Dynamics and patterns of species abundance in ocean: A mathematical modeling study

In the complex and competitive world of oceans, different size of plants and animals exist. All of them compete for the limited resources; e.g., nutrients, sunlight, minerals etc. Size-specific and intraspecific predation is common among zooplankton. We design a model food chain and explore dynamics, and patterns of species abundance in ocean. The proposed mathematical model is based on a parameter; exponent of closure, m. A value of m less than 1 represents both size-specific and intraspecific predation among zooplankton. The mathematical model has been extended to include random movements of all the constituent populations by adding Fickian diffusion. Eigenvalues and amplitude equations are used to figure out relevant parameter spaces for numerical exploration. An analysis of the spatial system in the neighborhood of a critical parameter is performed using amplitude equation. Choosing appropriate control parameter from the Turing space, existence conditions for stable patterns are derived. Equal density contours were plotted for all the constituents of the model food chain. Epidemiological significance of these spatial patterns is provided.