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We describe an equilibrium model to determine whether a random population o
f dynamic copolymer sequences could be driven by molecular recognition to a
subset of sequences that tightly bind a specific ligand, The model predict
s that the population's mean binding constant can be shifted, but because o
f competitive binding, only to a limited degree (ca. 2 orders of magnitude
larger than the original mean). True chemical evolution will require a mech
anism for selection and amplification.