Generalizing rate heterogeneity across sites in statistical phylogenetics. (August 2020)

• Record Type: Journal Article
• Authors: Heaps, Sarah E; Nye, Tom MW; Boys, Richard J; Williams, Tom A; Cherlin, Svetlana; Embley, T Martin
• Is Part Of: Statistical modelling. Volume 20:Number 4(2020)
• Page Start: 410
• Page End: 436
• Publication Date: 2020-08
• Subjects: across-site rate heterogeneity -- compositional heterogeneity -- multiplicative random effects -- phylogenetics -- selective coefficients -- tree of life; Linear models (Statistics) -- Periodicals; Mathematical models -- Periodicals; Modèles linéaires (Statistique) -- Périodiques; Modèles mathématiques -- Périodiques; Modèle statistique; Modèle linéaire; Modélisation statistique; Périodique électronique (Descripteur de forme); Ressource Internet (Descripteur de forme); 519.5011
• DOI: 10.1177/1471082X19829937
• Languages: English
• ISSNs: 1471-082X

Abstract

Phylogenetics uses alignments of molecular sequence data to learn about evolutionary trees relating species. Along branches, sequence evolution is modelled using a continuous-time Markov process characterized by an instantaneous rate matrix. Early models assumed the same rate matrix governed substitutions at all sites of the alignment, ignoring variation in evolutionary pressures. Substantial improvements in phylogenetic inference and model fit were achieved by augmenting these models with multiplicative random effects that describe the result of variation in selective constraints and allow sites to evolve at different rates which linearly scale a baseline rate matrix. Motivated by this pioneering work, we consider an extension using a quadratic, rather than linear, transformation. The resulting models allow for variation in the selective coefficients of different types of point mutation at a site in addition to variation in selective constraints. We derive properties of the extended models. For certain non-stationary processes, the extension gives a model that allows variation in sequence composition, both across sites and taxa. We adopt a Bayesian approach, describe an MCMC algorithm for posterior inference and provide software. Our quadratic models are applied to alignments spanning the tree of life and compared with site-homogeneous and linear models.