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

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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.