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The rock-paper-scissors game is a model example of the on-going cyclicturnover typical of many ecosystems, ranging from the terrestrial and aquaticto the microbial. Here we explore the evolution of a rock-paper-scissors systemwhere three species compete for space. The species are allowed to mutate andchange the speed by which they invade one another. In the case when all specieshave similar mutation rates, we observe a perpetual arms race where no singlespecies prevails. When only two species mutate, their aggressions increaseindefinitely until the ecosystem collapses and only the non-mutating speciessurvives. Finally we show that when only one species mutates, group selectionremoves individual predators with the fastest growth rates, causing the growthrate of the species to stabilize. We explain this group selectionquantitatively.

Clonal selection prevents tragedy of the commons when neighbors compete in a rock-paper-scissors game