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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…
Recent theoretical studies have shown that demographic stochasticity can greatly increase the tendency of asexually reproducing phenotypically diverse organisms to spontaneously evolve into localised clusters, suggesting a simple mechanism…
The paper reviews the results obtained for spatial population models and the evolution of the genealogies of these populations during the last decade by the author and his coworkers. The focus is on their large scale behaviour and on the…
Many life-history traits, like the age at maturity or adult longevity, are important determinants of the generation time. For instance, semelparous species whose adults reproduce once and die have shorter generation times than iteroparous…
Branching processes in a varying environment encompass a wide range of stochastic demographic models, and their complete understanding in terms of limit behaviour poses a formidable research challenge. In this paper, we conduct a thorough…
We consider a population of particles with unit life length. Dying each particle produces offspring whose size depends on the random environment specifying the reproduction law of all particles of the given generation and on the number of…
Interpretation of empirical results based on a taxa's lifetime distribution shows apparently conflicting results. Species' lifetime is reported to be exponentially distributed, whereas higher order taxa, such as families or genera, follow a…
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…
The correlation among the gene genealogies at different loci is crucial in biology, yet challenging to understand because such correlation depends on many factors including genetic linkage, recombination, natural selection and population…
We study voter models defined on large sets. Through a perspective emphasizing the martingale property of voter density processes, we prove that in general, their convergence to the Wright-Fisher diffusion only involves certain averages of…
Evolution occurs in populations of reproducing individuals. The structure of a biological population affects which traits evolve. Understanding evolutionary game dynamics in structured populations is difficult. Precise results have been…
Evolutionary graph theory has grown to be an area of intense study. Despite the amount of interest in the field, it seems to have grown separate from other subfields of population genetics and evolution. In the current work I introduce the…
Stellar populations carry information about the formation of galaxies and their evolution up to the present epoch. A wealth of observational data are available nowadays, which are analysed with stellar population models in order to obtain…
In a (two-type) Wright-Fisher diffusion with directional selection and two-way mutation, let $x$ denote today's frequency of the beneficial type, and given $x$, let $h(x)$ be the probability that, among all individuals of today's…
We build networks of genetic similarity in which the nodes are organisms sampled from biological populations. The procedure is illustrated by constructing networks from genetic data of a marine clonal plant. An important feature in the…
Standard neutral population genetics theory with a strictly fixed population size has important limitations. An alternative model that allows independently fluctuating population sizes and reproduces the standard neutral evolution is…
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 introduce a class of branching processes in which the reproduction or lifetime distribution at a given time depends on the total cumulative number of individuals who have been born in the population until that time. We focus on a…
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…
We consider a neutral dynamical model of biological diversity, where individuals live and reproduce independently. They have i.i.d. lifetime durations (which are not necessarily exponentially distributed) and give birth (singly) at constant…