МЕЛКОМАСШТАБНАЯ ПЯТНИСТОСТЬ В ПРОСТРАНСТВЕННОЙ МОДЕЛИ ТРОФИЧЕСКОЙ СИСТЕМЫ ДИАТОМОВЫЕ МИКРОВОДОРОСЛИ – ГАРПАКТИКОИДЫ

Abstract

A predator–prey model that describes littoral trophic communities consisting of diatom microalgae and benthic copepod crustaceans (order Harpacticoida) was built and investigated. The model is a system of three partial differential equations of the taxis–diffusion–reaction type. The Neumann boundary condition specifies zero-flux through the borders of a rectangular habitat. The movements of copepods is described by the classical Patlak – Keller – Segel flux expression, which includes both taxis and diffusion. The feeding migrations of consumers are modelled as indirect prey–taxis stimulated by harpacticoid satiety, i.e. with the diffusion coefficient being a decreasing function of individual satiety. Inasmuch as demographic processes in the predator population occur at slow time scale, the model includes no birth/death terms for predator. Hence, taking into account the boundary condition, the average density of predators remains constant. The analytical condition for the oscillatory instability of the homogeneous stationary state of species coexistence reveals the crucial role of the indirect prey–taxis for emergence of spatiotemporal patterns in the system. The proposed model can be viewed as the minimal model capable of explaining heterogeneity of the harpacticoid density. With parameters identified on the basis of field observation data, the model simulates small-scale spatial patterns with characteristic size and the expected lifetime of density patches typical for the considered community of benthic organisms. In spatially-heterogeneous dynamics both density of microalgae and individual consumption of harpacticoid copepods exceed equilibrium values observed without feeding migrations. This suggests that prey–taxis behavior is an evolutionary advantageous strategy