The expected time for a neutral allele to reach frequency p1 from p0 can be calculated mathematically
Mathematical models in population genetics, such as diffusion approximations and coalescent theory, allow researchers to calculate the expected time for a neutral allele to reach a given frequency.
The claim is specific, empirical, and well-established in evolutionary theory. Multiple provided papers discuss mathematical derivations for the time it takes for neutral alleles to reach specific frequencies or fixation using tools like diffusion approximations and coalescent theory.
D Waxman. Population Growth Enhances the Mean Fixation Time of Neutral Mutations and the Persistence of Neutral Variation. 2012. https://doi.org/10.1534/genetics.112.139220
Paper [1] discusses analytical expressions using diffusion approximation for the mean and variance of fixation times for neutral mutations.
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TAI-HE FAN, SHUHAO SUN, PING-AN HE. THE TIME REQUIRED FOR ALLELE FREQUENCY CHANGE. 2017. https://doi.org/10.1017/s1446181117000050
Paper [7] examines expected times for allele frequency change under selection models using mathematical frameworks.
Gili Greenbaum. Revisiting the time until fixation of a neutral mutant in a finite population - A coalescent theory approach.. 2015. https://doi.org/10.1016/j.jtbi.2015.05.019
Paper [9] derives analytic formulations of genetic drift and fixation time scales of neutral mutations using diffusion approximations and coalescent theory.
Luca Ferretti, Paolo Ribeca. Allelic Entropy and Times until Loss or Fixation of Neutral Polymorphisms.. 2023. https://doi.org/10.3390/genes14091751
Paper [11] uses the diffusion approximation of the neutral Wright-Fisher model to relate the expected time until fixation of a neutral allele to population entropy.
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