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The deterministic selection-recombination equation describes the evolution of the genetic type composition of a population under selection and recombination in a law of large numbers regime. So far, an explicit solution has seemed out of…
When organisms adapt to spatially heterogeneous environments, selection may drive divergence at multiple genes. If populations under divergent selection also exchange migrants, we expect genetic differentiation to be high at selected loci,…
Identifying drivers of complex traits from the noisy signals of genetic variation obtained from high throughput genome sequencing technologies is a central challenge faced by human geneticists today. We hypothesize that the variants…
We consider resequencing studies of associated loci and the problem of prioritizing sequence variants for functional follow-up. Working within the multivariate linear regression framework helps us to account for correlation across variants,…
In a (two-type) Wright-Fisher diffusion with directional selection and two-way mutation, let $x$ denote today's frequency of the beneficial type, and given $x$, let $h(x)$ be the probability that, among all individuals of today's…
Natural populations often show enhanced genetic drift consistent with a strong skew in their offspring number distribution. The skew arises because the variability of family sizes is either inherently strong or amplified by population…
Freshwater Unionid bivalves have recently faced ecological upheaval through pollution, barriers to dispersal, human harvesting, and changes in fish-host prevalence. Currently, over 70% of species are threatened, endangered or extinct. To…
The distribution and heritability of many traits depends on numerous loci in the genome. In general, the astronomical number of possible genotypes makes the system with large numbers of loci difficult to describe. Multilocus evolution,…
Adaptation in response to selection on polygenic phenotypes may occur via subtle allele frequencies shifts at many loci. Current population genomic techniques are not well posed to identify such signals. In the past decade, detailed…
In the analysis of complex traits, genetic effects are frequently modelled as either fixed or random effects. Such assumptions serve as a foundation of defining heritability and relatedness using genome-wide single nucleotide polymorphism…
We extend the spatial $\Lambda$-Fleming-Viot process introduced in [Electron. J. Probab. 15 (2010) 162-216] to incorporate recombination. The process models allele frequencies in a population which is distributed over the two-dimensional…
Biochemical and regulatory interactions central to biological networks are expected to cause extensive genetic interactions or epistasis affecting the heritability of complex traits and the distribution of genotypes in populations. However,…
Although a number of studies have shown that natural and laboratory populations initially well-adapted to their environment can evolve rapidly when conditions suddenly change, the dynamics of rapid adaptation are not well understood. Here a…
Coevolution is expected to follow two alternative dynamics, often called trench warfare and arms races in plant-pathogen systems. Trench warfare situations are stable cycles of allele frequencies at the coevolving loci of both host and…
The ancestral selection graph in population genetics was introduced by KroneNeuhauser (1997) as an analogue of the coalescent genealogy of a sample of genes from a neutrally evolving population. The number of particles in this graph,…
In recent years, a number of methods have been developed to infer complex demographic histories, especially historical population size changes, from genomic sequence data. Coalescent Hidden Markov Models have proven to be particularly…
We consider an infinitely large population under stabilising selection and mutation in which the allelic effects determining a polygenic trait vary between loci. We obtain analytical expressions for the stationary genetic variance as a…
We propose a resampling-based fast variable selection technique for detecting relevant single nucleotide polymorphisms (SNP) in a multi-marker mixed effect model. Due to computational complexity, current practice primarily involves testing…
We consider the Moran model of population genetics with two types, mutation, and selection, and investigate the line of descent of a randomly-sampled individual from a contemporary population. We trace this ancestral line back into the…
Human populations have experienced dramatic growth since the Neolithic revolution. Recent studies that sequenced a very large number of individuals observed an extreme excess of rare variants, and provided clear evidence of recent rapid…