A network perspective on the evolution of hybrid incompatibilities

Theory predicts that hybrid incompatibilities accumulate faster than linearly with genetic divergence, a phenomenon known as the snowball effect. While this prediction is mathematically robust under simplifying assumptions, accumulating evidence suggests that the structure of gene interaction networks can alter both the rate and organization of incompatibility evolution. Here, we extend classic DMI models with a network approach, where the assumptions of the Orr model correspond to the special case of a complete network of gene interactions (in which each gene interacts with every other gene). We simulate the evolution of hybrid incompatibilities under different gene interaction networks and evaluate the effects of network density, topology, and substitution model. We find that network density strongly governs the rate of DMI accumulation, particularly under models permitting multiple substitutions per locus, while network topology shapes the agglomeration of incompatibilities into large, connected clusters. Substitution rate heterogeneity, especially when anti-correlated with node degree, further suppresses both accumulation and clustering. These results highlight that while the snowball effect remains qualitatively valid, the structure and evolution of the incompatibility network exhibit nontrivial departures from previous expectations, with implications for observable quantities in empirical systems. Our findings underscore the importance of incorporating genomic architecture and network constraints into models of speciation.