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Organisms with external fertilisation exhibit a broad range of reproductive modes, from simple parthenogenesis to sexual reproduction encompassing isogamy, anisogamy, and oogamy, and including environmentally-mediated facultative sex. Here we develop a unifying mathematical model which explains the emergence of these modes via the coevolution of fertilization rate and cell size. Using a minimal assumption that survival is dependent on cell mass, and by carefully accounting for biological and evolutionary time scales, we find two distinct evolutionary outcomes: high fertilization rate (obligate sexuality) is selected when costs to cell fusion are low, while zero fertilization rate (obligate asexuality) is selected for when these costs are high. Surprisingly, in high fertilization rate scenarios evolving populations can transition from isogamy to anisogamy and oogamy via evolutionary branching. Furthermore, in variable environments we show that, without phenotypic plasticity, intermediate fertilization rates and isogamy can be maintained through bet-hedging. Allowing phenotypic plasticity can give rise to facultative sex; sexual reproduction in harsh environmental conditions, and asexuality in more benign conditions. These results parsimoniously explain a large range of empirically observed parthenogen reproduction strategies, and offer an hypothesis for the origin of binary cell fusion, a key step in the evolution of syngamy and sexual reproduction itself.

Organisms with external fertilization exhibit a variety of reproductive modes, from simple parthenogenesis to isogamy, anisogamy and oogamy. Here, we develop a mathematical model that helps to explain the evolution of these modes through the co-evolution of cell size and fertilization rate. By assuming that gametes can develop parthenogenetically should they fail to fertilize, and that survival of a propagule (zygote/unfertilized gamete) depends on size, we find that an isogamous population can evolve to anisogamy through evolutionary branching. Oogamy can then evolve from an anisogamous population under sexual conflict. Furthermore, we derive analytic results on the model parameters required to arrest evolution on this isogamy-oogamy trajectory. Low fertilization rates stabilise isogamy, while low fertilization costs stabilise anisogamy. Additionally we show using adaptive dynamics that isogamy can be maintained as a bet-hedging strategy in a stochastically switching environment.