SEXUAL selection is thought to be responsible for the evolution of exaggerated male characters and of female mate preferences(1-7). Evolutionary mechanisms driven by an advantage to the progeny are only effective if the preferred character has a large genetic component of variance; in most systems in which sexual selection operates, little is known of the relevant genetics(8), We have measured parent-offspring correlations, and report here that the preferred character (adult size) in seaweed flies has large additive genetic variance in males, but not in females, Virtually all the variance in male size is attributable to a chromosomal inversion system and, consequently, because this system is also a major determinant of larval viability(9,10), male size could be used by females as a reliable indicator of offspring survival.