The collapse of genetic incompatibilities in a hybridizing population

Genetic incompatibility has long been considered to be a hallmark of speciation due to its role in reproductive isolation. Previous analyses of the stability of epistatic incompatibility show that it is subject to collapse upon hybridization. In the present work, we derive explicitly the distribution of the lifespan of two-locus incompatibilities, and show that genetic drift, along with recombination, is critical in determining the time scale of collapse. The first class of incompatibilities, where derived alleles separated in parental populations act antagonistically in hybrids, survive longer in smaller populations when incompatible alleles are (co)dominant and tightly linked, but collapse more quickly when they are recessive. The second class of incompatibilities, where fitness is reduced by disrupting co-evolved elements in gene regulation systems, collapse on a time scale proportional to the exponential of effective recombination rate. Overall, our result suggests that the effects of genetic drift and recombination on incompatibilitys lifespan depend strongly on the underlying mechanisms of incompatibilities. As the time scale of collapse is usually shorter than the time scale of establishing a new incompatibility, the observed level of genetic incompatibilities in a particular hybridizing population may be shaped more by the collapse than by their initial accumulation. Therefore, a joint theory of accumulation-erosion of incompatibilities is in need to fully understand the genetic process under speciation with hybridization.