Do fecundity-time models really predict extreme optimal egg sizes?

In 1973, Vance published a mathematical model that explains differences in reproductive strategies such as planktotrophy and lecithotrophy found in marine invertebrates. The original model Vance (The American Naturalist, 107, 339-352) traded fecundity against development time and resulted in a U-shaped fitness function suggesting that only extreme levels of egg provisioning (referred to as egg size) are evolutionarily stable. Several later models independently predicted evolutionary stability of extreme egg sizes, and this has been commonly interpreted as a proof that the Vance model, albeit oversimplified, reflects the fundamental evolutionary principle of disruptive egg size evolution in marine invertebrates. However, empirical studies of the last several decades have illustrated that intermediate levels of egg provisioning are commonly observed in nature. As a result, the recent modifications of the original Vance model have attempted to explain evolution of such intermediate strategies. Here we re-examine the earlier fecundity-time models of the 'Vance family' and show that only Vance and its minor modification by Grant (The American Naturalist, 122, 549-555) invariably predict evolutionary stability of extreme egg sizes. Most modifications of the original Vance model in fact can predict at least some intermediate optimal egg sizes and reproductive strategies. There is no reason to assume that selection towards extreme egg sizes is the driving force in the evolution of marine invertebrate life histories.