Spatiotemporal Pattern Formation in a Prey-Predator System: The Case Study of Short-Term Interactions Between Diatom Microalgae and Microcrustaceans

Abstract

<jats:p>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.</jats:p>

Small‐scale spatiotemporal variability and distance–decay relationships in intertidal micro‐ and meiobenthic assemblages

“…Block AB was situated 9 m lower toward the low tide level (Figure 1b) and was exposed to a half‐hour shorter emersion during the low tides. All the groups studied, however, are known to perform diurnal vertical migrations (Saburova & Polikarpov, 2003; Saburova et al, 2004; Tyutyunov et al, 2020), so such a small difference in tidal regime seems unlikely to be substantial.…”

Stationary and non-stationary pattern formation over fragmented habitat

“…For each (n 1 , n 2 ), we find these curves by solving the equation ( 17) for d 2 with varying a. Specifically, two critical curves are marked (thick magenta curves) with the ) is a reasonable critical mode and the corresponding mode curve is close to the Turing bifurcation threshold [25]. Similarly, the mode curve for a = 2.25 and close to Turing bifurcation curve is determined by the mode numbers (n 1 , n 2 ) = (9, 47).…”

“…In order to have the right-hand patch with smaller width compared to the patch on the left, we consider the domain with L 2 = 200, L x 1 = 80, L x 2 = 90, L x 3 = 30 and L y = 5. Here, we choose the initial condition as (25) for the numerical simulation. We find a labyrinthine pattern in the left patch D 1 .…”

“…In order to see the formation of spatio-temporal chaotic pattern over the U-shaped domain, we choose a = 1, s = 2, d 1 = d 2 = 1. We take the initial condition (25) and domain size as L 1 = 400, L 2 = 200, L x 1 = L x 3 = 180, L x 2 = 40 and L y = 2. We plot the chaotic patterns at two different time steps in Fig.…”

Sufficient Conditions for the Existence and Uniqueness of the Solution of the Dynamics of Biogeochemical Cycles in Coastal Systems Problem

“…In [3], mathematical modeling methods are used to assess the state of the ecological system of the North Caspian shelf, biological pollution, including invasive species. In the works of Russian scientists [4,5], shallowwater ecosystems are researched, and forecasts of their development dynamics are made. In [6][7][8][9][10], the hydrological regime, dynamics of primary bioproduction, biogenic pollution of water bodies in the South of Russia were studied, and mathematical models of the movement of the aquatic environment, biochemistry, and biological kinetics were proposed.…”