From Equation (1), one can see that good estimation of insignificant adjusted P-values can be achieved with few permutations while many more are needed to estimate highly significant ones. Therefore, we implemented an alternative permutation scheme that adapts the number of permutations to the significance level of the variant–phenotype pairs (Hubner et al., 2005). The resulting approach saves time at insignificant hits and invests more for significant ones, thereby maintaining a reasonable overall computational cost. Specifically, this adaptive scheme permutes P until a given number B (typically 100) of null correlations stronger than the observed one are found. To prevent this strategy running too long for the most significant variant–phenotype pairs, the algorithm cannot perform more than M (typically 100 000) permutations in total. Then, an adjusted P-value of association for a candidate QTL is derived using: (2)pa=min(r,B)+1min(R,M)+1
