Minimal informational requirements for fitness

TL;DR

This paper develops a theoretical framework using rate-distortion theory to determine the minimal information required for populations to achieve specific growth rates or selection advantages, highlighting evolutionary trade-offs.

Contribution

It introduces a novel application of rate-distortion theory to evolutionary biology, linking information processing costs with fitness and providing analytical solutions for various systems.

Findings

Derived rate-distortion functions for different evolutionary systems

Established a correspondence between fitness and information distortion

Provided insights into energy-efficient information processing in evolution

Abstract

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.