A simple hierarchical model for heterogeneity in the evolutionary correlation on a phylogenetic tree

Abstract

Numerous questions in phylogenetic comparative biology revolve around the correlated evolution of two or more phenotypic traits on a phylogeny. In many cases, it may be sufficient to assume a constant value for the evolutionary correlation between characters across all the clades and branches of the tree. Under other circumstances, however, it is desirable or necessary to account for the possibility that the evolutionary correlation differs through time or in different sections of the phylogeny. Here, we present a method designed to fit a hierarchical series of models for heterogeneity in the evolutionary rates and correlation of two quantitative traits on a phylogenetic tree. We apply the method to two datasets: one for different attributes of the buccal morphology in sunfishes (Centrarchidae); and a second for overall body length and relative body depth in rock- and non-rock-dwelling South American iguanian lizards. We also examine the performance of the method for parameter estimation and model selection using a small set of numerical simulations.

phytools 2.0: An updated R ecosystem for phylogenetic comparative methods (and other things)

“…(In an empirical study we might imagine using a set of such trees sampled in proportion to their probabilities using stochastic mapping – and then averaging the result. E.g., see Revell et al 2022. )…”

“…Numerous continuous trait methods exist in the phytools package. For example, phytools can be used to measure phylogenetic signal (, Pagel 1999; Blomberg et al 2003; Revell et al 2008), it can fit multi-rate Brownian evolution models (, , , , , and , O’Meara et al 2006; Revell et al 2012, 2018; Revell 2021; Revell and Harmon 2022), it can perform phylogenetic canonical correlation and principal components analysis ( and , Revell and Harrison 2008; Revell 2009), it can reconstruct ancestral states under multiple evolutionary models (, , , and , Schluter et al 1997; Revell and Harmon 2022), it can use continuous trait data to place a fossil or missing lineage into a reconstructed tree ( and , Felsenstein 2002; Revell et al 2015), it can fit a multivariate Brownian model with multiple evolutionary correlations on the tree ( and , Revell and Collar 2009; Revell et al 2022), and it can perform various types of continuous character numerical simulation on phylogenies (e.g., , , , ).…”

“…Phylogenetic tree of rock- and non-rock dwelling tropidurid lizard species from Revell et al (2022). See main text for more details.…”

“…One of these is an interesting model (described in Revell and Collar 2009; Revell et al 2022) in which the rates and evolutionary correlations between traits are allowed to vary as a function of a set of mapped regimes on the tree. (Similar to O’Meara et al 2006, but for more than one trait at a time.)…”

“…To illustrate the method, I’ll use a phylogenetic tree and dataset of tropidurid lizard species from Revell et al (2022).…”