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We study a reaction-diffusion equation with an integral term describing nonlocal consumption of resources. We show that a homogeneous equilibrium can lose its stability resulting in appearance of stationary spatial structures. It is a new…
Let $(X_t)_{t \geq 0}$ be a continuous time Markov process on some metric space $M,$ leaving invariant a closed subset $M_0 \subset M,$ called the {\em extinction set}. We give general conditions ensuring either "Stochastic persistence"…
In any ecosystem, the conditions of the environment and the characteristics of the species that inhabit it are entangled, co-evolving in space and time. We introduce a model that couples active agents with a dynamic environment, interpreted…
A Markovian model of group-structured (two-level) population dynamics features births, deaths, and migrations of individuals, and fission and extinction of groups. These models are useful for studying group selection and other evolutionary…
For a one-locus haploid infinite population with discrete generations, the celebrated Kingman's model describes the evolution of fitness distributions under the competition of selection and mutation, with a constant mutation probability.…
We consider a population with two equal dominated species, dynamics of which is defined by one-dimensional piecewise-continuous, two parametric functions. It is shown that for any non-zero parameters this function has two fixed points and…
Consider a population whose size changes stepwise by its members reproducing or dying (disappearing), but is otherwise quite general. Denote the initial (non-random) size by $Z_0$ and the size of the $n$th change by $C_n$, $n= 1, 2,…
This article is a presentation of specific recent results describing scaling limits of individual-based models. Thanks to them, we wish to relate the time-scales typical of demographic dynamics and natural selection to the parameters of the…
We study an almost periodic version of a metapopulation model developed by Tilman \textit{et.al} and Nee \textit{et.al} in the nineties, which generalizes the classical Levins approach by considering several species in competition affected…
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…
Highly-diverse ecosystems exhibit a broad distribution of population sizes and species turnover, where species at high and low abundances are exchanged over time. We show that these two features generically emerge in the fluctuating phase…
To our knowledge, the populations are generally assumed to be homogeneous in the traditional approach to evolutionary game dynamics. Here, we focus on the inhomogeneous populations. A simple model which can describe the inhomogeneity of the…
We develop a stochastic two-patch epidemic model with nonlinear recidivism to investigate infectious disease dynamics in heterogeneous populations. Extending a deterministic framework, we introduce stochasticity to account for random…
Infectious diseases outbreaks are often characterized by a spatial component induced by hosts' distribution, mobility, and interactions. Spatial models that incorporate hosts' movements are being used to describe these processes, to…
The role of the selection pressure and mutation amplitude on the behavior of a single-species population evolving on a two-dimensional lattice, in a periodically changing environment, is studied both analytically and numerically. The…
Ecological systems are complex dynamical systems. Modelling efforts on ecosystems' dynamical stability have revealed that population dynamics, being highly nonlinear, can be governed by complex fluctuations. Indeed, experimental and field…
I study a population model in which the reproduction rate lambda is inherited with mutation, favoring fast reproducers in the short term, but conflicting with a process that eliminates agglomerations of individuals. The model is a variant…
A significant proportion of the infections driving the current {SARS-CoV-2} pandemic are transmitted asymptomatically. Here we introduce and study a simple epidemic model with separate compartments comprising asymptomatic and symptomatic…
The changes on abiotic features of ecosystems have rarely been taken into account by population dynamics models, which typically focus on trophic and competitive interactions between species. However, understanding the population dynamics…
The biological theory of adaptive dynamics proposes a description of the long-term evolution of a structured asexual population. It is based on the assumptions of large population, rare mutations and small mutation steps, that lead to a…