Impact of parity in rock-paper-scissors type models

TL;DR

This study explores how the parity of the number of species affects the abundance of weaker species in generalized rock-paper-scissors models, revealing significant parity effects and conditions favoring weak species.

Contribution

It demonstrates the influence of species number parity on weak species abundance in generalized rock-paper-scissors models through spatial stochastic simulations.

Findings

Odd number of species favors weak species over even numbers.

Weak species tend to have higher abundance when predation probability is sufficiently low.

Parity effects are significant for models with up to 8 species.

Abstract

We investigate the impact of parity on the abundance of weak species in the context of the simplest generalization of the rock-paper-scissors model to an arbitrary number of species -- we consider models with a total number of species ($N_S$) between 3 and 12, having one or more (weak) species characterized by a reduced predation probability (by a factor of ${\mathcal P}_w$ with respect to the other species). We show, using lattice based spatial stochastic simulations with random initial conditions, large enough for coexistence to prevail, that parity effects are significant. We find that the performance of weak species is dependent on whether the total number of species is even or odd, especially for $N_S \le 8$, with odd numbers of species being on average more favourable to weak species than even ones. We further show that, despite the significant dispersion observed among individual models, a weak species has on average a higher abundance than a strong one if ${\mathcal P}_w$ is sufficiently smaller than unity -- the notable exception being the four species case.