随机环境中正密度依赖结构种群的动力学剖分
A dynamical trichotomy for structured populations experiencing positive density-dependence in stochastic environments
摘要：
当个体经历随着人口密度增加而增加的生存、生长或繁殖时，会发生正密度依赖。导致这些积极关系的机制包括交配限制，饱和捕食风险，合作育种和觅食。这些群体中的个体可能在年龄、大小或地理位置上不同，从而构成这些群体。在这里，我研究结构化的人口模型占积极的密度依赖性和环境随机性，即随机波动的人口的人口率。在可访问性假设下（粗略地说，随机波动可以导致种群变小和变大），这些模型显示出动态的随机性：（i）对于所有初始条件，种群以概率1渐近灭绝，（ii）对于所有正初始条件，种群持续存在并渐近表现出无界增长，以及（iii）对于所有正初始条件，存在渐近灭绝的正概率和无限增长的互补正概率。的主要结果说明与应用程序的空间结构的人口与Allee效应和年龄结构的人口遇到配偶限制。
英文摘要：
Positive density-dependence occurs when individuals experience increased survivorship, growth, or reproduction with increased population densities. Mechanisms leading to these positive relationships include mate limitation, saturating predation risk, and cooperative breeding and foraging. Individuals within these populations may differ in age, size, or geographic location and thereby structure these populations. Here, I study structured population models accounting for positive density-dependence and environmental stochasticity i.e. random fluctuations in the demographic rates of the population. Under an accessibility assumption (roughly, stochastic fluctuations can lead to populations getting small and large), these models are shown to exhibit a dynamical trichotomy: (i) for all initial conditions, the population goes asymptotically extinct with probability one, (ii) for all positive initial conditions, the population persists and asymptotically exhibits unbounded growth, and (iii) for all positive initial conditions, there is a positive probability of asymptotic extinction and a complementary positive probability of unbounded growth. The main results are illustrated with applications to spatially structured populations with an Allee effect and age-structured populations experiencing mate limitation.
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