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The Evolutionary Unfolding of Complexity

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  • James P. Crutchfield
  • Erik van Nimwegen

Abstract

We analyze the population dynamics of a broad class of fitness functions that exhibit epochal evolution|a dynamical behavior, commonly observed in both natural and artificial evolutionary processes, in which long periods of stasis in an evolving population are punctuated by sudden bursts of change. Our approach---statistical dynamics---combines methods from both statistical mechanics and dynamical systems theory in a way that offers an alternative to current "landscape" models of evolutionary optimization. We describe the population dynamics on the macroscopic level of fitness classes or phenotype subbasins, while averaging out the genotypic variation that is consistent with a macroscopic state. Metastability in epochal evolution occurs solely at the macroscopic level of the fitness distribution. While a balance between selection and mutation maintains a quasistationary distribution of fitness, individuals diffuse randomly through selectively neutral subbasins in genotype space. Sudden innovations occur when, through this diffusion, a genotypic portal is discovered that connects to a new subbasin of higher fitness genotypes. In this way, we identify innovations with the unfolding and stabilization of a new dimension in the macroscopic state space. The architectural view of subbasins and portals in genotype space clarifies how frozen accidents and the resulting phenotypic constraints guide the evolution to higher complexity. To appear in Evolution as Computation, L. F. Landweber, E. Winfree, R. Lipton, and S. Freeland, editors, Lecture Notes in Computer Science, Springer-Verlag (1999). Proceedings of a DIMACS Workshop, 11-12 January 1999, Princeton University.

Suggested Citation

  • James P. Crutchfield & Erik van Nimwegen, 1999. "The Evolutionary Unfolding of Complexity," Working Papers 99-02-015, Santa Fe Institute.
  • Handle: RePEc:wop:safiwp:99-02-015
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    References listed on IDEAS

    as
    1. M. E. J. Newman & Robin Engelhardt, 1998. "Effects of Neutral Selection on the Evolution of Molecular Species," Working Papers 98-01-001, Santa Fe Institute.
    2. Erik van Nimwegen & James P. Crutchfield, 1998. "Optimizing Epochal Evolutionary Search: Population-Size Independent Theory," Working Papers 98-06-046, Santa Fe Institute.
    3. Walter Fontana & Peter Schuster, 1998. "Continuity in Evolution: On the Nature of Transition," Working Papers 98-04-030, Santa Fe Institute.
    4. W. Fontana & P. Schuster, 1998. "Continuity in Evolution: On the Nature of Transitions," Working Papers ir98039, International Institute for Applied Systems Analysis.
    5. Erik van Nimwegen & James P. Crutchfield, 1998. "Optimizing Epochal Evolutionary Search: Population-Size Dependent Theory," Working Papers 98-10-090, Santa Fe Institute.
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    Keywords

    Epochal evolution; statistical dynamics; maximum entropy; punctuated equilibrium;
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