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Generalizing rate heterogeneity across sites in statistical phylogenetics

Lookup NU author(s): Dr Sarah Heaps, Dr Tom Nye, Professor Richard Boys, Dr Svetlana CherlinORCiD, Emeritus Professor T. Martin Embley FMedSci FRSORCiD



This is the authors' accepted manuscript of an article that has been published in its final definitive form by Sage Publications Ltd, 2020.

For re-use rights please refer to the publisher's terms and conditions.


© 2019 SAGE Publications. 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.

Publication metadata

Author(s): Heaps SE, Nye TMW, Boys RJ, Williams TA, Cherlin S, Embley TM

Publication type: Article

Publication status: Published

Journal: Statistical Modelling

Year: 2020

Volume: 20

Issue: 4

Pages: 410-436

Online publication date: 10/03/2019

Acceptance date: 01/12/2018

Date deposited: 02/05/2019

ISSN (print): 1471-082X

ISSN (electronic): 1477-0342

Publisher: Sage Publications Ltd


DOI: 10.1177/1471082X18829937


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Funder referenceFunder name
Wellcome Trust