Dobzhansky–Muller incompatibilities and adaptation to a shared environment

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Abstract
Natural selection might drive the evolution of postzygotic reproductive isolation even when allopatric populations adapt to identical environments, an idea first suggested by Muller (1942). Here, we analyze this scenario mathematically, focusing on the evolution of a Dobzhansky–Muller incompatibility (DMI) between populations. Our results identify a potential problem with Muller's scenario: adaptation to identical environments can often involve substitution of the same alleles, precluding formation of a hybrid incompatibility. We show that the probability of evolving a DMI falls as selection coefficients among beneficial alleles become less similar. The reason is that if one locus is under much stronger selection than the other, that locus is much more likely to experience a substitution first in both populations. This precludes the development of a DMI, which requires different substitutions in the two populations.