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Biological evolution of a population is governed by the fitness landscape,which is a map from genotype to fitness. However, a fitness landscape dependson the organisms environment, and evolution in changing environments is stillpoorly understood. We study a particular model of antibiotic resistanceevolution in bacteria where the antibiotic concentration is an environmentalparameter and the fitness landscapes incorporate tradeoffs between adaptationto low and high antibiotic concentration. With evolutionary dynamics thatfollow fitness gradients, the evolution of the system under slowly changingantibiotic concentration resembles the athermal dynamics of disordered physicalsystems under external drives. Exploiting this resemblance, we show that ourmodel can be described as a system with interacting hysteretic elements. As inthe case of the driven disordered systems, adaptive evolution under antibioticconcentration cycling is found to exhibit hysteresis loops and memoryformation. We derive a number of analytical results for quasistaticconcentration changes. We also perform numerical simulations to study how theseeffects are modified under driving protocols in which the concentration ischanged in discrete steps. Our approach provides a general framework forstudying motifs of evolutionary dynamics in biological systems in a changingenvironment.

A Driven Disordered Systems Approach to Biological Evolution in Changing Environments