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: 2325076
• 负责人: Alan Hastings
• 金额: $ 13.84万
• 依托单位: University of California-Davis
• 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=2325076&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.

了解什么驱动生态动态是一个重要的挑战，在测量生态种群和确定相关的动态相互作用的困难。鉴于此，一个有用的方法是将想法建立在拥有最多信息的测量基础上，即使精度不是很高，这意味着使用在空间和时间上都不同的动态。本建议以这一前提为基础，结合从遥感获得的数据，开发统计物理模型。生态动力学和统计物理模型之间的基本对应关系是通过对生态数据进行粗粒化和使用只允许少数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。该项目的总体目标是为生态系统中的时空动态开发新的数学方法，重点是相关的时间尺度。了解导致生态种群在空间和多个时间尺度上空间同步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而变得更加紧迫。大多数长期存在的生态动力学的数学工具集中在渐近行为，但真实的生态系统很可能强烈的瞬态行为的影响。此外，生态数据往往是非常嘈杂的，产生大量的不确定性，我们的方法是强大的。研究人员将采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性的概念--在统计物理学中已经确立，但其潜在的生物学应用严重不足--以一种与细节无关的方式来考虑同步。然后，研究人员将应用现代机器学习技术，以更好地了解实际同步模式如何产生的细节，使用遥感果园数据作为案例研究。中等复杂性的机械模型将作为一个桥梁。通过将简化但通用的伊辛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性的方法。同步和空间图案化是保护生物学和公共卫生的核心，揭示图案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数学科学部（DMS）联合资助（MPS）和生物科学理事会环境生物学部（DEB）（BIO），人口和社区生态集群（PEC）。该奖项反映了NSF的法定使命，并已被认为是值得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的支持。