Critical Domain Sizes for Persistence in a Discrete-Time Stage-Structured Population Model

种群持续生存所需的临界域大小是生态学中的一个重要问题，它与生境的大小和配置密切相关。考虑到自然界中大多数物种表现出高度结构化的生命周期，我们在n维空间的有界域Ω中分析了一个由脉冲反应扩散方程控制的离散时间阶段结构种群模型。域Ω的外部被认为是不利的，但不能完全阻止种群扩散。因此，我们采用Robin边界条件来描述边界上的种群动态，并提供了n维超立方体和带半径的球体形状的域的临界结果。具体来说，我们利用主特征值理论和上下解的方法证明了当种群所居住的栖息地大小小于栖息地的临界域大小时，种群将会灭绝。反之，当生境空间范围大于临界域大小时，种群可以持续生存。The critical domain size required for population persistence is a significant problem in ecology, which is closely associated with habitat size and configuration. Given that most species in nature exhibit highly structured life cycles, we analyze a discrete-time stage-structured population model governed by an impulsive reaction-diffusion equation within a bounded domain Ω in an n-dimensional space. The exterior of the domain Ω is considered unfavorable but does not completely prevent population dispersal. We thus employ Robin boundary conditions to describe population dynamics at the boundary and provide critical results for domains shaped as n-dimensional hypercube and sphere with radius R. Specifically, we employ principal eigenvalue theory and the method of upper and lower solutions to demonstrate that when the habitat size where the population resides is smaller than the critical domain size of the habitat, the population will become extinct. Conversely, when the spatial extent of habitat is larger than the critical domain size, the population can persist and survive.