  The rock-paper-scissors game is a model example of the on-going cyclic
turnover typical of many ecosystems, ranging from the terrestrial and aquatic
to the microbial. Here we explore the evolution of a rock-paper-scissors system
where three species compete for space. The species are allowed to mutate and
change the speed by which they invade one another. In the case when all species
have similar mutation rates, we observe a perpetual arms race where no single
species prevails. When only two species mutate, their aggressions increase
indefinitely until the ecosystem collapses and only the non-mutating species
survives. Finally we show that when only one species mutates, group selection
removes individual predators with the fastest growth rates, causing the growth
rate of the species to stabilize. We explain this group selection
quantitatively.
