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The phenomenon of underpopulation has received scant attention from students of population dynamics. This work concerns the effect of rarity of mating in animal populations, and its evolutionary significance. Mathematical models are described and their use and limitations discussed. It is concluded that under certain ecological conditions, natural selection can be a very strong factor in the evolution of animals showing rarity in mating. This, coupled with the possible effects of gene drift in such populations could result in rapid evolution. It is suggested that conditions similar to those considered here are most likely to occur in tropical areas.