Denote the proportion of SNPs subsampled by xi;i = 1,2, …, where xi<xi+1 and xi are relative to the total number of SNPs used in the estimation. Denote the corresponding 5% quantile points yi. It follows that the effective number of independent tests defined by (2) should be proportional to xi when xi is small and should converge to an asymptote as xi grows large. To obtain these properties, we fit the Monod function to (xi,mi): This model is not claimed to be exact, but it has been found to fit data well in applications such as modeling population growth with limited resources [e.g. Cohen and Gürtler, 2001]. The parameters of this model are μ, the limit as x → ∞, and k, the half–saturation parameter representing the value of x for which f(x) = μ/2. We estimated the parameters by least squares to give the genomewide significance threshold as (4) We used a non–parametric bootstrap to estimate confidence intervals for ;genome. We resampled the minimum P–values with replacement from the permutation replicates, and for each resampling we subsampled SNPs, fitted the Monod function and calculated . We estimated 95% confidence intervals for ; k and from 1,000 bootstrap samples.
