Transitions in the evolution of meiosis

Meiosis may have evolved gradually within the eukaryotes with the earliest forms having a one-step meiosis. It has been speculated that the putative t ransition from a one-step meiosis without recombination to one with recombi nation may have been stimulated by the invasion of Killer alleles. These im aginary selfish elements are considered to act prior to recombination. They prime for destruction (which occurs after cell division) the half of the c ell on the opposite side of the meiotic spindle. Likewise the transition fr om one-step to two-step meiosis might have been stimulated by a subtly diff erent sort of imaginary distorter allele, a SisterKiller. These are propose d to act after recombination. It has yet to be established that the presenc e of such distorter alleles could induce the transitions in question. To in vestigate these issues we have analysed the dynamics of a modifier (1) of r ecombination and (2) of the number of steps of meiosis, as they enter a pop ulation with one-step meiosis. For the modifier of recombination, we find t hat invasion conditions are very broad and that persistence of Killer and m odifier is likely through most parameter space, even when the recombination rate is low. However, if we allow a Killer element to mutate into one that is self-tolerant, the modifier and the nonself-tolerant alleles are typica lly both lost from the population. The modifier of the number of steps can invade if the SisterKiller acts at meiosis II. However, a SisterKiller acti ng at meiosis I, far from promoting the modifier's spread, actually impedes it. In the former case the invasion is easiest if there is no recombinatio n. The SisterKiller hypothesis therefore fails to provide a reasonable acco unt of the evolution of two-step meiosis with recombination. As before, the evolution of self-tolerance on the part of the selfish element destroys th e process. We conclude that the conditions under which SisterKillers promot e the evolution of two-step meiosis are very much more limited than origina lly considered. We also conclude that there is no universal agreement betwe en ESS and modifier analyses of the same transitions.