Abstract
Two sets of sufficient conditions are given for convergence to stationary distributions, for some general models of two species competing in a randomly varying environment. The models are nonlinear stochastic difference equations which define Markov chains. One set of sufficient conditions involves strong continuity and φ-irreducibility of the transition probability for the chain. The second set has a much weaker irreducibility condition, but is only applicable to monotonic models. The results are applied to a stochastic two-species Ricker model, and to Chesson's “lottery model with vacant space”, to illustrate how the assumptions can be checked in specific models.
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Ellner, S. Convergence to stationary distributions in two-species stochastic competition models. J. Math. Biology 27, 451–462 (1989). https://doi.org/10.1007/BF00290639
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DOI: https://doi.org/10.1007/BF00290639