Stationary distributions of persistent ecological systems
Stationary distributions of persistent ecological systems
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DOI：
10.1007/s00285-021-01613-2
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发表时间：
2020-03
影响因子：
1.9
通讯作者：
Alexandru Hening;Yao Li
中科院分区：
文献类型：
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作者：
Alexandru Hening;Yao Li
我们分析受随机环境波动影响的生态系统。我们首先提供一般条件，确保物种共存和系统收敛到一个独特的不变的概率测度（平稳分布）。由于它通常是不可能的特征，这个不变的概率测度分析，我们开发了一个强大的方法，数值近似不变的概率措施。这使我们能够阐明生态系统的各种参数如何影响静态分布。我们分析不同类型的环境波动。首先，我们研究随机微分方程模拟的生态系统。在第二个设置中，我们看看分段确定性马尔可夫过程。在这些过程中，一个人在随机时间内遵循微分方程系统，之后环境状态发生变化，另一个人遵循不同的微分方程组-这个过程然后无限重复。最后，我们看看随机微分方程开关，其中考虑到白色噪声波动和随机环境开关。作为我们的理论和数值分析的应用程序，我们看看竞争的Lotka-Volterra，Beddington-DeAngelis捕食者-猎物，和石头剪刀布动态。我们通过分析生态系统的静态分布，并通过观察各种类型的环境波动如何影响种群的长期命运，来突出新的生物学见解。
We analyze ecological systems that are influenced by random environmental fluctuations. We first provide general conditions which ensure that the species coexist and the system converges to a unique invariant probability measure (stationary distribution). Since it is usually impossible to characterize this invariant probability measure analytically, we develop a powerful method for numerically approximating invariant probability measures. This allows us to shed light upon how the various parameters of the ecosystem impact the stationary distribution. We analyze different types of environmental fluctuations. At first we study ecosystems modeled by stochastic differential equations. In the second setting we look at piecewise deterministic Markov processes. These are processes where one follows a system of differential equations for a random time, after which the environmental state changes, and one follows a different set of differential equations—this procedure then gets repeated indefinitely. Finally, we look at stochastic differential equations with switching, which take into account both the white noise fluctuations and the random environmental switches. As applications of our theoretical and numerical analysis, we look at competitive Lotka–Volterra, Beddington–DeAngelis predator–prey, and rock–paper–scissors dynamics. We highlight new biological insights by analyzing the stationary distributions of the ecosystems and by seeing how various types of environmental fluctuations influence the long term fate of populations.