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

  • Tini GarskeEmail author
Original Article

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.

Keywords

Mutation–selection model Hopfield model Error threshold Maximum principle 

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Copyright information

© Society for Mathematical Biology 2006

Authors and Affiliations

  1. 1.Fakultät für MathematikUniversität BielefeldBielefeldGermany
  2. 2.Applied Maths Department, Faculty of Mathematics and ComputingThe Open UniversityMilton KeynesUK

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