Rock-scissors-paper and the survival of the weakest

In the children's game of rock-scissors-paper, players each choose one of t hree strategies. A rock beats a pair of scissors, scissors beat a sheet of paper and paper beats a rock, so the strategies form a competitive cycle. A lthough cycles in competitive ability appear to be reasonably rare among te rrestrial plants, they are common among marine sessile organisms and have b een reported in other contexts. Here we consider a system with three specie s in a competitive loop and show that this simple ecology exhibits two coun terintuitive phenomena. First, the species that is least competitive is exp ected to have the largest population and, where there are oscillations in a finite population, to he the least likely to die out. As a consequence an apparent weakening of a species leads to an increase in its population. Sec ond, evolution favours the most competitive individuals within a species, w hich leads to a decline in its population. This is analogous to the tragedy of the commons, bur here, rather than leading to a collapse, the 'tragedy' acts to maintain diversity.