Statistical Dynamics of Epochal Evolution
    Erik van Nimwegen
Santa Fe Institute 
1399 Hyde Park,  Santa Fe, NM 87501 
        erik@santafe.edu 

 
In epochal evolution, some macroscopic state variables that describe the evolving population exhibit an alternation of periods of stasis (epochs) and sudden transitions (innovations). In constant selective environments, such metastable evolutionary dynamics may either come about through the existence of ``fitness barriers'' in the fitness landscape of the evolving population, or through the existence of ``entropy barriers''. A new mathematical approach that combines ideas and methods from statistical mechanics, mathematical population genetics, and dynamical systems theory
was developed to study epochal evolutionary dynamics. In particular, the maximum entropy formalism of statistical mechanics can be extended to apply to simple evolutionary systems, such that "macroscopic" equations of motion can be constructed from an underlying "microscopic" evolutionary dynamics. For a wide class of simple fitness functions, this analytic approach is shown to accurate predict many quantitative features of the evolutionary dynamics. The analysis shows that, on the macroscopic level of description, epochal evolution is described as the unfolding of a macroscopic phase space, where each evolutionary innovation corresponds to the unfolding of a new macroscopic dimension through dynamical symmetry breaking at the microscopic level of genotypes. The analysis further shows that wide fitness barriers cannot be crossed on reasonable evolutionary time scales, and suggests that the crossing of entropy barriers, by diffusion of the population through neutral networks of iso-fitness genotypes, is the main mechanism by which epochal dynamics is brought about in evolution. Finally, if time permits, I will discuss recent results on the evolution of mutational robustness for populations that diffuse over neutral networks in genotype space.
 
 

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