Volume 94, No. 2 THE QUARTERLY REVIEW OF BIOLOGY June 2019 MATHEMATICAL MODELS OF FERTILIZATION—AN ECO-EVOLUTIONARY PERSPECTIVE Jussi Lehtonen School of Life and Environmental Sciences, University of Sydney Sydney, New South Wales 2006 Australia Evolution and Ecology Research Centre, School of Biological, Earth and Environmental Sciences, University of New South Wales Sydney, New South Wales 2052 Australia e-mail: jussi.lehtonen@iki.fi Louis Dardare Evolution and Ecology Research Centre, School of Biological, Earth and Environmental Sciences, University of New South Wales Sydney, New South Wales 2052 Australia e-mail:
[email protected] keywords fertilization functions, egg, sperm, gamete, fertilization models, sperm limitation abstract Mathematical models of fertilization have been developed for many taxa, for both external and inter- nal 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 pre- dictive 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 fertiliza- tion success must decrease as sperm density approaches zero.