Optimal size and number of propagules: allowance for discrete stages and effects of maternal size on reproductive output and offspring fitness.

Existing optimality models of propagule size and number are not appropriate for many organisms. First, existing models assume a monotonically increasing offspring fitness/propagule size relationship. However, offspring survival during certain stages may decrease with increasing propagule size, generating a peaked offspring fitness/propagule size function (e.g., egg size in oxygen-limited aquatic environments). Second, existing models typically do not consider maternal effects on total reproductive output and the expression of offspring survival/propagule size relationships. However, larger females often have greater total egg production and may provide better habitats for their offspring. We develop a specific optimality model that incorporates these effects and test its predictions using data from salmonid fishes. We then outline a general model without assuming specific functional forms and test its predictions using data from freshwater fishes. Our theoretical and empirical results illustrate that, when offspring survival is negatively correlated with propagule size, optimal propagule size is larger in better habitats. When larger females provide better habitats, their optimal propagule size is larger. Nevertheless, propagule number should increase more rapidly than propagule size for a given increase in maternal size. In the absence of density dependence, females with greater relative reproductive output (i.e., for a given body size) should produce more but not larger propagules.