A Selfish Herd with a Target

TL;DR

This paper introduces a generalized model of the selfish herd hypothesis allowing agents to target specific domain areas, revealing how domain preferences influence collective behaviors like aggregation and milling.

Contribution

It extends previous models by enabling agents to aim for particular domain sizes and incorporates limited perception, uncovering new phases of collective motion.

Findings

Agents targeting specific domain areas exhibit diverse collective behaviors.

Limited perception influences the emergence of collective motion.

Different domain size preferences lead to distinct behavioral phases.

Abstract

One of the most striking phenomena in biological systems is the tendency for biological agents to spatially aggregate, and subsequently display further collective behaviours such as rotational motion. One prominent explanation for why agents tend to aggregate is known as the selfish herd hypothesis (SHH). The SHH proposes that each agent has a "domain of danger" whose area is proportional to the risk of predation. The SHH proposes that aggregation occurs as a result of agents seeking to minimise the area of their domain. Subsequent attempts to model the SHH have had varying success in displaying aggregation, and have mostly been unable to exhibit further collective behaviours, such as aligned motion or milling. Here, we introduce a model that seeks to generalise the principles of previous SHH models, by allowing agents to aim for domains of a specific (possibly non-minimal) area or a range of areas and study the resulting collective dynamics. Moreover, the model incorporates the lack of information that biological agents have by limiting the range of movement and vision of the agents. The model shows that the possibility of further collective motion is heavily dependent on the domain area the agents aim for - with several distinct phases of collective behaviour.