Hysteretic dynamics of driven disordered systems provide insights into biological evolution in a changing environment*

Biological evolution of a population is governed by the fitness landscape, which is a map from genotype to fitness. However, a fitness landscape depends on the organism’s environment, and evolution in changing environments is still poorly understood. We study a particular model of antibiotic resistance evolution in bacteria where the antibiotic concentration is an environmental parameter, and the landscapes incorporate tradeoffs between adaptation to low and high antibiotic concentration. With evolutionary dynamics that follow fitness gradients, the evolution of the system under slowly changing antibiotic concentration resembles the athermal dynamics of disordered physical systems under quasistatic external drives. Specifically, our model can be described as a Preisach system with interacting hysterons, and it exhibits effects of memory such as hysteresis loops under antibiotic concentration cycling. Indeed the model can show a rich variety of phenomena, including the existence of return point memory for certain biologically relevant parameter choices. This approach provides a novel way of discovering and studying motifs of evolutionary dynamics in biological systems in a changing environment.