Mathematical Models of Fertilization—An Eco-Evolutionary Perspective

Abstract

Mathematical models of fertilization have been developed for many taxa, for both external and internal fertilizers. They estimate the proportion or number of fertilized gametes based on gamete concentrations and parameters relating to the biology of the model organism, as well as serve multiple purposes: a predictive purpose, with applications in, for example, artificial insemination; they clarify causal components of fertilization success such as concentration, size, collision rates and swimming speed of gametes, and polyspermy block times; and they function as components of models in evolutionary ecology, which often require understanding of fitness consequences of resource allocation between gametes and other traits. We pay particular attention to this last category, which has received less attention than other uses. Many evolutionary models assume the simplest relationship between fertilization success and gamete numbers: all eggs are fertilized. In nature, however, it is not uncommon for eggs to be sperm limited, and fertilization success must decrease as sperm density approaches zero. Fertilization functions become important in the range between these two extremes. We focus on models in evolutionary ecology, but aim for a resource that is useful regardless of topic or taxon by reviewing models developed for different purposes in a common mathematical framework.