Branching with selection and mutation I: Mutant fitness of Fr\'echet type
arxiv(2022)
摘要
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 Fr\'echet 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.
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关键词
mutant fitness,mutation,branching,selection,type
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