Mutual Invadability Implies Coexistence in Spatial Models - Softcover

Durrett, Richard

Softcover

ISBN 10: 0821827685 ISBN 13: 9780821827680

Publisher: Amer Mathematical Society, 2002

Synopsis

In (1994) Durrett and Levin proposed that the equilibrium behaviour 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 Durrett proves a general result in support of that picture. He gives 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, he shows 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: Amer Mathematical Society
• Publication date: 2002
• Language: English
• ISBN 10: 0821827685
• ISBN 13: 9780821827680
• Binding: Mass Market Paperback
• Number of pages: 118