The quasi-deterministic limit of population dynamics
نویسندگان
چکیده
We discuss and compare three different, but related, approximations to the stochastic dynamics of populations, all of them having as limit the same deterministic dynamics. The diffusion approximation (van Kampen (1981a); Arnold (1997)), linearized diffusion approximation (Kurtz (1971)) and the Poisson approximation (Aparicio & Solari (2001a); Solari & Natiello (2003b)) are briefly revisited and their quality as approximations for large, but given, populations is addressed analytically as well as with demonstrative examples.
منابع مشابه
Noise-driven transition to quasi-deterministic limit cycle dynamics in excitable systems
The effect of small-amplitude noise on excitable systems with large time-scale separation is analyzed. It is found that small random perturbations of the fast excitatory variable result in the onset of a quasi-deterministic limit cycle behavior, absent without noise. The limit cycle is established at a critical value of the amplitude of the noise, and its period is nontrivially determined by th...
متن کاملQuasi-stationary Distributions and Diffusion Models in Population Dynamics by Patrick Cattiaux, Pierre Collet,
In this paper we study quasi-stationarity for a large class of Kolmogorov diffusions. The main novelty here is that we allow the drift to go to −∞ at the origin, and the diffusion to have an entrance boundary at +∞. These diffusions arise as images, by a deterministic map, of generalized Feller diffusions, which themselves are obtained as limits of rescaled birth–death processes. Generalized Fe...
متن کاملQuasi-stationary distributions for population processes
Key-words: population dynamics, quasi-stationarity, Yaglom’s limit, birth and death process, logistic Feller diffusion.
متن کاملMultilocus selection in subdivided populations I. Convergence properties for weak or strong migration.
The dynamics and equilibrium structure of a deterministic population-genetic model of migration and selection acting on multiple multiallelic loci is studied. A large population of diploid individuals is distributed over finitely many demes connected by migration. Generations are discrete and nonoverlapping, migration is irreducible and aperiodic, all pairwise recombination rates are positive, ...
متن کاملMetastable states and quasicycles in a stochastic Wilson-Cowan model of neuronal population dynamics.
We analyze a stochastic model of neuronal population dynamics with intrinsic noise. In the thermodynamic limit N→∞ , where N determines the size of each population, the dynamics is described by deterministic Wilson-Cowan equations. On the other hand, for finite N the dynamics is described by a master equation that determines the probability of spiking activity within each population. We first c...
متن کامل