An ESS model to better understand the evolutionary dynamics of a primitive non-mating type gamete size was developed with reference to the PBS (Parker, Baker and Smith's) theory, which was based on total numbers of zygotes formed and the zygote survival rates. We did not include mating types since it has been suggested that primitive mating systems did not have mating types. As input parameters, we used experimental data on gamete motility of marine green algae. Based on hard sphere collision mechanics, we detailed the fertilization kinetics of gametes that swim in water prior to fusing with their partners through a set of coupled, non-linear differential equations. These equations were integrated numerically using typical values of the constant parameters. To estimate the relative zygote survival rate, we used a function that is sigmoid in shape and examined some evolutionarily stable strategies in mating systems that depend on optimizing values of the invasion success ratio.
