Assessing postzygotic isolation using zygotic disequilibria in natural hybrid zones

Hybrid zones as windows on evolutionary processes provide a natural laboratory for studying the genetic basis and mechanisms of postzygotic isolation. One resultant pattern in hybrid zones is the Hardy-Weinberg disequilibrium (HWD) for a single locus or the linkage disequilibrium (LD) for multiple loci produced by natural selection against hybrids. However, HWD and the commonly used low-order gametic or composite digenic LD cannot fully reflect the pattern of the high-order genotypic interactions. Here we propose the use of zygotic LD to elucidate the selection mechanisms of postzygotic isolation, and its calculation is based on genotypic frequencies only, irrespective of the type of mating system. We numerically and analytically show that the maximum composite digenic LD is always greater than the maximum absolute zygotic LD under the linear-additive selection, but is comparable to or smaller than the maximum absolute zygotic LD under the strong epistatic selection. Selection mechanisms can be inferred by testing such differences. We analyze a previously reported mouse hybrid zone assayed with genome-wide SNPs, and confirm that the composite digenic LD cannot appropriately indicate all possible significant genotypic interactions for a given SNP pair. A large proportion of significant zygotic LDs, ∼75% in general in the mouse hybrid zone, cannot be revealed from the composite digenic LD analysis. Statistical tests indicate that epistatic selection occurred among multiple loci in the mouse hybrid zone. The results highlight that the joint patterns of the composite digenic and zygotic LDs can help to elucidate the selection mechanism that is potentially involved in postzygotic isolation.