Bateman demonstrated differences in variance for fertility and mating success between the sexes, with males usually having a greater variance than females. Thus in general, male reproductive success increases with number of mates acquired. These results have been referred to as “Bateman's principles” and taken together with other parameters (e.g., relative parental investment) have been proposed to estimate a component of sexual selection. For this review I examine patterns of parental care and sexual selection in teleost fishes (substrate brooding and with internal fertilization). I present data for the pumpkinseed sunfish Lepomis gibbosus, in which I estimated cost of paternal care and compared direct measures of the intensity of selection on possible sexually selected traits to measures of sexual selection based on Bateman's principles.

Despite high levels of paternal care in substrate brooding fishes, sexual selection tends to act more strongly on males than on females, which suggests that maternal investment is higher than paternal investment and that parental care does not limit the reproductive rate for males. In pumpkinseed sunfish, selection favors parents with high levels of defense that may exclude predators more effectively and, as suggested by Bateman's measures, alternative reproductive strategies may decrease the opportunity for sexual selection within the parental strategy. In teleost fishes with internal fertilization, patterns of parental investment and intensity of sexual selection seem to support Bateman's principles, but further studies using these systems and these measures of selection will improve the understanding of factors affecting the intensity of sexual selection and its relation to mating systems.