Making sense of recent models of the "sheltering" hypothesis for recombination arrest between sex chromosomes

In their most extreme form, sex chromosomes exhibit a complete lack of genetic recombination along much of their length in the heterogametic sex. Some recent models explain the evolution of such suppressed recombination by the "sheltering" of deleterious mutations by chromosomal inversions that prevent recombination around a polymorphic locus controlling sex. This sheltering hypothesis is based on the following reasoning. An inversion that is associated with the male-determining allele (with male heterogamety) is present only in the heterozygous state. If such an inversion carries a lower-than-average number of deleterious mutations, it will accrue a selective advantage and will be sheltered from homozygosity for any mutations that it carries due to the enforced heterozygosity for the inversion itself. It can, therefore, become fixed among all carriers of the male-determining allele. Recent population genetics models of this process are discussed. It is shown that, except under the unlikely scenario of a high degree of recessivity of most deleterious mutations, inversions of this type that lack any other fitness effects will have, at best, a modest selective advantage; they will usually accumulate on proto-Y chromosomes at a rate close to, or less than, the neutral expectation. While the existence of deleterious mutations does not necessarily prevent the spread of Y-linked inversions, it is unlikely to provide a significant selective advantage to them.