Bernoulli Lecture II - Populations and communities as fluid on a landscape: rising to the challenge of long-term environmental change, past, present, and future   07 August 2014

16:15 - 17:15


Peter Chesson, University of Arizona

By Peter Chesson (University of Arizona)

All natural populations and communities occupy spatially heterogeneous landscapes. Individual fitnesses vary in space, and the contributions to population growth from different localities can be profoundly unequal even though directed dispersal, and retention of organisms in favorable localities, reduce the potential inequalities. Elaborate methods have been developed for solving models of population and community dynamics on heterogeneous landscapes, but to be science rather than technology, they must also impart understanding. Scale transition theory aims to provide this understanding through concepts that explain how the rules for population dynamics on local spatial scales interact with heterogeneity between localities, leading to novel outcomes on larger spatial scales. These novel outcomes include changes in population densities, stabilization of population dynamics, and promotion of species coexistence. Scale transition theory is founded on the idea of nonlinear averaging: the average of a nonlinear function is in general different from the average of the nonlinear function. Jensen’s inequality is a simple instance of nonlinear averaging where the function is convex and the average of the function is uniformly greater than the function of the average. More generally, the function is multidimensional and not necessarily convex. A product of two variables is a simple but extremely important example of a nonlinear function of multiple variables. The average of the product is the product of the averages (the function of the average), plus the covariance between the two variables in space. Two key concepts emerge from this simple observation: (1) fitness-density covariance, which explains how fitness at the landscape scale differs from the simple spatial average of local scale fitness, and (2) covariance between environment and competition, which explains how the ability of an organism to benefit from favorable environmental conditions can be limited by competition. Both concepts have powerful roles showing how population stabilization and species coexistence can emerge from the interaction between nonlinearities and spatial heterogeneity. Another concept, nonlinear competitive variance, shows how different nonlinear reactions to the same underlying spatially varying density-dependent processes can profoundly change higher scale dynamics. Scale transition theory can be applied to models using quadratic approximations related to moment closure techniques. However, exact approaches are being developed. In general these exact approaches require numerical evaluation of the key quantities, but still provide general understanding through elucidation of the role of the key ideas in specific instances. Other approximations use spatially implicit models and Laplace transforms to provide detailed understanding of the interactions between different kinds of spatial variation and nonlinear functions. Recent developments in scale transition theory abandon the usual stationary assumptions that the environment repeats statistically in time and space, allowing realistic landscapes, and the consequences of temporal nonstationarity, including long-term climate change, to be studied rigorously with mathematical models, extending traditional theory to richer more realistic domains.

Name University Dates of visit
Peter Chesson University of Arizona 07/08/2014 - 07/08/2014
Total Guests : 1
Name University Dates of visit
Total Guests : 0