  The existing concept of the "fitness value of information" provides a
theoretical upper bound on the fitness advantage of using information
concerning a fluctuating environment. Using concepts from rate-distortion
theory, we develop a theoretical framework to answer a different pair of
questions: What is the minimal amount of information needed for a population to
achieve a certain growth rate? What is the minimal amount of information gain
needed for one sub-population to achieve a certain average selection
coefficient over another? We introduce a correspondence between fitness and
distortion and solve for the rate-distortion functions of several systems using
analytical and numerical methods. Because accurate information processing is
energetically costly, our approach provides a theoretical basis for
understanding evolutionary "design principles" underlying information-cost
trade-offs.
