Abstract: The optimal tradeoff between offspring size and number can depend on details of the mode of reproduction or development. In marine organisms, broadcast spawning is widespread, and external coats are a common feature of spawned eggs. Egg jelly coats are thought to influence several aspects of fertilization and early development, including the size of the target for sperm, fertilization efficiency, egg suspension time, polyspermy, embryo survival, and fecundity. These costs and benefits of investment in jelly result in tradeoffs that can influence optimal reproductive allocation and the evolution of egg size. I develop an optimization model that sequentially incorporates assumptions about the function of egg coats in fertilization. The model predicts large variation in coat size and limited variation in ovum size under a broad range of conditions. Heterogeneity among spawning events further limits the range of ovum sizes predicted to evolve under sperm limitation. In contrast, variation in larval mortality predicts a broad range of optimal ovum sizes that more closely reflects natural variation among broadcastspawning invertebrates. By decoupling physical and energetic size, egg coats can enhance fertilization, maintain high fecundity, and buffer the evolution of ovum size from variation in spawning conditions
