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

2025/02/20 by Su‐Chan Park, Park, Su-Chan, Joachim Krug +3
Biochemistry, Genetics and Molecular Biology · #60J80 #60J85 #92D25 #Biological Physics (physics.bio-ph) #Evolution and Genetic Dynamics #FOS: Mathematics #FOS: Physical sciences #Probability (math.PR) #Statistical Mechanics (cond-mat.stat-mech)

paper · pdf · doi:10.48550/arxiv.2502.14774

openalex publication_date 2025/02/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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.

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