Stochastic and information-thermodynamic structures of population dynamics in a fluctuating environment.Adaptation in a fluctuating environment is a process of fueling environmental information to gain fitness.  In this work, we elucidate the underlying stochastic and information-thermodynamic structure in this process, by deriving causal fluctuation relations (FRs) of fitness and information.  Furthermore, the FRs generalize the concept of the evolutionary stable state (ESS) for fluctuating environment by giving the probability that the optimal strategy on average can be invaded by a suboptimal one owing to rare environmental fluctuation.  These results clarify the information-thermodynamic structures in adaptation and evolution.
THERM