Frontiers in Science Colloquium
Date/Time/Room: Friday (3/2/2001) at 12:00 noon in 114 Chemistry Research Building
Hal L. Smith,
Department of Mathematics,
Arizona State University
``How Many Species Can a Given
Number of Resources Support?''
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
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.