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We describe the onset of condensation in the simple model for the balancebetween selection and mutation given by Kingman in terms of a scaling limittheorem. Loosely speaking, this shows that the wave moving towards genes ofmaximal fitness has the shape of a gamma distribution. We conjecture that thiswave shape is a universal phenomenon that can also be found in a variety ofmore complex models, well beyond the genetics context, and provide some furtherevidence for this.

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