A search for maximum species abundances in ecological communities under conditional diversity optimization

We study a multispecies community of autotrophic microorganisms which grow in a batch culture regime with several perfectly complementary resources. A basic hypothesis is that a stationary phase of the polyculture corresponds to a maximum diversity under the constraints having the meaning of matter conservation laws. The corresponding conditional extremum problem is studied in detail. It is shown that a unique solution to this problem-a ''species structure formula''-adequately describes the experimental data. We prove a number of strict statements concerning the domain of definition and maxima of the obtained solutions. These statements find an adequate interpretation as limitation principles in ecology and in the problems of community structure control. (C) 1997 Society for Mathematical Biology.