A stochastic differential equation model for foraging behavior of fish schools

TL;DR

This paper introduces a stochastic differential equation model to simulate fish school foraging behavior in various spatial configurations, including obstacles, revealing how school size influences foraging success.

Contribution

The paper develops a new stochastic differential equation model that incorporates obstacles and analyzes how school size affects foraging success in different spatial setups.

Findings

Larger schools generally have higher foraging success.

An optimal school size maximizes foraging probability.

Fish maintain school structure during foraging.

Abstract

We present a novel model of stochastic differential equations for foraging behavior of fish schools in space including obstacles. We then study the model numerically. Three configurations of space with different locations of food resource are considered. In the first configuration, fish move in free but limited space. All individuals can find food almost surely. In the second and third configurations, fish move in limited space with one or two obstacles. Our results reveal that on one hand, when school size increases, so does the probability of foraging success. On the other hand, when it exceeds an optimal value, the probability decreases. In all configurations, fish always keep a school structure through the process of foraging.