Optimized Bacteria are Environmental Prediction Engines.

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.