What do egg size distributions in marine invertebrates tell us about validity of fecundity-time models?

An early mathematical model of egg size evolution in marine invertebrates (American Naturalist, 1973a, 107, 353) traded fecundity against development time and resulted in a U-shaped optimality curve suggesting that only extremes of egg sizes should be evolutionary stable. It was later suggested that the model predicts a bimodal distribution of egg sizes and therefore can be tested by examining histograms of egg sizes. More recent fecundity-time models (American Naturalist, 1997, 150, 48; American Naturalist, 2000, 156, 175) came up with predictions of intermediate optimal egg sizes; however, comparisons of optimality curves with histograms of egg sizes remained central to model testing. Here the question whether the bimodality assumption has any basis has been addressed theoretically. Simulation modeling and analysis show that egg size distributions generally do not match the optimality curves produced by fecundity-time models and that the shape of predicted frequency distributions depends on both the optimality curve and other model parameters. Therefore, egg size frequency distributions alone cannot be used for model testing.