Modeling the Evolution of Rates of Continuous Trait Evolution

Abstract

Rates of phenotypic evolution vary markedly across the tree of life, from the accelerated evolution apparent in adaptive radiations to the remarkable evolutionary stasis exhibited by so-called "living fossils". Such rate variation has important consequences for large-scale evolutionary dynamics, generating vast disparities in phenotypic diversity across space, time, and taxa. Despite this, most methods for estimating trait evolution rates assume rates vary deterministically with respect to some variable of interest or change infrequently during a clade's history. These assumptions may cause underfitting of trait evolution models and mislead hypothesis testing. Here, we develop a new trait evolution model that allows rates to vary gradually and stochastically across a clade. Further, we extend this model to accommodate generally decreasing or increasing rates over time, allowing for flexible modeling of "early/late bursts" of trait evolution. We implement a Bayesian method, termed "evolving rate" (evorates for short), to efficiently fit this model to comparative data. Through simulation, we demonstrate that evorates can reliably infer both how and in which lineages trait evolution rates varied during a clade's history. We apply this method to body size evolution in cetaceans, recovering substantial support for an overall slowdown in body size evolution over time with recent bursts among some oceanic dolphins and relative stasis among beaked whales of the genus Mesoplodon. These results unify and expand on previous research, demonstrating the empirical utility of evorates.

Jointly Modeling the Evolution of Discrete and Continuous Traits

“…Continuous character models which initially relied on either single rate Brownian motion or simple Ornstein-Uhlenbeck models (Felsenstein 1985;Hansen 1997) have seen several extensions to allow for heterogeneity in the evolutionary process as well as the deterministic influence of underlying independent variables. Generally, these models can be classified as either being "hypothesis driven" or "data driven" (Martin et al 2022). Hypothesis driven models are those which require a priori hypotheses regarding where evolutionary rates may differ throughout the phylogeny.…”

“…Furthermore, some recently developed methods have allowed for rate variation without the assumption of constant regimes at all. Instead, these models assume the rates themselves evolve and change throughout the phylogeny under various Brownian motionlike processes (Lemey et al 2010;Eastman et al 2013;Revell 2021;Martin et al 2022) or single optima Ornstein-Uhlenbeck processes (Hansen et al 2008;Mitov et al 2019). The method presented here is most like the latter group.…”