The evolution of parthenogen fertilization rates in switching environments: from facultative cell-fusion to oogamy

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. Surprisingy, 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.