Collaborative Research: Modeling and Inference for Spatiotemporal Climate Impacts on Complex Ecosystems

Regents Of The University Of Idaho, Moscow ID

Investigators

Abstract

In many hierarchical dynamical systems, synchrony between multiple fluctuating variables (i.e., correlations or other similarities in fluctuations between variables through time) is more important than the individual variables themselves. For instance, a neuron may fire only when all of its input neurons fire synchronously, or the electrical grid may crash only when demands of multiple users become synchronized, producing total-usage spikes. Ecosystems can show this type of dependency on synchrony. Ecosystems include multiple trophic levels, with population signals from lower levels often being spatially aggregated to affect higher levels and human concerns such as fisheries. For instance, a predator is only harmed if its prey are scarce over its whole hunting area. And human fish exploitation is only reduced if fish decline synchronously everywhere. For systems of this type, it is primarily the synchronous components of signals that matter in the average signal that affects the next hierarchical level - non-synchronous components tend to cancel in the spatial average. Thus, spatial synchrony of population dynamics is very important to ecosystem dynamics generally. Spatial synchrony of population dynamics has been widely observed in organisms as diverse as mammals and protists, at distances up to thousands of kilometers. Synchrony is closely related to large-scale outbreaks and shortages. Synchrony has conservation implications because populations are at greater risk of simultaneous extinction if they are simultaneously rare. But in spite of the importance of synchrony in ecology, possible impacts of climate change on synchrony are very little studied. In this context, climate change constitutes not just warming, but also changes in other statistical aspects of environmental signals. It is also unknown the extent to which synchrony, and climate-change-induced changes therein, can be transmitted through predator-prey interacts and hence throughout entire food webs in complex patterns. The goals of this research are: (1) to develop mathematical models and statistics to build understanding of how potential changes in synchrony induced by climate change will ramify through complex ecosystems; (2) and to develop mathematical models and use them to understand the consequences of changes in synchrony for a widely observed empirical pattern called Taylor's law, a phenomenon fundamental to spatial ecology and applied in a variety of areas including fisheries management, conservation, and agriculture. Researchers will also strive, as time allows, to understand the consequences of changes in synchrony for species extinction risk. To meet goal (1) above, the researchers will perform stochastic-process modeling in a network context, to understand how changes in synchrony should theoretically cascade through complex species interaction networks; and will develop statistical methods combining wavelets and statistical path analysis, to be used to help infer how synchrony cascades through empirical interaction networks. A vector autoregressive moving average modelling framework will be constructed consisting of multiple habitat patches, with several species interacting within patches, migrating between patches, and being affected by a stochastic environment in each patch. For each species independently, dispersal and/or environmental synchronizing effects can be independently set to act directly on the species as synchronizing influences, or not. A given species may also be synchronized through its interactions with other synchronized species. The primary utility of the models is to make it possible to derive analytically, for each species, the relative importance of these direct and trophically-mediated synchronizing effects, thereby understanding the nature of trophic transmission of synchrony through the network. To meet goal (2) above, researchers will use the theory of ergodic stationary stochastic processes to represent population levels at different locations. If time allows, consequences of synchrony for extinction risk will be assessed through mathematical analysis within a classic stochastic matrix modelling framework, expanded to represent multiple populations across space.