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In considering evolution of transcribed regions, regulatory modules, and other genomic loci of interest, we are often faced with a situation in which the number of allelic states greatly exceeds the population size. In this limit, the…
We study the evolution of allele frequencies in a large population where random mating is violated in a particular way that is related to recent works on speciation. Specifically, we consider non-random encounters in haploid organisms…
This survey focuses on the most important aspects of the mathematical theory of population genetic models of selection and migration between discrete niches. Such models are most appropriate if the dispersal distance is short compared to…
We investigate sufficient conditions for the presence of coexistence states for different genotypes in a diploid diallelic population with dominance distributed on a heterogeneous habitat, considering also the interaction between genes at…
We study the evolution of the probability density of an asexual, one locus population under natural selection and random evolution. This evolution is governed by a Fokker-Planck equation with degenerate coefficients on the boundaries,…
We review models of biological evolution in which the population frequency changes deterministically with time. If the population is self-replicating, although the equations for simple prototypes can be linearised, nonlinear equations arise…
In the absence of selection, the structure of allelic diversity is described by the elegant sampling formula of Ewens. This formula has helped shape our expectations of empirical patterns of molecular variation. Along with coalescent…
A steady influx of a single deleterious multilocus genotype will impose genetic load on the resident population and leave multiple descendants carrying various numbers of the foreign alleles. Provided that the foreign types are rare at…
We consider a single genetic locus with two alleles $A_1$ and $A_2$ in a large haploid population. The locus is subject to selection and two-way, or recurrent, mutation. Assuming the allele frequencies follow a Wright-Fisher diffusion and…
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…
The shape of allele-frequency clines maintained by migration-selection balance depends not only on the properties of migration and selection, but also on the dominance relations among alleles and on linkage to other loci under selection. We…
We study existence and stability of stationary solutions of a system of semilinear parabolic partial differential equations that occurs in population genetics. It describes the evolution of gamete frequencies in a geographically structured…
We investigate the evolutionary dynamics of a population structured in phenotype, subjected to trait dependent selection with a linearly moving optimum and an asexual mode of reproduction. Our model consists of a non-local and non-linear…
We study the population genetics of two neutral alleles under reversible mutation in the \Lambda-processes, a population model that features a skewed offspring distribution. We describe the shape of the equilibrium allele frequency…
The dynamics of adaptation is difficult to predict because it is highly stochastic even in large populations. The uncertainty emerges from number fluctuations, called genetic drift, arising in the small number of particularly fit…
We revisit the classical population genetics model of a population evolving under multiplicative selection, mutation and drift. The number of beneficial alleles in a multi-locus system can be considered a trait under exponential selection.…
To understand the effect of assortative mating on the genetic evolution of a population, we consider a finite population in which each individual has a type, determined by a sequence of n diallelic loci. We assume that the population…
An Allee effect occurs when the per-capita growth rate increases at low densities. Here, we investigate the evolutionary stability of a partial migration population with migrant population experiencing Allee effects. Partial migration is a…
Genetic diversity is central to the process of evolution. Both natural selection and random genetic drift are influenced by the level of genetic diversity of a population; selection acts on diversity while drift samples from it. At a given…
Game theoretic tools are utilized to analyze a one-locus continuous selection model of sex-specific meiotic drive by considering nonequivalence of the viabilities of reciprocal heterozygotes that might be noticed at an imprinted locus. The…