Appendix 1—figure 3. $p{Q}_X(k)$ statistics for $k\mathrm{=}\mathrm{1}\mathrm{:}\mathrm{150}$ for the HapMap5k dataset.

The x axis gives the average physical distance between all pairs of SNPs contributing to a given $p\mathit{}{Q}_X\mathit{}\mathrm{(}k\mathrm{)}$ statistic. The boxplots give an empirical null distribution of $p\mathit{}{Q}_X\mathit{}\mathrm{(}k\mathrm{)}$ statistics derived from permuting the signs of all effect sizes independently (this empirical null was omitted from Appendix 1—figure 1 due to computational expense). The uptick in signal from pairs of SNPs physically nearby to one another is present in this dataset, again suggesting a role for physical linkage in contributing to the signal. However, note that in contrast to the 20 k and 5 k ascertainments, the HapMap5k ascertainment also has a large amount of signal from $p\mathit{}{Q}_X\mathit{}\mathrm{(}\mathrm{\infty }\mathrm{)}$, which cannot be explained by linkage.