We investigated the evolution of monogamy (one male, one female) and polygyny (one male, more than one female). In particular, we studied whether it is possible for a mutant polygynous mating strategy to invade a resident population of monogamous breeders and, alternatively, whether a mutant monogamy can invade resident polygyny. Our population obeys discrete–time Ricker dynamics. The role of males and females in the breeding system is incorporated via the harmonic birth function. The results of the invasability analysis are straightforward. Polygyny is an evolutionarily stable strategy mating system; this holds throughout the examined range of numbers of offspring produced per female. So that the two strategies can coexist, polygyny has to be punished. The coexistence of monogamy and polygyny is achieved by reducing the offspring number for polygyny relative to monogamy. This yields long–term persistence of the strategies for all offspring numbers studied. An alternative punishment is to increase the sensitivity of polygynous breeders to population density. The coexistence is possible only with a limited range of offspring produced. The third way to achieve coexistence of the two mating strategies is to assume that individuals live in a spatially structured population, where dispersal links population subunits to a network. Reducing the dispersal rate of polygynous breeders relative to that of monogamous individuals makes the coexistence feasible. However, for monogamy to persist, the number of offspring produced has to be relatively high.