  Motivated by the cyclic pattern of reproductive regimes observed in some
species of green flies (``{\it aphids}''), we simulate the evolution of a
population enduring harsh seasonal conditions for survival. The reproductive
regime of each female is also seasonal in principle and genetically acquired,
and can mutate for each newborn with some small probability. The results show a
sharp transition at a critical value of the survival probability in the winter,
between a reproductive regime in the fall that is predominantly sexual, for low
values of this probability, or asexual, for high values.
