Abstract
Changes in population size is a useful quantity for understanding the evolutionary history of a species. Genetic variation within a species can be summarized by the site frequency spectrum (SFS). For a sample of size n, the SFS is a vector of length n − 1 where entry i is the number of sites where the mutant base appears i times and the ancestral base appears n − i times. We present a new method, CubSFS, for estimating the changes in population size of a panmictic population from an observed SFS. First, we provide a straightforward proof for the expression of the expected site frequency spectrum depending only on the population size. Our derivation is based on an eigenvalue decomposition of the instantaneous coalescent rate matrix. Second, we solve the inverse problem of determining the changes in population size from an observed SFS. Our solution is based on a cubic spline for the population size. The cubic spline is determined by minimizing the weighted average of two terms, namely (i) the goodness of fit to the observed SFS, and (ii) a penalty term based on the smoothness of the changes. The weight is determined by cross-validation. The new method is validated on simulated demographic histories and applied on unfolded and folded SFS from 26 different human populations from the 1000 Genomes Project.
Funding source: Lundbeck Foundation
Award Identifier / Grant number: R155–2014–1724
Funding statement: BLW is funded by The Lundbeck Foundation Initiative for Integrative Psychiatric Research, iPSYCH, Denmark. Grant number R155–2014–1724.
Acknowledgement
We are grateful to two anonymous reviewers who provided very careful and constructive questions and suggestions on the first version of this paper. The helpful comments resulted in a much improved paper. We thank X. Liu and Y.-X. Fu for providing the SFS of the 9 populations. We also thank J. Terhorst and Y. Song for providing key insight into the SMC++ method. We further thank Bjarni Vilhjalmsson, for providing the folded SFS of the 1000 Genomes Project phase 3 data.
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Supplemental Material
The online version of this article offers supplementary material (https://doi.org/10.1515/sagmb-2017-0061).
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