Related papers: Analysis of a Population Genetics Model with Mutat…
We consider a model of a population of fixed size $N$ undergoing selection. Each individual acquires beneficial mutations at rate $\mu_N$, and each beneficial mutation increases the individual's fitness by $s_N$. Each individual dies at…
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…
We consider a (sub) critical Galton-Watson process with neutral mutations (infinite alleles model), and decompose the entire population into clusters of individuals carrying the same allele. We specify the law of this allelic partition in…
McNamara and Dall (2011) identified novel relationships between the abundance of a species in different environments, the temporal properties of environmental change, and selection for or against dispersal. Here, the mathematics underlying…
We consider an approximating sequence of interacting population models with branching, mutation and competition. Each individual is characterized by its trait and the traits of its ancestors. Birth- and death-events happen at exponential…
Cheek and Johnston (Journal of Mathematical Biology, 2023) consider a continuous-time Bienaym\'e-Galton-Watson tree conditioned on being alive at time $T$. They study the reproduction events along the ancestral lineage of an individual…
Demographic noise causes unlimited population growth in a broad class of models which, without noise, would predict a stable finite population. We study this effect on the example of a stochastic birth-death model which includes…
This review is about statistical genetics, an interdisciplinary topic between statistical physics and population biology. The focus is on the phase of quasi-linkage equilibrium (QLE). Our goals here are to clarify under which conditions the…
This survey concerns the study of quasi-stationary distributions with a specific focus on models derived from ecology and population dynamics. We are concerned with the long time behavior of different stochastic population size processes…
While Neutral Theory famously describes the number of discrete genetic differences in populations, we consider the number of genetic backgrounds under which such differences are observed - setting limits to the generalizability of their…
A phenomenon that strongly influences the demography of small introduced populations and thereby potentially their genetic diversity is the Allee effect, a reduction in population growth rates at small population sizes. We take a stochastic…
In population genetics, extant samples are usually used for inference of past population genetic forces. With the Kingman coalescent and the backward diffusion equation, inference of the marginal likelihood proceeds from an extant sample…
The goal of this paper is to provide mathematically rigorous tools for modelling the evolution of a community of interacting individuals. We model the population by a measure space where the measure determines the abundance of individual…
We study the dynamics of phenotypically structured populations in environments with fluctuations. In particular, using novel arguments from the theories of Hamilton-Jacobi equations with constraints and homogenization, we obtain results…
A density-dependent branching process is a particle system in which individuals reproduce independently, but in a way that depends on the current population size. This feature can model a wide range of ecological interactions at the cost of…
We are interested in the long-time behavior of a diploid population with sexual reproduction, characterized by its genotype composition at one bi-allelic locus. The population is modeled by a 3-dimensional birth-and-death process with…
We study the convergence towards a unique equilibrium distribution of the solutions to a time-discrete model with non-overlapping generations arising in quantitative genetics. The model describes the dynamics of a phenotypic distribution…
The evolution of dispersal is a classical question in evolutionary biology, and it has been studied in a wide range of mathematical models. A selection-mutation model, in which the population is structured by space and a phenotypic trait,…
Sweepstakes reproduction refers to a highly skewed individual recruitment success without involving natural selection and may apply to individuals in broadcast spawning populations characterised by Type III survivorship. We consider an…
The goal of this paper is to study the lookdown model with selection in the case of a population containing two types of individuals, with a reproduction model which is dual to the $\Lambda$-coalescent. In particular we formulate the…