论文标题
随机生态社区共存和灭绝的一般理论
A general theory of coexistence and extinction for stochastic ecological communities
论文作者
论文摘要
我们分析了一种一般理论，该理论是生态社区共存和灭绝的，该理论受到随机时间环境波动影响的生态群落。结果适用于离散时间（随机差方程），连续时间（随机微分方程），紧凑和非紧密的状态空间以及退化或非分类噪声。此外，我们还可以包括模拟环境波动，种群结构，生态环境反馈或其他内部或外部因素的动力学辅助变量。 我们能够将Benaim和Schreiber（数学生物学杂志'19杂志）的最新离散时间结果显着概括到非紧密的状态空间，并且我们提供了更强的持久性和灭绝结果。 Hening和Nguyen（应用概率'18的年鉴）的连续时间结果得到了加强，以包括退化噪声和辅助变量。 使用一般理论，我们列出了几个示例。在离散的时间内，我们在有一个或两个物种时对动态进行了分类，并查看Ricker模型，对数正态分布的后代模型，彩票模型，离散Lotka-Volterra模型以及多年生和年生物体的模型。对于连续的时间设置，我们使用资源变量，随机复制器模型和三维Lotka-Volterra模型探索模型。
We analyze a general theory for coexistence and extinction of ecological communities that are influenced by stochastic temporal environmental fluctuations. The results apply to discrete time (stochastic difference equations), continuous time (stochastic differential equations), compact and non-compact state spaces and degenerate or non-degenerate noise. In addition, we can also include in the dynamics auxiliary variables that model environmental fluctuations, population structure, eco-environmental feedbacks or other internal or external factors. We are able to significantly generalize the recent discrete time results by Benaim and Schreiber (Journal of Mathematical Biology '19) to non-compact state spaces, and we provide stronger persistence and extinction results. The continuous time results by Hening and Nguyen (Annals of Applied Probability '18) are strengthened to include degenerate noise and auxiliary variables. Using the general theory, we work out several examples. In discrete time, we classify the dynamics when there are one or two species, and look at the Ricker model, Log-normally distributed offspring models, lottery models, discrete Lotka-Volterra models as well as models of perennial and annual organisms. For the continuous time setting we explore models with a resource variable, stochastic replicator models, and three dimensional Lotka-Volterra models.
