phenotypic change across phylogenetic space. Based on the available phenotypic and phylogenetic information, we estimate measures of the rate of evolution on each individual branch and, subsequently, these estimates are used to parameterize a multiple variance BM model inferring the phenotypic values at all internal nodes. We demonstrate the validity of our approach with a series of simulations and an empirical example. We show that values for internal nodes inferred using our approach are equivalent to those inferred with a constant variance BM model if phenotypic evolution occurs according to standard BM. When evolution occurs at different rates along different branches of the phylogeny, our approach greatly outperforms constant variance BM. We further demonstrate that our approach accurately detects bursts of change in phylogenetic space. An empirical analysis of the evolution of primate brain and body mass reveals that our approach yields an improved statistical fit relative to both traditional and recent methods, and provides estimates of nodal values that lie within a range expected based on the fossil record.