Related papers: Localization for Linear Stochastic Evolutions
In this paper we focus on spatial Markov population models, describing the stochastic evolution of populations of agents, explicitly modelling their spatial distribution, representing space as a discrete, finite graph. More specifically, we…
We consider a class of stochastic growth models on the integer lattice which includes various interesting examples such as the number of open paths in oriented percolation and the binary contact path process. Under some mild assumptions, we…
This paper is concerned with spatial spreading dynamics of a nonlocal dispersal population model in a shifting environment where the favorable region is shrinking. It is shown that the species will become extinct in the habitat once the…
We introduce a nonlinear and nonlocal model that describes the range expansion of a population resulting from growth and competition for space. This type of phenomenon underlies the expansion of colonies of immotile cells which motivated…
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…
We study a stochastic spatial model of biological competition in which two species have the same birth and death rates, but different diffusion constants. In the absence of this difference, the model can be considered as an off-lattice…
Winner-take-all phenomena are observed in various competitive systems. We find similar phenomena in replicator models with randomly fluctuating growth rates. The disparity between winners and losers increases indefinitely, even if all…
The evolution of dispersal rate is studied with a model of several local populations linked by dispersal. Three dispersal strategies are considered where all, half, or none of the offspring disperse. The spatial scale (number of patches)…
The presence of one or more species at some spatial locations but not others is a central matter in ecology. This phenomenon is related to ecological pattern formation. Nonlocal interactions can be considered as one of the mechanisms…
There is mounting empirical evidence that many communities of living organisms display key features which closely resemble those of physical systems at criticality. We here introduce a minimal model framework for the dynamics of a community…
We employ Monte Carlo simulations to study a stochastic Lotka-Volterra model on a two-dimensional square lattice with periodic boundary conditions. If the (local) prey carrying capacity is finite, there exists an extinction threshold for…
In this paper, we investigate a generalised model of $N$ particles undergoing second-order non-local interactions on a lattice. Our results have applications across many research areas, including the modelling of migration, information…
We derive an alternative expression for a delayed logistic equation in which the rate of change in the population involves a growth rate that depends on the population density during an earlier time period. In our formulation, the delay in…
We model and study the genetic evolution and conservation of a population of diploid hermaphroditic organisms, evolving continuously in time and subject to resource competition. In the absence of mutations, the population follows a 3-type…
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 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…
Positive density-dependence occurs when individuals experience increased survivorship, growth, or reproduction with increased population densities. Mechanisms leading to these positive relationships include mate limitation, saturating…
We propose new analytical tools for describing growth-rate distributions generated by stationary time-series. Our analysis shows how deviations from normality are not pathological behaviour, as suggested by some traditional views, but…
This article is concerned with a version of the contact process with sexual reproduction on a graph with two levels of interactions modeling metapopulations. The population is spatially distributed into patches and offspring are produced in…
Stochastic, spatially extended models for predator-prey interaction display spatio-temporal structures that are not captured by the Lotka-Volterra mean-field rate equations. These spreading activity fronts reflect persistent correlations…