The choice of a proper global significance threshold for nominal P-values is very difficult due to the fact that we test multiple variants per phenotype, correlated because of LD, across a wide allele frequency spectrum, while all this varies from one phenotype to another. To account for this, significance of a candidate QTL is assessed via permutations. Specifically, we repeat the cis-window scan procedure for R random permutations of P, leaving the genotype data G unchanged to preserve the correlation between variants. Each time, we store the strongest correlation; the goal is to produce a sample from the distribution of the strongest correlation under the complete null hypothesis of no genetic associations. Then, the observed correlation is compared with this empirical null distribution to obtain an adjusted P-value characterizing the significance of the candidate QTL. When very few null correlations are found to be stronger than the observed one, it means that reaching this correlation level by chance is very unlikely and therefore that the QTL candidate is likely to be true. More formally, if r correlations in the null
