The fitness value of information

TL;DR

This paper explores the relationship between information-theoretic and decision-theoretic measures of information in biological evolution, showing how mutual information relates to fitness benefits in uncertain environments.

Contribution

It demonstrates that the fitness value of information combines Shannon's mutual information with decision-theoretic value, and establishes conditions where they are equivalent.

Findings

Fitness increase due to information can be quantified in an evolutionary model.

Mutual information can exactly equal the fitness value of a cue in certain cases.

Environmental entropy bounds the fitness value of information.

Abstract

Biologists measure information in different ways. Neurobiologists and researchers in bioinformatics often measure information using information-theoretic measures such as Shannon's entropy or mutual information. Behavioral biologists and evolutionary ecologists more commonly use decision-theoretic measures, such the value of information, which assess the worth of information to a decision maker. Here we show that these two kinds of measures are intimately related in the context of biological evolution. We present a simple model of evolution in an uncertain environment, and calculate the increase in Darwinian fitness that is made possible by information about the environmental state. This fitness increase -- the fitness value of information -- is a composite of both Shannon's mutual information and the decision-theoretic value of information. Furthermore, we show that in certain cases the fitness value of responding to a cue is exactly equal to the mutual information between the cue and the environment. In general the Shannon entropy of the environment, which seemingly fails to take anything about organismal fitness into account, nonetheless imposes an upper bound on the fitness value of information.