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A stochastic differential equation model for predator-avoidance fish schooling.

Aditya Dewanto Hartono¹, Linh Thi Hoai Nguyen², Tôn Việt Tạ³

¹Mathematical Modeling Laboratory, Division of Bioproduction Environmental Sciences, Department of Agro-environmental Sciences, Faculty of Agriculture, Kyushu University, 744 Motooka Nishi Ward, Fukuoka, 819-0395, Japan.

Mathematical Biosciences

|December 3, 2023

Summary

This summary is machine-generated.

This study models predator-prey dynamics using stochastic differential equations, revealing four schooling prey avoidance patterns. Large prey groups effectively reduce predation risk in aquatic ecosystems.

Keywords:

Fish schooling Particle-based model Predator-avoiding patterns Predator–prey system Stochastic differential equations Swarm behavior

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Area of Science:

Mathematical Biology
Ecology
Physics

Background:

Predator-prey dynamics are crucial in ecological systems.
Schooling behavior in prey influences survival strategies.
Mathematical models can simulate complex biological interactions.

Purpose of the Study:

To develop a mathematical model for predator-prey dynamics with schooling prey.
To investigate prey schooling behavior and predator hunting tactics.
To identify predator-avoidance patterns.

Main Methods:

Utilized stochastic differential equations (SDEs) for modeling.
Employed a particle-like approach with attractive and repulsive forces.
Simulated two predator hunting strategies: center-attacking and nearest-attacking.

Main Results:

Identified four distinct prey avoidance patterns: Split and Reunion, Split and Separate into Two Groups, Scattered, and Maintain Formation and Distance.
Demonstrated that large schooling prey groups significantly mitigate predation risk.
Validated model predictions against real-world aquatic ecosystem observations.

Conclusions:

The developed SDE model accurately captures predator-prey interactions with schooling behavior.
Schooling is an effective anti-predation strategy for aquatic prey.
The model provides insights into the collective behavior of schooling organisms.