A generalized model of a resource-population system

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Abstract
A basic structure [Eqs. (5), (6), (3), (12), (30)] for mathematical models of resource-population systems is presented. This basic structure may be specified in order to include different alternative hypotheses and it represents, therefore, a family of particular models. The study of one of its particular realizations [Eqs. (31) and (39)] shows that its behavior agrees qualitatively with what should be expected from biological considerations. Even when the system of nonlinear differential equations could not be solved explicitly, important information has been obtained, by studying its properties in the limiting cases, its sensitivity to changes in the parameters, and the results of computer simulation. The proposed model, duplicating some of the basic features of a population living under resource limitation, and allowing a coupling with a predator population, is intended to be used as an elementary component in food web or ecosystem theoretical studies. The studies need not include detailed descriptions of the population variables, but rather only its essential, gross features, in order to explore the properties that characterize the complete systems.