Adaptive walks by the fittest among finite random mutants on a Mt. Fuji-type fitness landscape II. Effect of small non-additivity (original) (raw)

Abstract.

We examined properties of adaptive walks by the fittest on “rough Mt. Fuji-type” fitness landscapes, which are modeled by superposing small uncorrelated random component on an additive fitness landscape. A single adaptive walk is carried out by repetition of the evolution cycle composed of (1) mutagenesis process that produces random _d_-fold point mutants of population size N and (2) selection process that picks out the fittest mutant among them. To comprehend trajectories of the walkers, the fitness landscape is mapped into a (x, y, z)-space, where x, y and z represent, respectively, normalized Hamming distance from the peak on the additive fitness landscape, scaled additive fitness and scaled non-additive fitness. Thus a single adaptive walk is expressed as the dynamics of a particle in this space. We drew the “hill-climbing” vector field, where each vector represents the most probable step for a walker in a single step. Almost all of the walkers are expected to move along streams of vectors existing on a particular surface that overlies the (x, y)-plane, toward the neighborhood of a characteristic point at which a mutation-selection-random drift balance is reached. We could theoretically predict this reachable point in the case of random sampling search strategy.

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Authors and Affiliations

  1. Takarazuka Research Institute, Novartis Pharma K. K., 10-66, Miyuki-cho, Takarazuka, 665 Japan and Department of Functional Materials Science, Saitama University, Urawa 338, Japan. e-mail: aita@evolve.fms.saitama-u.ac.jp, , , , , , JP
    Takuyo Aita
  2. Department of Functional Materials Science, Saitama University, Urawa 338, Japan. e-mail: husimi@fms.saitama-u.ac.jp, , , , , , JP
    Yuzuru Husimi

Authors

  1. Takuyo Aita
  2. Yuzuru Husimi

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Received: 1 March 2000 / Published online: 3 August 2000

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Aita, T., Husimi, Y. Adaptive walks by the fittest among finite random mutants on a Mt. Fuji-type fitness landscape II. Effect of small non-additivity.J Math Biol 41, 207–231 (2000). https://doi.org/10.1007/s002850000046

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