Related papers: Persistence and extinction dynamics in a stochasti…
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 consider a nonlocal parabolic equation describing the dynamics of a population structured by a spatial position and a phenotypic trait, submitted to dispersion , mutations and growth. The growth term may be of the Fisher-KPP type but may…
In this paper, we analyse a recently proposed predator-prey model with ratio dependence and Holling type III functional response, with particular emphasis on the dynamics close to extinction. By using Briot-Bouquet transformation we…
Mutual interference and prey refuge are important drivers of predator-prey dynamics. The "exponent" or degree of mutual interference has been under much debate in theoretical ecology. In the present work, we investigate the interplay of the…
Including spatial structure and stochastic noise invalidates the classical Lotka-Volterra picture of stable regular population cycles emerging in models for predator-prey interactions. Growth-limiting terms for the prey induce a continuous…
In this paper we present the simplest individual level model of predator-prey dynamics and show, via direct calculation, that it exhibits cycling behavior. The deterministic analogue of our model, recovered when the number of individuals is…
We introduce a spatial stochastic process on the lattice Z^d to model mass extinctions. Each site of the lattice may host a flock of up to N individuals. Each individual may give birth to a new individual at the same site at rate \phi until…
In recent years there has been a growing interest in the study of the dynamics of stochastic populations. A key question in population biology is to understand the conditions under which populations coexist or go extinct. Theoretical and…
This study assessed the effects of migration on the dynamics of a species population. It was considered that the species in its natural state and without the presence of migration exhibited Allee effect. This work also considered migration…
We are interested in the impact of natural selection in a prey-predator community. We introduce an individual-based model of the community that takes into account both prey and predator phenotypes. Our aim is to understand the phenotypic…
We consider a nonlocal bistable reaction-diffusion equation, which serves as a model for a population structured by a phenotypic trait, subject to mutation, trait-dependent fitness, and nonlocal competition. Within this replicator-mutator…
We study the effects of demographic stochasticity on the long-term dynamics of biological coevolution models of community assembly. The noise is induced in order to check the validity of deterministic population dynamics. While mutualistic…
We analyze the role of the Allee effect, a positive correlation between population density and mean individual fitness, for ecological communities formed by a large number of species. Our study is performed using the generalized…
In this paper, we investigate the effect of dispersal and advection on the dynamics of a predator-prey model. More precisely, we show that the linear stability of the semi-trivial steady state is determined by the dispersal rate, the…
Two mathematical models of macroevolution are studied. These models have population dynamics at the species level, and mutations and extinction of species are also included. The population dynamics are updated by difference equations with…
How diffusion impacts on ecological dynamics under the Allee effect and spatial constraints? That is the question we address. Employing a microscopic minimal model in a metapopulation (without imposing nonlinear birth and death rates) we…
Populations of competing biological species exhibit a fascinating interplay between the nonlinear dynamics of evolutionary selection forces and random fluctuations arising from the stochastic nature of the interactions. The processes…
We consider a recently introduced model of mosquito dynamics that includes mating and progression through breeding, questing and egg-laying stages of mosquitoes using human and other vertebrate sources for blood meals. By exploiting a…
The coupling between evolutionary and ecological changes (eco-evolutionary dynamics) has been shown to be relevant among diverse species, and is also of interest outside of ecology, i.e. in cancer evolution. These dynamics play an important…
We examine the switching dynamics of a stochastic population subjected to a deterministically time-varying environment. Our approach is demonstrated in the realm of ecology on a problem of population establishment. Here, by assuming a…