Inference of directional selection and mutation parameters assuming equilibrium

The expected sample allele frequencies from populations of changing size via orthogonal polynomials

In this article, discrete and stochastic changes in (effective) population size are incorporated into the spectral representation of a biallelic diffusion process for drift and small mutation rates. A forward algorithm inspired by Hidden-Markov-Model (HMM) literature is used to compute exact sample allele frequency spectra for three demographic scenarios: single changes in (effective) population size, boom-bust dynamics, and stochastic fluctuations in (effective) population size. An approach for fully agnostic demographic inference from these sample allele spectra is explored, and sufficient statistics for stepwise changes in population size are found. Further, convergence behaviours of the polymorphic sample spectra for population size changes on different time scales are examined and discussed within the context of inference of the effective population size. Joint visual assessment of the sample spectra and the temporal coefficients of the spectral decomposition of the forward diffusion process is found to be important in determining departure from equilibrium. Stochastic changes in (effective) population size are shown to shape sample spectra particularly strongly.

Purifying selection against spurious splicing signals contributes to the base composition evolution of the polypyrimidine tract

Among eukaryotes, the major spliceosomal pathway is highly conserved. While long introns may contain additional regulatory sequences, the ones in short introns seem to be nearly exclusively related to splicing. Although these regulatory sequences involved in splicing are well-characterized, little is known about their evolution. At the 3' end of introns, the splice signal nearly universally contains the dimer AG, which consists of purines, and the polypyrimidine tract upstream of this 3' splice signal is characterized by over-representation of pyrimidines. If the over-representation of pyrimidines in the polypyrimidine tract is also due to avoidance of a premature splicing signal, we hypothesize that AG should be the most under-represented dimer. Through the use of DNA-strand asymmetry patterns, we confirm this prediction in fruit flies of the genus Drosophila and by comparing the asymmetry patterns to a presumably neutrally evolving region, we quantify the selection strength acting on each motif. Moreover, our inference and simulation method revealed that the best explanation for the base composition evolution of the polypyrimidine tract is the joint action of purifying selection against a spurious 3' splice signal and the selection for pyrimidines. Patterns of asymmetry in other eukaryotes indicate that avoidance of premature splicing similarly affects the nucleotide composition in their polypyrimidine tracts.

Evolutionary dynamics of pseudoautosomal region 1 in humans and great apes

BACKGROUND

The pseudoautosomal region 1 (PAR1) is a 2.7 Mb telomeric region of human sex chromosomes. PAR1 has a crucial role in ensuring proper segregation of sex chromosomes during male meiosis, exposing it to extreme recombination and mutation processes. We investigate PAR1 evolution using population genomic datasets of extant humans, eight populations of great apes, and two archaic human genome sequences.

RESULTS

We find that PAR1 is fast evolving and closer to evolutionary nucleotide equilibrium than autosomal telomeres. We detect a difference between substitution patterns and extant diversity in PAR1, mainly driven by the conflict between strong mutation and recombination-associated fixation bias at CpG sites. We detect excess C-to-G mutations in PAR1 of all great apes, specific to the mutagenic effect of male recombination. Despite recent evidence for Y chromosome introgression from humans into Neanderthals, we find that the Neanderthal PAR1 retained similarity to the Denisovan sequence. We find differences between substitution spectra of these archaics suggesting rapid evolution of PAR1 in recent hominin history. Frequency analysis of alleles segregating in females and males provided no evidence for recent sexual antagonism in this region. We study repeat content and double-strand break hotspot regions in PAR1 and find that they may play roles in ensuring the obligate X-Y recombination event during male meiosis.

CONCLUSIONS

Our study provides an unprecedented quantification of population genetic forces governing PAR1 biology across extant and extinct hominids. PAR1 evolutionary dynamics are predominantly governed by recombination processes with a strong impact on mutation patterns across all species.

