Dresden 2017 – scientific programme

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DY: Fachverband Dynamik und Statistische Physik

DY 22: Posters - Statistical Physics of Biological Systems

DY 22.9: Poster

Tuesday, March 21, 2017, 14:00–16:00, P1A

Local optima in NK fitness landscapes — •Benjamin Schmiegelt, Sungmin Hwang, and Joachim Krug — Institute for Theoretical Physics, University of Cologne

Fitness landscapes, the assigment of fitness values to genotypes, determine the structural impact of selection on population dynamics. Populations will, especially under strong selection pressure, cluster around local optima. The number of local optima is also considered a measure of ruggedness, complexity and difficulty for a population to move on the landscape. The NK model models landscapes with parameter-controlled ruggedness and many possible interaction schemes between loci, sharinf similarities with p-spin glass models. For a quasi-one dimensional circular interaction layout the expected number of local optima is well established. We consider instead the case of random interaction networks, mean field and other variations and find, contrary to traditional assumptions, quantitatively different asymptotics for the expected numbers of local optima from the circular case.

[1] Weinberger, E. D. (1991). Local properties of Kauffman's N-k model: A tunably rugged energy landscape. Physical Review A, 44(10), 6399.

[2] Limic, V., & Pemantle, R. (2004). More rigorous results on the Kauffman-Levin model of evolution. The Annals of Probability, 32(3), 2149-2178.

[3] Schmiegelt, B., & Krug, J. (2014). Evolutionary accessibility of modular fitness landscapes. Journal of Statistical Physics, 154(1-2), 334-355.