@article {Mashayekhi6244,
author = {Mashayekhi, Somayeh and Beerli, Peter},
title = {Fractional coalescent},
volume = {116},
number = {13},
pages = {6244--6249},
year = {2019},
doi = {10.1073/pnas.1810239116},
publisher = {National Academy of Sciences},
abstract = {The fractional coalescent is a generalization of Kingman{\textquoteright}s n-coalescent. It facilitates the development of the theory of population genetic processes that deviate from Poisson-distributed waiting times. It also marks the use of methods developed in fractional calculus in population genetics. The fractional coalescent is an extension of Canning{\textquoteright}s model, where the variance of the number of offspring per parent is a random variable. The distribution of the number of offspring depends on a parameter α, which is a potential measure of the environmental heterogeneity that is commonly ignored in current inferences.An approach to the coalescent, the fractional coalescent (f-coalescent), is introduced. The derivation is based on the discrete-time Cannings population model in which the variance of the number of offspring depends on the parameter α. This additional parameter α affects the variability of the patterns of the waiting times; values of α\<1 lead to an increase of short time intervals, but occasionally allow for very long time intervals. When α=1, the f-coalescent and the Kingman{\textquoteright}s n-coalescent are equivalent. The distribution of the time to the most recent common ancestor and the probability that n genes descend from m ancestral genes in a time interval of length T for the f-coalescent are derived. The f-coalescent has been implemented in the population genetic model inference software Migrate. Simulation studies suggest that it is possible to accurately estimate α values from data that were generated with known α values and that the f-coalescent can detect potential environmental heterogeneity within a population. Bayes factor comparisons of simulated data with α\<1 and real data (H1N1 influenza and malaria parasites) showed an improved model fit of the f-coalescent over the n-coalescent. The development of the f-coalescent and its inclusion into the inference program Migrate facilitates testing for deviations from the n-coalescent.},
issn = {0027-8424},
URL = {https://www.pnas.org/content/116/13/6244},
eprint = {https://www.pnas.org/content/116/13/6244.full.pdf},
journal = {Proceedings of the National Academy of Sciences}
}