Efficient search and responsiveness trade-offs in a Markov chain model of evolution in dynamic environments

• Evolution in dynamic environments may be captured by a simple, tunable Markov chain.
• The method is not gradient-based, but dwells longer in states that are more fit.
• Derived conditions for optimal search efficiency are met in biology and in physics.
• Resilience losses from highly tuned selection may impact directed evolution efforts.
• A Lyapunov function links the method’s fitness maximization to search information.

Motivated by the desire to study evolutionary responsiveness in fluctuating environments, and by the current interest in analyses of evolution that merge notions of fitness maximization with dynamical systems concepts such as Lyapunov functions, this paper models natural evolution with a simple stochastic dynamical system that can be represented as a Markov chain. The process maximizes fitness globally via search and has links to information and entropy. These links suggest that a possible rationale for evolution with the exponential fitness functions observed in nature is that of optimally-efficient search in a dynamic environment, which represents the quickest trade-off of prior information about the genotype search space for search effort savings after an environment perturbation. A Lyapunov function is also provided that relates the stochastic dynamical system model with search information, and the model shows that evolution is not gradient-based but dwells longer on more fit outcomes. The model further indicates that tuning the amount of selection trades off environment responsiveness with the time to reach fit outcomes, and that excessive selection causes a loss of responsiveness, a result that is validated by the literature and impacts efforts in directed evolution.