Persistence in fluctuating environments |
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Authors: | Sebastian J Schreiber Michel Benaïm Kolawolé A S Atchadé |
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Institution: | 1.Department of Evolution and Ecology and the Center for Population Biology,University of California,Davis,USA;2.Institut de Mathématiques,Université de Neuchatel,Neuchatel,Switzerland |
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Abstract: | 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 and environmental fluctuations
are key factors that can facilitate or disrupt coexistence. To better understand this interplay between these deterministic
and stochastic forces, we develop a mathematical theory extending the nonlinear theory of permanence for deterministic systems
to stochastic difference and differential equations. Our condition for coexistence requires that there is a fixed set of weights
associated with the interacting populations and this weighted combination of populations’ invasion rates is positive for any
(ergodic) stationary distribution associated with a subcollection of populations. Here, an invasion rate corresponds to an
average per-capita growth rate along a stationary distribution. When this condition holds and there is sufficient noise in
the system, we show that the populations approach a unique positive stationary distribution. Moreover, we show that our coexistence
criterion is robust to small perturbations of the model functions. Using this theory, we illustrate that (i) environmental
noise enhances or inhibits coexistence in communities with rock-paper-scissor dynamics depending on correlations between interspecific
demographic rates, (ii) stochastic variation in mortality rates has no effect on the coexistence criteria for discrete-time
Lotka–Volterra communities, and (iii) random forcing can promote genetic diversity in the presence of exploitative interactions.
One day is fine, the next is black.—The Clash |
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