Parthenogenesis, sexual conflict, and selection on fertilization rates in switching environments

In the face of varying environments, organisms exhibit a variety of reproductive modes, from asexuality to obligate sexuality. Should reproduction be sexual, the morphology of the sex cells (gametes) produced by these organisms has important evolutionary implications; these cells can be the same size (isogamy), one larger and one smaller (anisogamy), and finally the larger cell can lose its capacity for motility (oogamy, the familiar sperm-egg system). Understanding the origin of the sexes, which lies in the types of gametes they produce, thus amounts to explaining these evolutionary transitions. Here we extend classic results in this area by exploring these transitions in a model in which organisms can reproduce both sexually and asexually (a reproductive mode present in many algae). In particular, we investigate the co-evolution of gamete cell size with fertilization rate, which is a proxy for motility and pheromone production but usually held constant in such models. Using adaptive dynamics generalized to the case of switching environments, we find that isogamy can evolve to anisogamy through evolutionary branching, and that anisogamy can evolve to oogamy or suppressed pheromone production through a further branching driven by sexual conflict. We also derive analytic conditions on the model parameters required to arrest evolution on this isogamy-oogamy trajectory, with low fertilization rates and stochastically switching environments stabilizing isogamy under a bet-hedging strategy, and low fertilization costs stabilizing anisogamy and pheromone production.