Globally, humans are causing substantial environmental perturbations, and these perturbations are likely to become more frequent and more severe in the future. Such disturbances can have profound impacts on the structure of ecological communities (e.g. species diversity and abundance) and on the ecosystem services that those communities provide. Given the potential significance of such changes for human well-being, it is essential that we develop effective tools to predict these ecological and ecosystem impacts. Traditionally, the study of the resilience of ecological communities to severe environmental perturbations (e.g. hurricanes, floods) has focused on ecological processes. However, there is mounting evidence that feedbacks between the ecological and evolutionary processes (eco-evolutionary feedbacks) occur over commensurate time scales. This raises the possibility that evolutionary processes may play an important role in community resilience and species persistence. This project tackles the challenges posed by this possibility by developing a mathematical framework for analyzing models of disturbance which account for eco-evolutionary feedbacks and applying this framework to two real world systems whose properties have not been synthetically treated. In addition, this project will also support multiple outreach activities to K-12 education. The investigators will develop new analytical methods models accounting for environmental stochasticity, eco-evolutionary feedbacks, and demographic stochasticity. Stochastic difference equations (SDEs) will be used to model eco-evolutionary feedbacks in disturbed habitats. For these SDEs, new methods will be developed for verifying persistence of species and exponential rates of convergence to positive stationary distributions (which provides a measure of resilience). For models also accounting for finite population sizes, large deviation methods will be used to prove that stochastic persistence for the mean field SDE implies that the mean time to extinction of any species or genotype increases exponentially with habitat size, and the meta-stable behavior of the system dynamics are characterized by the positive stationary distributions of the mean field SDE. These mathematical methods will be applied to a nested set of common models associated with two prominent empirical systems: Anolis lizards on Bahamian Islands recovering from hurricanes, and stickleback fish in streams on Vancouver Island recovering from catastrophic floods. Using such different model systems provides the unique opportunity to more readily find generalities and plays to the two systems' complementary experimental strengths. Field experiments and observations as well as existing data will be used to parameterize the individual-based eco-evolutionary models. These models will be used to examine the impact of an environmental disturbance on (1) local adaptation of a focal predator (Anolis or stickleback), (2) community resilience, (3) long-term species persistence, and (4) projections about the rate and nature of ecological and evolutionary recovery under present and future climatic conditions. For outreach, the investigators will run and develop material for the modelling in the life sciences cluster of the California State Summer School for Mathematics and Science, will develop short educational videos about field research, ecology, and evolution for K-12 students in Austin, and create additional educational opportunities for local Bahamian school children in collaboration with Friends of the Environment (a Bahamian conservation organization).
Division Of Mathematical Sciences (DMS)