Speciation is fundamental to understanding the huge diversity of life on Earth. Although still
controversial, empirical evidence suggests that the rate of speciation is larger for smaller
populations. Here, we explore a biophysical model of speciation by developing a simple
coarse-grained theory of transcription factor-DNA binding and how their co-evolution in two
geographically isolated lineages leads to incompatibilities. To develop a tractable analytical
theory, we derive a Smoluchowski equation for the dynamics of binding energy evolution …