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Originally published as Genetics Published Articles Ahead of Print on October 18, 2007.
Genetics, Vol. 178, 325-337, January 2008, Copyright © 2008
doi:10.1534/genetics.107.073361
Population Genetics of Polymorphism and Divergence Under Fluctuating Selection
Emilia Huerta-Sanchez*,
Rick Durrett
and
Carlos D. Bustamante
,1
* Center for Applied Mathematics, Department of Mathematics, Department of Biological Statistics and Computational Biology, Cornell University, Ithaca, New York 14853
1 Corresponding author: 101 Biotechnology Bldg., Cornell University, Ithaca, NY 14853.
E-mail: cdb28{at}cornell.edu
Current methods for detecting fluctuating selection require time series data on genotype frequencies. Here, we propose an alternative approach that makes use of DNA polymorphism data from a sample of individuals collected at a single point in time. Our method uses classical diffusion approximations to model temporal fluctuations in the selection coefficients to find the expected distribution of mutation frequencies in the population. Using the Poisson random-field setting we derive the site-frequency spectrum (SFS) for three different models of fluctuating selection. We find that the general effect of fluctuating selection is to produce a more "U"-shaped site-frequency spectrum with an excess of high-frequency derived mutations at the expense of middle-frequency variants. We present likelihood-ratio tests, comparing the fluctuating selection models to the neutral model using SFS data, and use Monte Carlo simulations to assess their power. We find that we have sufficient power to reject a neutral hypothesis using samples on the order of a few hundred SNPs and a sample size of 
20 and power to distinguish between selection that varies in time and constant selection for a sample of size 20. We also find that fluctuating selection increases the probability of fixation of selected sites even if, on average, there is no difference in selection among a pair of alleles segregating at the locus. Fluctuating selection will, therefore, lead to an increase in the ratio of divergence to polymorphism similar to that observed under positive directional selection.
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