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   https://doi.org/10.1073/pnas.1810239116  

   Mashayekhi, Somayeh; Beerli, Peter (March 2019, Proceedings of the National Academy of Sciences)

   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 $\alpha <1$lead to an increase of short time intervals, but occasionally allow for very long time intervals. When $\alpha =1$, 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 $\alpha <1$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 Migratefacilitates testing for deviations from the n-coalescent. 

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   null (Ed.)
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   Bhattacharya, Anirban; Pati, Debdeep; Yang, Yun (February 2019, The Annals of Statistics)
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   Antil, Harbir; Dondl, Patrick; Striet, Ludwig (January 2021, SIAM Journal on Scientific Computing)