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In this paper, we consider time-inhomogeneous branching processes and time-inhomogeneous birth-and-death processes, in which the offspring distribution and birth and death rates (respectively) vary in time. A classical result of branching…
Branching Processes in Random Environment (BPREs) $(Z_n:n\geq0)$ are the generalization of Galton-Watson processes where in each generation the reproduction law is picked randomly in an i.i.d. manner. In the supercritical case, the process…
Wright-Fisher diffusions describe the evolution of the type composition of an infinite haploid population with two types (say type $0$ and type $1$) subject to neutral reproductions, and possibly selection and mutations. In the present…
Wright-Fisher diffusions and their dual ancestral graphs occupy a central role in the study of allele frequency change and genealogical structure, and they provide expressions, explicit in some special cases but generally implicit, for the…
We investigate the impact of parity on the abundance of weak species in the context of the simplest generalization of the rock-paper-scissors model to an arbitrary number of species -- we consider models with a total number of species…
Rapid progress is now being made in the study of stellar populations of galaxies at large lookback times, both in dense clusters and the field. Dramatic transformations in star formation histories (even morphologies) appear to prevail among…
We study a density-dependent Markov jump process describing a population where each individual is characterized by a type, and reproduces at rates depending both on its type and on the population type distribution. We are interested in the…
In this paper, we show that a Galton-Watson tree conditioned to have a fixed number of particles in generation $n$ converges in distribution as $n\rightarrow\infty$, and with this tool we study the span and gap statistics of a branching…
The ways in which natural selection can allow the proliferation of cooperative behavior have long been seen as a central problem in evolutionary biology. Most of the literature has focused on interactions between pairs of individuals and on…
This paper deals with branching processes in varying environment, namely, whose offspring distributions depend on the generations. We provide sufficient conditions for survival or extinction which rely only on the first and second moments…
Biological organisms have to cope with stochastic variations in both the external environment and the internal population dynamics. Theoretical studies and laboratory experiments suggest that population diversification could be an effective…
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,…
This article is concerned with a version of the contact process with sexual reproduction on a graph with two levels of interactions modeling metapopulations. The population is spatially distributed into patches and offspring are produced in…
This paper deals with the stochastic modeling of a class of heterogeneous population in a random environment, called birth-death-swap. In addition to demographic events, swap events, i.e. moves between subgroups, occur in the population.…
We consider branching random walks in $d$-dimensional integer lattice with time-space i.i.d. offspring distributions. This model is known to exhibit a phase transition: If $d \ge 3$ and the environment is "not too random", then, the total…
We investigate the behaviour of the genealogy of a Wright-Fisher population model under the influence of a strong seed-bank effect. More precisely, we consider a simple seed-bank age distribution with two atoms, leading to either classical…
It seems paradoxical to have observed the absence of reduced effective population sizes $N_{\mathrm{e}}$ under marine hatchery practices. This paper studies the Ryman-Laikre, or two-demographic-component, model of the hatchery impact…
Recurrent mutations are a common phenomenon in population genetics. They may be at the origin of the fixation of a new genotype, if they give a phenotypic advantage to the carriers of the new mutation. In this paper, we are interested in…
A key question in evolution is how likely a mutant is to take over. This depends on natural selection and on stochastic fluctuations. Population spatial structure can impact mutant fixation probabilities. We introduce a model for structured…
We study an extension of the so-called defective Galton-Watson processes obtained by allowing the offspring distribution to change over the generations. Thus, in these processes, the individuals reproduce independently of the others and in…