The accumulation of beneficial mutations and convergence to a Poisson process
Issued Date
2025-05-01
Resource Type
ISSN
03044149
Scopus ID
2-s2.0-85215989591
Journal Title
Stochastic Processes and their Applications
Volume
183
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SCOPUS
Bibliographic Citation
Stochastic Processes and their Applications Vol.183 (2025)
Suggested Citation
Udomchatpitak N., Schweinsberg J. The accumulation of beneficial mutations and convergence to a Poisson process. Stochastic Processes and their Applications Vol.183 (2025). doi:10.1016/j.spa.2025.104578 Retrieved from: https://repository.li.mahidol.ac.th/handle/123456789/103122
Title
The accumulation of beneficial mutations and convergence to a Poisson process
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Abstract
We consider a model of a population with fixed size N, which is subjected to an unlimited supply of beneficial mutations at a constant rate μN. Individuals with k beneficial mutations have the fitness (1+sN)k. Each individual dies at rate 1 and is replaced by a random individual chosen with probability proportional to its fitness. We show that when μN≪1/(NlogN) and N−η≪sN≪1 for some η<1, the fixation times of beneficial mutations, after a time scaling, converge to the times of a Poisson process, even though for some choices of sN and μN satisfying these conditions, there will sometimes be multiple beneficial mutations with distinct origins in the population, competing against each other.