随机Holt-Lawton表观竞争模型中的$P^*$规则
The $P^*$ rule in the stochastic Holt-Lawton model of apparent competition
摘要：
在$1993$中，Holt和Lawton引入了一个两种寄主被一种寄生蜂寄生的随机模型。我们介绍和分析了这些随机差分方程的泛化与任何数量的主机物种，随机变化的寄生率，随机变化的主机固有的适合度，和随机移民的寄生蜂。尽管缺乏直接的，主机的密度依赖性，我们表明，该系统是耗散的，即在有限时间内进入一个紧凑的集合的所有初始条件。当有一个单一的主机物种，随机持久性和灭绝的主机的特点是使用外部李雅普诺夫指数对应的平均人均增长率的主机时，罕见的。当一个单一的主机持续，说物种$i$，一个明确的表达式是来自平均密度，$P_i^*$，寄生蜂在固定分布支持两个物种。当有多个宿主物种时，我们证明了具有最大$P_i^*$值的宿主物种随机持续存在，而其他宿主物种则渐进地走向灭绝。回顾了主要的数学方法来证明的结果和未来的挑战。
英文摘要：
In $1993$, Holt and Lawton introduced a stochastic model of two host species parasitized by a common parasitoid species. We introduce and analyze a generalization of these stochastic difference equations with any number of host species, stochastically varying parasitism rates, stochastically varying host intrinsic fitnesses, and stochastic immigration of parasitoids. Despite the lack of direct, host density-dependence, we show that this system is dissipative i.e. enters a compact set in finite time for all initial conditions. When there is a single host species, stochastic persistence and extinction of the host is characterized using external Lyapunov exponents corresponding to the average per-capita growth rates of the host when rare. When a single host persists, say species $i$, a explicit expression is derived for the average density, $P_i^*$, of the parasitoid at the stationary distributions supporting both species. When there are multiple host species, we prove that the host species with the largest $P_i^*$ value stochastically persists, while the other host species are asymptotically driven to extinction. A review of the main mathematical methods used to prove the results and future challenges are given.
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