Open AccessProbability of Gene Fixation in an Expanding Finite Population
Author(s) -
Motoo Kimura,
Takao Ohta
Publication year - 1974
Publication title -
proceedings of the national academy of sciences of the united states of america
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 5.011
H-Index - 771
eISSN - 1091-6490
pISSN - 0027-8424
DOI - 10.1073/pnas.71.9.3377
Subject(s) - fixation (population genetics) , population , monte carlo method , mathematics , statistical physics , heavy traffic approximation , allele , statistics , genetics , biology , gene , physics , demography , sociology
A mathematical theory was developed, based on diffusion models, that enables us to compute the probability of a rare mutant allele eventually spreading through a population when the population size changes with time. In particular, we elaborated the case in which the mutant allele has a definite selective advantage and the population expands following the logistic law. In this case, the probability of ultimate fixation of a single mutant is given byu =2s (Z/N ), wheres is the selective advantage andZ/N is a factor by which the probability of fixation is modified through population expansion. Analytical expression was obtained forZ/N , and the validity of the formula foru was checked by Monte Carlo experiments.