Emergence of condensation in Kingman's model of selection and mutation

Steffen Dereich, P Morters

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We describe the onset of condensation in the simple model for the balance between selection and mutation given by Kingman in terms of a scaling limit theorem. Loosely speaking, this shows that the wave moving towards genes of maximal fitness has the shape of a gamma distribution. We conjecture that this wave shape is a universal phenomenon that can also be found in a variety of more complex models, well beyond the genetics context, and provide some further evidence for this.
Original languageEnglish
Pages (from-to)17-26
Number of pages10
JournalActa Applicandae Mathematicae
Issue number1
Publication statusPublished - Oct 2013


  • House of cards model
  • Bose-Einstein condensation
  • condensation wave
  • selection, mutation
  • fitness distribution
  • universality
  • Gamma distribution


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