Species pairs often become genetically incompatible during divergence, which is an important source of reproductive isolation. An idealized picture is often painted where incompatibility alleles accumulate and fix between diverging species. However, recent studies have shown both that incompatibilities can collapse with ongoing hybridization, and that incompatibility loci can be polymorphic within species. This paper suggests some general rules for the behavior of incompatibilities under hybridization. In particular, we argue that redundancy of genetic pathways can strongly affect the dynamics of intrinsic incompatibilities. Since fitness in genetically redundant systems is unaffected by introducing a few foreign alleles, higher redundancy decreases the stability of incompatibilities during hybridization, but also increases tolerance of incompatibility polymorphism within species. We use simulations and theories to show that this principle leads to two types of collapse: in redundant systems, exemplified by classical Dobzhansky–Muller incompatibilities, collapse is continuous and approaches a quasi‐neutral polymorphism between broadly sympatric species, often as a result of isolation‐by‐distance. In nonredundant systems, exemplified by co‐evolution among genetic elements, incompatibilities are often stable, but can collapse abruptly with spatial traveling waves. As both types are common, the proposed principle may be useful in understanding the abundance of genetic incompatibilities in natural populations.

Hybridization is a major evolutionary force that can erode genetic differentiation between species, whereas reproductive isolation maintains such differentiation. In studying a hybrid zone between the swallowtail butterflies Papilio syfanius and Papilio maackii (Lepidoptera: Papilionidae), we made the unexpected discovery that genomic substitution rates are unequal between the parental species. This phenomenon creates a novel process in hybridization, where genomic regions most affected by gene flow evolve at similar rates between species, while genomic regions with strong reproductive isolation evolve at species-specific rates. Thus, hybridization mixes evolutionary rates in a way similar to its effect on genetic ancestry. Using coalescent theory, we show that the rate-mixing process provides distinct information about levels of gene flow across different parts of genomes, and the degree of rate-mixing can be predicted quantitatively from relative sequence divergence (FST) between the hybridizing species at equilibrium. Overall, we demonstrate that reproductive isolation maintains not only genomic differentiation, but also the rate at which differentiation accumulates. Thus, asymmetric rates of evolution provide an additional signature of loci involved in reproductive isolation.

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Two empirical rules arise from the incompatibility of interspecific hybrids: Haldane's Rule predicts that the chromosomally heterogametic sex (XY or ZW) is more unfit after hybridization; the large-X/Z effect posits that sex chromosomes play a major role in incompatibility. Classical theories on these two rules rely on evidence mainly from taxa with male heterogamety, while female heterogamety received little investigation. Here, we reveal the genetic architectures of the two rules in hybrids between the butterfliesPapilio bianorandPapilio dehaanii, where the female is the heterogametic sex. In these crosses, hybrid females suffer from both body size abnormality and ovary dysgenesis, while males appear normal and fertile. Curiously, abnormal size in females is mapped to a continuum of Z-linked polygenes, each acting quantitatively with small phenotypic effects. This polygenic system, perhaps spanning the entire Z chromosome, also correctly predicts weaker incompatibility effects in males. For ovary dysgenesis, the underlying genetic architecture can be monogenic or polygenic with different maternal backgrounds. Most peculiarly, when comparing ovary dysgenesis in certain maternal backgrounds betweenPapilioandHeliconius, we find that F1 recombination on the Z chromosome often rescues incompatibilities among backcross individuals, while a non-recombined Z chromosome almost always produces strong ovary defects regardless of ancestry. These results suggest that high fitness in these maternal backgrounds requires a balance between the total quantities of introgression on autosomes and the Z chromosome. Our study highlights that, in addition to incompatibility factors with large effects, genomically dispersed polygenes are also abundant in creating butterfly reproductive isolation.

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 incompatibility’s 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.