Persistence and extinction for stochastic ecological models with internal and external variables
Persistence and extinction for stochastic ecological models with internal and external variables
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DOI：
10.1007/s00285-019-01361-4
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发表时间：
2019-07-01
影响因子：
1.9
通讯作者：
Schreiber, Sebastian J.
中科院分区：
文献类型：
--
作者：
Benaim, Michel;Schreiber, Sebastian J.
物种密度的动态取决于内部和外部变量。内部变量包括表现出不同表型或生活在不同空间位置的个体的频率。外部变量包括非生物因素或非焦点物种。这些内部或外部变量可能由于环境条件的随机波动而波动。这些变量和物种密度之间的相互作用可以决定特定种群是否持续存在或灭绝。为了理解这种相互作用，我们证明了考虑内部和外部变量的随机生态差分方程的随机持久性和排除定理。具体来说，我们使用平均李亚普诺夫函数的随机模拟来开发充分和必要的条件：（i）所有种群密度在低密度下花费很少的时间，即随机持久性，以及（ii）种群轨迹以正概率渐近接近灭绝集。对于（i）和（ii），我们分别提供了系统接近灭绝集合的时间分数的定量估计，以及渐近灭绝的概率作为系统初始状态的函数。此外，在持久性的情况下，我们提供了逃离灭绝集邻域的预期时间的下限。为了说明我们的结果的适用性，我们分析了进化博弈、Lotka-Volterra 动力学、性状进化和空间结构疾病动力学的随机模型。我们对这些模型的分析表明，环境随机性促进了鹰鸽博弈中策略的共存，但抑制了石头剪刀布博弈和 Lotka-Volterra 捕食者-猎物模型中的共存。此外，具有正自相关的环境波动可以促进不断进化的种群的持续存在和斑块景观中疾病的持续存在。虽然我们的结果有助于缩小确定性系统和随机系统的持久性理论之间的差距，但我们强调了未来研究的几个挑战。
The dynamics of species' densities depend both on internal and external variables. Internal variables include frequencies of individuals exhibiting different phenotypes or living in different spatial locations. External variables include abiotic factors or non-focal species. These internal or external variables may fluctuate due to stochastic fluctuations in environmental conditions. The interplay between these variables and species densities can determine whether a particular population persists or goes extinct. To understand this interplay, we prove theorems for stochastic persistence and exclusion for stochastic ecological difference equations accounting for internal and external variables. Specifically, we use a stochastic analog of average Lyapunov functions to develop sufficient and necessary conditions for (i) all population densities spending little time at low densities i.e. stochastic persistence, and (ii) population trajectories asymptotically approaching the extinction set with positive probability. For (i) and (ii), respectively, we provide quantitative estimates on the fraction of time that the system is near the extinction set, and the probability of asymptotic extinction as a function of the initial state of the system. Furthermore, in the case of persistence, we provide lower bounds for the expected time to escape neighborhoods of the extinction set. To illustrate the applicability of our results, we analyze stochastic models of evolutionary games, Lotka-Volterra dynamics, trait evolution, and spatially structured disease dynamics. Our analysis of these models demonstrates environmental stochasticity facilitates coexistence of strategies in the hawk-dove game, but inhibits coexistence in the rock-paper-scissors game and a Lotka-Volterra predator-prey model. Furthermore, environmental fluctuations with positive auto-correlations can promote persistence of evolving populations and persistence of diseases in patchy landscapes. While our results help close the gap between the persistence theories for deterministic and stochastic systems, we highlight several challenges for future research.