The Value of Information for Populations in Varying Environments

TL;DR

This paper develops a mathematical model of population dynamics in varying environments, revealing how biological systems can violate traditional information bounds due to individual stochasticity, and proposes generalized measures of information.

Contribution

It introduces a model linking information theory to biological population dynamics, extending the concept of information bounds to account for biological stochasticity.

Findings

Mutual information bounds can be violated in biological systems.

Individual stochasticity affects the value of information in populations.

Generalized measures of uncertainty are proposed for biological contexts.

Abstract

The notion of information pervades informal descriptions of biological systems, but formal treatments face the problem of defining a quantitative measure of information rooted in a concept of fitness, which is itself an elusive notion. Here, we present a model of population dynamics where this problem is amenable to a mathematical analysis. In the limit where any information about future environmental variations is common to the members of the population, our model is equivalent to known models of financial investment. In this case, the population can be interpreted as a portfolio of financial assets and previous analyses have shown that a key quantity of Shannon's communication theory, the mutual information, sets a fundamental limit on the value of information. We show that this bound can be violated when accounting for features that are irrelevant in finance but inherent to biological systems, such as the stochasticity present at the individual level. This leads us to generalize the measures of uncertainty and information usually encountered in information theory.