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Mathematical Physics Seminar

Evolution in changing environments and driven disordered systems

Joachim Krug - University of Cologne

Location:  Zoom
Date & time: Wednesday, 18 January 2023 at 10:45AM - 11:45AM

Abstract : Biological evolution is governed by the fitness landscape, a map from the genetic sequence of an organism to its fitness.  Here fitness denotes some quantitative measure of reproductive success, such as the expected number of offspring. A fitness landscape depends on the organism's environment, and evolution in changing environments is still poorly understood. After introducing the concept of fitness landscapes and their mathematical description, the talk will focus on a particular model of antibiotic resistance  evolution in bacteria, where the drug concentration is an environmental parameter. Tradeoffs between adaptation to low and high concentration lead to a rugged landscape with an exponentially large number of fitness peaks. With evolutionary dynamics that follow  fitness gradients, resistance evolution under slowly changing antibiotic concentration resembles the zero temperature dynamics of  a disordered spin system under quasistatic driving. Specifically, the set of genetic sequences that form a fitness peak at some concentration maps exactly to the metastable states in an equivalent Preisach system, a paradigmatic model of hysteresis in random  magnets. Making use of the conceptual tool of state transition graphs developed in the context of driven disordered systems, we quantify the degree of genotypic and phenotypic reversibility in the response of the population to antibiotic concentration  cycling, and ask to what extent a memory of past concentration changes is stored in the current genetic sequence. The talk is based on joint work with Suman G. Das and Muhittin Mungan.

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