Related papers: Extinction, periodicity and multistability in a Ri…
We study the evolution in discrete time of certain age-structured populations, such as adults and juveniles, with a Ricker fitness function. We determine conditions for the convergence of orbits to the origin (extinction) in the presence of…
A model of the dynamics of natural rotifer populations is described as a discrete nonlinear map depending on three parameters, which reflect characteristics of the population and environment. Model dynamics and their change by variation of…
Species extinction occurs regularly and unavoidably in ecological systems. The time scales for extinction can broadly vary and inform on the ecosystem's stability. We study the spatio-temporal extinction dynamics of a paradigmatic…
The statistical properties of an ecosystem composed of species interacting via pairwise, random interactions and deterministic, concentration limiting self-interaction are studied analytically with tools of equilibrium statistical mechanics…
We study bifurcations in a spatially extended nonlinear system representing population dynamics with the help of analytic calculations based on the time-independent Schr\"{o}dinger equation for a quantum particle subjected to a uniform…
We present an explicit unified stochastic model of fluctuations in population size due to random birth, death, density-dependent competition and environmental fluctuations. Stochastic dynamics provide insight into small populations,…
We investigate extinction dynamics in the paradigmatic model of two competing species A and B that reproduce (A-->2A, B-->2B), self-regulate by annihilation (2A-->0, 2B-->0), and compete (A+B-->A, A+B-->B). For a finite system that is in…
We present numerical results based on a simplified ecological system in evolution, showing features of extinction similar to that claimed for the biosystem on Earth. In the model each species consists of a population in interaction with the…
We consider a system of two stochastic differential equations (SDEs) with competing two-way interactions driven by Brownian motions and spectrally positive $\alpha$-stable random measures. Such a SDE system can be identified as a…
We study the biodiversity problem for resource competition systems with extinctions and self-limitation effects. Our main result establishes estimates of biodiversity in terms of the fundamental parameters of the model. We also prove the…
We study the multi-species replicator model with linear fitness and random fitness matrices of various classes. By means of numerical resolution of the replicator equations, we determine the survival probability of a species in terms of its…
We investigate the bifurcation structure of equilibria in a class of non-autonomous ordinary differential equations governed by a season length parameter, $\tau$, which determines the alternation between growth and decline dynamics. This…
We study the ABC model (A + B --> 2B, B + C --> 2C, C + A --> 2A), and its counterpart: the three--component neutral drift model (A + B --> 2A or 2B, B + C --> 2B or 2C, C + A --> 2C or 2A.) In the former case, the mean field approximation…
We study the non-equilibrium phase transition between survival and extinction of spatially extended biological populations using an agent-based model. We especially focus on the effects of global temporal fluctuations of the environmental…
Recent biological evidence suggests the presence of a two-phase ageing process in several species. We introduce a system of two age-structured partial differential equations (PDE) representing two phases of ageing of a wild population. The…
A model for large-scale evolution recently introduced by Amaral and Meyer is studied analytically and numerically. Species are located at different trophic levels and become extinct if their prey becomes extinct. It is proved that this…
Population dynamics reflects an underlying birth-death process, where the rates associated with different events may depend on external environmental conditions and on the population density. A whole family of simple and popular…
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…
Understanding the conditions ensuring the persistence of a population is an issue of primary importance in population biology. The first theoretical approach to the problem dates back to the 50's with the KiSS (after Kierstead, Slobodkin…
Competitive birth-death processes often exhibit an oscillatory behavior. We investigate a particular case where the oscillation cycles are marginally stable on the mean-field level. An iconic example of such a system is the Lotka-Volterra…