Related papers: Diffusion approximation of a multilocus model with…
In this paper, the replicator dynamics of the two-locus two-allele system under weak mutation and weak selection is investigated in a generation-wise non-overlapping unstructured population of individuals mating at random. Our main finding…
We study a population model of fixed size undergoing strong selection where individuals accumulate beneficial mutations, namely the Moran model with selection. In a specific setting with strong selection, Schweinsberg showed that the…
Competition between random genetic drift and natural selection plays a central role in evolution: Whereas non-beneficial mutations often prevail in small populations by chance, mutations that sweep through large populations typically confer…
A general multi-type population model is considered, where individuals live and reproduce according to their age and type, but also under the influence of the size and composition of the entire population. We describe the dynamics of the…
Many species are unsustainable at small population densities (Allee Effect), i.e., below a threshold named Allee threshold, the population decreases instead of growing. In a closed local population, environmental fluctuations always lead to…
We consider integro-differential models describing the evolution of a population structured by a quantitative trait. Individuals interact competitively, creating a strong selection pressure on the population. On the other hand, mutations…
We consider a fixed size population that undergoes an evolutionary adaptation in the weak mutuation rate limit, which we model as a biased Langevin process in the genotype space. We show analytically and numerically that, if the fitness…
This paper gives a new flavor of what Peter Jagers and his co-authors call `the path to extinction'. In a neutral population with constant size $N$, we assume that each individual at time $0$ carries a distinct type, or allele. We consider…
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…
We study a continuous time model for the frequency distribution of an infinitely large asexual population in which both beneficial and deleterious mutations occur and the fitness is additive. When beneficial mutations are ignored, the exact…
Understanding the temporal spread of gene drive alleles -- alleles that bias their own transmission -- through modeling is essential before any field experiments. In this paper, we present a deterministic reaction-diffusion model describing…
We discuss two different ways of chromosomes' and genomes' evolution. Purifying selection dominates in large panmictic populations, where Mendelian law of independent gene assortment is valid. If the populations are small, recombination…
A model of mutation rate evolution for multiple loci under arbitrary selection is analyzed. Results are obtained using techniques from Karlin (1982) that overcome the weak selection constraints needed for tractability in prior studies of…
Many experimental and field studies have shown that adaptation can occur very rapidly. Two qualitatively different modes of fast adaptation have been proposed: selective sweeps wherein large shifts in the allele frequencies occur at a few…
Fundamental properties of macroscopic gene-mating dynamic evolutionary systems are investigated. We focus on a single locus, any number of alleles in a two-gender dioecious population, for a large class of systems within population…
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…
Large populations may contain numerous simultaneously segregating polymorphisms subject to natural selection. Since selection acts on individuals whose fitness depends on many loci, different loci affect each other's dynamics. This leads to…
We consider a branching model in discrete time where each individual has a trait in some general state space. Both the reproduction law and the trait inherited by the offsprings may depend on the trait of the mother and the environment. We…
In this paper, we study a finite population undergoing discrete, nonoverlapping generations, that is structured into $D$ demes, each containing $N$ individuals of two possible types, $A$ and $B$, whose viability coefficients, $s_A$ and…
The strong Allee effect plays an important role on the evolution of population in ecological systems. One important concept is the Allee threshold that determines the persistence or extinction of the population in a long time. In general, a…