Genetic maps in linkage disequilibrium (LD) units play the same role for association mapping as maps in centimorgans provide at much lower resolution for linkage mapping. Association mapping of genes determining disease susceptibility and other phenotypes is based on the theory of LD, here applied to relations with three phenomena. To test the theory, markers at high density along a 10-Mb continuous segment of chromosome 20q were studied in African-American, Asian, and Caucasian samples. Population structure, whether created by pooling samples from divergent populations or by the mating pattern in a mixed population, is accurately bioassayed from genotype frequencies. The effective bottleneck time for Eurasians is substantially less than for migration out of Africa, reflecting later bottlenecks. The classical dependence of allele frequency on mutation age does not hold for the generally shorter time span of inbreeding and LD. Limitation of the classical theory to mutation age justifies the assumption of constant time in a LD map, except for alleles that were rare at the effective bottleneck time or have arisen since. This assumption is derived from the Malecot model and verified in all samples. Tested measures of relative efficiency, support intervals, and localization error determine the operating characteristics of LD maps that are applicable to every sexually reproducing species, with implications for association mapping, high-resolution linkage maps, evolutionary inference, and identification of recombinogenic sequences.