A model for optimal offspring size in fish, including live-bearing and parental effects

Since Smith and Fretwell's seminal article in 1974 on the optimal offspring size, most theory has assumed a trade-off between offspring number and offspring fitness, where larger offspring have better survival or fitness, but with diminishing returns. In this article, we use two ubiquitous biological mechanisms to derive the shape of this trade-off: the offspring's growth rate combined with its size-dependent mortality (predation). For a large parameter region, we obtain the same sigmoid relationship between offspring size and offspring survival as Smith and Fretwell, but we also identify parameter regions where the optimal offspring size is as small or as large as possible. With increasing growth rate, the optimal offspring size is smaller. We then integrate our model with strategies of parental care. Egg guarding that reduces egg mortality favors smaller or larger offspring, depending on how mortality scales with size. For live-bearers, the survival of offspring to birth is a function of maternal survival; if the mother's survival increases with her size, then the model predicts that larger mothers should produce larger offspring. When using parameters for Trinidadian guppies Poecilia reticulata, differences in both growth and size-dependent predation are required to predict observed differences in offspring size between wild populations from high- and low-predation environments.