Abstract
A simple mathematical model capable of reproducing formation of small-scale spatial structures in prey–predator system is presented. The migration activity of predators is assumed to be determined by the degree of their satiation. The hungrier individual predators migrate more frequently, randomly changing their spatial position. It has previously been demonstrated that such an individual response to local feeding conditions leads to prey–taxis and emergence of complex spatiotemporal dynamics at population level, including periodic, quasi-periodic and chaotic regimes. The proposed taxis–diffusion–reaction model is applied to describe the trophic interactions in system consisting of benthic diatom microalgae and harpacticoid copepods. The analytical condition for the oscillatory instability of the homogeneous stationary state of species coexistence is given. The model parameters are identified on the basis of field observation data and knowledge on the species ecology in order to explain micro-scale spatial patterns of these organisms, which still remain obscure, and to reproduce in numerical simulations characteristic size and the expected lifetime of density patches.
Highlights
In nature, spatial distribution of benthic copepod crustaceans is highly heterogeneous, varying over a wide range of spatial and temporal scales
In [11] for the case study of copepod movements we have proved applicability of the PKS-flux model to sporadically migrating organisms
In the model presented here, predator’s migrations are explicitly formalized as indirect prey–taxis stimulated by the degree of starvation, which leads to the Patlak–Keller–Segel flux of the predator population density [8,11]
Summary
Spatial distribution of benthic copepod crustaceans (order Harpacticoida) is highly heterogeneous, varying over a wide range of spatial and temporal scales. It is reasonable to assume that the prevailing mechanism causing the small-scale spatial heterogeneity of harpacticoid population density is related to species biology and behavior [1,2]. Rigorous substantiation of using the PKS-flux expression for abundant animals performing sporadic stick-slip replacements of individuals being locally stimulated by an external factor is given in [11]. Mathematical models of this type are of theoretical and practical importance in various fields of science, including biology, medicine and biophysics (see [12] and references therein)
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