Joint

Frontiers in Science Colloquium

and

Date/Time/Room: Friday (3/2/2001) at 12:00 noon in 114 Chemistry Research Building

Speaker: Hal L. Smith, Department of Mathematics, Arizona State University

``How Many Species Can a Given Number of Resources Support?''

Abstract: Given k essential resources, how many species can be supported in purely exploitative competition for the given resources in a spatially and temporally homogeneous environment? It has long been known that generically speaking, equilibrium coexistence is impossible if n>k and, as competition rarely generates oscillations, one might expect that not more than k species can be supported by k (non-reproducing) resources. However, numerical simulations of the standard mathematical model in a recent Nature article of Huisman and Weissing strongly suggest that up to six species can be supported by three resources and as many as twelve species can be supported on five resources. Their simulations show that certain solutions of the standard model of k species with k resources oscillate (periodically if k=3 and chaotically if k=5) and that these oscillatory communities (solutions) can be successively invaded by one species after another up to the total numbers given above. These results have important implications for the planktonic paradox-Why can so many plankton species seemingly coexist on so few limiting resources?

Without going into great mathematical detail, we review what can actually be proved mathematically, focusing on the case of two resources and n>=2 species, and 3 resources and 3 species.