The kinetics of monospermic and polyspermic fertilization in free-spawning marine invertebrates.

The equation of Vogel et al. (1982) is widely used in fertilization studies of free-spawning marine invertebrates to predict the percentage of viable eggs that will be fertilized at any specified levels of gamete concentration and contact time. Here, the random collision model that underlies the Vogel et al. equation is extended to distinguish between monospermic and polyspermic fertilization, and separate equations for the percentages of monospermic and polyspermic fertilization are obtained. These equations provide an explanation for empirical observations which have shown a decreased percentage of successful egg development at high sperm concentrations. Comparison is made with an earlier heuristic attempt (Styan, 1998) to predict the extent of polyspermic fertilization, and it is found that this earlier method can underestimate the percentage of polyspermic fertilization by up to 10 percent. Moreover, the approach used here retains the flexibility to model changes in sperm concentration due to dispersal mechanisms, and is able to model different mechanisms for the block to polyspermy.