Related papers: Extinction statistics in N random interacting spec…
How do interactions between species influence their spatial distribution in an ecosystem? To answer this question, we introduce a spatially-extended ecosystem of Generalized Lotka-Volterra type, where species can diffuse and interactions…
We study a stochastic predator-prey model on a square lattice, where each of the six species has two superior and two inferior partners. The invasion probabilities between species depend on the predator-prey pair and are supplemented by…
Introducing the effect of extinction into the so-called replicator equations in mathematical biology, we construct a general model of ecosystems. The present model shows mass extinction by its own extinction dynamics when the system…
Motivated by the traditional Lotka-Volterra competitive models, this paper proposes and analyzes a class of stochastic reaction-diffusion partial differential equations. In contrast to the models in the literature, the new formulation…
We analyze ecological systems that are influenced by random environmental fluctuations. We first provide general conditions which ensure that the species coexist and the system converges to a unique invariant probability measure (stationary…
We study the asymptotics of a two-dimensional stochastic differential system with a degenerate diffusion matrix. This system describes the dynamics of a population where individuals contribute to the degradation of their environment through…
Time evolution of number of species (genera, families, and others), population of them, and size distribution of present ones and life times are studied in terms of a new model, where population of each genetic taxon increases by a (random)…
We use an effective Markovian description to study the long-time behaviour of a nonlinear second order Langevin equation with Gaussian noise. When dissipation is neglected, the energy of the system grows as with time a power-law with an…
When four species compete stochastically in a cyclic way, the formation of two teams of mutually neutral partners is observed. In this paper we study through numerical simulations the extinction processes that can take place in this system…
The influence of an external random field on the competition process in a nonlinear open spatially extended system is analyzed numerically. A three-component model is chosen as the competition model in which a "weak" species can move in…
We introduce and study a stochastic model for the dynamics of colonial species, which reproduce through fission or fragmentation. The fission rate depends on the relative sizes of colonies in the population, and the growth rate of colonies…
The enigmatic stability of population oscillations within ecological systems is analyzed. The underlying mechanism is presented in the framework of two interacting species free to migrate between two spatial patches. It is shown that that…
We investigate stochastic extinction in an epidemic model and the impact of random vaccinations in large populations. We show that, in the absence of vaccinations, the effective entropic barrier for extinction displays scaling with the…
Stochasticity can play an important role in the dynamics of biologically relevant populations. These span a broad range of scales: from intra-cellular populations of molecules to population of cells and then to groups of plants, animals and…
Isolated populations ultimately go extinct because of the intrinsic noise of elementary processes. In multi-population systems extinction of a population may occur via more than one route. We investigate this generic situation in a simple…
We define a model of Galton Watson processes in dynamical environments where the environment evolves according to a dynamical system (X, T). Three behaviours are possible: uniformly subcritical, critical, and uniformly supercritical. We…
Game theory ideas provide a useful framework for studying evolutionary dynamics in a well-mixed environment. This approach, however, typically enforces a strictly fixed overall population size, deemphasizing natural growth processes. We…
We study the density fluctuations at equilibrium of the multi-species stirring process, a natural multi-type generalization of the symmetric (partial) exclusion process. In the diffusive scaling limit, the resulting process is a system of…
Quantification of chaos is a challenging issue in complex dynamical systems. In this paper, we discuss the chaotic properties of generalized Lotka-Volterra and May-Leonard models of biodiversity, via the Hamming distance density. We…
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…