  Information theory has explained the organization of many biological
phenomena, from the physiology of sensory receptive fields to the variability
of certain DNA sequence ensembles. Some scholars have proposed that information
should provide the central explanatory principle in biology, in the sense that
any behavioral strategy that is optimal for an organism's survival must
necessarily involve efficient information processing. We challenge this view by
providing a counterexample. We present an analytically tractable model for a
particular instance of a perception-action loop: a creature searching for a
food source confined to a one-dimensional ring world. The model incorporates
the statistical structure of the creature's world, the effects of the
creature's actions on that structure, and the creature's strategic decision
process. The model takes the form of a Markov process on an infinite
dimensional state space. To analyze it we construct an exact coarse graining
that reduces the model to a Markov process on a finite number of "information
states". This technique allows us to make quantitative comparisons between the
performance of an information-theoretically optimal strategy with other
candidate strategies on a food gathering task. We find that: 1. Information
optimal search does not necessarily optimize utility (expected food gain). 2.
The rank ordering of search strategies by information performance does not
predict their ordering by expected food obtained. 3. The relative advantage of
different strategies depends on the statistical structure of the environment,
in particular the variability of motion of the source. We conclude that there
is no simple relationship between information and utility. Behavioral
optimality does not imply information efficiency, nor is there a simple
tradeoff between gaining information about a food source versus obtaining the
food itself.
