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Error Thresholds in a Mutation–selection Model with Hopfield-type Fitness

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Abstract

The deterministic limit of a Hopfield-type mutation–selection model in the sequence space approach is investigated. Genotypes are identified with two-letter sequences. Mutation is modelled as a Markov process, fitness functions are of Hopfield type, where the fitness of a sequence is determined by the Hamming distances to a number of predefined patterns. Using a maximum principle for the population mean fitness in equilibrium, the error threshold phenomenon is studied for quadratic Hopfield-type fitness functions with small numbers of patterns. Different from previous investigations of the Hopfield model, the system shows error threshold behaviour not for all fitness functions, but only for certain parameter values.

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Authors and Affiliations

  1. Fakultät für Mathematik, Universität Bielefeld, Bielefeld, Postfach 100131, D-33501, Germany

    Tini Garske

  2. Applied Maths Department, Faculty of Mathematics and Computing, The Open University, Walton Hall, Milton Keynes, MK7 6AA, UK

    Tini Garske

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  1. Tini Garske
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Correspondence to Tini Garske.

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Garske, T. Error Thresholds in a Mutation–selection Model with Hopfield-type Fitness. Bull. Math. Biol. 68, 1715–1746 (2006). https://doi.org/10.1007/s11538-006-9072-1

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