Nonrandom associations between alleles at different loci can be tested for using Fisher's exact test. Extensive simulations show that there is a substantial probability of obtaining significant nonrandom associations between closely or completely linked polymorphic neutral loci in a population of constant size at equilibrium under mutation and genetic drift. In a rapidly growing population, however, there will be little chance of finding significant nonrandom associations even between completely linked loci if the growth has been sufficiently rapid. This result is illustrated by the analysis of mitochondrial DNA sequence data from humans. In comparing all pairs of informative sites, fewer than 5% of the pairs show significant disequilibrium in Sardinians, which have apparently undergone rapid population growth, while 20% to 30% in !Kung and Pygmies, which apparently have not undergone rapid growth, show significance. The extent of linkage disequilibrium in a population is closely related to the gene genealogies of the loci examined, with "star-like" genealogies making significant linkage disequilibrium unlikely.