| Summary: | 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.
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