Models of sexual and asexual coexistence in aphids based on constraints

Two models are presented to test the hypothesis that in aphids, a particular constraint (the necessity to resist frost) could be the proximal cause for the maintenance of sex. Both models are based on temporal variability in winter survival of asexuals. They show that: i) only cyclical parthenogenesis is maintained below a threshold frequency of mild winters, because of the cold-resistance of sexually-produced eggs. ii) above a second threshold, only obligate parthenogenesis is maintained. iii) in-between, the first model predicts a mixed evolutionarily stable strategy (ESS). This would reflect well the geographic distribution of the different types of reproduction. The second model, based on the genetic control of the reproduction system in two aphid species, predicts the maintenance of polymorphism with fluctuating proportions of the two life-cycles. Males produced by obligate parthenogens play an essential role in this equilibrium (no stable polymorphism exists if this male production is set to zero). The value of the lowest possible fitness achieved by overwintering asexuals is critical.