Recent work has shown that the expression levels of genes transcribed in the brains of humans and chimpanzees have changed less than those of genes transcribed in other tissues [1]. However, when gene expression changes are mapped onto the evolutionary lineage in which they occurred, the brain shows more changes than other tissues in the human lineage compared to the chimpanzee lineage [1], [2] and [3]. There are two possible explanations for this: either positive selection drove more gene expression changes to fixation in the human brain than in the chimpanzee brain, or genes expressed in the brain experienced less purifying selection in humans than in chimpanzees, i.e. gene expression in the human brain is functionally less constrained. The first scenario would be supported if genes that changed their expression in the brain in the human lineage showed more selective sweeps than other genes. Unfortunately, current human genome-wide DNA sequence variation do not allow signatures of selective sweeps to be inferred using frequency-based approaches [4] and [5]. However, estimates of linkage disequilibrium (LD) - i.e. the extent of non-random association of alleles along chromosomes - are expected to be largely unaffected by frequency ascertainment bias [5], and selective sweeps are expected to increase the amount of LD around a selected gene variant [6], [7], [8] and 9 P.C. Sabeti, D.E. Reich, J.M. Higgins, H.Z. Levine, D.J. Richter and S.F. Schaffner et al., Detecting recent positive selection in the human genome from haplotype structure, Nature 419 (2002), pp. 832-837.