The accumulation of beneficial mutations and convergence to a Poisson process

Nantawat Udomchatpitak and Jason Schweinsberg

Stochastic Processes and their Applications, 2025, vol. 183, issue C

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.

Keywords: Population model; Mutation; Selection; Poisson process (search for similar items in EconPapers)
Date: 2025
References: Add references at CitEc
Citations:

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0304414925000195
Full text for ScienceDirect subscribers only

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:spapps:v:183:y:2025:i:c:s0304414925000195

Ordering information: This journal article can be ordered from
http://http://www.elsevier.com/wps/find/supportfaq.cws_home/regional
https://shop.elsevie ... _01_ooc_1&version=01

DOI: 10.1016/j.spa.2025.104578

Access Statistics for this article

Stochastic Processes and their Applications is currently edited by T. Mikosch

More articles in Stochastic Processes and their Applications from Elsevier
Bibliographic data for series maintained by Catherine Liu ().