Rock-paper-scissors models with a preferred mobility direction

TL;DR

This study explores how a preferred movement direction affects species competition in a modified rock-paper-scissors model, revealing that directional preference influences species advantage and extinction probabilities.

Contribution

It introduces a spatial stochastic Lotka-Volterra model with asymmetric mobility and analyzes how preferred movement direction impacts species dynamics and coexistence.

Findings

Preferred mobility gives an advantage to the species with asymmetric movement.

An optimal noise level maximizes the advantage of the preferred-moving species.

Higher noise levels decrease the critical population size for extinction, reducing coexistence chances.

Abstract

We investigate a modified spatial stochastic Lotka-Volterra formulation of the rock-paper-scissors model using off-lattice stochastic simulations. In this model one of the species moves preferentially in a specific direction -- the level of preference being controlled by a noise strength parameter $\eta \in [0, 1]$ ($\eta = 0$ and $\eta = 1$ corresponding to total preference and no preference, respectively) -- while the other two species have no referred direction of motion. We study the behaviour of the system starting from random initial conditions, showing that the species with asymmetric mobility has always an advantage over its predator. We also determine the optimal value of the noise strength parameter which gives the maximum advantage to that species. Finally, we find that the critical number of individuals, below which the probability of extinction becomes significant, decreases as the noise level increases, thus showing that the addition of a preferred mobility direction studied in the present paper does not favour coexistence.