Related papers: Moran models and Wright--Fisher diffusions with se…
We establish a genealogical framework for an existing analytical moment duality between a Wright--Fisher type SDE and a counting process with interaction. To achieve this, we construct a finite-population Moran model featuring interactive…
We consider two versions of stochastic population models with mutation and selection. The first approach relies on a multitype branching process; here, individuals reproduce and change type (i.e., mutate) independently of each other,…
We consider a population of N individuals, whose dynamics through time is represented by a biparental Moran model with two types: an advantaged type and a disadvantaged type. The advantage is due to a mutation, transmitted in a Mendelian…
$\Lambda$-Wright--Fisher processes provide a robust framework to describe the type-frequency evolution of an infinite neutral population. We add a polynomial drift to the corresponding stochastic differential equation to incorporate…
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…
Consider a population of $N$ individuals, each of them carrying a type in $\mathbb N_0$. The population evolves according to a Moran dynamics with selection and mutation, where an individual of type $k$ has the same selective advantage over…
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…
Several groups have recently modeled evolutionary transitions from an ancestral allele to a beneficial allele separated by one or more intervening mutants. The beneficial allele can become fixed if a succession of intermediate mutants are…
We consider a population constituted by two types of individuals; each of them can produce offspring in two different islands (as a particular case the islands can be interpreted as active or dormant individuals). We model the evolution of…
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…
We construct an individual-based metapopulation model of population genetics featuring migration, mutation, selection and genetic drift. In the case of a single `island', the model reduces to the Moran model. Using the diffusion…
We consider the classical Wright-Fisher model with mutation and selection. Mutations occur independently in each locus, and selection is performed according to the sharp peak landscape. In the asymptotic regime studied in [3], a…
We study two types of stochastic processes, a mean-field spatial system of interacting Fisher-Wright diffusions with an inferior and an advantageous type with rare mutation (inferior to advantageous) and a (mean-field) spatial system of…
We present a model for growth in a multi-species population. We consider two types evolving as a logistic branching process with mutation, where one of the types has a selective advantage, and are interested in the regime in which the…
We study the large population limit of the Moran process, assuming weak-selection, and for different scalings. Depending on the particular choice of scalings, we obtain a continuous model that may highlight the genetic-drift (neutral…
Many mathematical models of evolution assume that all individuals experience the same environment. Here, we study the Moran process in heterogeneous environments. The population is of finite size with two competing types, which are exposed…
In evolutionary games the fitness of individuals is not constant but depends on the relative abundance of the various strategies in the population. Here we study general games among n strategies in populations of large but finite size. We…
The entropy rates of the Wright-Fisher process, the Moran process, and generalizations are computed and used to compare these processes and their dependence on standard evolutionary parameters. Entropy rates are measures of the variation…
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…
We study a class of processes that are akin to the Wright-Fisher model, with transition probabilities weighted in terms of the frequency-dependent fitness of the population types. By considering an approximate weak formulation of the…