The Trivers-Willard hypothesis: sex ratio or investment?

The Trivers-Willard hypothesis has commonly been considered to predict two things. First, that a mother in good condition should bias the sex ratio of her offspring towards males (if males exhibit greater variation in reproductive value). Second, that a mother in good condition should invest more per son than per daughter. These two predictions differ empirically, mechanistically and, as we demonstrate here, theoretically too. We construct a simple model of sex allocation that allows simultaneous analysis of both versions of the Trivers-Willard hypothesis. We show that the sex ratio version holds under very general conditions, being valid for a large class of male and female fitness functions. The investment version, on the other hand, is shown to hold only for a small subset of male and female fitness functions. Our results help to make sense of the observation that the sex ratio version is empirically more successful than the investment version.