A Stochastic Differential Equation Model for Predator-Avoidance Fish Schooling

TL;DR

This paper introduces a stochastic differential equation model to simulate predator-prey interactions in aquatic environments, revealing prey schooling behaviors and the advantages of large groups in predator avoidance, validated through numerical simulations.

Contribution

It develops a novel SDE-based model incorporating predator tactics and prey schooling, capturing complex predator-avoidance patterns and group benefits in aquatic ecosystems.

Findings

Four predator-avoidance patterns identified

Large prey groups reduce predation risk

Model aligns with real-world observations

Abstract

This paper presents a system of stochastic differential equations (SDEs) as mathematical model to describe the spatial-temporal dynamics of predator-prey system in an artificial aquatic environment with schooling behavior imposed upon the associated prey. The proposed model follows the particle-like approach where interactions among the associated units are manifested through combination of attractive and repulsive forces analogous to the ones occurred in molecular physics. Two hunting tactics of the predator are proposed and integrated into the general model, namely the center-attacking and the nearest-attacking strategy. Emphasis is placed upon demonstrating the capacity of the proposed model in: (i) discovering the predator-avoidance patterns of the schooling prey, and (ii) showing the benefit of constituting large prey school in better escaping the predator's attack. Based on numerical simulations upon the proposed model, four predator-avoidance patterns of the schooling prey are discovered, namely Split and Reunion, Split and Separate into Two Groups, Scattered, and Maintain Formation and Distance. The proposed model also successfully demonstrates the benefit of constituting large group of schooling prey in mitigating predation risk. Such findings are in agreement with real-life observations of the natural aquatic ecosystem, hence confirming the validity and exactitude of the proposed model.