Inference on the strength of balancing selection for epistatically interacting loci

Exact simulation of coupled Wright–Fisher diffusions

In this paper an exact rejection algorithm for simulating paths of the coupled Wright–Fisher diffusion is introduced. The coupled Wright–Fisher diffusion is a family of multivariate Wright–Fisher diffusions that have drifts depending on each other through a coupling term and that find applications in the study of networks of interacting genes. The proposed rejection algorithm uses independent neutral Wright–Fisher diffusions as candidate proposals, which are only needed at a finite number of points. Once a candidate is accepted, the remainder of the path can be recovered by sampling from neutral multivariate Wright–Fisher bridges, for which an exact sampling strategy is also provided. Finally, the algorithm’s complexity is derived and its performance demonstrated in a simulation study.

Inference from the stationary distribution of allele frequencies in a family of Wright-Fisher models with two levels of genetic variability

The distribution of allele frequencies obtained from diffusion approximations to Wright-Fisher models is useful in developing intuition about the population level effects of evolutionary processes. The statistical properties of the stationary distributions of K-allele models have been extensively studied under neutrality or under selection. Here, we introduce a new family of Wright-Fisher models in which there are two hierarchical levels of genetic variability. The genotypes composed of alleles differing from each other at the selected level have fitness differences with respect to each other and evolve under selection. The genotypes composed of alleles differing from each other only at the neutral level have the same fitness and evolve under neutrality. We show that with an appropriate scaling of the mutation parameter with respect to the number of alleles at each level, the frequencies of alleles at the selected and the neutral level are conditionally independent of each other, conditional on knowing the number of alleles at all levels. This conditional independence allows us to simulate from the joint stationary distribution of the allele frequencies. We use these simulated frequencies to perform inference on parameters of the model with two levels of genetic variability using Approximate Bayesian Computation.

Positive selection on human gamete-recognition genes

Coevolution of genes that encode interacting proteins expressed on the surfaces of sperm and eggs can lead to variation in reproductive compatibility between mates and reproductive isolation between members of different species. Previous studies in mice and other mammals have focused in particular on evidence for positive or diversifying selection that shapes the evolution of genes that encode sperm-binding proteins expressed in the egg coat or zona pellucida (ZP). By fitting phylogenetic models of codon evolution to data from the 1000 Genomes Project, we identified candidate sites evolving under diversifying selection in the human genes ZP3 and ZP2. We also identified one candidate site under positive selection in C4BPA, which encodes a repetitive protein similar to the mouse protein ZP3R that is expressed in the sperm head and binds to the ZP at fertilization. Results from several additional analyses that applied population genetic models to the same data were consistent with the hypothesis of selection on those candidate sites leading to coevolution of sperm- and egg-expressed genes. By contrast, we found no candidate sites under selection in a fourth gene (ZP1) that encodes an egg coat structural protein not directly involved in sperm binding. Finally, we found that two of the candidate sites (in C4BPA and ZP2) were correlated with variation in family size and birth rate among Hutterite couples, and those two candidate sites were also in linkage disequilibrium in the same Hutterite study population. All of these lines of evidence are consistent with predictions from a previously proposed hypothesis of balancing selection on epistatic interactions between C4BPA and ZP3 at fertilization that lead to the evolution of co-adapted allele pairs. Such patterns also suggest specific molecular traits that may be associated with both natural reproductive variation and clinical infertility.

KIR and HLA under pressure: evidences of coevolution across worldwide populations

KIR (killer cell immunoglobulin-like receptors) and HLA (human leukocyte antigens) are two distinct gene families with remarkable importance for human immune responses. The recognition of HLA molecules by activating and inhibitory KIR promotes a balance of signals that regulates NK cell function and is especially important for the innate defense against pathogens and early placentation. There is no documented gametic association between these two gene families and no evidence of common regulation. However, due to the critical role of KIR recognition for immunity and reproduction, the possibility of KIR-HLA combinations being under selective pressure is not surprising. In this manuscript, we first summarize the HLA-KIR system, the HLA molecules that are the putative ligands for KIR, and then we review the evidences that suggest these two gene families are coevolving as an integrated system.

Recent human adaptation: genomic approaches, interpretation and insights

The recent availability of genomic data has spurred many genome-wide studies of human adaptation in different populations worldwide. Such studies have provided insights into novel candidate genes and pathways that are putatively involved in adaptation to different environments, diets and disease prevalence. However, much work is needed to translate these results into candidate adaptive variants that are biologically interpretable. In this Review, we discuss methods that may help to identify true biological signals of selection and studies that incorporate complementary phenotypic and functional data. We conclude with recommendations for future studies that focus on opportunities to use integrative genomics methodologies in human adaptation studies.

An explicit transition density expansion for a multi-allelic Wright-Fisher diffusion with general diploid selection

Characterizing time-evolution of allele frequencies in a population is a fundamental problem in population genetics. In the Wright-Fisher diffusion, such dynamics is captured by the transition density function, which satisfies well-known partial differential equations. For a multi-allelic model with general diploid selection, various theoretical results exist on representations of the transition density, but finding an explicit formula has remained a difficult problem. In this paper, a technique recently developed for a diallelic model is extended to find an explicit transition density for an arbitrary number of alleles, under a general diploid selection model with recurrent parent-independent mutation. Specifically, the method finds the eigenvalues and eigenfunctions of the generator associated with the multi-allelic diffusion, thus yielding an accurate spectral representation of the transition density. Furthermore, this approach allows for efficient, accurate computation of various other quantities of interest, including the normalizing constant of the stationary distribution and the rate of convergence to this distribution.

Efficient simulation and likelihood methods for non-neutral multi-allele models

Throughout the 1980s, Simon Tavaré made numerous significant contributions to population genetics theory. As genetic data, in particular DNA sequence, became more readily available, a need to connect population-genetic models to data became the central issue. The seminal work of Griffiths and Tavaré (1994a , 1994b , 1994c) was among the first to develop a likelihood method to estimate the population-genetic parameters using full DNA sequences. Now, we are in the genomics era where methods need to scale-up to handle massive data sets, and Tavaré has led the way to new approaches. However, performing statistical inference under non-neutral models has proved elusive. In tribute to Simon Tavaré, we present an article in spirit of his work that provides a computationally tractable method for simulating and analyzing data under a class of non-neutral population-genetic models. Computational methods for approximating likelihood functions and generating samples under a class of allele-frequency based non-neutral parent-independent mutation models were proposed by Donnelly, Nordborg, and Joyce (DNJ) (Donnelly et al., 2001). DNJ (2001) simulated samples of allele frequencies from non-neutral models using neutral models as auxiliary distribution in a rejection algorithm. However, patterns of allele frequencies produced by neutral models are dissimilar to patterns of allele frequencies produced by non-neutral models, making the rejection method inefficient. For example, in some cases the methods in DNJ (2001) require 10(9) rejections before a sample from the non-neutral model is accepted. Our method simulates samples directly from the distribution of non-neutral models, making simulation methods a practical tool to study the behavior of the likelihood and to perform inference on the strength of selection.