Optimal phenotypic adaptation in fluctuating environments.

Phenotypic adaptation is a universal feature of biological systems navigating highly variable environments. Recent empirical data support the role of memory-driven decision making in cellular systems navigating uncertain future nutrient landscapes, wherein a distinct growth phenotype emerges in fluctuating conditions. We develop a simple stochastic mathematical model to describe memory-driven cellular adaptation required for systems to optimally navigate such uncertainty. In this framework, adaptive populations traverse dynamic environments by inferring future variation from a memory of prior states, and memory capacity imposes a fundamental trade-off between the speed and accuracy of adaptation to new fluctuating environments. Our results suggest that the observed growth reductions that occur in fluctuating environments are a direct consequence of optimal decision making and result from bet hedging and occasional phenotypic-environmental mismatch. We anticipate that this modeling framework will be useful for studying the role of memory in phenotypic adaptation, including in the design of temporally varying therapies against adaptive systems.