  We investigate the equilibrium state of the model of Peng, \textit{et al.}
for molecular breeding. In the model, a population of DNA sequences is
successively culled by removing the sequences with the lowest binding affinity
to a particular target sequence. The remaining sequences are then amplified to
restore the original population size, undergoing some degree of
point-substitution of nucleotides in the process. Working in the infinite
population size limit, we derive an equation for the equilibrium distribution
of binding affinity, here modeled by the number of matches to the target
sequence. The equation is then solved approximately in the limit of large
sequence length, in the three regimes of strong, intermediate and weak
selection. The approximate solutions are verified via comparison to exact
numerical results.
