A simple, deterministic analysis predicts that accumulation of Dobzhansky-Muller incompatibilities by a spatially structured population strongly depends on the number of negative interactions of an allele. If an allele can be incompatible with alleles at only one locus, incompatibilities accumulate linearly with time. In contrast, if an allele can participate in multiple pairwise incompatibilities with alleles at different loci, the expected number of incompatibilities eventually increases quadratically.