Exploring Fast Computational Strategies for Probabilistic Phylogenetic Analysis

Robustness of phylogenetic inference to model misspecification caused by pairwise epistasis

Likelihood-based phylogenetic inference posits a probabilistic model of character state change along branches of a phylogenetic tree. These models typically assume statistical independence of sites in the sequence alignment. This is a restrictive assumption that facilitates computational tractability, but ignores how epistasis, the effect of genetic background on mutational effects, influences the evolution of functional sequences. We consider the effect of using a misspecified site-independent model on the accuracy of Bayesian phylogenetic inference in the setting of pairwise-site epistasis. Previous work has shown that as alignment length increases, tree reconstruction accuracy also increases. Here, we present a simulation study demonstrating that accuracy increases with alignment size even if the additional sites are epistatically coupled. We introduce an alignment-based test statistic that is a diagnostic for pairwise epistasis and can be used in posterior predictive checks.

Detecting amino acid preference shifts with codon-level mutation-selection mixture models

BACKGROUND

In recent years, increasing attention has been placed on the development of phylogeny-based statistical methodologies for uncovering site-specific changes in amino acid fitness profiles over time. The few available random-effects approaches, modelling across-site variation in amino acid profiles as random variables drawn from a statistical law, either lack a mechanistic codon-level formulation, or pose significant computational challenges.

RESULTS

Here, we bring together a few existing ideas to explore a simple and fast method based on a predefined finite mixture of amino acid profiles within a codon-level substitution model following the mutation-selection formulation. Our study is focused on the detection of site-specific shifts in amino acid profiles over a known sub-clade of a tree, using simulations with and without shifts over the sub-clade to study the properties of the method. Through modifications of the values of the amino acid profiles, our simulations show different levels of reliability under different forms of finite mixture models. Sites identified by our method in a real data set show obvious overlap with those identified using previous methods, with some notable differences.

CONCLUSION

Overall, our results show that when a site-specific shift in amino acid profile is strongly pronounced, involving two clearly different sets of profiles, the method performs very well; but shifts between profiles that share many features are difficult to correctly identify, highlighting the challenging nature of the problem.

A Not-So-Long Introduction to Computational Molecular Evolution

In this chapter, we give a not-so-long and self-contained introduction to computational molecular evolution. In particular, we present the emergence of the use of likelihood-based methods, review the standard DNA substitution models, and introduce how model choice operates. We also present recent developments in inferring absolute divergence times and rates on a phylogeny, before showing how state-of-the-art models take inspiration from diffusion theory to link population genetics, which traditionally focuses at a taxonomic level below that of the species, and molecular evolution. Although this is not a cookbook chapter, we try and point to popular programs and implementations along the way.

Relaxing the Molecular Clock to Different Degrees for Different Substitution Types

Rates of molecular evolution can vary over time. Diverse statistical techniques for divergence time estimation have been developed to accommodate this variation. These typically require that all sequence (or codon) positions at a locus change independently of one another. They also generally assume that the rates of different types of nucleotide substitutions vary across a phylogeny in the same way. This permits divergence time estimation procedures to employ an instantaneous rate matrix with relative rates that do not differ among branches. However, previous studies have suggested that some substitution types (e.g., CpG to TpG changes in mammals) are more clock-like than others. As has been previously noted, this is biologically plausible given the mutational mechanism of CpG to TpG changes. Through stochastic mapping of sequence histories from context-independent substitution models, our approach allows for context-dependent nucleotide substitutions to change their relative rates over time. We apply our approach to the analysis of a 0.15 Mb intergenic region from eight primates. In accord with previous findings, we find comparatively little rate variation over time for CpG to TpG substitutions but we find more for other substitution types. We conclude by discussing the limitations and prospects of our approach.

On the statistical interpretation of site-specific variables in phylogeny-based substitution models

Phylogeny-based modeling of heterogeneity across the positions of multiple-sequence alignments has generally been approached from two main perspectives. The first treats site specificities as random variables drawn from a statistical law, and the likelihood function takes the form of an integral over this law. The second assigns distinct variables to each position, and, in a maximum-likelihood context, adjusts these variables, along with global parameters, to optimize a joint likelihood function. Here, it is emphasized that while the first approach directly enjoys the statistical guaranties of traditional likelihood theory, the latter does not, and should be approached with particular caution when the site-specific variables are high dimensional. Using a phylogeny-based mutation-selection framework, it is shown that the difference in interpretation of site-specific variables explains the incongruities in recent studies regarding distributions of selection coefficients.

The essentials of computational molecular evolution

In this chapter, we give a brief yet self-contained introduction to computational molecular evolution. In particular, we present the emergence of the use of likelihood-based methods, review the standard DNA substitution models, and introduce how model choice operates. We also present recent developments in inferring absolute dates and rates on a phylogeny and show how state-of-the-art models take inspiration from diffusion theory to link population genetics, which traditionally focuses at a taxonomic level under that of species, and molecular evolution.

Rapid likelihood analysis on large phylogenies using partial sampling of substitution histories

Likelihood-based approaches can reconstruct evolutionary processes in greater detail and with better precision from larger data sets. The extremely large comparative genomic data sets that are now being generated thus create new opportunities for understanding molecular evolution, but analysis of such large quantities of data poses escalating computational challenges. Recently developed Markov chain Monte Carlo methods that augment substitution histories are a promising approach to alleviate these computational costs. We analyzed the computational costs of several such approaches, considering how they scale with model and data set complexity. This provided a theoretical framework to understand the most important computational bottlenecks, leading us to combine novel variations of our conditional pathway integration approach with recent advances made by others. The resulting technique ("partial sampling" of substitution histories) is considerably faster than all other approaches we considered. It is accurate, simple to implement, and scales exceptionally well with dimensions of model complexity and data set size. In particular, the time complexity of sampling unobserved substitution histories using the new method is much faster than previously existing methods, and model parameter and branch length updates are independent of data set size. We compared the performance of methods on a 224-taxon set of mammalian cytochrome-b sequences. For a simple nucleotide substitution model, partial sampling was at least 10 times faster than the PhyloBayes program, which samples substitutions in continuous time, and about 100 times faster than when using fully integrated substitution histories. Under a general reversible model of amino acid substitution, the partial sampling method was 1,600 times faster than when using fully integrated substitution histories, confirming significantly improved scaling with model state-space complexity. Partial sampling of substitutions thus dramatically improves the utility of likelihood approaches for analyzing complex evolutionary processes on large data sets.

Bayesian comparisons of codon substitution models

In 1994, Muse and Gaut (MG) and Goldman and Yang (GY) proposed evolutionary models that recognize the coding structure of the nucleotide sequences under study, by defining a Markovian substitution process with a state space consisting of the 61 sense codons (assuming the universal genetic code). Several variations and extensions to their models have since been proposed, but no general and flexible framework for contrasting the relative performance of alternative approaches has yet been applied. Here, we compute Bayes factors to evaluate the relative merit of several MG and GY styles of codon substitution models, including recent extensions acknowledging heterogeneous nonsynonymous rates across sites, as well as selective effects inducing uneven amino acid or codon preferences. Our results on three real data sets support a logical model construction following the MG formulation, allowing for a flexible account of global amino acid or codon preferences, while maintaining distinct parameters governing overall nucleotide propensities. Through posterior predictive checks, we highlight the importance of such a parameterization. Altogether, the framework presented here suggests a broad modeling project in the MG style, stressing the importance of combining and contrasting available model formulations and grounding developments in a sound probabilistic paradigm.