Resilience of Cyclic Ecosystems in the Presence of R- and P-Tipping

政权转移，一个“正常”状态突然出乎意料地转移到一个非常不同的状态（例如，通常丰富的种群变得稀少，森林让位于草原），是气候变化下生态系统保护的一个重大关切。从数学上讲，这些状态转变是由临界点引起的：参数的微小变化会导致动力学系统从一个静止基态切换到另一个静止基态。传统上，这些小费事件被归因于B-小费，即，所述参数穿过所述第一基态变得不稳定或消失的分叉值。然而，最近发现了基于速率的倾斜：如果参数变化足够快并且不存在任何经典分叉，则固定基态之间会发生R倾斜。甚至最近，我和我的同事发现了P-倾斜，一种介于振荡基态和静止基态之间的新型倾斜：在这里，重要的是参数变化时振荡的相位。这些动态倾翻行为通常发生在B倾翻预期之前，因此在预测生态系统对气候变化的反应方面可能至关重要。我的研究计划是一个全面的调查R-和P-小费在捕食者-猎物和食物网模型。由于R-和P-倾斜只是轻轻地探索到目前为止，这些动态的倾斜过程中的生态系统的生存作用在很大程度上是未知的。因此，我和我的学生将对关键生态系统模型中的R-和P-倾斜进行彻底的数学研究。我们将开始，将扩大对P-小费的初步工作，重点是两个经典的捕食者-猎物模型，通过检查更复杂的模型，包括生态系统的其他关键特征，如捕食者行为的季节性变化，额外的物种（例如，三物种食物链和食物网模型），以及栖息地斑块之间的移动。在应对气候变化时，决策者需要知道生态系统中何时会发生R-和P-倾翻事件。然而，生态模型中结构敏感性的存在使得预测极其困难，因为不知道什么数学函数准确地表示被建模的物种相互作用和行为。此外，气候变化预计将大大改变气候敏感模型参数的平均值和变异性（自相关性，振幅）。因此，我的研究计划包括一个详细的数学研究的结构敏感性和气候敏感的参数值的时间变化在上述研究的生态系统模型的范围。 这项工作将提供重要的信息，我们有能力预测生态系统何时容易受到R-和P-倾斜，以及这些事件在气候变化下的可能性有多大。我恭敬地承认，拟议中的研究将在Syilx Okanagan国家的传统、祖传和未割让领土上进行。

Regime shifts, where a "normal" state suddenly and unexpectedly shifts to a very different one (e.g., a population that is normally abundant becomes scarce, a forest gives way to grassland), are a significant concern in the conservation of ecosystems under climate change. Mathematically, these regime shifts are caused by tipping points: A small change in a parameter causes a dynamical system to switch from one stationary base state to another. Traditionally, these tipping events are ascribed to B-tipping, i.e., the parameter crosses through a bifurcation value at which the first base state becomes unstable or disappears. Recently, however, a tipping based on rate was discovered: R-tipping between stationary base states occurs if the parameter change is fast enough, and in the absence of any classical bifurcations. Even more recently, my colleagues and I discovered P-tipping, a new type of tipping between oscillatory and stationary base states: Here it is the phase of the oscillation at the moment of parameter change that matters. These dynamic tipping behaviours typically occur before B-tipping is expected, and may thus be critically important in predicting ecosystem response to climate change. My research program is a comprehensive investigation of R- and P-tipping in predator-prey and food web models. As R- and P-tipping are only lightly explored to date, the role of these dynamic tipping processes in the survival of ecosystems is largely unknown. My students and I will therefore carry out a thorough mathematical study of R- and P-tipping in key ecosystem models. We will begin by will extending the initial work on P-tipping, which focussed on two classic predator-prey models, by examining more complex models that include other key features of ecosystems such as seasonal changes in predator behaviours, additional species (e.g., three-species food chain and food web models), and movement between habitat patches. In tackling climate change, decision-makers need to know when R- and P-tipping events will occur in ecosystems. The presence of structural sensitivity in ecological models, however, makes prediction extremely difficult, as it is unknown what mathematical functions accurately represent the species interactions and behaviours being modeled. In addition, climate change is predicted to significantly alter the mean and variability (autocorrelation, amplitude) of climate-sensitive model parameters. My research program thus includes a detailed mathematical study of structural sensitivity and temporal variation of climate-sensitive parameter values across the range of ecosystem models studied above.  This work will provide important information regarding our ability to predict when ecosystems are vulnerable to R- and P-tipping, and how likely these events are under climate change. I respectfully acknowledge that the proposed research will be done on the traditional, ancestral and unceded territory of the Syilx Okanagan Nation.