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

eMB：协作研究：理解生态学空间同步的新数学方法

• 批准号: 2325077
• 负责人: Jonathan Machta
• 金额: $ 5.77万
• 依托单位: University of Massachusetts Amherst
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2023
• 资助国家: 美国
• 起止时间: 2023-09-01 至 2026-08-31
• 项目状态: 未结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=2325077&HistoricalAwards=false
• 关键词: eMB; Collaborative; Research; New; mathematical

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.

了解驱动生态动态的是什么是一个重要的挑战，在衡量生态种群和确定相关的动态相互作用方面遇到了困难。鉴于此，一种有用的方法是基于有关具有最多信息的测量的想法，即使精度不是很好，这表明使用在时空和时间上不同的动力学。该提案建立在此前提之上，以开发从统计物理学以及从遥控性获得的数据结合使用的模型。生态动力学和统计物理模型之间的基本对应关系是通过粗糙的生态数据和仅允许少数人口状态的模型来完成的。这种方法符合基于动态系统的更传统的数学方法，并且非常适合粗数据。总体目标是预测促进或防止在时间上跨越时间动力学同步的功能。这将产生对生态动力学的新理解，具有改善保护和农业实践的潜力。该项目的总体目标是开发生态系统中时空动态的新型数学方法，重点是相关时间尺度。了解导致在空间和多个临时尺度上生态人群中空间同步的过程是一个重大挑战，这使得需要理解和预测气候变化的影响更加紧迫。生态动力学的大多数长期数学工具都集中在不对称行为上，但是实际的生态系统可能会受到瞬态行为的强烈影响。此外，生态数据通常是非常噪音的，产生了很大的不确定性，我们的方法很鲁棒。研究人员将将新颖和高度互补的定量方法应用于有关生态同步的起源和后果的问题。首先，研究人员将使用ISING普遍性的想法 - 在统计物理学中良好确定，但由于其潜在的生物学应用而严重不发达 - 以详细的独立方式考虑同步。然后，研究人员将使用现代的机器学习技术，以更好地了解实际同步模式如何出现的细节，并使用远程感知的果园数据作为案例研究。中间复杂性的机械模型将用作桥梁。通过将简化但通用的模型描述与研究人员寻求验证，改进和更好地理解这两种方法了解生态同步的方法的数据密集型机器学习方法。同步和空间图案是保护生物学和公共卫生的核心，并且揭示图案形成的普遍规则将为这些领域的新见解打开通往新见解的途径。该项目由数学科学（DMS）在数学和物理科学（MPS）的数学科学局（MPS）和竞赛（MPS）的数学和物理生物学（MPS）中（Bioological in Ci acience in Ci Incience in Ci acience in Ci aciention）共同资助。 （PEC）。该奖项反映了NSF的法定使命，并通过使用基金会的知识分子优点和更广泛的影响审查标准来评估，被认为是宝贵的支持。