Dynamics of Simple Food Webs

We consider a simple food web with commensal relationship, where organisms utilize both external resources and resources produced by other organisms. We show that in such a community with no competition, there is at most one possible equilibrium for each fixed set of surviving species, and develop a natural condition that determines which species survive based on available resource. Our main result shows that among all possible communities described by equilibria, the one which is stable has the largest number of surviving species and largest combined biomass and hence maximizes utilization of available resources.