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 increasi ng offspring fitness/propagule size relationship. However, offspring surviv al during certain stages may decrease with increasing propagule size, gener ating 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 express ion of offspring survival/propagule size relationships. However, larger fem ales often have greater total egg production and may provide better habitat s for their offspring. We develop a specific optimality model that incorpor ates these effects and test its predictions using data from salmonid fishes . We then outline a general model without assuming specific functional form s and test its predictions using data from freshwater fishes. Our theoretic al and empirical results illustrate that, when offspring survival is negati vely correlated with propagule size, optimal propagule size is larger in be tter habitats. When larger females provide better habitats, their optimal p ropagule size is larger. Nevertheless, propagule number should increase mor e 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 pro pagules.