Evolution of autosomal suppression of the sex-ratio trait in Drosophila

The sex-ratio trait is the production of female-biased progenies due to X-linked meiotic drive in males of several Drosophila species. The driving X chromosome (called SR) is not fixed due to at least two stabilizing factors: natural selection (favoring ST, the nondriving standard X) and drive suppression by either Y-linked or autosomal genes. The evolution of autosomal suppression is explained by Fisher's principle, a mechanism of natural selection that leads to equal proportion of males and females in a sexually reproducing population. In fact, sex-ratio expression is partially suppressed by autosomal genes in at least three Drosophila species. The population genetics of this system is not completely understood. In this article we develop a mathematical model for the evolution of autosomal suppressors of SR (sup alleles) and show that: (i) an autosomal suppressor cannot invade when SR is very deleterious in males (c < 1/3, where c is the fitness of SR/Y males); (ii) 'SR/ST, sup/+' polymorphisms occur when SR is partially deleterious (~0.3 < c < 1); while (iii) SR neutrality (c = 1) results in sup fixation and thus in total abolishment of drive. So, surprisingly, as long as there is any selection against SR/Y males, neutral autosomal suppressors will not be fixed. In that case, when a polymorphic equilibrium exists, the average female proportion in SR/Y males' progeny is given approximately by (ac + 1 - a + [square root of ([a.sup.2][(c + 1).sup.2] + 1 - 4ac))]/4ac, where a is the fitness of SR/ST females.