Enrichment Effects in a Simple Stoichiometric Producer-consumer Population Growth Model

A rudimentary predator-prey model is considered that is stoichometric, in that the nutrient content of the producer species affects the ability of the consumer to produce biomass. We show that the model supports biologically important dynamical properties that differ from the corresponding non-stoichiometric model. Specifically, under the assumption of Holling II-type functional response, for all sufficiently high system nutrient levels energy enrichment of the producer induces the loss of stability for the consumer-free (producer “monoculture”) system and the transcritical creation of a non-trivial coexistence equilibrium. Under further energy enrichment, this equilibrium undergoes a loss of stability (generically via Hopf bifurcation.) The model then supports a nontrivial periodic coexistence solution. In contrast to the non-stoichiometric case, here further energy enrichment induces restabilization of the monoculture equilibrium. Moreover, under sufficiently high energy enrichment, the system supports no nontrivial periodic solutions. The details of the bifurcation structure are computed for a simple case. Our results suggest that the energy-induced loss of periodic coexistence state can be attributed to the dilution of a consumer-limiting nutrient when the producer population is large, resulting in a carbon-rich / nutrient-poor food source that cannot sustain the consumer’s nutrient needs. AMS (MOS) Subject Classification. 92D25, 37J45.