论文标题
$ p^*$规则在随机的Holt-Lawton明显竞争模型中
The $P^*$ rule in the stochastic Holt-Lawton model of apparent competition
论文作者
论文摘要
霍尔特（Holt）和劳顿（Lawton）在$ 1993 $中引入了一个随机模型，该模型是由普通寄生虫物种寄生的两个寄主物种。我们介绍和分析了这些随机差异方程的概括，与任何数量的宿主物种，随机变化的寄生虫率，随机变化的宿主内在适应性以及寄生虫的随机移民。尽管缺乏直接的宿主密度依赖性，但我们表明该系统是耗散性的，即在所有初始条件下进入有限时间的紧凑型设置。当有单个宿主物种时，使用外部Lyapunov指数对应于宿主的平均人均生长速率时，将宿主的随机持久性和灭绝来表征。当单个宿主持续存在时，例如物种$ i $，在支撑这两个物种的固定分布中的平均密度（$ p_i^*$）的平均密度（$ p_i^*$）得出了明显的表达。当有多种寄主物种时，我们证明了最大的$ p_i^*$值随机持续存在的宿主物种，而其他宿主物种则渐近地驱动为灭绝。对用于证明结果和未来挑战的主要数学方法的回顾。
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.
