Mutual Invadability Implies Coexistence in Spatial Models (Memoirs of the American Mathematical Society) - Softcover

Durrett, Richard

Softcover

ISBN 10: 0821827685 ISBN 13: 9780821827680

Publisher: American Mathematical Society, 2002

Synopsis

In (1994) Durrett and Levin proposed that the equilibrium behavior of stochastic spatial models could be determined from properties of the solution of the mean field ordinary differential equation (ODE) that is obtained by pretending that all sites are always independent. Here we prove a general result in support of that picture. We give a condition on an ordinary differential equation which implies that densities stay bounded away from 0 in the associated reaction-diffusion equation, and that coexistence occurs in the stochastic spatial model with fast stirring. Then using biologists' notion of invadability as a guide, we show how this condition can be checked in a wide variety of examples that involve two or three species: epidemics, diploid genetics models, predator-prey systems, and various competition models.

Edition details

• Publisher: American Mathematical Society
• Publication date: 2002
• Language: English
• ISBN 10: 0821827685
• ISBN 13: 9780821827680
• Binding: Mass Market Paperback
• Number of pages: 118