# Uneven rock-paper-scissors models: patterns and coexistence

## TL;DR

This paper investigates how introducing unevenness in a stochastic rock-paper-scissors model affects pattern formation and species coexistence, revealing that asymmetry influences spatial structures and survival probabilities.

## Contribution

It demonstrates that asymmetry in species strength alters pattern dynamics and coexistence in May-Leonard models, highlighting the role of unevenness in ecological interactions.

## Key findings

- Unevenness prevents spiral wave formation from random initial conditions.
- Spatial patterns emerge through cyclic dominance of single-species domains.
- Species survival depends on asymmetry level and individual mobility.

## Abstract

We study a class of the stochastic May-Leonard models, with three species dominating each other in a cyclic nonhierarchical way, according to the rock-paper-scissors game. We introduce an unevenness in the system, by considering that one of the species is weaker because of a lower selection probability. The simulation results show that the pattern formation is drastically affected by the presence of the weaker species, with no spiral waves arising immediately from random initial conditions. Instead, single-species spatial domains cyclically dominate the entire territory until a region occupied by the weaker species is sufficiently narrow to be crossed by individuals without being selected. This leads to the appearance of spatial patterns responsible for the species coexistence. We verify that the asymmetry in the selection probabilities leads to different spatial autocorrelation function and average relative species abundances. Finally, we investigate the coexistence probability and show that the surviving species depends on the level of unevenness of the model and the mobility of individuals.