  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.
