Branching with selection and mutation I: Mutant fitness of Fréchet type

Abstract

We investigate two stochastic models of a growing population subject to selection and mutation. In our models each individual carries a fitness which determines its mean offspring number. Many of these offspring inherit their parent's fitness, but some are mutants and obtain a fitness randomly sampled from a distribution in the domain of attraction of the Fréchet distribution. We give a rigorous proof for the precise rate of superexponential growth of these stochastic processes and support the argument by a heuristic and numerical study of the mechanism underlying this growth.

29 pages, 3 figures

References in corpus (6)

• Population genetics of neutral mutations in exponentially growing cancer cell populations
• Evolutionary dynamics of tumor progression with random fitness values
• Evolution in random fitness landscapes: the infinite sites model
• Stochastic clonal dynamics and genetic turnover in exponentially growing populations
• Unpredictable repeatability in molecular evolution
• Kingman's model with random mutation probabilities: convergence and condensation II