Collaborative Research: Modeling and Inference for Spatiotemporal Climate Impacts on Complex Ecosystems

在许多分层动态系统中，多个波动变量（即，变量之间波动的相关性或其他相似性）比单个变量本身更重要。例如，一个神经元可能只有在所有输入神经元同步激发时才会激发，或者电网可能只有在多个用户的需求同步时才会崩溃，从而产生总使用量尖峰。生态系统可以表现出这种对同步性的依赖。生态系统包括多个营养层次，来自较低层次的种群信号往往在空间上聚集起来，影响较高层次和渔业等人类关切的问题。例如，只有当猎物在整个狩猎区域都很稀少时，捕食者才会受到伤害。只有在各地鱼类数量同步下降的情况下，人类对鱼类的开发才会减少。对于这种类型的系统，主要是信号的同步分量在影响下一个层次级别的平均信号中起作用-非同步分量往往在空间平均中抵消。因此，种群动态的空间同步性对生态系统动态具有重要意义。种群动态的空间同步性已经在哺乳动物和原生生物等多种生物中广泛观察到，距离可达数千公里。同步性与大规模疫情和短缺密切相关。同步性具有保护意义，因为如果它们同时稀少，则种群同时灭绝的风险更大。但是，尽管同步性在生态学中的重要性，气候变化对同步性的可能影响却很少被研究。在这方面，气候变化不仅是变暖，而且还包括环境信号其他统计方面的变化。同步性和气候变化引起的变化在多大程度上可以通过捕食者-被捕食者的相互作用，从而以复杂的模式在整个食物网中传播，这一点也是未知的。本研究的目标是：（1）建立数学模型和统计数据，以了解气候变化引起的潜在同步变化如何通过复杂的生态系统产生影响;（2）建立数学模型，并利用它们来理解同步变化的后果，这是一个被广泛观察到的经验模式，称为泰勒定律，这是空间生态学的基本现象，并应用于包括渔业管理、保护和农业在内的各种领域。在时间允许的情况下，研究人员还将努力了解同步性变化对物种灭绝风险的影响。为了实现上述目标（1），研究人员将在网络环境中进行随机过程建模，以了解同步性变化在理论上如何通过复杂的物种相互作用网络级联;并将开发结合小波和统计路径分析的统计方法，用于帮助推断同步级联如何通过经验相互作用网络。一个向量自回归移动平均建模框架将构建多个栖息地补丁，补丁内的几个物种相互作用，补丁之间的迁移，并在每个补丁的随机环境的影响。对于每个物种独立地，扩散和/或环境同步效应可以独立地设置为直接作用于物种作为同步影响，或不。一个给定的物种也可以通过与其他同步物种的相互作用而同步。该模型的主要效用是使之有可能得到分析，为每个物种，这些直接和trophically介导的同步效应的相对重要性，从而了解通过网络的同步性的营养传输的性质。为了实现上述目标（2），研究人员将使用遍历平稳随机过程理论来表示不同位置的种群水平。如果时间允许，灭绝风险的同步后果将通过经典随机矩阵建模框架内的数学分析进行评估，扩展到代表跨空间的多个种群。

In many hierarchical dynamical systems, synchrony between multiple fluctuating variables (i.e., correlations or other similarities in fluctuations between variables through time) is more important than the individual variables themselves. For instance, a neuron may fire only when all of its input neurons fire synchronously, or the electrical grid may crash only when demands of multiple users become synchronized, producing total-usage spikes. Ecosystems can show this type of dependency on synchrony. Ecosystems include multiple trophic levels, with population signals from lower levels often being spatially aggregated to affect higher levels and human concerns such as fisheries. For instance, a predator is only harmed if its prey are scarce over its whole hunting area. And human fish exploitation is only reduced if fish decline synchronously everywhere. For systems of this type, it is primarily the synchronous components of signals that matter in the average signal that affects the next hierarchical level - non-synchronous components tend to cancel in the spatial average. Thus, spatial synchrony of population dynamics is very important to ecosystem dynamics generally. Spatial synchrony of population dynamics has been widely observed in organisms as diverse as mammals and protists, at distances up to thousands of kilometers. Synchrony is closely related to large-scale outbreaks and shortages. Synchrony has conservation implications because populations are at greater risk of simultaneous extinction if they are simultaneously rare. But in spite of the importance of synchrony in ecology, possible impacts of climate change on synchrony are very little studied. In this context, climate change constitutes not just warming, but also changes in other statistical aspects of environmental signals. It is also unknown the extent to which synchrony, and climate-change-induced changes therein, can be transmitted through predator-prey interacts and hence throughout entire food webs in complex patterns. The goals of this research are: (1) to develop mathematical models and statistics to build understanding of how potential changes in synchrony induced by climate change will ramify through complex ecosystems; (2) and to develop mathematical models and use them to understand the consequences of changes in synchrony for a widely observed empirical pattern called Taylor's law, a phenomenon fundamental to spatial ecology and applied in a variety of areas including fisheries management, conservation, and agriculture. Researchers will also strive, as time allows, to understand the consequences of changes in synchrony for species extinction risk.To meet goal (1) above, the researchers will perform stochastic-process modeling in a network context, to understand how changes in synchrony should theoretically cascade through complex species interaction networks; and will develop statistical methods combining wavelets and statistical path analysis, to be used to help infer how synchrony cascades through empirical interaction networks. A vector autoregressive moving average modelling framework will be constructed consisting of multiple habitat patches, with several species interacting within patches, migrating between patches, and being affected by a stochastic environment in each patch. For each species independently, dispersal and/or environmental synchronizing effects can be independently set to act directly on the species as synchronizing influences, or not. A given species may also be synchronized through its interactions with other synchronized species. The primary utility of the models is to make it possible to derive analytically, for each species, the relative importance of these direct and trophically-mediated synchronizing effects, thereby understanding the nature of trophic transmission of synchrony through the network. To meet goal (2) above, researchers will use the theory of ergodic stationary stochastic processes to represent population levels at different locations. If time allows, consequences of synchrony for extinction risk will be assessed through mathematical analysis within a classic stochastic matrix modelling framework, expanded to represent multiple populations across space.