Related papers: Some stochastic models for structured populations …
Understanding how stochastic and non-linear deterministic processes interact is a major challenge in population dynamics theory. After a short review, we introduce a stochastic individual-centered particle model to describe the evolution in…
We are interested in modelling Darwinian evolution, resulting from the interplay of phenotypic variation and natural selection through ecological interactions. Our models are rooted in the microscopic, stochastic description of a population…
We are interested in modeling some two-level population dynamics, resulting from the interplay of ecological interactions and phenotypic variation of individuals (or hosts) and the evolution of cells (or parasites) of two types living in…
Evolutionary branching is analysed in a stochastic, individual-based population model under mutation and selection. In such models, the common assumption is that individual reproduction and life career are characterised by values of a…
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…
The aim of this paper is to tackle part of the program set by Diekmann et al. in their seminal paper Diekmann et al. (2001). We quote "It remains to investigate whether, and in what sense, the nonlinear determin-istic model formulation is…
We propose a modelling framework to analyse the stochastic behaviour of heterogeneous, multi-scale cellular populations. We illustrate our methodology with a particular example in which we study a population with an oxygen-regulated…
We address a novel approach for stochastic individual-based modelling of a single species population. Individuals are distinguished by their remaining lifetimes, which are regulated by the interplay between the inexorable running of time…
In this work we address the analysis of discrete-time models of structured metapopulations subject to environmental stochasticity. Previous works on these models made use of the fact that migrations between the patches can be considered…
We analyze the long-term stability of a stochastic model designed to illustrate the adaptation of a population to variation in its environment. A piecewise-deterministic process modeling adaptation is coupled to a Feller logistic diffusion…
Discrete time, spatially extended models play an important role in ecology, modelling population dynamics of species ranging from micro-organisms to birds. An important question is how 'bottom up', individual-based models can be…
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 stochastic individual-based population model with competition, trait-structure affecting reproduction and survival, and changing environment. The changes of traits are described by jump processes, and the dynamics can be…
We design a stochastic individual-based model structured in energy, for single species consuming an external resource, where populations are characterized by a typical energy at birth in $\mathbb{R}^{*}_{+}$. The resource is maintained at a…
Traditionally, population models distinguish individuals on the basis of their current state. Given a distribution, a discrete time model then specifies (precisely in deterministic models, probabilistically in stochastic models) the…
We study population dynamics through a general growth/degrowth-fragmentation process, with resource consumption and unbounded growth/degrowth, birth and death rates. Our model is structured in a positive trait called energy (which is a…
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 present an explicit unified stochastic model of fluctuations in population size due to random birth, death, density-dependent competition and environmental fluctuations. Stochastic dynamics provide insight into small populations,…
This work is devoted to studying the dynamics of a structured population that is subject to the combined effects of environmental stochasticity, competition for resources, spatio-temporal heterogeneity and dispersal. The population is…
Over the past century, nonlinear difference and differential equations have been used to understand conditions for species coexistence. However, these models fail to account for random fluctuations due to demographic and environmental…