Dynamics of hybrid incompatibility in gene networks in a constant environment

After an ancestral population splits into two allopatric populations, different mutations may fix in each. When pairs of mutations are brought together in a hybrid offspring, epistasis may cause reduced fitness. Such pairs are known as Bateson-Dobzhansky-Muller (BDM) incompatibilities. A well-known model of BDM incompatibility due to Orr suggests that the fitness load on hybrids should initially accelerate, and continue to increase as the number of potentially incompatible substitutions increases (the "snowball effect"). In the gene networks model, which violates a key assumption of Orr's model (independence of fixation probabilities), the snowball effect often does not occur. Instead, we describe three possible dynamics in a constant environment: (1) Stabilizing selection can constrain two allopatric populations to remain near-perfectly compatible. (2) Despite constancy of environment, punctuated evolution may obtain; populations may experience rare adaptations asynchronously, permitting incompatibility. (3) Despite stabilizing selection, developmental system drift may permit genetic change, allowing two populations to drift in and out of compatibility. We reinterpret Orr's model in terms of genetic distance. We extend Orr's model to the finite loci case, which can limit incompatibility. Finally, we suggest that neutral evolution of gene regulation in nature, to the point of speciation, is a distinct possibility.