Berlin 2015 – scientific programme

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BP: Fachverband Biologische Physik

BP 26: Posters: Statistical Physics of Biological Systems

BP 26.14: Poster

Tuesday, March 17, 2015, 14:00–16:00, Poster A

Evolutionary accessibility in the NK Model for fitness landscapes — •Benjamin Schmiegelt — Institute for Theoretical Physics, Cologne, Germany

Fitness landscapes are biological evolution’s equivalent to energy landscapes, on which populations move as genotype distribution clouds [1]. In the limit of weak mutation and strong selection, the population’s dynamic can be described by an uphill climb. Accessibility refers here to the probability that the landscape’s global maximum is reachable from the antipodal genotype [2]. The NK model for such a landscape with L binary loci resembles a spin glass where each spin/locus interacts with k other spins/loci. A key determinant of evolutionary accessibility is the degree of sign epistasis, the fraction of loci having both positive and negative fitness effects depending on the state of other loci. Using that the NK model at fixed k for L→∞ almost surely exhibits global reciprocal epistasis, i.e. reciprocal sign epistasis between two loci on all generic background, it is shown that the accessibility tends to zero, and does so faster than in the House-of-Cards model (random energy model), generalizing results obtained previously for a special case of the NK-model where the groups of interacting loci are disjoint [3].

[1] J.A.G.M. de Visser and J. Krug, Nature Reviews Genetics 15, 480-490 (2014)

[2] J. Franke, A. Klözer, J.A.G.M. de Visser and J. Krug, PLoS Computational Biology 7, e1002134 (2011).

[3] B. Schmiegelt and J. Krug, Journal of Statistical Physics 154, 334-355 (2014).