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 transition from a one‐step meiosis without recombination to one with recombination may have been stimulated by the invasion of Killer alleles. These imaginary selfish elements are considered to act prior to recombination. They prime for destruction (which occurs after cell division) the half of the cell on the opposite side of the meiotic spindle. Likewise the transition from one‐step to two‐step meiosis might have been stimulated by a subtly different sort of imaginary distorter allele, a SisterKiller. These are proposed to act after recombination. It has yet to be established that the presence of such distorter alleles could induce the transitions in question. To investigate these issues we have analysed the dynamics of a modifier (1) of recombination and (2) of the number of steps of meiosis, as they enter a population with one‐step meiosis. For the modifier of recombination, we find that invasion conditions are very broad and that persistence of Killer and modifier 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 typically both lost from the population. The modifier of the number of steps can invade if the SisterKiller acts at meiosis II. However, a SisterKiller acting 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 recombination. The SisterKiller hypothesis therefore fails to provide a reasonable account of the evolution of two‐step meiosis with recombination. As before, the evolution of self‐tolerance on the part of the selfish element destroys the process. We conclude that the conditions under which SisterKillers promote the evolution of two‐step meiosis are very much more limited than originally considered. We also conclude that there is no universal agreement between ESS and modifier analyses of the same transitions.