Models of fertilization kinetics

Fertilization functions describe how the number of realized fertilizations depends on gamete numbers or density. They provide insight into the fertilization process, and are important components in models on the evolution of reproductive and sex-specific traits. Existing fertilization functions generally examine the proportion of fertilized eggs as a function of sperm numbers or density in a given fertilization environment. Because these functions have been developed for species with highly diverged gametes, there is an inbuilt (and well justified) asymmetry in them: they treat eggs and sperm, and therefore the two sexes, differently. Although very useful, such functions cannot therefore be used to consistently model early stages in the evolution of the two sexes, or extant species where sex-specific gamete sizes and numbers are similar. Here, I derive fertilization functions that describe the fertilization process without making prior assumptions about the two sexes, and are therefore consistent under any level of gamete dimorphism. These functions are compatible with simpler fertilization functions under appropriate conditions. Such functions can be particularly useful in understanding the early stages in the differentiation of the two sexes, as well as its consequences, where the gametes from the two sexes should be treated on an equal basis.