We analyze patterns of nucleotide variability at 15 X-linked loci and 14 autosomal loci from a North American population of Drosophila simulans. We show that there is significantly more linkage disequilibrium on the X chromosome than on chromosome arm 3R and much more linkage disequilibrium on both chromosomes than expected from estimates of recombination rates, mutation rates, and levels of diversity. To explore what types of evolutionary models might explain this observation, we examine a model of recurrent, nonoverlapping selective sweeps and a model of a recent drastic bottleneck (e.g., founder event) in the demographic history of North American populations of D. simulans. The simple sweep model is not consistent with the observed patterns of linkage disequilibrium nor with the observed frequencies of segregating mutations. Under a restricted range of parameter values, a simple bottleneck model is consistent with multiple facets of the data. While our results do not exclude some influence of selection on X vs. autosome variability levels, they suggest that demography alone may account for patterns of linkage disequilibrium and the frequency spectrum of segregating mutations in this population of D. simulans.