Sperm competition and sex allocation in simultaneous hermaphrodites: A new look at Charnov’s invariance principle

Recently, Charnov (1996) investigated the consequences of sperm competition for optimal sex allocation in simultaneous hermaphrodites. Charnov argued that the optimal sex allocation strategy can be derived on the basis of the ‘sperm displacement rule’; that is, the function describing the relationship between sperm production and sperm displacement. Based on three specific examples of such sperm displacement rules, Charnov claimed that the details of the relationship between ejaculate volume and sperm displacement have only a minor effect on the optimal sex allocation strategy. We demonstrate that this ‘invariance principle’ is less general than suggested. The optimal sex allocation strategy as a function of the dimensionless quantity δ (ratio of maximum sperm volume to sperm storage volume) can have a wide variety of shapes. This is because Charnov’s results depend crucially on two assumptions of questionable generality: diminishing displacement with investment in sperm and linear fitness returns with investment in eggs. We argue that deeper insights into optimal sex allocation are obtained if the allocation decision is partitioned into multiple components. Using this approach, we find a novel invariance principle: if egg survival only depends on the investment per egg (and not on clutch size), then the shape of this relationship has no effect whatsoever on optimal allocation to eggs versus sperm.