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A model of natural selection that exhibits a dynamic phase transition

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Abstract

A simple, stochastic model is developed of an asexual biological population that is undergoing natural selection. It is then observed that the size of the population, like the temperature parameter in the simulated annealing algorithm, is a measure of the amount of randomness to be allowed in the system. Exploiting the formal analogy between the two processes, it is shown that the distribution of different types of organisms in the population model converges to a stationary distribution if the population is growing more slowly thanO(lnt) (“annealing”), but can fail to converge at all if the population is growing faster thanO(lnt) (“quenching”). The results may be related to the “historical accidents” that permeate biological structures.

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Authors and Affiliations

  1. Department of Biochemistry and Biophysics, University of Pennsylvania, 19104, Philadelphia, Pennsylvania

    Ed Weinberger

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  1. Ed Weinberger
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Weinberger, E. A model of natural selection that exhibits a dynamic phase transition. J Stat Phys 49, 1011–1028 (1987). https://doi.org/10.1007/BF01017557

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  • DOI: https://doi.org/10.1007/BF01017557

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