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

本研究计划将：(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-食饵系统中温度依赖性物候；(3)研究种群动态中的暂态行为。对于(1)，重点将是双重的：我将研究物种在间接捕食风险下的竞争结果，以及在两个以上营养水平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之前关于具有恐惧效应的捕食者-猎物系统的结果扩展到涉及空间和时间异质性的系统。这将导致对元群落恐惧效应的深入研究，丰富我们对物种相互作用的理解，并促进实施适当的生态系统管理策略。(2)重点研究季节环境下物候事件对物种空间分布的影响。物候事件，如出现时间或繁殖，影响猎物和捕食者相互作用的时间和时间，并受到气候变化等环境变化的影响。此外，对于一个大类别的物种，不同季节的扩散模式差异显著。我计划建立结合这两种效应的季节模型，并研究它们对物种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作出反应，我将研究导致解从一种状态突然变化到另一种状态的潜在机制，例如种群动力学模型中低密度和高密度之间的跳跃，在渐近收敛之前。我还将把获得的瞬态动力学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.