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A five-species predator-prey model is studied on a square lattice where eachspecies has two prey and two predators on the analogy to theRock-Paper-Scissors-Lizard-Spock game. The evolution of the spatialdistribution of species is governed by site exchange and invasion between theneighboring predator-prey pairs, where the cyclic symmetry can be characterizedby two different invasion rates. The mean-field analysis has indicated periodicoscillations in the species densities with a frequency becoming zero for aspecific ratio of invasion rates. When varying the ratio of invasion rates, theappearance of this zero-eigenvalue mode is accompanied by neutrality betweenthe species associations. Monte Carlo simulations of the spatial system revealdiverging fluctuations at a specific invasion rate, which can be related to thevanishing dominance between all pairs of species associations.

Diverging fluctuations in a spatial five-species cyclic dominance game