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Speciation is fundamental to the huge diversity of life on Earth. Evidencesuggests reproductive isolation arises most commonly in allopatry with a higherspeciation rate in small populations. Current theory does not address thisdependence in the important weak mutation regime. Here, we examine abiophysical model of speciation based on the binding of a protein transcriptionfactor to a DNA binding site, and how their independent co-evolution, in astabilizing landscape, of two allopatric lineages leads to incompatibilities.Our results give a new prediction for the monomorphic regime of evolution,consistent with data, that smaller populations should develop incompatibilitiesmore quickly. This arises as: 1) smaller populations having a greater initialdrift load, as there are more sequences that bind poorly than well, so fewersubstitutions are needed to reach incompatible regions of phenotype space; 2)slower divergence when the population size is larger than the inverse ofdiscrete differences in fitness. Further, we find longer sequences developincompatibilities more quickly at small population sizes, but more slowly atlarge population sizes. The biophysical model thus represents a robustmechanism of rapid reproductive isolation for small populations and largesequences, that does not require peak-shifts or positive selection.

A simple biophysical model predicts more rapid accumulation of hybrid incompatibilities in small populations