eMB: Collaborative Research: New mathematical approaches for understanding spatial synchrony in ecology

理解驱动生态动态的因素是一个重要的挑战，在测量生态种群和确定相关的动态相互作用方面都存在困难。考虑到这一点，一个有用的方法是将想法建立在拥有最多信息的测量上，即使精度不是很高，这建议使用在空间和时间上都变化的动力学。本提案建立在这一前提下，从统计物理结合遥感数据开发模型。生态动力学和统计物理模型之间的潜在对应关系是通过对生态数据进行粗粒度处理和使用只允许少量种群状态的模型来实现的。这种方法补充了基于动力系统的更传统的数学方法，并且非常适合于原始数据。总体目标将是预测促进或阻止时空动态同步的特征。这将产生对生态动态的新认识，并有可能改善保护和农业实践。该项目的总体目标是开发新的数学方法来研究生态系统的时空动态，重点关注相关的时间尺度。了解导致跨空间和多时间尺度生态种群空间同步性的过程是一项重大挑战，由于需要了解和预测气候变化的影响，这一挑战变得更加紧迫。大多数长期存在的生态动力学数学工具都关注于渐近行为，但真实的生态系统可能受到瞬态行为的强烈影响。此外，生态数据通常非常嘈杂，产生了大量的不确定性，我们的方法可能是稳健的。研究人员将运用新颖和高度互补的定量方法来研究生态同步的起源和后果。首先，研究人员将使用伊辛普适的思想——在统计物理学中已经建立，但在其潜在的生物学应用方面严重不发达——以独立于细节的方式考虑同步。然后，研究人员将应用现代机器学习技术，以遥感果园数据作为案例研究，更好地了解实际同步模式如何产生的细节。中等复杂程度的机械模型将充当桥梁。通过将简化但通用的Ising模型描述与数据密集型机器学习方法联系起来，研究人员试图验证、改进和更好地理解这两种理解生态同步的方法。同步和空间模式是保护生物学和公共卫生的核心，揭示模式形成的普遍规则将为这些领域的新见解开辟道路。该项目由数学和物理科学理事会（MPS）的数学科学部（DMS）和生物科学理事会（BIO）的环境生物学部（DEB）、人口和社区生态集群（PEC）共同资助。该奖项反映了美国国家科学基金会的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。

Understanding what drives ecological dynamics is an important challenge, with difficulties arising both in measuring ecological populations and identifying the relevant dynamical interactions. Given this, a useful approach is to base ideas on measurements that have the most information, even when the accuracy is not great, which suggests using dynamics that vary both in space and time. This proposal builds on this premise to develop models from statistical physics combined with data obtained from remote sensing. The underlying correspondence between ecological dynamics and statistical physics models is accomplished by coarse graining the ecological data and using models that permit only a small number of states of the population. This approach complements more traditional mathematical approaches based on dynamical systems and is well suited to crude data. The overall goal will be to predict the features that either facilitate or prevent synchrony in dynamics across space through time. This will yield new understanding of ecological dynamics with potential for improving conservation and agricultural practices.The overall goal of this project is to develop novel mathematical approaches for spatio-temporal dynamics in ecological systems, with a focus on relevant time scales. Understanding the processes that have led to spatial synchrony in ecological populations across space and at multiple temporal scales is a substantial challenge, made more urgent by the need to understand and predict the impacts of a changing climate. Most of the longstanding mathematical tools for ecological dynamics focus on asymptotic behavior, but real ecological systems are likely strongly influenced by transient behavior. In addition, ecological data are often very noisy, generating substantial uncertainty to which our methods much be robust. The Investigators will apply novel and highly complementary quantitative methods to questions about the origins and consequences of ecological synchrony. First, the Investigators will use the idea of Ising universality – well established in statistical physics but severely underdeveloped for its potential biological applications – to consider synchronization in a detail-independent manner. The Investigators will then apply modern machine learning techniques to better understand the details of how actual synchrony patterns arise, using remotely sensed orchard data as a case study. Mechanistic models of intermediate complexity will serve as a bridge. By connecting the simplified but universal Ising model description with the data-intensive machine learning methods the Investigators seek to validate, improve and better understand both approaches to understanding ecological synchrony. Synchrony and spatial patterning are central to conservation biology and public health, and uncovering universal rules for pattern formation will open a path to new insights in these fields.This project is jointly funded by the Division of Mathematical Sciences (DMS) in the Directorate for Mathematical and Physical Sciences (MPS) and the Division of Environmental Biology (DEB) in the Directorate for Biological Sciences (BIO), Population and Community Ecology Cluster (PEC).This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.