Assessment of positive selection across SARS-CoV-2 variants via maximum likelihood.

Study of the genome of the SARS-CoV-2 virus, particularly with regard to understanding evolution of the virus, is crucial for managing the COVID-19 pandemic. To this end, we sample viral genomes from the GISAID repository and use several of the maximum likelihood approaches implemented in PAML, a collection of open source programs for phylogenetic analyses of DNA and protein sequences, to assess evidence for positive selection in the protein-coding regions of the SARS-CoV-2 genome. Across all major variants identified by June 2021, we find limited evidence for positive selection. In particular, we identify positive selection in a small proportion of sites (5-15%) in the protein-coding region of the spike protein across variants. Most other variants did not show a strong signal for positive selection overall, though there were indications of positive selection in the Delta and Kappa variants for the nucleocapsid protein. We additionally use a forward selection procedure to fit a model that allows branch-specific estimates of selection along a phylogeny relating the variants, and find that there is variation in the selective pressure across variants for the spike protein. Our results highlight the utility of computational approaches for identifying genomic regions under selection.

Bayesian inference of selection in the Wright-Fisher diffusion model.

The increasing availability of population-level allele frequency data across one or more related populations necessitates the development of methods that can efficiently estimate population genetics parameters, such as the strength of selection acting on the population(s), from such data. Existing methods for this problem in the setting of the Wright-Fisher diffusion model are primarily likelihood-based, and rely on numerical approximation for likelihood computation and on bootstrapping for assessment of variability in the resulting estimates, requiring extensive computation. Recent work has provided a method for obtaining exact samples from general Wright-Fisher diffusion processes, enabling the development of methods for Bayesian estimation in this setting. We develop and implement a Bayesian method for estimating the strength of selection based on the Wright-Fisher diffusion for data sampled at a single time point. The method utilizes the latest algorithms for exact sampling to devise a Markov chain Monte Carlo procedure to draw samples from the joint posterior distribution of the selection coefficient and the allele frequencies. We demonstrate that when assumptions about the initial allele frequencies are accurate the method performs well for both simulated data and for an empirical data set on hypoxia in flies, where we find evidence for strong positive selection in a region of chromosome 2L previously identified. We discuss possible extensions of our method to the more general settings commonly encountered in practice, highlighting the advantages of Bayesian approaches to inference in this setting.

Identifiability of the unrooted species tree topology under the coalescent model with time-reversible substitution processes, site-specific rate variation, and invariable sites.

The inference of the evolutionary history of a collection of organisms is a problem of fundamental importance in evolutionary biology. The abundance of DNA sequence data arising from genome sequencing projects has led to significant challenges in the inference of these phylogenetic relationships. Among these challenges is the inference of the evolutionary history of a collection of species based on sequence information from several distinct genes sampled throughout the genome. It is widely accepted that each individual gene has its own phylogeny, which may not agree with the species tree. Many possible causes of this gene tree incongruence are known. The best studied is the incomplete lineage sorting, which is commonly modeled by the coalescent process. Numerous methods based on the coalescent process have been proposed for the estimation of the phylogenetic species tree given DNA sequence data. However, use of these methods assumes that the phylogenetic species tree can be identified from DNA sequence data at the leaves of the tree, although this has not been formally established. We prove that the unrooted topology of the n-leaf phylogenetic species tree is generically identifiable given observed data at the leaves of the tree that are assumed to have arisen from the coalescent process under a time-reversible substitution process with the possibility of site-specific rate variation modeled by the discrete gamma distribution and a proportion of invariable sites.

Quartet inference from SNP data under the coalescent model.

MOTIVATION: Increasing attention has been devoted to estimation of species-level phylogenetic relationships under the coalescent model. However, existing methods either use summary statistics (gene trees) to carry out estimation, ignoring an important source of variability in the estimates, or involve computationally intensive Bayesian Markov chain Monte Carlo algorithms that do not scale well to whole-genome datasets. RESULTS: We develop a method to infer relationships among quartets of taxa under the coalescent model using techniques from algebraic statistics. Uncertainty in the estimated relationships is quantified using the nonparametric bootstrap. The performance of our method is assessed with simulated data. We then describe how our method could be used for species tree inference in larger taxon samples, and demonstrate its utility using datasets for Sistrurus rattlesnakes and for soybeans. AVAILABILITY AND IMPLEMENTATION: The method to infer the phylogenetic relationship among quartets is implemented in the software SVDquartets, available at www.stat.osu.edu/∼lkubatko/software/SVDquartets.

Monte Carlo estimation of total variation distance of Markov chains on large spaces, with application to phylogenetics.

Markov chains are widely used for modeling in many areas of molecular biology and genetics. As the complexity of such models advances, it becomes increasingly important to assess the rate at which a Markov chain converges to its stationary distribution in order to carry out accurate inference. A common measure of convergence to the stationary distribution is the total variation distance, but this measure can be difficult to compute when the state space of the chain is large. We propose a Monte Carlo method to estimate the total variation distance that can be applied in this situation, and we demonstrate how the method can be efficiently implemented by taking advantage of GPU computing techniques. We apply the method to two Markov chains on the space of phylogenetic trees, and discuss the implications of our findings for the development of algorithms for phylogenetic inference.

Nuclear versus mitochondrial DNA: evidence for hybridization in colobine monkeys.

BACKGROUND: Colobine monkeys constitute a diverse group of primates with major radiations in Africa and Asia. However, phylogenetic relationships among genera are under debate, and recent molecular studies with incomplete taxon-sampling revealed discordant gene trees. To solve the evolutionary history of colobine genera and to determine causes for possible gene tree incongruences, we combined presence/absence analysis of mobile elements with autosomal, X chromosomal, Y chromosomal and mitochondrial sequence data from all recognized colobine genera. RESULTS: Gene tree topologies and divergence age estimates derived from different markers were similar, but differed in placing Piliocolobus/Procolobus and langur genera among colobines. Although insufficient data, homoplasy and incomplete lineage sorting might all have contributed to the discordance among gene trees, hybridization is favored as the main cause of the observed discordance. We propose that African colobines are paraphyletic, but might later have experienced female introgression from Piliocolobus/Procolobus into Colobus. In the late Miocene, colobines invaded Eurasia and diversified into several lineages. Among Asian colobines, Semnopithecus diverged first, indicating langur paraphyly. However, unidirectional gene flow from Semnopithecus into Trachypithecus via male introgression followed by nuclear swamping might have occurred until the earliest Pleistocene. CONCLUSIONS: Overall, our study provides the most comprehensive view on colobine evolution to date and emphasizes that analyses of various molecular markers, such as mobile elements and sequence data from multiple loci, are crucial to better understand evolutionary relationships and to trace hybridization events. Our results also suggest that sex-specific dispersal patterns, promoted by a respective social organization of the species involved, can result in different hybridization scenarios.