Haldane's rule and X-chromosome size in Drosophila

The "dominance theory" of HALDANE'S rule postulates that hybrids of the heterogametic sex are more likely to be inviable or sterile than the homogametic sex because some of the epistatic incompatibilities contributing to postzygotic isolation behave as X-linked partial recessives. When this is true, pairs of taxa with relatively large X chromosomes should require less divergence time, on average, to produce HALDANE'S rule than pairs with smaller Xs. Similarly, if the dominance theory is correct and if the X chromosome evolves at a similar rate to the autosomes, the size of the X should not influence the rate at which homogametic hybrids become inviable or sterile. We use Drosophila data to examine both of these predictions. As expected under the dominance theory, pairs of taxa with large X chromosomes (approximately 40% of the nuclear genome) show HALDANE's rule for sterility at significantly smaller genetic distances than pairs with smaller X chromosomes (approximately 20% of the genome). As also predicted, the genetic distances between taxa that exhibit female inviability/sterility show no differences between "large X" vs. "small X" pairs. We present some simple mathematical models to relate these data to the dominance theory and alternative hypotheses involving faster evolution of the X vs. the autosomes and/or faster evolution of incompatibilities that produce male-specific vs. female-specific sterility. Although the data agree qualitatively with the predictions of the dominance theory, they depart significantly from the quantitative predictions of simple models of the dominance theory and the other hypotheses considered. These departures probably stem from the many simplifying assumptions needed to tractably model epistatic incompatibilities and to analyze heterogeneous data from many taxa.