Dobzhansky and Muller proposed a general mechanism through which microevolution, the gradual substitution of alleles within species, can cause the evolution of postzygotic reproductive isolation between species and, therefore, macroevolution. They argued that, as genetic differences accumulate between allopatric populations, derived alleles from one population may be incompatible with alleles at one or more loci in the other population because most combinations of alleles differing between the populations would not have been tested by natural selection. Indeed, the kinds of genetic incompatibilities envisaged by Dobzhansky and Muller have been shown to exist and to cause inviability or sterility in hybrids between closely related species. Furthermore, the number of such genetic incompatibilities has been found to grow with the genetic distance between the diverging populations. However, what determines the rate and pattern of accumulation of incompatibilities remains unclear. Here we investigate this question by simulating the evolution of RNA secondary structures on a holey fitness landscape. We demonstrate that the rate at which genetic incompatibilities accumulate depends critically on genetic robustness: the higher the genetic robustness within populations, the slower genetic incompatibilities accumulate between them. We go on to identify two population genetic parameters that influence the rate of accumulation of genetic incompatibilities: recombination probability and population size. In large populations with abundant genetic variation, recombination selects for increased genetic robustness and, as a consequence, genetic incompatibilities accumulate more slowly. In small populations, genetic drift interferes with this process by reducing the amount of genetic variation, weakening the effect of recombination on genetic robustness and, thereby, promoting the accumulation of genetic incompatibilities. Our results suggest a novel mechanism by which genetic drift promotes and recombination hinders speciation.