A five-species predator-prey model is studied on a square lattice where each
species has two prey and two predators on the analogy to the
Rock-Paper-Scissors-Lizard-Spock game. The evolution of the spatial
distribution of species is governed by site exchange and invasion between the
neighboring predator-prey pairs, where the cyclic symmetry can be characterized
by two different invasion rates. The mean-field analysis has indicated periodic
oscillations in the species densities with a frequency becoming zero for a
specific ratio of invasion rates. When varying the ratio of invasion rates, the
appearance of this zero-eigenvalue mode is accompanied by neutrality between
the species associations. Monte Carlo simulations of the spatial system reveal
diverging fluctuations at a specific invasion rate, which can be related to the
vanishing dominance between all pairs of species associations.Comment: accepted for publication in Physical Review
