Convergence to stationary distributions in two-species stochastic competition models.
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 phi-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.
Ellner
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Department of Statistics, North Carolina State University, Raleigh 27695-8203.
D004463:Ecology; D004777:Environment; D015233:Models, Statistical; D011153:Population; D011336:Probability; D013269:Stochastic Processes