and African-American samples were recruited in parallel and evaluated with the same SNPs, the racial/ethnic differences between the participants suggest that the samples are likely to manifest differences in fine patterns of linkage disequilibrium and in phase of association at many loci. Apparent replication “failures” using approach (1) could thus relate to sample-to-sample differences in fine patterns of linkage disequilibrium and/or different amounts of information provided by markers with population-specific differences in allele frequencies. Allelic heterogeneities could also make contributions. Conceivably, genes for which the Monte Carlo p values determined by approach (2) are much stronger than the estimates based on approach (1) might provide interesting candidates for such allelic heterogeneity. Positive findings in the “cluster than converge” approach that are supported by evidence from other studies might be especially attractive candidates. NRXN3 and GABBR2 were identified using this approach and also in linkage studies of opiate dependence [45] and association studies of nicotine dependence [6], [46], for example.