Related papers: L\'evy flights in ecology
Many populations, e.g. of cells, bacteria, viruses, or replicating DNA molecules, start small, from a few individuals, and grow large into a noticeable fraction of the environmental carrying capacity $K$. Typically, the elements of the…
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…
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…
Representations of population models in terms of countable systems of particles are constructed, in which each particle has a `type', typically recording both spatial position and genetic type, and a level. For finite intensity models, the…
Predicting the adaptation of populations to a changing environment is crucial to assess the impact of human activities on biodiversity. Many theoretical studies have tackled this issue by modeling the evolution of quantitative traits…
We consider a continuous-time Bienaym\'e-Galton-Watson process with logistic competition in a regime of weak competition, or equivalently of a large carrying capacity. Individuals reproduce at random times independently of each other but…
Evolution by Natural Selection is a process by which progeny inherit some properties from their progenitors with small variation. These properties are subject to Natural Selection and are called adaptive traits and carriers of the latter…
We investigate the thermodynamics as well as the population dynamics of ecosystems based on a stochastic approach in which the number of individuals of the several species of the ecosystem are treated as stochastic variables. The several…
Heterogeneities in environmental conditions often induce corresponding heterogeneities in the distribution of species. In the extreme case of a localized patch of increased growth rates, reproducing populations can become strongly…
We study the influence of stochastic effects due to finite population size in the evolutionary dynamics of populations interacting in the multi-person Prisoner's Dilemma game. This paper is an extension of the investigation presented in a…
We consider two versions of stochastic population models with mutation and selection. The first approach relies on a multitype branching process; here, individuals reproduce and change type (i.e., mutate) independently of each other,…
An infinite population of point entities dwelling in the habitat $X=\mathds{R}^d$ is studied. Its members arrive at and depart from $X$ at random. The departure rate has a term corresponding to a logistic-type interaction between the…
We are interested in the evolving genealogy of a birth and death process with trait structure and ecological interactions. Traits are hereditarily transmitted from a parent to its offspring unless a mutation occurs. The dynamics may depend…
Population structure can have a significant effect on evolution. For some systems with sufficient symmetry, analytic results can be derived within the mathematical framework of evolutionary graph theory which relate to the outcome of the…
We consider an individual based model of phenotypic evolution in hermaphroditic populations which includes random and assortative mating of individuals. By increasing the number of individuals to infinity we obtain a nonlinear transport…
Comprehensive models of stochastic, clonally reproducing populations are defined in terms of general branching processes, allowing birth during maternal life, as for higher organisms, or by splitting, as in cell division. The populations…
We consider the duration of discussions in face-to-face contacts and propose a stochastic model to describe it. It is based on the points of a Levy flight where the duration of each contact corresponds to the size of the clusters produced…
Genetic data are often used to infer demographic history and changes or detect genes under selection. Inferential methods are commonly based on models making various strong assumptions: demography and population structures are supposed…
The prediction and control of rare events is an important task in disciplines that range from physics and biology, to economics and social science. The Big Jump principle deals with a peculiar aspect of the mechanism that drives rare…
Models of population growth and extinction are an increasingly popular subject of study. However, consequences of stochasticity and noise in shaping distributions and outcomes are not sufficiently explored. Here we consider a distributed…