SYMP 8-2
Optimal control and beyond in life history theory and theories of ecosystem management
Optimal control theory and related approaches to dynamic optimization have had a long history of application within ecology. Two major areas of application are the identification of optimal behavior and management of ecosystems. Various mathematical approaches can be used to find behaviors, broadly defined, ranging from life histories to actual behavior, that would be optimal and therefore the outcome of selection. These optimal solutions can then be compared to observations of organisms as a way to check how well causes for behavior are understood. A second long standing set of applications has been to understand and develop approaches for management of ecosystems, such as setting harvest levels in fisheries or determining approaches for the control of invasive species. Exact solutions for both these classes of problems can be difficult to find except in the simplest cases, so an important question is how well approximate solutions provide meaningful biological answers. These issues are particularly important and challenging in the presence of stochasticity.
Results/Conclusions
Examples will first be presented that show when the approach of simplifying the model, for example, by ignoring stochasticity and using a deterministic model, to produce one that can be completely optimized, is not advisable. Examples will then be presented that show how approximations that yield solutions that are not necessarily optimal (in the mathematical sense) to models that do incorporate complexities provide good answers to questions of both life history dynamics and in management. Applications to specific management questions including control of the spread of invasive species will be used to illustrate general principles.