Do deleterious mutations promote the evolution ofrecombination suppression between X and Y chromosomes?

An interesting new model has recently been proposed for the evolution of suppressed recombination between newly evolving X and Y chromosomes, where males are heterozygous for a locus determining sex and females are homozygous (the same principles apply to systems with female heterogamety, with the role of the two sexes reversed). The model appeals to the selective advantage that accrues to a recombination suppressor (e.g., an inversion), which arises on a male-determining haplotype that carries a smaller number of deleterious mutations than average and remains completely associated with the sex determining locus. The underlying logic of the model rests on the idea that, because such an inversion cannot become homozygous, it is "sheltered" from selection against any deleterious recessive mutations it may carry, in contrast to an autosomal inversion. It has been claimed that computer simulations of this process show that the probability that a new inversion becomes fixed within the population of Y chromosomes is substantially higher than expected under selective neutrality, and higher than that for a comparable autosomal inversion. However, analytical population genetic models of some special cases cast doubt on the magnitude of the selective advantage claimed for Y-linked inversions under this process, demanding re-evaluation of the simulation results. The published estimates of fixation probabilities of Y-linked inversions were in fact calculated after excluding inversions that were lost in the first 20 generations. This generates a substantial bias towards high fixation probabilities and obscures comparisons with neutrality. If all simulation runs are included, most parameter sets yield estimates of fixation probabilities that are close to neutral expectation, unless deleterious mutations are close to being completely recessive. The proposed sheltering mechanism is unlikely to provide a robust selective advantage to inversions suppressing recombination between evolving X and Y (or Z and W) chromosomes.