Nonequilibrium adaptation and phenotypic switching to big environmental changes, like booms and busts

In statistical physics, systems can exchange energy or matter with baths that provide fixed resources. But, in biological evolution, systems face highly fluctuating environments, including those that undergo booms and busts. The ability to sense the environment and adapt are thus the key for the system to thrive. We make the simplest possible model of an adaptive process: a binary sensor in a stochastic two-state (boom or bust) environment. Our goal is to identify and analyze all essential parameters that characterize this system's adaptation to its environment. We first show analytically that the total system must be out of equilibrium for the sensor to outperform a random oscillator. A novel relation among the system's sensing performance, the environment changing rate, and the level of nonequilibrium is derived. We then analytically find the optimal sensor when the system's adaptation rates are bounded by their physical limits. Lastly, we generalize our results above to describe the interplay between phenotype switching and population growth under a stochastic boom-bust environment.