This paper is the first to attempt global identification of population-specific fixations due to natural selection, and is thus an important contribution to the literature. However, the authors themselves note that their particular approach yields a sizeable number of false positives, making it of limited usefulness for an investigator who wonders whether their favorite gene has experienced selection. A couple possible improvements:

1. as the chimanzee genome is available, it might be useful to polarize SNPs as either ancestral or derived. A comparison between populations could then take this information into account (it may be less likely that the ancestral allele has experienced population-specific pressure, for example).

2. the analysis in the discussion of which genes have been under selection makes informal use of Bayesian reasoning. In may be useful to formally implement some sort of Bayesian framework, altering the prior probability of being under selection for a gene according to previous studies.