Related papers: The effective strength of selection in random envi…
A two-types, discrete-time population model with finite, constant size is constructed, allowing for a general form of frequency-dependent selection and skewed offspring distribution. Selection is defined based on the idea that individuals…
Wright-Fisher diffusions and their dual ancestral graphs occupy a central role in the study of allele frequency change and genealogical structure, and they provide expressions, explicit in some special cases but generally implicit, for the…
Discrete ancestral problems arising in population genetics are investigated. In the neutral case, the duality concept has proved of particular interest in the understanding of backward in time ancestral process from the forward in time…
Duality plays an important role in population genetics. It can relate results from forwards-in-time models of allele frequency evolution with those of backwards-in-time genealogical models; a well known example is the duality between the…
The purpose of this article is to study some asymptotic properties of the \Lambda-Wright-Fisher process with selection. This process represents the frequency of a disadvantaged allele. The resampling mechanism is governed by a finite…
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…
In populations competing for resources, it is natural to ask whether consuming fewer resources provides any selective advantage. To answer this question, we propose a Wright- Fisher model with two types of individuals: the inefficient…
Consider a two-type Moran population of size $N$ with selection and mutation, where the selective advantage of the fit individuals is amplified at extreme environmental conditions. Assume selection and mutation are weak with respect to $N$,…
Mathematical models of genetic evolution often come in pairs, connected by a so-called duality relation. The most seminal example are the Wright-Fisher diffusion and the Kingman coalescent, where the former describes the stochastic…
We investigate the $\Lambda$-Seed-Bank-Wright-Fisher process, a model describing allele frequency dynamics in populations exhibiting both skewed offspring distributions and dormancy. By performing a change of measure, we condition this…
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…
Evolution occurs in populations of reproducing individuals. The structure of a biological population affects which traits evolve. Understanding evolutionary game dynamics in structured populations is difficult. Precise results have been…
We introduce a multi-allele Wright-Fisher model with non-recurrent, reversible mutation and directional selection. In this setting, the allele frequencies at a single locus track the path of a hybrid jump-diffusion process with state space…
Evolutionary models for populations of constant size are frequently studied using the Moran model, the Wright-Fisher model, or their diffusion limits. When evolution is neutral, a random genealogy given through Kingman's coalescent is used…
Competition between biological species in marine environments is affected by the motion of the surrounding fluid. An effective 2D compressibility can arise, for example, from the convergence and divergence of water masses at the depth at…
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…
A number of discrete time, finite population size models in genetics describing the dynamics of allele frequencies are known to converge (subject to suitable scaling) to a diffusion process in the infinite population limit, termed the…
The stationary distribution of allele frequencies under a variety of Wright--Fisher $k$-allele models with selection and parent independent mutation is well studied. However, the statistical properties of maximum likelihood estimates of…
This paper investigates the long-term behavior of a class of $\Lambda$-Wright--Fisher processes incorporating frequency-dependent selection, coordinated (bidirectional) selection, as well as individual and coordinated mutation. Our primary…
We study a model of selection acting on a diploid population (one in which each individual carries two copies of each gene) living in one spatial dimension. We suppose a particular gene appears in two forms (alleles) $A$ and $a$, and that…