Persistence in fluctuating environments

• DOI: 10.1007/s00285-010-0349-5
• Publication Date: 2010-06-07T11:45:34Z
• Authors: Sebastian J. Schr...; Michel Benaïm; Kolawolé A. S. At...
• Keywords: Stationary distribution; Persistence (discontinuity)

Understanding under what conditions interacting populations, whether they be plants, animals, or viral particles, coexist is a question of theoretical and practical importance in population biology. Both biotic interactions environmental fluctuations are key factors that can facilitate disrupt coexistence. To better understand this interplay between these deterministic stochastic forces, we develop mathematical theory extending the nonlinear permanence for systems to difference differential equations. Our condition coexistence requires there fixed set weights associated with populations weighted combination populations’ invasion rates positive any (ergodic) stationary distribution subcollection populations. Here, an rate corresponds average per-capita growth along distribution. When holds sufficient noise system, show approach unique Moreover, our criterion robust small perturbations model functions. Using theory, illustrate (i) enhances inhibits communities rock-paper-scissor dynamics depending on correlations interspecific demographic rates, (ii) variation mortality has no effect criteria discrete-time Lotka–Volterra communities, (iii) random forcing promote genetic diversity presence exploitative interactions. One day fine, next black.—The Clash