Mathematical Models for Continuous Culture Growth Dynamics of Mixed Populations Subsisting on a Heterogeneous Resource Base. II. Predation and Trophic Structure*

In an earlier paper @mouse, 1980), I described an extension of the classical mode1 of chemostat dynamics (Monod, 1949), which extension allows one to deal with competion for multiple limiting substrates. The object of the present paper is similarly to extend a simple chemostat mode1 of predation (Tsuchiya et al., 1972) to the case of multiple predators and multiple prey, both. underpinned by multiple limiting substrates. I shall also extend the model to multiple trophic layers, and shall indicate the changes necessary to deal with trophic-layer “leap-frogging.” In keeping with the strategy of the earlier paper, I shall translate the input parameters of the continuous flow chemostat system into comparable parameters of a modified predation analogue of the sort described by Schoener (1973, 1974). This latter type of description, basically an extension of the classic Lotka (1925)-Volterra (1926) predation model, is more familiar to the population biologist. The present treatment may be viewed as a particularization of a more general formulation by Levin et al., (1977), who did not specify the manner in which multiple substrates and multiple prey were to be utilized. It is an alternative to models proposed by Jost et al., (1973), who deal with a different sort of multiple-substrate utilization. There are three questions of primary interest: (1) How do the parameters of the modified predation mode1 relate to those of the chemostat system? (2) What are the parametric conditions for the existence and stability of various possible steady states, and how do these translate into comparable statements about the chemostat