Related papers: A central limit theorem for the spatial Lambda Fle…
We review and extend results for mutation, selection, genetic drift, and migration in a one-dimensional continuous population. The population is described by a continuous limit of the stepping stone model, which leads to the stochastic…
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…
We introduce a broad class of spatial models to describe how spatially heterogeneous populations live, die, and reproduce. Individuals are represented by points of a point measure, whose birth and death rates can depend both on spatial…
Following some recent works, we investigate the problem of optimising the total population size for logistic diffusive models with respect to resources distributions. Using the spatially heterogeneous Fisher-KPP equation, we obtain a…
We consider a mutation-selection model of a population structured by the spatial variables and a trait variable which is the diffusion rate. Competition for resource is local in spatial variables, but nonlocal in the trait variable. We…
We study the role of demographic fluctuations in typical endemics as exemplified by the stochastic SIRS model. The birth-death master equation of the model is simulated using exact numerics and analysed within the linear noise…
We are interested in modeling Darwinian evolution resulting from the interplay of phenotypic variation and natural selection through ecological interactions. The population is modeled as a stochastic point process whose generator captures…
We consider an individual-based spatially structured population for Darwinian evolution in an asexual population. The individuals move randomly on a bounded continuous space according to a reflected brownian motion. The dynamics involves…
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…
We investigate the behaviour of an establishing mutation which is subject to rapidly fluctuating selection under the Lambda-Fleming-Viot model and show that under a suitable scaling it converges to the Feller diffusion in a random…
We consider a system of multiscale stochastic differential equations whose slow component is drivenby a fractional Brownian motion with Hurst parameter H greater than 1/2. Under ergodic assumptions ensuring the applicability of the…
We introduce a stochastic individual model for the spatial behavior of an animal population of dispersive and competitive species, considering various kinds of biological effects, such as heterogeneity of environmental conditions, mutual…
We obtain the Brownian net of Sun and Swart (2008) as the scaling limit of the paths traced out by a system of continuous (one-dimensional) space and time branching and coalescing random walks. This demonstrates a certain universality of…
We study a generalized discrete-time multi-type Wright-Fisher population process. The mean-field dynamics of the stochastic process is induced by a general replicator difference equation. We prove several results regarding the asymptotic…
The Fleming-Viot (FV) process is a measure-valued diffusion that models the evolution of type frequencies in a countable population which evolves under resampling (genetic drift), mutation, and selection. In the classic FV model the fitness…
Populations evolving under the joint influence of recombination and resampling (traditionally known as genetic drift) are investigated. First, we summarise and adapt a deterministic approach, as valid for infinite populations, which assumes…
In this article, a stochastic individual-based model describing Darwinian evolution of asexual, phenotypic trait-structured population, is studied. We consider a large population with constant population size characterised by a resampling…
Phenotypes of individuals in a population of organisms are not fixed. Phenotypic fluctuations, which describe temporal variation of the phenotype of an individual or individual-to-individual variation across a population, are present in…
This paper focuses on the maximum speed at which biological evolution can occur. I derive inequalities that limit the rate of evolutionary processes driven by natural selection, mutations, or genetic drift. These \emph{rate limits} link 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…