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Domesticated Asian rice (Oryza sativa) is one of the oldest domesticated crop species in the world, having fed more people than any other plant in human history. We report the patterns of DNA sequence variation in rice and its wild ancestor, O. rufipogon, across 111 randomly chosen gene fragments, and use these to infer the evolutionary dynamics that led to the origins of rice. There is a genome-wide excess of high-frequency derived single nucleotide polymorphisms (SNPs) in O. sativa varieties, a pattern that has not been reported for other crop species. We developed several alternative models to explain contemporary patterns of polymorphisms in rice, including a (i) selectively neutral population bottleneck model, (ii) bottleneck plus migration model, (iii) multiple selective sweeps model, and (iv) bottleneck plus selective sweeps model. We find that a simple bottleneck model, which has been the dominant demographic model for domesticated species, cannot explain the derived nucleotide polymorphism site frequency spectrum in rice. Instead, a bottleneck model that incorporates selective sweeps, or a more complex demographic model that includes subdivision and gene flow, are more plausible explanations for patterns of variation in domesticated rice varieties. If selective sweeps are indeed the explanation for the observed nucleotide data of domesticated rice, it suggests that strong selection can leave its imprint on genome-wide polymorphism patterns, contrary to expectations that selection results only in a local signature of variation.