AI 中文总结
研究空间异质环境中两竞争物种生态动力学长期行为，通过构建连续和有限维模型，得出相互入侵是稳定共存充分必要条件，且有限维模型低估物种持久性，揭示空间异质性对物种生存的促进作用。
AI 中文摘要
我们关注由两种栖息地类型组成的空间异质环境中两个竞争物种生态动力学的长期行为，目标是为两个种群的持久性提供条件。首先考虑空间连续模型，形式化为无限维积分 - 微分方程组，表明若各物种单独存在时能持久，相互入侵对方单物种平衡是两物种长期生存的充分条件。接着引入有限维常微分方程组，通过对有限数量栖息地类型平均近似空间动力学，得出类似稳定共存充分条件并证明存在正共存平衡。最后用模拟研究完善理论结果，表明相互入侵也是两种模型中稳定共存的必要条件，还显示有限维模型低估物种持久性，即空间异质性促进生存。
英文摘要
We are interested in the long-time behaviour of the ecological dynamics of two competing species in a spatially heterogeneous environment consisting of two habitat types. Our goal is to provide conditions for the persistence of the two populations. First, we consider a spatially continuous model, formalized as an infinite-dimensional system of integro-differential equations. We show that if each species would persist if it were alone, then mutual invasibility of each other's monospecific equilibrium is a sufficient condition for long time survival of both species. Second, we introduce a finite-dimensional system of ordinary differential equations which approximate the spatial dynamics by averaging over a finite number of habitat types. We derive an analogous sufficient condition for stable coexistence, and show that in this case, there exists a positive coexistence equilibrium. Finally, we complete our theoretical result using a simulation study. Our results indicate that mutual invasibility also is a necessary condition for stable coexistence in both models. In addition, we show that the finite-dimensional model underestimates species' persistance, which indicates that spatial heterogeneity promotes survival.
