Regensburg 2019 – scientific programme
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DY: Fachverband Dynamik und Statistische Physik
DY 60: Statistical Physics in Biological Systems III
DY 60.6: Talk
Friday, April 5, 2019, 11:15–11:30, H3
NK Fitness Landscapes Interpolated between K=2 and K=3 — James E Sullivan, Dmitry Nerukh, and •Jens Christian Claussen — Department of Mathematics, Aston University, Birmingham B4 7ET, U.K.
The NK model was introduced by Stuart Kauffmann and coworkers [1] as a model for fitness landscapes with tunable ruggedness, to understand epistasis and pleiotropy in evolutionary biology. It has also raised interest in combinatorial optimisation, study of spinglasses and in organizational theory. In the original formulation, fitness is defined as a sum of fitness functions for each locus, each depending on the locus itself and K other loci. Varying K from K=0 to K=N−1 leads to different ruggedness of the landscape. Here we introduce a generalization that allows to interpolate between integer values of K by allowing Ki to assume different values for each locus. We focus on the interpolation between the most widely studied cases of K=2 and K=3 and characterize the landscapes by study of their local minima. While we largely see a linear interpolation, small deviations are observed. Finally we discuss applications of this approach in economic systems and biology.
[1] Kauffman, S.; Levin, S., Journal of Theoretical Biology. 128, 11 (1987); Kauffman, S.; Weinberger, E., Journal of Theoretical Biology. 141, 211 (1989).