Related papers: Stochastic models in population biology and their …

This paper studies a general class of stochastic population processes in which agents interact with one another over a network. Agents update their behaviors in a random and decentralized manner according to a policy that depends only on…

Traditional approaches to ecosystem modelling have relied on spatially homogeneous approximations to interaction, growth and death. More recently, spatial interaction and dispersal have also been considered. While these leads to certain…

Competition between species and genotypes is a dominant factor in a variety of ecological and evolutionary processes. Biological dynamics are typically highly stochastic, and therefore, analyzing a competitive system requires accounting for…

We study the limit of many small mutations of a model of population dynamics. The population is structured by phonological traits and is spatially inhomogeneous. The various sub-populations compete for the same nutrient which diffuses…

Spatial metapopulation models are fundamental to theoretical ecology, enabling to study how landscape structure influences global species dynamics. Traditional models, including recent generalizations, often rely on the deterministic limit…

Quantitative predictions about the processes that promote species coexistence are a subject of active research in ecology. In particular, competitive interactions are known to shape and maintain ecological communities, and situations where…

Generalizing the cyclically competing three-species model (often referred to as the rock-paper-scissors game), we consider a simple system of population dynamics without spatial structures that involves four species. Unlike the previous…

In this paper, we study the relationship between certain stochastic and deterministic versions of Hanski's incidence function model and the spatially realistic Levins model. We show that the stochastic version can be well approximated in a…

Here, we consider an SIS epidemic model where the individuals are distributed on several distinct patches. We construct a stochastic model and then prove that it converges to a deterministic model as the total population size tends to…

Stochastic models of diffusion with excluded-volume effects are used to model many biological and physical systems at a discrete level. The average properties of the population may be described by a continuum model based on partial…

Evolutionary game theory has traditionally employed deterministic models to describe population dynamics. These models, due to their inherent nonlinearities, can exhibit deterministic chaos, where population fluctuations follow complex,…

Stochastic diffusion is the noisy and uncertain process through which dynamics like epidemics, or agents like animal species, disperse over a larger area. Understanding these processes is becoming increasingly important as we attempt to…

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 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…

A stochastic model for behavioral changes by imitative pair interactions of individuals is developed. `Microscopic' assumptions on the specific form of the imitative processes lead to a stochastic version of the game dynamical equations.…

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…

I discuss the so-called stochastic individual based model of adaptive dynamics and in particular how different scaling limits can be obtained by taking limits of large populations, small mutation rate, and small effect of single mutations…

Over the last few decades, ecologists have come to appreciate that key ecological patterns, which describe ecological communities at relatively large spatial scales, are not only scale dependent, but also intimately intertwined. The…

Identifying the critical domain size necessary for a population to persist is an important question in ecology. Both demographic and environmental stochasticity impact a population's ability to persist. Here we explore ways of including…

The theory of slow manifolds is an important tool in the study of deterministic dynamical systems, giving a practical method by which to reduce the number of relevant degrees of freedom in a model, thereby often resulting in a considerable…