具有种内竞争的随机Lotka-Volterra食物链的持久性
Persistence in Stochastic Lotka--Volterra food chains with intraspecific competition
摘要：
本文研究了随机环境下一类简单的Lotka-Volterra食物链的演化问题。它可以被看作是Hening和Nguyen（J. of Math. Biol.'18）的配套论文，其中我们在假设捕食者之间没有种内竞争的情况下描述了这种食物链的持久性和灭绝。在目前的文件中，我们专注于当所有物种的经验内竞争的情况下。我们分析的食物链由一个猎物和$n-1$捕食者组成。$j$第一种捕食者吃掉$j-1$第一种，然后被$j+1$第一种捕食者吃掉;这样，每个物种最多只与两个其他物种相互作用--在营养链中，这些物种直接位于它的上方或下方。我们表明，一个可以分类，基于入侵率的捕食者（我们可以确定通过算法的系统的相互作用系数），物种灭绝，收敛到他们独特的不变概率测度。我们得到更强的结果比在没有种内竞争的情况下，因为在这种情况下，我们可以利用的一般结果的Hening和Nguyen（Ann.的应用概率）。与文献中的大多数结果不同，我们对非退化和退化噪声进行了深入分析。我们展示我们的一般结果，通过分析植物-食草动物-捕食系统中的营养级联，并提供持久性/灭绝的食物链长度$n\leq 3$的标准。
英文摘要：
This paper is devoted to the analysis of a simple Lotka-Volterra food chain evolving in a stochastic environment. It can be seen as the companion paper of Hening and Nguyen (J. of Math. Biol. `18) where we have characterized the persistence and extinction of such a food chain under the assumption that there is no intraspecific competition among predators. In the current paper we focus on the case when all the species experience intracompetition. The food chain we analyze consists of one prey and $n-1$ predators. The $j$th predator eats the $j-1$st species and is eaten by the $j+1$st predator; this way each species only interacts with at most two other species - the ones that are immediately above or below it in the trophic chain. We show that one can classify, based on the invasion rates of the predators (which we can determine from the interaction coefficients of the system via an algorithm), which species go extinct and which converge to their unique invariant probability measure. We obtain stronger results than in the case with no intraspecific competition because in this setting we can make use of the general results of Hening and Nguyen (Ann. of Appl. Probab.). Unlike most of the results available in the literature, we provide an in depth analysis for both non-degenerate and degenerate noise. We exhibit our general results by analysing trophic cascades in a plant--herbivore--predator system and providing persistence/extinction criteria for food chains of length $n\leq 3$.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
