  Experimentalists have observed phenotypic variability in isogenic bacteria
populations. We explore the hypothesis that in fluctuating environments this
variability is tuned to maximize a bacterium's expected log growth rate,
potentially aided by epigenetic markers that store information about past
environments. We show that, in a complex, memoryful environment, the maximal
expected log growth rate is linear in the instantaneous predictive
information---the mutual information between a bacterium's epigenetic markers
and future environmental states. Hence, under resource constraints, optimal
epigenetic markers are causal states---the minimal sufficient statistics for
prediction. This is the minimal amount of information about the past needed to
predict the future as well as possible. We suggest new theoretical
investigations into and new experiments on bacteria phenotypic bet-hedging in
fluctuating complex environments.
