Abstract
Markov models of character substitution on phylogenies form the foundation of phylogenetic inference frameworks. Early models made the simplifying assumption that the substitution process is homogeneous over time and across sites in the molecular sequence alignment. While standard practice adopts extensions that accommodate heterogeneity of substitution rates across sites, heterogeneity in the process over time in a site-specific manner remains frequently overlooked. This is problematic, as evolutionary processes that act at the molecular level are highly variable, subjecting different sites to different selective constraints over time, impacting their substitution behavior. We propose incorporating time variability through Markov-modulated models (MMMs), which extend covarion-like models and allow the substitution process (including relative character exchange rates as well as the overall substitution rate) at individual sites to vary across lineages. We implement a general MMM framework in BEAST, a popular Bayesian phylogenetic inference software package, allowing researchers to compose a wide range of MMMs through flexible XML specification. Using examples from bacterial, viral, and plastid genome evolution, we show that MMMs impact phylogenetic tree estimation and can substantially improve model fit compared to standard substitution models. Through simulations, we show that marginal likelihood estimation accurately identifies the generative model and does not systematically prefer the more parameter-rich MMMs. To mitigate the increased computational demands associated with MMMs, our implementation exploits recent developments in BEAGLE, a high-performance computational library for phylogenetic inference. [Bayesian inference; BEAGLE; BEAST; covarion, heterotachy; Markov-modulated models; phylogenetics.]
Highlights
VOL. 70 with an implementation in BEAST (Suchard et al 2018)—a software package for Bayesian evolutionary analysis—that accommodates phylogenetic uncertainty
We here analyze the psaB gene with standard nucleotide substitution models and Markov-modulated models (MMMs) and compare the inferred phylogenies and model fit; we refer to Supplementary material available on Dryad for our analysis of the ndhD gene
We use a simple counting procedure to quantify the number of differences between the ancestral model states as a means to reconstruct which sites evolve according to which CTMC within the MMM(GTR)33A, and we observe a relatively small amount of CTMC switching throughout the phylogeny
Summary
VOL. 70 with an implementation in BEAST (Suchard et al 2018)—a software package for Bayesian evolutionary analysis—that accommodates phylogenetic uncertainty. We strive for optimal generality by allowing switching between evolutionary models within the MMM that have different substitution rates, relative character exchange rates and stationary distributions.
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