Estimating the Distribution of Selection Coefficients from Phylogenetic Data Using Sitewise Mutation-Selection Models

Abstract

Estimation of the distribution of selection coefficients of mutations is a long-standing issue in molecular evolution. In addition to population-based methods, the distribution can be estimated from DNA sequence data by phylogenetic-based models. Previous models have generally found unimodal distributions where the probability mass is concentrated between mildly deleterious and nearly neutral mutations. Here we use a sitewise mutation–selection phylogenetic model to estimate the distribution of selection coefficients among novel and fixed mutations (substitutions) in a data set of 244 mammalian mitochondrial genomes and a set of 401 PB2 proteins from influenza. We find a bimodal distribution of selection coefficients for novel mutations in both the mitochondrial data set and for the influenza protein evolving in its natural reservoir, birds. Most of the mutations are strongly deleterious with the rest of the probability mass concentrated around mildly deleterious to neutral mutations. The distribution of the coefficients among substitutions is unimodal and symmetrical around nearly neutral substitutions for both data sets at adaptive equilibrium. About 0.5% of the nonsynonymous mutations and 14% of the nonsynonymous substitutions in the mitochondrial proteins are advantageous, with 0.5% and 24% observed for the influenza protein. Following a host shift of influenza from birds to humans, however, we find among novel mutations in PB2 a trimodal distribution with a small mode of advantageous mutations.

Contingency and entrenchment in protein evolution under purifying selection

“…Indeed, although some more sophisticated models have been proposed (e.g., refs. [45][46][47][48][49][50], all commonly used phylogenetic models of long-term protein evolution assume that epistasis is absent so that sites evolve independently (51)(52)(53)(54)(55)(56).…”

Extensively Parameterized Mutation–Selection Models Reliably Capture Site-Specific Selective Constraint

“…Findings from previous mutation-selection model studies would suggest that natural simulations would favor the swMutSel platform, which is known to estimate large proportions of deleterious changes, and conversely DMS simulations would favor the pbMutSel platform, which tends to infer strictly unimodal S distributions (Rodrigue et al 2010;Tamuri et al 2012Tamuri et al , 2014Rodrigue 2013). Therefore, the different features across our simulation sets allowed us to directly contrast how each mutation-selection inference platform behaves on data with realistic levels of evolutionary heterogeneity, without biasing results towards one particular implementation.…”

“…The first implementation, known as swMutSel, estimates site-specific fitness parameters as fixed-effect variables through a maximum penalized-likelihood (MPL) approach (Tamuri et al 2012(Tamuri et al , 2014. The second implementation, available in the PhyloBayes software package, instead employs a Dirichlet Process (DP) Bayesian framework and models site-specific fitness parameters as random effects (Rodrigue et al 2010;Rodrigue and Lartillot 2014).…”

“…Whether the amino-acid fitnesses estimated by either swMutSel or pbMutSel truly reflect evolutionary constraint remains an open question, in particular because these two implementations produce seemingly incompatible results: swMutSel infers S distributions with two peaks representing nearly neutral (centered at S ¼ 0) and highly deleterious changes, commonly defined as S < À10 in the context of mutation-selection models (Tamuri et al 2012(Tamuri et al , 2014Rodrigue 2013). In contrast, pbMutSel infers unimodal distributions centered at S ¼ 0, without a peak of highly deleterious changes.…”

“…Previous quantitative comparisons of swMutSel and pbMutSel inferences have focused nearly exclusively on asking how well they recapitulate the gene-wide distribution of S, or similarly the gene-wide proportions of deleterious and beneficial substitutions (Rodrigue et al 2010;Tamuri et al 2012Tamuri et al , 2014Rodrigue 2013;Rodrigue and Lartillot 2014). In spite of these efforts, however, there remains no conclusive evidence supporting either swMutSel or pbMutSel as the more reliable inference approach.…”