Related papers: Diffusion approximation of a multilocus model with…
Cryptic genetic sequences have attenuated effects on phenotypes. In the classic view, relaxed selection allows cryptic genetic diversity to build up across individuals in a population, providing alleles that may later contribute to…
The adaptation of biological species to their environment depends on their traits. When various biological processes occur (survival, reproduction, migration, etc.), the trait distribution may change with respect to time and space. In the…
The population dynamics that evolves in the radial symmetric geometry is investigated. The nonlinear reaction-diffusion model, which depends on population density, is employed as the governing equation for this system. The approximate…
For a genetic locus carrying a strongly beneficial allele which has just fixed in a large population, we study the ancestry at a linked neutral locus. During this ``selective sweep'' the linkage between the two loci is broken up by…
The sample frequency spectrum of a segregating site is the probability distribution of a sample of alleles from a genetic locus, conditional on observing the sample to have more than one clearly different phenotypes. We present a model for…
The spreading of evolutionary novelties across populations is the central element of adaptation. Unless population are well-mixed (like bacteria in a shaken test tube), the spreading dynamics not only depends on fitness differences but also…
The Moran discrete process and the Wright-Fisher modelare the most popular models in population genetics. It is common tounderstand the dynamics of these models to use an approximating diffusionprocess, called Wright-Fisher diffusion. Here,…
We study the genealogical distance of two randomly chosen individuals in a population that evolves according to a two type Moran model with mutation and selection. We prove that this distance is stochastically smaller than the corresponding…
We study the stability of non-conservative deterministic cross diffusion models and prove that they are approximated by stochastic population models when the populations become locally large. In this model, the individuals of two species…
The problem of natural selection in dispersal-structured populations consisting of individuals characterized by different diffusion coefficients is studied. The competition between the organisms is taken into account through the assumption…
We model and study the genetic evolution and conservation of a population of diploid hermaphroditic organisms, evolving continuously in time and subject to resource competition. In the absence of mutations, the population follows a 3-type…
The coevolutionary dynamics in finite populations currently is investigated in a wide range of disciplines, as chemical catalysis, biological evolution, social and economic systems. The dynamics of those systems can be formulated within the…
Species growing in environments that change in time and space will vary in their abundance across locations, even in the absence of persistent location preferences. Here we quantify this non-equilibrium effect by studying a minimal model of…
We consider a metapopulation made up of $K$ demes, each containing $N$ individuals bearing a heritable quantitative trait. Demes are connected by migration and undergo independent Moran processes with mutation and selection based on trait…
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…
The forest of mutations associated to a multitype branching forest is obtained by merging together all vertices of its clusters and by preserving connections between them. We first show that the forest of mutations of any mulitype branching…
In this article, discrete and stochastic changes in (effective) population size are incorporated into the spectral representation of a biallelic diffusion process for drift and small mutation rates. A forward algorithm inspired by…
Dispersal of species to find a more favorable habitat is important in population dynamics. Dispersal rates evolve in response to the relative success of different dispersal strategies. In a simplified deterministic treatment (J. Dockery, V.…
The Wright-Fisher model and the Moran model are both widely used in population genetics. They describe the time evolution of the frequency of an allele in a well-mixed population with fixed size. We propose a simple and tractable model…
We describe a continuous-time modelling framework for biological population dynamics that accounts for demographic noise. In the spirit of the methodology used by statistical physicists, transitions between the states of the system are…