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The Value of Information for Populations in Varying Environments

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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.

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Authors and Affiliations

  1. LIPhy UMR 5588, CNRS, Grenoble, France

    Olivier Rivoire

  2. Laboratory of Living Matter, The Rockefeller University, New York, NY, USA

    Stanislas Leibler

  3. School of Natural Sciences, The Simons Center for Systems Biology, The Institute for Advanced Study, Princeton, NJ, USA

    Stanislas Leibler

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  1. Olivier Rivoire
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  2. Stanislas Leibler
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Correspondence to Olivier Rivoire.

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Rivoire, O., Leibler, S. The Value of Information for Populations in Varying Environments. J Stat Phys 142, 1124–1166 (2011). https://doi.org/10.1007/s10955-011-0166-2

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  • DOI: https://doi.org/10.1007/s10955-011-0166-2

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