Evidence for a force favoring GC over AT at short intronic sites in Drosophila simulans and Drosophila melanogaster

Population genetics studies often make use of a class of nucleotide site free from selective pressures, in order to make inferences about population size changes or natural selection at other sites. If such neutral sites can be identified, they offer the opportunity to avoid any confounding effects of selection. Here, we investigate evolution at putatively neutrally evolving short intronic sites in natural populations of Drosophila melanogaster and Drosophila simulans, in order to understand the properties of spontaneous mutations and the extent of GC-biased gene conversion in these species. Use of data on the genetics of natural populations is advantageous because it integrates information from large numbers of individuals over long timescales. In agreement with direct evidence from observations of spontaneous mutations in Drosophila, we find a bias in the spectrum of mutations toward AT basepairs. In addition, we find that this bias is stronger in the D. melanogaster lineage than in the D. simulans lineage. The evidence for GC-biased gene conversion in Drosophila has been equivocal. Here, we provide evidence for a weak force favoring GC in both species, which is correlated with the GC content of introns and is stronger in D. simulans than in D. melanogaster.

Population dynamics of GC-changing mutations in humans and great apes

The nucleotide composition of the genome is a balance between origin and fixation rates of different mutations. For example, it is well-known that transitions occur more frequently than transversions, particularly at CpG sites. Differences in fixation rates of mutation types are less explored. Specifically, recombination-associated GC-biased gene conversion (gBGC) may differentially impact GC-changing mutations, due to differences in their genomic distributions and efficiency of mismatch repair mechanisms. Given that recombination evolves rapidly across species, we explore gBGC of different mutation types across human populations and great ape species. We report a stronger correlation between segregating GC frequency and recombination for transitions than for transversions. Notably, CpG transitions are most strongly affected by gBGC in humans and chimpanzees. We show that the overall strength of gBGC is generally correlated with effective population sizes in humans, with some notable exceptions, such as a stronger effect of gBGC on non-CpG transitions in populations of European descent. Furthermore, species of the Gorilla and Pongo genus have a greatly reduced gBGC effect on CpG sites. We also study the dependence of gBGC dynamics on flanking nucleotides and show that some mutation types evolve in opposition to the gBGC expectation, likely due to hypermutability of specific nucleotide contexts. Our results highlight the importance of different gBGC dynamics experienced by GC-changing mutations and their impact on nucleotide composition evolution.

A nearly-neutral biallelic Moran model with biased mutation and linear and quadratic selection

In this article, a biallelic reversible mutation model with linear and quadratic selection is analysed. The approach reconnects to one proposed by Kimura (1979), who starts from a diffusion model and derives its equilibrium distribution up to a constant. We use a boundary-mutation Moran model, which approximates a general mutation model for small effective mutation rates, and derive its equilibrium distribution for polymorphic and monomorphic variants in small to moderately sized populations. Using this model, we show that biased mutation rates and linear selection alone can cause patterns of polymorphism within and substitution rates between populations that are usually ascribed to balancing or overdominant selection. We illustrate this using a data set of short introns and fourfold degenerate sites from Drosophila simulans and Drosophila melanogaster.

Maximum likelihood estimators for scaled mutation rates in an equilibrium mutation-drift model

The stationary sampling distribution of a neutral decoupled Moran or Wright-Fisher diffusion with neutral mutations is known to first order for a general rate matrix with small but otherwise unconstrained mutation rates. Using this distribution as a starting point we derive results for maximum likelihood estimates of scaled mutation rates from site frequency data under three model assumptions: a twelve-parameter general rate matrix, a nine-parameter reversible rate matrix, and a six-parameter strand-symmetric rate matrix. The site frequency spectrum is assumed to be sampled from a fixed size population in equilibrium, and to consist of allele frequency data at a large number of unlinked sites evolving with a common mutation rate matrix without selective bias. We correct an error in a previous treatment of the same problem (Burden and Tang, 2017) affecting the estimators for the general and strand-symmetric rate matrices. The method is applied to a biological dataset consisting of a site frequency spectrum extracted from short autosomal introns in a sample of Drosophila melanogaster individuals.

