Biological Dynamics at Intermediate Time Scales

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The goal of this project is to develop a general theory for the dynamics of biological systems at intermediate time scales. At short time scales, the current state or the current direction of a biological system provides a good description of the future state. At very long time scales, systems settle into predictable patterns that are relatively easy to study. Intermediate time scales lie in between these two states and may include rapid, and harder to predict yet important, changes in system behavior. As a first step toward understanding intermediate time scales, specific case studies based on a) ecological models with a small number of interacting species, b) neural models with a few neurons or c) epidemic models will be studied numerically on a computer. These numerical results will then be generalized using mathematical theory based on the study of dynamical physical systems. The resulting generalizations will allow the determination of when phenomena like turbulence (apparently irregular changes in population size) or bursting (rapid, apparently random large changes in population size separated by periods without change) will arise in systems with interacting species distributed over space, and also in a variety of other biological systems.The theory developed will be general and of wide applicability across levels of biological organization ranging from the cellular level to neuroscience to the dynamics of individual populations to ecosystems. A particular set of important applications will be fisheries management, the impact of global climate change on ecosystem services, and the dynamics of diseases, all of which will require prediction on scales appropriate for human dominated systems. In the course of this work postdoctoral scholars and graduate students will receive interdisciplinary training that will develop the human capital to meet future challenges in understanding complex biological systems.