Related papers: Stochastic population growth in spatially heteroge…
Continuum models for the spatial dynamics of growing cell populations have been widely used to investigate the mechanisms underpinning tissue development and tumour invasion. These models consist of nonlinear partial differential equations…
A two-species spatially extended system of hosts and parasitoids is studied. There are two distinct kinds of coexistence; one with populations distributed homogeneously in space and another one with spatiotemporal patterns. In the latter…
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.…
Microbial populations in the natural environment are likely to experience growth conditions very different from those of a typical laboratory xperiment. In particular, removal rates of biomass and substrate are unlikely to be balanced under…
We study a stochastic spatial epidemic model where the $N$ individuals carry two features: a position and an infection state, interact and move in $\R^d$. In this Markovian model, the evolution of the infection states are described with the…
The spatial heterogeneity of cities -- the uneven distribution of population and activities -- is fundamental to urban dynamics and related to critical issues such as infrastructure overload, housing affordability, and social inequality.…
We discuss several models of the dynamics of interacting populations. The models are constructed by nonlinear differential equations and have two sets of parameters: growth rates and coefficients of interaction between populations. We…
The effects of demographic stochasticity in the long term behaviour of endemic infectious diseases have been considered for long as a necessary addition to an underlying deterministic theory. The latter would explain the regular behaviour…
The time evolution of spatial fluctuations in inhomogeneous d-dimensional biological systems is analyzed. A single species continuous growth model, in which the population disperses via diffusion and convection is considered.…
Climate change impacts population distributions, forcing some species to migrate poleward if they are to survive and keep up with the suitable habitat that is shifting with the temperature isoclines. Previous studies have analyzed whether…
An ab-initio numerical study of the density-dependent, evolutionary stable dispersal strategy is presented. The simulations are based on a simple discretei generation island model with four processes: reproduction, dispersal, competition…
We consider a stochastic individual-based model for the evolution of a haploid, asexually reproducing population. The space of possible traits is given by the vertices of a (possibly directed) finite graph $G=(V,E)$. The evolution of the…
Ecologists have long argued about the strength of density dependence and population regulation, respectively defined as the short-term and long-term rates of return to equilibrium. Here, I give three arguments for the intractability of…
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…
Phenotypically structured equations arise in population biology to describe the interaction of species with their environment that brings the nutrients. This interaction usually leads to selection of the fittest individuals. Models used in…
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"…
We analyze an interacting particle system with a Markov evolution of birth-and-death type. We have shown that a local competition mechanism (realized via a density dependent mortality) leads to a globally regular behavior of the population…
Biodiversity widely observed in ecological systems is attributed to the dynamical balance among the competing species. The time-varying populations of the interacting species are often captured rather well by a set of deterministic…
Many models of population dynamics are formulated as deterministic iterated maps although real populations are stochastic. This is justifiable in the limit of large population sizes, as the stochastic fluctuations are negligible then.…
Understanding the mechanisms of species coexistence has always been a fundamental topic in ecology. Classical theory predicts that interspecific competition may select for traits that stabilize niche differences, although recent work shows…