A Bayesian extension of phylogenetic generalized least squares: Incorporating uncertainty in the comparative study of trait relationships and evolutionary rates

Abstract

Phylogenetic comparative methods use tree topology, branch lengths, and models of phenotypic change to take into account nonindependence in statistical analysis. However, these methods normally assume that trees and models are known without error. Approaches relying on evolutionary regimes also assume specific distributions of character states across a tree, which often result from ancestral state reconstructions that are subject to uncertainty. Several methods have been proposed to deal with some of these sources of uncertainty, but approaches accounting for all of them are less common. Here, we show how Bayesian statistics facilitates this task while relaxing the homogeneous rate assumption of the well‐known phylogenetic generalized least squares (PGLS) framework. This Bayesian formulation allows uncertainty about phylogeny, evolutionary regimes, or other statistical parameters to be taken into account for studies as simple as testing for coevolution in two traits or as complex as testing whether bursts of phenotypic change are associated with evolutionary shifts in intertrait correlations. A mixture of validation approaches indicates that the approach has good inferential properties and predictive performance. We provide suggestions for implementation and show its usefulness by exploring the coevolution of ankle posture and forefoot proportions in Carnivora.

Relaxing Selective Pressures on Developmentally Complex Integumentary Structures: Feather Vane Symmetry Evolves in Addition to Body Mass and Wing Length After Flight Loss in Recent Birds

“…Our other approach to rates was fitting a two-slope, two-rate phylogenetic regression using RJAGS following Fuentes-G et al . (2020).…”

Integrative Phylogenetics: Tools for Palaeontologists to Explore the Tree of Life

“…Uncertainty exists with respect the measured traits, the shape of the phylogeny, and the estimates of the rates themselves. Fuentes-G. [ 114 ] recently extended phylogenetic regressions to accommodate these different levels and degrees of uncertainty. In their study [ 114 ], they explored how allometric relationships vary in posture across a phylogeny of mammals, although their flexible approach is applicable to any dataset.…”

“…Such models are increasingly used in palaeobiological and macroevolutionary studies [ 108 , 109 , 114 , 115 , 116 , 117 , 118 ]. Once rates have been estimated using these approaches, hierarchical Bayesian regressions [ 108 ] can be used to identify associations between diversification rates and abiotic/biotic variables (such as climate, traits, and local richness) to evaluate the relative importance of each variable in driving diversification.…”

Body size correlates with discrete-character morphological proxies

“…A linear null-model approach incorporating mixed effects, such as that used here, can be applied to decouple size from morphological proxies and examine size-independent proxies along with body-size evolution, separately. Interestingly, such approaches could simultaneously incorporate phylogenetic topological uncertainties (Fuentes et al 2020). These are particularly relevant when examining time-series analyses and can be built into models that evaluate morphology and disparity over time (Adams et al 2019; Fig.…”