title: Optimal Egg Size in Marine Invertebrates: Theory and Phylogenetic Analysis of the Critical Relationship between Egg Size and Development Time in Echinoids.
abstract: Life-history models for marine invertebrate larvae generally predict a dichotomy in egg size in different species: eggs should be either minimal in size or large enough to support development fully without larval feeding. This prediction is contradicted, however, by the empirical observation of wide, continuous variation in egg size between these extremes. The prediction of dichotomy rests on the assumption of a negative linear relationship between egg size and development time. Here, I present a simple model in which development time is inversely proportional to egg size. Incorporating this relationship into an optimality model produces predictions of intermediate rather than extreme egg size. Modeled variations in mortality, food availability, fertilization rates, and temperature all produce continuous shifts in the value of the intermediate optimal size, in direct contrast to those produced by previous models, which predict shifts between two extreme optima. Empirical data on echinoid egg size and development time strongly support the model's assumption of an inverse proportional relationship between egg size and development time. A composite phylogeny is constructed of the 37 species for which egg size, development time, water temperature, and phylogenetic relatedness are known. Independent contrasts are made of the evolutionary changes in egg size and development time. This analysis indicates that evolutionary shifts in development time are correlated with the inversely proportional shifts in egg size assumed in the model. The assumption of a negative linear relationship used in previous models is rejected. This model provides a potential explanation for intraspecific variation in egg size along environmental gradients, sympatric differences in egg size among species, and biogeographic trends in egg size and development mode across taxa.
authors.forename: Don R
authors.initials: DR
authors.lastname: Levitan