An important goal of population genetics is to determine the forces that have shaped the pattern of genetic variation in natural populations. We developed a maximum likelihood method that allows us to infer demographic changes and detect recent positive selection (selective sweeps) in populations of varying size from DNA polymorphism data. Applying this approach to single nucleotide polymorphism data at more than 250 noncoding loci on the X chromosome of Drosophila melanogaster from an (ancestral) African population and a (derived) European, we found that the African population expanded about 60,000 y ago and that the European population split off from the African lineage about 15,800 y ago, thereby suffering a severe population size bottleneck. We estimated that about 160 beneficial mutations (with selection coefficients s between 0.05% and 0.5%) were fixed in the euchromatic portion of the X in the African population since population size expansion, and about 60 mutations (with s around 0.5%) in the diverging European lineage.