Genotypes studied in our model and the possible mutational pathways (blue arrows).

Pleiotropy can evolve from a genetic architecture in which the private trait (p, P) and cooperation (c, C) are unlinked (mutation I) and is either allowed or not allowed to revert (mutation II). All other mutations are always possible. During reproduction, a mutation occurs with probability μ in each offspring, in which case either one randomly chosen locus or the pleiotropic link in cooperators is changed. We also performed simulations with more realistic mutation rates, for which the probability of gaining a function (either cooperation, the private trait, or pleiotropy) was reduced by a factor of either 10 or 100 (S5 and S6 Figs).