QEIB: Theory for communities in nonstationary environments

尽管自然界几乎总是在变化，但生态学理论在很大程度上是利用数学模型发展起来的，这些模型假定生态系统达到稳定的平衡。近几十年来，这样的模型得到了补充，部分被物理环境在时间和空间上变化的模型所取代。然而，这些模型环境总是具有平稳性，这意味着它们可以通过一组固定的统计数据来表征，例如发生波动的平均值，以及波动的大小和性质的衡量标准。虽然已经从这些模型中学到了很多，但现在很明显，平稳性的假设在本质上是站不住脚的，因为环境不会随着时间的推移而稳定。人为气候变化的挑战意味着，关于物理环境的更现实的非静态假设对未来至关重要，但为了更准确地理解过去和现在的生态，这些假设也是必要的。这项研究将开发受非稳定环境影响的物种相互作用模型，以预测非稳定环境对维持生物多样性的影响。该项目将开发数学工具，用于做出关于多样性维持的生态预测，允许针对更现实、更非稳定的条件替换或修改固定预测。这将有助于表明，与以前的固定假设相比，在非固定情况下，物种和环境的哪些方面对维持多样性有很大影响。该项目还将研究不同物种因环境变化而以不同速度迁徙如何影响物种间相互作用和维持生物多样性的结果。研究结果将应用于自然环境的保护和管理，并帮助社会应对全球环境变化的挑战，而非平稳理论对此至关重要。此外，还将为学生和博士后研究员提供一个主要的教育和培训部分，让他们学习非静态环境中生态模型的新工具。高中教师还将接受针对环境变化的生态模型的培训，以促进课堂教学材料的开发。

Although the natural world is almost always in flux, ecological theory has been largely developed using mathematical models that assume that ecosystems come to a stable equilibrium. In recent decades, such models have been supplemented and partially replaced by models in which the physical environment varies in time and space. However, those model environments have invariably had the property of stationarity, which means that they can be characterized by a fixed set of statistics, such as averages, about which fluctuations occur, and measures of the magnitude and nature of the fluctuations. Although much has been learned from these models, it is now clear that the assumption of stationarity does not hold in nature, because environments are not stable over time. The challenge of anthropogenic climate change means that more realistic nonstationary assumptions about the physical environment are essential for the future, but they are also needed for more accurate understanding of past and present ecology. This research will develop models of interacting species subject to nonstationary environments to predict the impact of nonstationarity on the maintenance of biological diversity. The project will develop mathematical tools for making ecological predictions about diversity maintenance that allow stationary predictions to be replaced or modified for more realistic, nonstationary conditions. This will help show which aspects of species and of the environment have large effects on the maintenance of diversity in the nonstationary case as compared with the previous stationary assumptions. The project will also study how migration of different species at different rates in response to a changing environment affects the outcomes of the interactions between species and the maintenance of biological diversity. The results of the research will have application to the conservation and management of natural environments, and help society face the challenges of global environmental change, for which nonstationary theory is essential. In addition, there will be a major education and training component for students and postdoctoral fellows in new tools for ecological models in nonstationary environments. High school teachers also will be given training in ecological models for changing environments to foster the development of materials for classroom instruction.