Simple Biophysical Model Predicts Faster Accumulation of Hybrid Incompatibilities in Small Populations Under Stabilizing Selection

Speciation is fundamental to the process of generating the huge diversity of life on Earth. However, we are yet to have a clear understanding of its molecular-genetic basis. Here, we examine a computational model of reproductive isolation that explicitly incorporates a map from genotype to phenotype based on the biophysics of protein-DNA binding. In particular, we model the binding of a protein transcription factor to a DNA binding site and how their independent coevolution, in a stabilizing fitness landscape, of two allopatric lineages leads to incompatibilities. Complementing our previous coarse-grained theoretical results, our simulations give a new prediction for the monomorphic regime of evolution that smaller populations should develop incompatibilities more quickly. This arises as (1) smaller populations have a greater initial drift load, as there are more sequences that bind poorly than well, so fewer substitutions are needed to reach incompatible regions of phenotype space, and (2) slower divergence when the population size is larger than the inverse of discrete differences in fitness. Further, we find longer sequences develop incompatibilities more quickly at small population sizes, but more slowly at large population sizes. The biophysical model thus represents a robust mechanism of rapid reproductive isolation for small populations and large sequences that does not require peak shifts or positive selection. Finally, we show that the growth of DMIs with time is quadratic for small populations, agreeing with Orr's model, but nonpower law for large populations, with a form consistent with our previous theoretical results.