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<p>We study a model of a branching process subject to <i>selection</i>, modeled by giving each family an individual fitness acting as a branching rate, and <i>mutation</i>, modeled by resampling the fitness of a proportion of offspring in each generation. For two large classes of fitness distributions of Gumbel type we determine the growth of the population, almost surely on survival. We then study the empirical fitness distribution in a simplified model, which is numerically indistinguishable from the original model, and show the emergence of a Gaussian travelling wave.</p>

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Branching with selection and mutation II: Mutant fitness of Gumbel type

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年10月25日

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  • Su-Chan Park,
  • Joachim Krug,
  • Peter Mörters

摘要

We study a model of a branching process subject to selection, modeled by giving each family an individual fitness acting as a branching rate, and mutation, modeled by resampling the fitness of a proportion of offspring in each generation. For two large classes of fitness distributions of Gumbel type we determine the growth of the population, almost surely on survival. We then study the empirical fitness distribution in a simplified model, which is numerically indistinguishable from the original model, and show the emergence of a Gaussian travelling wave.