SG: The stochastic shielding heuristic in ecological networks

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Making good decisions about ecological resources requires understanding how changes in one part of an ecosystem can affect important species both nearby and far away. Developing a theory on ecosystem change is complicated by several factors. Animal and plant species interact with a variety of other species, and migrate from one location in an ecosystem to another. The changes in plant and animal species involve factors that are predictable, like seasonal migrations, and other factors that are unpredictable, like week-to-week and day-to-day changes in temperature and rainfall. In this project, the investigators develop new theoretical approaches for understanding how unpredictable changes affect complex ecosystems, providing managers with a better framework for making decisions that affect society and students with training. Species in ecosystems affect one another in a variety of ways, directly and indirectly, and thereby are connected by an ecological network. In current mathematical models of ecological networks, unpredictable events (referred to as stochasticity), are omitted for simplicity, in order to make the computations tractable. In this project, the investigators will develop a theory of stochastic processes in ecological networks to provide guidelines for when and how stochastic fluctuations should be included in computational models. Ecological network models with realistic complexity (large numbers of nodes and connections) and population sizes (finite rather than infinite) naturally exhibit random fluctuations due to demographic stochasticity (variation in birth and death rates) and environmental stochasticity (unpredictable events such as extreme weather, earthquakes and landslides). Fluctuations around average population behavior can play an important role, for instance in extinction events or invasions, but modeling all stochastic elements in a realistic ecological network is conceptually and numerically taxing. Building on recent innovations in theoretical neuroscience (the "stochastic shielding" heuristic) the investigators will develop a framework that can greatly reduce the number of independent stochastic processes needed to accurately represent the fluctuations in a select set of nodes of interest (e.g. representing focal species or critical habitat patches). The project will create a framework for exploiting data on not only average population sizes but also variances, by developing the theoretical underpinnings that complement existing efforts to bring ecological science into the age of big data.