Related papers: Analysis of a Population Genetics Model with Mutat…

In large populations, multiple beneficial mutations may be simultaneously spreading. In asexual populations, these mutations must either arise on the same background or compete against each other. In sexual populations, recombination can…

Both evolution and ecology have long been concerned with the impact of variable environmental conditions on observed levels of genetic diversity within and between species. We model the evolution of a quantitative trait under selection that…

Coalescent processes, including mutation, are derived from Moran type population models admitting large offspring numbers. Including mutation in the coalescent process allows for quantifying the turnover of alleles by computing the…

Whether evolution can be predicted is a key question in evolutionary biology. Here we set out to better understand the repeatability of evolution. We explored experimentally the effect of mutation supply and the strength of selective…

We study the long-time behaviour of a population structured by age and a phenotypic trait under a selection-mutation dynamics. By analysing spectral properties of a family of positive operators on measure spaces, we show the existence of…

In this article we present a new p-adic generalization of the Eigen-Schuster model where the genomes (sequences) are represented by words written in the alphabet 0,1,,p-1, where p is a prime number, with a time variable length. The time…

We introduce a population dynamics model, where individual genomes are represented by bit-strings. Selection is described by death probabilities which depend on these genomes, and new individuals continuously replace the ones that die,…

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…

We introduce a stochastic model of a population with overlapping generations and arbitrary levels of self-fertilization versus outcrossing. We study how the global graph of reproductive relationships, or population pedigree, influences the…

We consider a stochastic model describing a constant size $N$ population that may be seen as a directed polymer in random medium with $N$ sites in the transverse direction. The population dynamics is governed by a noisy traveling wave…

This article presents a comprehensive study of the continuous McKendrick model, which serves as a foundational framework in population dynamics and epidemiology. The model is formulated through partial differential equations that describe…

Genetically identical cells in the same population can take on phenotypically variable states, leading to differentiated responses to external signals, such as nutrients and drug-induced stress. Many models and experiments have focused on a…

This paper extends earlier work by Cox and Durrett, who studied the coalescence times for two lineages in the stepping stone model on the two-dimensional torus. We show that the genealogy of a sample of size n is given by a time change of…

We pursue the task of developing a finite population counterpart to Eigen's model. We consider the classical Wright-Fisher model describing the evolution of a population of size $m$ of chromosomes of length $\ell$ over an alphabet of…

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…

We consider birth-and-death stochastic evolution of genotypes with different lengths. The genotypes might mutate that provides a stochastic changing of lengthes by a free diffusion law. The birth and death rates are length dependent which…

With a view to connecting random mutation on the molecular level to punctuated equilibrium behavior on the phenotype level, we propose a new model for biological evolution, which incorporates random mutation and natural selection. In this…

Several results of large deviations are obtained for distributions that are associated with the Poisson--Dirichlet distribution and the Ewens sampling formula when the parameter $\theta$ approaches infinity. The motivation for these results…

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…

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…