A Predator-Prey Model for Zooplankton Grazing on Competing Algal Populations

Abstract

The typical freshwater algal community can be roughly categorised into two groups according to the distribution of biomass with cell size. Algae in the small size group are known to be edible for zooplankton grazers; large algae are much less edible. To model population dynamics of a size selective zoaplankton predator like Daphnia we thus consider a 3-species predator-prey model with an "edible" and an "inedible" prey. We show that a system which in the absence of inedible algae exhibits cyclic dynamics may exhibit a stable equilibrium if inedible algae are introduced. This stabilisation can be caused by one or both of the following mechanisms: (a) "indirect interaction" involving interspecific competition between the prey which reduces the effective carrying capacity of the edible species, and (b) "direct interaction" in which there is a reduction of the attack rate on the edible prey when the predator spends time handling inedibles. We study the behaviour of the system under enrichment. With only the indirect interaction, the equilibrium density of the edible prey is unaffected by enrichment, but the density of both inedible prey and predator increases. With sufficient enrichment the system can always be destabilised. If there is direct interaction, the equilibrium density of all three species increases with enrichment: the edible fraction decreases, but has a lower bound. If the direct interaction is sufficiently strong there are regions of parameter space for which the system can never be destabilised by enrichment.