Modelling of Spatially Distributed Predator–Prey System with Periodically Migrating Predator (Case Study of the White Sea Intertidal Harpacticoids and Benthic Microalgae)

Abstract

A time-continuous, spatially discrete motile predator–immobile prey model has been developed to describe the interactions between harpacticoid copepods and benthic microalgae in the intertidal zone. Harpacticoids perform periodic and nondirectional migrations; the local intensity of these migrations is trophic-dependent, related to the ratio of real to maximum food consumption rates. The zero-dimensional (non-spatial) analog of the model has three nontrivial equilibrium states, two of which are stable: one corresponds to overgrazing (permanently low abundance of prey controlled by hungry predator); the second is “welfare” (well-fed predator and resource-limited prey). Simulations show that in the spatially distributed model with close-to-real parameter values, two regimes can be realized: either total overgrazing or a persistent heterogeneous dynamic regime with short-lived patches of both populations, similar to that observed in nature. The predator’s ability to migrate narrows the “welfare” domain in parametric space, but increases the trophic efficiency of the system: in this domain, both average prey abundance and average consumption rate for the predator are higher than without migrations. The migrating gain is larger in an environment that is spatially heterogeneous for prey. Assumption of local awareness of the predator (preferred migrations toward a high abundance of prey) has no significant effect on the state of the system.