Residual linkage: why do linkage peaks not disappear after an association study?

Family-based candidate gene and genome-wide association studies are a logical progression from linkage studies for the identification of gene and polymorphisms underlying complex traits. An efficient way to analyse phenotypic and genotypic data is to model linkage and association simultaneously. An important result from such an analysis is whether any evidence for linkage remains after fitting polymorphisms at candidate genes (residual linkage), because this may indicate locus and allelic heterogeneity in the population and will influence subsequent molecular strategies. Here we report that substantial residual linkage is to be expected, even under genetic homogeneity and when the underlying causal polymorphisms are genotyped and fitted in the model. We simulated a powerful design to detect linkage to quantitative trait loci, with 5, 10 or 20 causal SNPs spread throughout the genome. These SNPs were responsible for all genetic variation, and hence for both linkage and association. Residual linkage at the largest linkage peak from a genome-wide scan was substantial, with mean LOD scores of 0.4, 0.7, and 1.4 for the case of 5, 10 and 20 underlying causal SNPs, respectively. For less powerful designs, the proportion of the original LOD scores that remains after association will be even larger. All cases of 'significant' residual linkage are false positives. The reason for the apparent paradox of detecting residual linkage after fitting causal polymorphisms is that the linkage signals at the largest peaks in a genome-scan are severely inflated, even if all peaks correspond to true linkage. Our findings are general and apply to linkage mapping of any phenotype and to any pedigree structure.