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Optimal evolutionary control for artificial selection on molecular phenotypes

Controlling an evolving population is an important task in modern molecular genetics, including directed evolution for improving the activity of molecules and enzymes, in breeding experiments in animals and in plants, and in devising public health strategies to suppress evolving pathogens. An optimal intervention to direct evolution should be designed by considering its impact over an entire stochastic evolutionary trajectory that follows. As a result, a seemingly suboptimal intervention at a given time can be globally optimal as it can open opportunities for desirable actions in the future. Here, we propose a feedback control formalism to devise globally optimal artificial selection protocol to direct the evolution of molecular phenotypes. We show that artificial selection should be designed to counter evolutionary tradeoffs among multi-variate phenotypes to avoid undesirable outcomes in one phenotype by imposing selection on another. Control by artificial selection is challenged by our ability to predict molecular evolution. We develop an information theoretical framework and show that molecular time-scales for evolution under natural selection can inform how to monitor a population in order to acquire sufficient predictive information for an effective intervention with artificial selection. Our formalism opens a new avenue for devising artificial selection methods for directed evolution of molecular functions.