# Apex predator and the cyclic competition in a rock-paper-scissors game of three species

## TL;DR

This paper investigates how introducing an apex predator affects the dynamics of three species engaged in cyclic competition, revealing that it promotes uniform spread, disrupts spiral patterns, and reduces cluster sizes while maintaining biodiversity.

## Contribution

It introduces a novel approach to simulate the impact of an apex predator in a rock-paper-scissors model with stochastic simulations.

## Key findings

- Apex predator promotes uniform distribution of species.
- It destroys spiral patterns in the system.
- Biodiversity is maintained despite reduced cluster sizes.

## Abstract

This work deals with the effects of an apex predator on the cyclic competition among three distinct species that follow the rules of the rock-paper-scissors game. The investigation develops standard stochastic simulations but is motivated by a novel procedure which is explained in the work. We add the apex predator as the fourth species in the system that contains three species that evolve following the standard rules of migration, reproduction and predation, and study how the system evolves in this new environment, in comparison with the case in the absence of the apex predator. The results show that the apex predator engenders the tendency to spread uniformly in the lattice, contributing to destroy the spiral patterns, keeping biodiversity but diminishing the average size of the clusters of the species that compete cyclically.