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

TL;DR

This paper models how populations balance exploring new phenotypes and exploiting resources in fluctuating environments, revealing conditions where exploration enhances growth and providing analytical insights into optimal strategies.

Contribution

It introduces a minimal model linking exploration-exploitation trade-offs to environmental fluctuation statistics, identifying when exploration improves population fitness.

Findings

Non-zero exploration rate maximizes fitness under random environmental fluctuations.

Pure exploitation is optimal in two-state environments regardless of switching times.

Analytical results connect exploration rates to environmental dynamics.

Abstract

We study a minimal model for the growth of a phenotypically heterogeneous population of cells subject to a fluctuating environment in which they can replicate (by exploiting available resources) and modify their phenotype within a given landscape (thereby exploring novel configurations). The model displays an exploration-exploitation trade-off whose specifics depend on the statistics of the environment. Most notably, the phenotypic distribution corresponding to maximum population fitness (i.e. growth rate) requires a non-zero exploration rate when the magnitude of environmental fluctuations changes randomly over time, while a purely exploitative strategy turns out to be optimal in two-state environments, independently of the statistics of switching times. We obtain analytical insight into the limiting cases of very fast and very slow exploration rates by directly linking population growth to the features of the environment.