Asymptotic and transient dynamics in predator-prey systems with spatial and temporal heterogeneity

该研究计划将：（1）研究食物网系统中恐惧诱导的种间和种内相互作用;（2）探索捕食者-被捕食者系统中温度依赖的物候学;（3）研究种群动态中的瞬态行为。对于（1），重点将是双重的：我将研究间接捕食风险下的物种竞争结果和两个以上营养级的生态系统中恐惧的级联效应。我在（1）中建立的模型将我们以前关于具有恐惧效应的捕食者-食饵系统的结果推广到具有时空异质性的系统。这将导致对Meta社区中恐惧效应的彻底检查，丰富我们对物种如何相互作用的理解，并促进实施适当的生态系统管理策略。对于（2），重点将是研究在季节环境中，温度依赖的物候事件如何影响物种的空间分布。物候事件，如出现时间或繁殖，影响猎物和捕食者互动的时间和时间，并受到气候变化等环境变化的影响。此外，对于一个大类的物种，不同的季节之间的扩散模式有显着差异。我计划制定的季节模型，结合联合收割机的两种效果在一个机械的方法，并研究其对物种的持久性和空间分布的影响。这将加深我们对气候变化如何恶化生态系统生物多样性的认识。对于（3），重点也将是双重的：我将探索系统如何在短期和中期时间尺度上对扰动做出反应，我将研究导致解从一个状态到另一个状态的突然变化的潜在机制，例如在渐近收敛之前，种群动力学模型中的低密度和高密度之间的跳跃。我还将把瞬态动力学的结果应用于生态系统和传染病模型，以便对人口密度变化或疾病传播进行短期预测。

This proposed research program will: (1) study the fear induced interspecific and intraspecific interactions in food-web systems; (2) explore the temperature-dependent phenology in predator-prey systems; (3) study the transient behavior in population dynamics. For (1), the focus will be two-fold: I will study both the competition outcome of species under indirect predation risk and the cascading effect of fear in ecological systems with more than two trophic levels. The models I develop in (1) will extend our previous results of the predator-prey systems with fear effect to systems involving spatial and temporal heterogeneity. This will lead to a thorough examination of the fear effect in the meta community, enrich our understanding of how species interact, and facilitate implementing appropriate strategies for ecosystem management. For (2), the focus will be on studying how temperature-dependent phenological events affect species' spatial distribution in a seasonal environment. Phenological events such as, emergence time or reproduction, impact when and for how long prey and predator interact and are subject to environmental variations such as the climatic change. Moreover, for a large class of species, the dispersal patterns vary significantly among different seasons. I plan to formulate seasonal models that combine the two effects in a mechanistic approach and study their impact on species persistence and spatial distribution. This will deepen our recognition of how climatic change deteriorates ecosystem biodiversity. For (3), the focus will also be two-fold: I will explore how systems respond to perturbations in short and intermediate time scales and I will investigate the underlying mechanisms that induce abrupt change of solutions from one state to another, such as the jump between low densities and high densities in population dynamics models, before the asymptotic convergence. I will also apply the obtained results on transient dynamics to ecological systems and infectious disease models, such that short-term predictions of the population density variation or disease spread can be made.