Related papers: Stochastic models for a chemostat and long time be…
We study the long-time behavior of stochastic models with an absorbing state, conditioned on survival. For a large class of processes, in which saturation prevents unlimited growth, statistical properties of the surviving sample attain…
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…
Frequency dependent selection and demographic fluctuations play important roles in evolutionary and ecological processes. Under frequency dependent selection, the average fitness of the population may increase or decrease based on…
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…
This article studies the quasi-stationary behaviour of population processes with unbounded absorption rate, including one-dimensional birth and death processes with catastrophes and multi-dimensional birth and death processes, modeling…
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…
Microbial ecosystems are remarkably diverse, stable, and often consist of a balanced mixture of core and peripheral species. Here we propose a conceptual model exhibiting all these emergent properties in quantitative agreement with real…
We study the existence and uniqueness of the solution of a non-linear coupled system constituted of a degenerate diffusion-growth-fragmentation equation and a differential equation, resulting from the modeling of bacterial growth in a…
We are interested in the long time behavior of a two-type density-dependent biological population conditioned to non-extinction, in both cases of competition or weak cooperation between the two species. This population is described by a…
Protein distributions measured under a broad set of conditions in bacteria and yeast were shown to exhibit a common skewed shape, with variances depending quadratically on means. For bacteria these properties were reproduced by temporal…
Horizontal gene transfer consists in exchanging genetic materials between microorganisms during their lives. This is a major mechanism of bacterial evolution and is believed to be of main importance in antibiotics resistance. We consider a…
We present a model for the dynamics of a population of bacteria with a continuum of traits, who compete for resources and exchange horizontally (transfer) an otherwise vertically inherited trait with possible mutations. Competition…
We study how environmental stochasticity influences the long-term population size in certain one- and two-species models. The difficulty is that even when one can prove that there is persistence, it is usually impossible to say anything…
How are granular details of stochastic growth and division of individual cells reflected in smooth deterministic growth of population numbers? We provide an integrated, multiscale perspective of microbial growth dynamics by formulating a…
We present a model for continuous cell culture coupling intra-cellular metabolism to extracellular variables describing the state of the bioreactor, taking into account the growth capacity of the cell and the impact of toxic byproduct…
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…
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…
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,…
Extinction of a long-lived isolated stochastic population can be described as an exponentially slow decay of quasi-stationary probability distribution of the population size. We address extinction of a population in a two-population system…
We consider a hierarchically structured population in which the amount of resources an individual has access to is affected by individuals that are larger, and that the intake of resources by an individual only affects directly the growth…