The site frequency spectrum of an exponentially growing population: Theory and evolutionary history inference

Einar BjarkiGunnarsson

Science Institute, University of Iceland

"The site frequency spectrum of an exponentially growing population: Theory and evolutionary history inference"

The site frequency spectrum (SFS) is a popular summary statistic of genomic data. In population genetics, the SFS has provided a simple means of inferring the rate of adaptation of a population and for distinguishing between neutral evolution and evolution under selection. The rapidly growing amount of cancer genomic data has attracted interest in the SFS of an exponentially growing population. In this talk, we discuss recent results on the expected value of the SFS of a population that grows according to a stochastic branching process, as well as (first-order) almost sure convergence results for the SFS in the large-time and large-population limits. Our results show that while the SFS depends linearly on the mutation rate, the branching process parameters of birth and death control the fundamental shape of the SFS at the low-frequency end. For the special case of a birth-death process (binary branching process), our results give rise to statistically consistent estimators for the mutation rate and extinction probability of the population, which stands in contrast to previous work which has indicated the need for additional data to decouple these two parameters. Overall, our work shows how single timepoint data on the SFS of an exponentially growing population can be used to infer important evolutionary parameters.
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