Quantifying GC-Biased Gene Conversion in Great Ape Genomes Using Polymorphism-Aware Models

As multi-individual population-scale data become available, more complex modeling strategies are needed to quantify genome-wide patterns of nucleotide usage and associated mechanisms of evolution. Recently, the multivariate neutral Moran model was proposed. However, it was shown insufficient to explain the distribution of alleles in great apes. Here, we propose a new model that includes allelic selection. Our theoretical results constitute the basis of a new Bayesian framework to estimate mutation rates and selection coefficients from population data. We apply the new framework to a great ape dataset, where we found patterns of allelic selection that match those of genome-wide GC-biased gene conversion (gBGC). In particular, we show that great apes have patterns of allelic selection that vary in intensity-a feature that we correlated with great apes' distinct demographies. We also demonstrate that the AT/GC toggling effect decreases the probability of a substitution, promoting more polymorphisms in the base composition of great ape genomes. We further assess the impact of GC-bias in molecular analysis, and find that mutation rates and genetic distances are estimated under bias when gBGC is not properly accounted for. Our results contribute to the discussion on the tempo and mode of gBGC evolution, while stressing the need for gBGC-aware models in population genetics and phylogenetics.

Stationary distribution of a 2-island 2-allele Wright-Fisher diffusion model with slow mutation and migration rates

The stationary distribution of the diffusion limit of the 2-island, 2-allele Wright-Fisher with small but otherwise arbitrary mutation and migration rates is investigated. Following a method developed by Burden and Tang (2016, 2017) for approximating the forward Kolmogorov equation, the stationary distribution is obtained to leading order as a set of line densities on the edges of the sample space, corresponding to states for which one island is bi-allelic and the other island is non-segregating, and a set of point masses at the corners of the sample space, corresponding to states for which both islands are simultaneously non-segregating. Analytic results for the corner probabilities and line densities are verified independently using the backward generator and for the corner probabilities using the coalescent.

Variation in the Intensity of Selection on Codon Bias over Time Causes Contrasting Patterns of Base Composition Evolution in Drosophila

Four-fold degenerate coding sites form a major component of the genome, and are often used to make inferences about selection and demography, so that understanding their evolution is important. Despite previous efforts, many questions regarding the causes of base composition changes at these sites in Drosophila remain unanswered. To shed further light on this issue, we obtained a new whole-genome polymorphism data set from D. simulans. We analyzed samples from the putatively ancestral range of D. simulans, as well as an existing polymorphism data set from an African population of D. melanogaster. By using D. yakuba as an outgroup, we found clear evidence for selection on 4-fold sites along both lineages over a substantial period, with the intensity of selection increasing with GC content. Based on an explicit model of base composition evolution, we suggest that the observed AT-biased substitution pattern in both lineages is probably due to an ancestral reduction in selection intensity, and is unlikely to be the result of an increase in mutational bias towards AT alone. By using two polymorphism-based methods for estimating selection coefficients over different timescales, we show that the selection intensity on codon usage has been rather stable in D. simulans in the recent past, but the long-term estimates in D. melanogaster are much higher than the short-term ones, indicating a continuing decline in selection intensity, to such an extent that the short-term estimates suggest that selection is only active in the most GC-rich parts of the genome. Finally, we provide evidence for complex evolutionary patterns in the putatively neutral short introns, which cannot be explained by the standard GC-biased gene conversion model. These results reveal a dynamic picture of base composition evolution.

An alternative derivation of the stationary distribution of the multivariate neutral Wright-Fisher model for low mutation rates with a view to mutation rate estimation from site frequency data

Recently, Burden and Tang (2016) provided an analytical expression for the stationary distribution of the multivariate neutral Wright-Fisher model with low mutation rates. In this paper we present a simple, alternative derivation that illustrates the approximation. Our proof is based on the discrete multivariate boundary mutation model which has three key ingredients. First, the decoupled Moran model is used to describe genetic drift. Second, low mutation rates are assumed by limiting mutations to monomorphic states. Third, the mutation rate matrix is separated into a time-reversible part and a flux part, as suggested by Burden and Tang (2016). An application of our result to data from several great apes reveals that the assumption of stationarity may be inadequate or that other evolutionary forces like selection or biased gene conversion are acting. Furthermore we find that the model with a reversible mutation rate matrix provides a reasonably good fit to the data compared to the one with a non-reversible mutation rate matrix.