Extinction in neutrally stable stochastic Lotka-Volterra models

Dobrinevski, Alexander und Frey, Erwin (Mai 2012): Extinction in neutrally stable stochastic Lotka-Volterra models. In: Physical Review E, Bd. 85, Nr. 5: 051903-1

Abstract

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 leading to extinction of species, whose understanding is a key component in the study of evolution and biodiversity, are influenced by both of these factors. Here, we investigate a class of stochastic population dynamics models based on generalized Lotka-Volterra systems. In the case of neutral stability of the underlying deterministic model, the impact of intrinsic noise on the survival of species is dramatic: It destroys coexistence of interacting species on a time scale proportional to the population size. We introduce a new method based on stochastic averaging which allows one to understand this extinction process quantitatively by reduction to a lower-dimensional effective dynamics. This is performed analytically for two highly symmetrical models and can be generalized numerically to more complex situations. The extinction probability distributions and other quantities of interest we obtain show excellent agreement with simulations.

• Dokumententyp: Zeitschriftenartikel
• Publikationsform: Publisher's Version
• Fakultät: Physik
• Themengebiete: 500 Naturwissenschaften und Mathematik > 530 Physik
• ISSN: 1539-3755
• Ort: ONE PHYSICS ELLIPSE, COLLEGE PK, MD 20740-3844 USA
• Sprache: Englisch