局部调节竞争种群的共存与分支湮灭随机游动的生存
Coexistence in locally regulated competing populations and survival of branching annihilating random walk
摘要：
我们提出了两个模型的一对竞争种群的进化。两者都是基于网格的。第一个是完全空间模型之间的妥协，这似乎不服从分析结果，和相互作用的粒子系统模型，不，目前，将所有的竞争策略，人口可能采取。第二种方法是第一种方法的简化，即竞争只发生在格点内，每个格点内的总总体规模为常数。在特殊情况下，第二个模型是一个分支零化随机游动的对偶。对于每个模型，使用定向渗流的比较，我们表明，对于某些参数值，两个人口将共存的所有时间与正概率。作为推论，我们推导出的所有时间的分支零化随机游动足够大的分支率的生存。我们还提出了一些与空间在两个种群的生存概率中的作用有关的图表。
英文摘要：
We propose two models of the evolution of a pair of competing populations. Both are lattice based. The first is a compromise between fully spatial models, which do not appear amenable to analytic results, and interacting particle system models, which do not, at present, incorporate all of the competitive strategies that a population might adopt. The second is a simplification of the first, in which competition is only supposed to act within lattice sites and the total population size within each lattice point is a constant. In a special case, this second model is dual to a branching annihilating random walk. For each model, using a comparison with oriented percolation, we show that for certain parameter values, both populations will coexist for all time with positive probability. As a corollary, we deduce survival for all time of branching annihilating random walk for sufficiently large branching rates. We also present a number of conjectures relating to the rôle of space in the survival probabilities for the two populations.
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