Prof. Hastings, Distinguished Professor in the Dept. of Environmental Science and Policy, received a collaborative $1M grant from the National Science Foundation for "Integrating statistical physics and nonlinear dynamics to understand emergent synchrony and phase transitions in biological systems" for 2018–2022 and another NSF grant for "Metacommunity dynamics: integrating local dynamics, stochasticity and connectivity".

Those who wish to learn more about Prof. Hastings' research area may find his recent coauthored review article in Science, "Transient phenomena in ecology", interesting.

Details about the new grants follow.

DMS - 1840221: RoL:FELS:RAISE: Integrating statistical physics and nonlinear dynamics to understand emergent synchrony and phase transitions in biological systems. National Science Foundation 9/1/2018-8/31/2022 (PI, with Karen Abbott and Jonathon Machta) $999,992

This research will use ideas from statistical physics to examine the transitions to synchrony across space in biological systems. Tools in physics first developed primarily to explain how magnetism arises at large scale from the alignment of magnets at the small scale will be employed to develop detail-independent explanations for the emergence of synchrony. The work will determine general rules that govern the propagation of information or dynamics in biological systems from short range interactions to large scales with an emphasis on ecological systems. Phenomena in this category range from synchrony across space of oscillations in predator and prey systems to synchrony in dynamics of neural activity in the brain. Synchrony is strongly linked to extinction risk, which may either be beneficial (e.g. epidemic burnout, invasive species) or detrimental (e.g. threatened species). Similarly, synchronous neural dynamics may have large implications for human health.

This research will build upon previous research demonstrating that the transitions in the two-dimensional Ising model of theoretical physics map onto models of spatial population dynamics on a lattice and can be used to explain data for the yield of individual trees across space and time in a pistachio orchard. A pattern of synchrony across space is prevalent at many scales of biological systems, so a detail-independent explanation should exist to explain its occurrence. However, real biological systems have significant heterogeneities, so further work will build both on various extensions and modifications of the Ising model as well as look at other biological systems. The work will depend on extensive simulations and analysis of models from statistical physics. The overall goal of finding detail-independent universal explanations of large scale synchronous dynamics will advance understanding of ecological systems as well as a range of other biological systems. Tying together ideas and methods from ecology, neuroscience and animal behavior will advance the quest for universal rules of life.

DMS- 1817124 Metacommunity dynamics: integrating local dynamics, stochasticity and connectivity. National Science Foundation 6/15/2018-5/31/2021 (PI) $290,670

This project will develop a novel mathematical approach for describing the dynamics of ecological communities at large spatial scales, a description of dynamics called metacommunities. From a mathematical standpoint, the project will start with relatively simple descriptions of interactions among species, such as competition and predation, at small spatial scales, coupled with descriptions of connectivity, the way species move between locations. The mathematical descriptions will then be expanded to include more detailed and realistic descriptions of interactions among species and underlying environmental changes. The models will be analyzed to determine both long term behavior and dynamics. The mathematical models will then be used to answer important ecological questions focused on how changes in habitat quality and availability and connectivity between different habitats will affect the composition and dynamics of these metacommunities. This, in turn, will provide information about how human activities which affect habitats and connectivity will affect species composition and dynamics and can provide guidance for both conservation and restoration efforts.

The mathematical models of netacommunities used will be primarily phrased in discrete time with a time step of one year, both to reflect dynamics in seasonal environments and how data is gathered. The simplest models will focus only on species presence or absence and will be difference equations, so a relatively complete analytical treatment will be possible. Equilibria and their stability can be calculated. The more complex descriptions will all be phrased as integro-difference equations where time is discrete, but the state space is continuous. The underlying dependent variables will be density functions for the abundance of the species under consideration, and the kernels in the integro-difference equations will describe the underlying ecological dynamics. Initial analyses will be numerical with the expectation that analytic treatment of conditions for persistence and coexistence will be possible, building on recent mathematical work on integro-difference equations. To treat changing conditions through time, the kernels will be modified to include explicit time dependence. The mathematical analyses will then be used to answer the underlying ecological questions.