Sarah E.; Crutchfield, James P.

Experimentalists observe phenotypic variability even 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 (all inheritable nongenetic) markers that store information about past environments. Crucially, we assume a time delay between sensing and action, so that a past epigenetic marker is used to generate the present phenotypic variability. 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-or lossy approximations thereof. We propose new theoretical investigations into and new experiments on bacteria phenotypic bet-hedging in fluctuating complex environments.