page_title: Stuart Kauffman
section_title: Fitness landscapes
hierarchical_section_title: Stuart Kauffman / Fitness landscapes
caption_attribution_description: English: This is a visualization of two dimensions of a NK fitness landscape. The X and Y axes represent a combination of bits that encode the genotype. The height of the peaks represents the fitness, or reproductive success, or organisms with that particular genotype. The paths drawn on the landscape represent different paths that a population could follow while evolving on this fitness landscape.
context_page_description: Stuart Alan Kauffman is an American medical doctor, theoretical biologist, and complex systems researcher who studies the origin of life on Earth. He was a professor at the University of Chicago, University of Pennsylvania, and University of Calgary. He is currently emeritus professor of biochemistry at the University of Pennsylvania and affiliate faculty at the Institute for Systems Biology. He has a number of awards including a MacArthur Fellowship and a Wiener Medal.
  He is best known for arguing that the complexity of biological systems and organisms might result as much from self-organization and far-from-equilibrium dynamics as from Darwinian natural selection as discussed in his book Origins of Order. In 1967 and 1969 he used random boolean networks to investigate generic self-organizing properties of gene regulatory networks, proposing that cell types are dynamical attractors in gene regulatory networks and that cell differentiation can be understood as transitions between attractors. Recent evidence suggests that cell types in humans and other organisms are attractors.
context_section_description: Kauffman's NK model defines a combinatorial phase space, consisting of every string (chosen from a given alphabet) of length . For each string in this search space, a scalar value (called the fitness) is defined. If a distance metric is defined between strings, the resulting structure is a landscape.
  Fitness values are defined according to the specific incarnation of the model, but the key feature of the NK model is that the fitness of a given string  is the sum of contributions from each locus  in the string:
  and the contribution from each locus in general depends on the value of  other loci:
  where  are the other loci upon which the fitness of  depends.
  Hence, the fitness function  is a mapping between strings of length K + 1 and scalars, which Weinberger's later work calls "fitness contributions". Such fitness contributions are often chosen randomly from some specified probability distribution.
  In 1991, Weinberger published a detailed analysis of the case in which  and the fitness contributions are chosen randomly. His analytical estimate of the number of local optima was later shown to be flawed. However, numerical experiments included in Weinberger's analysis support his analytical result that the expected fitness of a string is normally distributed with a mean of approximately
  
  and a variance of approximately
  .
caption: Visualization of two dimensions of a NK fitness landscape. The arrows represent various mutational paths that the population could follow while evolving on the fitness landscape.
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