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We have studied a genome-wide set of single-nucleotide polymorphism (SNP) allele frequency measures for African-American, East Asian, and European-American samples. For this analysis we derived a simple, closed mathematical formulation for the spectrum of expected allele frequencies when the sampled populations have experienced nonstationary demographic histories. The direct calculation generates the spectrum orders of magnitude faster than coalescent simulations do and allows us to generate spectra for a large number of alternative histories on a multidimensional parameter grid. Model-fitting experiments using this grid reveal significant population-specific differences among the demographic histories that best describe the observed allele frequency spectra. European and Asian spectra show a bottleneck-shaped history: a reduction of effective population size in the past followed by a recent phase of size recovery. In contrast, the African-American spectrum shows a history of moderate but uninterrupted population expansion. These differences are expected to have profound consequences for the design of medical association studies. The analytical methods developed for this study, i.e., a closed mathematical formulation for the allele frequency spectrum, correcting the ascertainment bias introduced by shallow SNP sampling, and dealing with variable sample sizes provide a general framework for the analysis of public variation data.