Universality Classes of Interaction Structures for NK Fitness Landscapes

  title={Universality Classes of Interaction Structures for NK Fitness Landscapes},
  author={Sungmin Hwang and Benjamin Schmiegelt and Luca Ferretti and Joachim H A Krug},
  journal={Journal of Statistical Physics},
Kauffman’s NK-model is a paradigmatic example of a class of stochastic models of genotypic fitness landscapes that aim to capture generic features of epistatic interactions in multilocus systems. Genotypes are represented as sequences of L binary loci. The fitness assigned to a genotype is a sum of contributions, each of which is a random function defined on a subset of $$k \le L$$k≤L loci. These subsets or neighborhoods determine the genetic interactions of the model. Whereas earlier work on… 
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Kauffman and Levin introduced a class of models for the evolution of hereditary systems which they called NK fitness landscapes. Inspired by spinglasses, these models have the attractive feature of
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The block model can be viewed as a special case of Kauffman’s NK-model, and it is shown that the number of accessible paths can be written as a product of the path numbers within the blocks, which provides a detailed analytic description of the paths statistics.
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Evolutionary Accessibility in Tunably Rugged Fitness Landscapes
Some measures of accessibility behave non-monotonically as a function of K, indicating a special role of the most sparsely connected, non-trivial cases K=1 and 2, and the relation between models for fitness landscapes and spin glasses is addressed.
Genotypic Complexity of Fisher’s Geometric Model
The analysis shows that thephenotypic dimension, which is often referred to as phenotypic complexity, does not generally correlate with the complexity of fitness landscapes and that even organisms with a single Phenotypic trait can have complex landscapes.
Adaptation in Tunably Rugged Fitness Landscapes: The Rough Mount Fuji Model
A simple fitness landscape model with tunable ruggedness based on the rough Mount Fuji (RMF) model originally introduced by Aita et al. in the context of protein evolution is proposed and compared to the known behavior in the MLM model.
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It is proved that NK landscapes can be represented by parametric linear interaction models where model coefficients have meaningful interpretations and the statistical properties of the model coefficients are derived, providing insight into how the NK algorithm parses importance to main effects and interactions.