Genetic incompatibilities do not snowball in a demographic model of speciation

Two populations evolving in isolation can accumulate genetic differences over time that cause incompatibilities in their hybrid offspring. These "Dobzhansky-Muller incompatibilities" (DMIs) are predicted to accumulate at a rate faster than linear as the number of incompatible gene interactions "snowballs". Here we show that this snowball prediction is an artifact of two unrealistic modeling assumptions that stem from ignoring demography. We introduce a new alternative "demographic speciation model" in which the rate of DMI accumulation between populations is affected by the efficiency of purifying selection to remove incompatibilities that arise within populations. This model yields new testable predictions for understanding the tempo and mode of speciation based on population demographic parameters. A large-scale empirical analysis of bird and mammal datasets supports a unique prediction of our model: a negative relationship between effective population sizes and speciation rates. Our results challenge views of the snowball theory, and of ecological speciation models rooted in positive selection, showing instead that purifying selection may play a major role in mediating speciation rates.