  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.
