New explicit expressions for relative frequencies of single-nucleotide polymorphisms with application to statistical inference on population growth.

We present new methodology for calculating sampling distributions of single-nucleotide polymorphism (SNP) frequencies in populations with time-varying size. Our approach is based on deriving analytical expressions for frequencies of SNPs. Analytical expressions allow for computations that are faster and more accurate than Monte Carlo simulations. In contrast to other articles showing analytical formulas for frequencies of SNPs, we derive expressions that contain coefficients that do not explode when the genealogy size increases. We also provide analytical formulas to describe the way in which the ascertainment procedure modifies SNP distributions. Using our methods, we study the power to test the hypothesis of exponential population expansion vs. the hypothesis of evolution with constant population size. We also analyze some of the available SNP data and we compare our results of demographic parameters estimation to those obtained in previous studies in population genetics. The analyzed data seem consistent with the hypothesis of past population growth of modern humans. The analysis of the data also shows a very strong sensitivity of estimated demographic parameters to changes of the model of the ascertainment procedure.