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Proc Natl Acad Sci U S A. 2019 Mar 26;116(13):6244-6249. doi: 10.1073/pnas.1810239116. Epub 2019 Mar 13.

Fractional coalescent.

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Department of Scientific Computing, Florida State University, Tallahassee, FL 32306
Department of Scientific Computing, Florida State University, Tallahassee, FL 32306.


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 [Formula: see text] lead to an increase of short time intervals, but occasionally allow for very long time intervals. When [Formula: see text], the f-coalescent and the Kingman'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 [Formula: see text] 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.


Bayesian inference; coalescent; environmental heterogeneity; fractional calculus; population genetics

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