A single predator charging a herd of prey: effects of self volume and predator-prey decision-making

TL;DR

This study models predator-prey interactions on a lattice, highlighting how prey sighting range and self-volume influence hunting success, with prey sighting range being a critical factor for prey survival.

Contribution

It introduces an explicit lattice-based model incorporating prey self-volume and decision-making, analyzing predator-prey dynamics with a novel focus on sighting ranges and effective two-body approximations.

Findings

Prey sighting range significantly affects prey survival.

Predator benefits more from prey having poor eyesight than from its own good eyesight.

The predator-prey distance dynamics can be approximated by an Ornstein-Uhlenbeck process.

Abstract

We study the degree of success of a single predator hunting a herd of prey on a two dimensional square lattice landscape. We explicitly consider the self volume of the prey restraining their dynamics on the lattice. The movement of both predator and prey is chosen to include an intelligent, decision making step based on their respective sighting ranges, the radius in which they can detect the other species (prey cannot recognise each other besides the self volume interaction): after spotting each other the motion of prey and predator turns from a nearest neighbour random walk into direct escape or chase, respectively. We consider a large range of prey densities and sighting ranges and compute the mean first passage time for a predator to catch a prey as well as characterise the effective dynamics of the hunted prey. We find that the prey's sighting range dominates their life expectancy and the predator profits more from a bad eyesight of the prey than from his own good eye sight. We characterise the dynamics in terms of the mean distance between the predator and the nearest prey. It turns out that effectively the dynamics of this distance coordinate can be captured in terms of a simple Ornstein-Uhlenbeck picture. Reducing the many-body problem to a simple two-body problem by imagining predator and nearest prey to be connected by a Hookean bond, all features of the model such as prey density and sighting ranges merge into the effective binding constant.