TY - JOUR
T1 - Generalizing rate heterogeneity across sites in statistical phylogenetics
AU - Heaps, Sarah E.
AU - Nye, Tom M W
AU - Boys, Richard J.
AU - Williams, Tom
AU - Cherlin, Svetlana
AU - Embley, T. Martin
PY - 2019/3/10
Y1 - 2019/3/10
N2 - 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.
AB - 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.
KW - Across-site rate heterogeneity
KW - Compositional heterogeneity
KW - multiplicative random effects
KW - phylogenetics
KW - selective coefficients
KW - tree of life
UR - https://arxiv.org/abs/1702.05972
UR - http://www.scopus.com/inward/record.url?scp=85062773778&partnerID=8YFLogxK
U2 - 10.1177/1471082X18829937
DO - 10.1177/1471082X18829937
M3 - Article (Academic Journal)
SN - 1471-082X
JO - Statistical Modelling
JF - Statistical Modelling
ER -