Dynamics of competitive evolution on a smooth landscape

We study competitive DNA sequence evolution directed by in vitro protein binding. The steady-state dynamics of this process is well described by a shape-preserving pulse which decelerates and eventually reaches equilibrium. We explain this dynamical behavior within a continuum mean-field framework. Analytical results obtained on the motion of the pulse agree with simulations. Furthermore, finite population correction to the mean-field results are found to be insignificant.