Ellner S
Department of Statistics, North Carolina State University, Raleigh 27695-8203.
J Math Biol. 1989;27(4):451-62. doi: 10.1007/BF00290639.
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.
针对在随机变化环境中竞争的两种群的一些一般模型，给出了两组收敛到平稳分布的充分条件。这些模型是非线性随机差分方程，它们定义了马尔可夫链。一组充分条件涉及链的转移概率的强连续性和φ-不可约性。第二组具有弱得多的不可约性条件，但仅适用于单调模型。结果应用于一个随机两种群里克特模型和切森的“有空位的彩票模型”，以说明如何在具体模型中检验这些假设。
