Collaborative Research: Consequences of Environmental Stochasticity for the Spatial Dynamics of Savanna-Forest Transitions

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Changing temperature and rainfall patterns globally will have major effects on vegetation patterns, in some cases shifting the nature of ecosystems dramatically with consequences for wildlife, and for the services that natural systems provide to humans. These “critical transitions” are possible outcomes of environmental shifts in a wide variety of systems, including the savanna and forest transitions that this project will address, in which changes in frequency of fires can be especially important in changing the nature of these key ecosystem types. Building on previous work by the project leaders, this research will develop and apply state-of-the-art mathematical models, in concert with empirical studies, to predict how changing environmental conditions will mediate shifts in the savanna-forest boundary. This project will also enhance education and training at multiple levels, including the training of a postdoctoral fellow; development of graduate and undergraduate research projects; and data visualization through collaboration with artist and educator Neil Goldberg.The potential for multiple stable states, respectively forest and savanna, in vegetation systems has been previously demonstrated, combining empirical work with dynamical systems models. The introduction of spatial effects leads to systems of partial-differential or partial differential-integral equations, including stochastic influences, which of course are more complicated to analyze, but are crucial for predicting the shifts of boundaries. This project will develop and apply new methodologies drawn from non-equilibrium statistical mechanics, and will generate novel mathematical results, in particular in terms of fluctuations around the mean-field limit, developing new approaches to these stochastic systems, and applying a novel landscape-flux approach. A key element will involve the training of a truly interdisciplinary postdoctoral fellow to be fluent both in the mathematical dimensions of the project and the ecological data analysis.This award is funded jointly by the MPS Division of Mathematical Sciences (DMS) through the Mathematical Biology Program and BIO/DEB through the Cluster of Population and Community Ecology.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.