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We study a minimal model for the growth of a phenotypically heterogeneouspopulation of cells subject to a fluctuating environment in which they canreplicate (by exploiting available resources) and modify their phenotype withina given landscape (thereby exploring novel configurations). The model displaysan exploration-exploitation trade-off whose specifics depend on the statisticsof the environment. Most notably, the phenotypic distribution corresponding tomaximum population fitness (i.e. growth rate) requires a non-zero explorationrate when the magnitude of environmental fluctuations changes randomly overtime, while a purely exploitative strategy turns out to be optimal in two-stateenvironments, independently of the statistics of switching times. We obtainanalytical insight into the limiting cases of very fast and very slowexploration rates by directly linking population growth to the features of theenvironment.

Exploration-exploitation tradeoffs dictate the optimal distributions of phenotypes for populations subject to fitness fluctuations