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Abstract Epistasis refers to gene interaction effect involving two or more genes. Statistical methods for mapping quantitative trait loci (QTL) with epistasis effects have become available recently. However, little is known about the statistical power and sample size requirements for mapping epistatic QTL using genetic markers. In this study, we developed analytical formulae to calculate the statistical power and sample requirement for detecting each epistasis effect under the F-2 design based on crossing inbred lines. Assuming two unlinked interactive QTL and the same absolute value for all epistasis effects, the heritability of additive × additive (a × a) effect is twice as large as that of additive × dominance (a × d) or dominance × additive (d × a) effect, and is four times as large as that of dominance × dominance (d × d) effect. Consequently, among the four types of epistasis effects involving two loci, 'a × a' effect is the easiest to detect whereas 'd × d' effect is the most difficult to detect. The statistical power for detecting 'a × a' effect is similar to that for detecting dominance effect of a single QTL. The sample size requirements for detecting 'a × d', 'd × a' and 'd × d' are highly sensitive to increased distance between the markers and the interacting QTLs. Therefore, using dense marker coverage is critical to detecting those effects.

Abstract A strategy of multi-step minimal conditional regression analysis has been developed to determine the existence of statistical testing and parameter estimation for a quantitative trait locus (QTL) that are unaffected by linked QTLs. The estimation of marker-QTL recombination frequency needs to consider only three cases: 1) the chromosome has only one QTL, 2) one side of the target QTL has one or more QTLs, and 3) either side of the target QTL has one or more QTLs. Analytical formula was derived to estimate marker-QTL recombination frequency for each of the three cases. The formula involves two flanking markers for case 1), two flanking markers plus a conditional marker for case 2), and two flanking markers plus two conditional markers for case 3). Each QTL variance and effect, and the total QTL variance were also estimated using analytical formulae. Simulation data show that the formulae for estimating marker-QTL recombination frequency could be a useful statistical tool for fine QTL mapping. With 1 000 observations, a QTL could be mapped to a narrow chromosome region of 1.5 cM if no linked QTL is present, and to a 2.8 cM chromosome region if either side of the target QTL has at least one linked QTL.