Effectiveness of marker-assisted selection (MAS) and quantitative trait loci (QTL) mapping using population-wide linkage disequilibrium (LD) between markers and QTL depends on the extent of LD and how it declines with distance in a population. Because marker–QTL LD cannot be observed directly, the objective of this study was to evaluate alternative measures of observable LD between multi-allelic markers as predictors of usable LD of multi-allelic markers with presumed biallelic QTL. Observable LD between marker pairs was evaluated using eight existing measures and one new measure. These consisted of two pooled and standardized measures of LD between pairs of alleles at two markers based on Lewontin's LD measure, two pooled measures of squared correlations between alleles, one standardized measure using Hardy–Weinberg heterozygosities, and four measures based on the chi-square statistic for testing for association between alleles at two loci. In simulated populations with a range of LD generated by drift and a range of marker polymorphism, marker–marker LD measured by a standardized chi-square statistic (denoted χ2′) was found to be the best predictor of useable marker–QTL LD for a group of multi-allelic markers. Estimates of the level and decline of marker–marker LD with distance obtained from χ2′ were linearly and highly correlated with usable LD of those markers with QTL across population structures and marker polymorphism. Corresponding relationships were poorer for the other marker–marker LD measures. Therefore, when LD is generated by drift, χ2′ is recommended to quantify the amount and extent of usable LD in a population for QTL mapping and MAS based on multi-allelic markers.

W. G. Hill and X.-S. Zhang (2004). Effects on phenotypic variability of directional selection arising through genetic differences in residual variability. Genetical Research83, 121–132.

We thank Herman Mulder for noting errors in the published equations. The correct formulae were used in calculations.