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Journal of Statistical Physics

, Volume 142, Issue 6, pp 1124–1166 | Cite as

The Value of Information for Populations in Varying Environments

  • Olivier Rivoire
  • Stanislas Leibler
Article

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.

Keywords

Information Regulation Fitness Population dynamics Branching processes Control Investment 

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Copyright information

© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  1. 1.LIPhy UMR 5588CNRSGrenobleFrance
  2. 2.Laboratory of Living MatterThe Rockefeller UniversityNew YorkUSA
  3. 3.School of Natural Sciences, The Simons Center for Systems BiologyThe Institute for Advanced StudyPrincetonUSA

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