- Response to Cavalli-Sforza Interview[Human Biology 82(3):245-266 (June 2010)]
Luigi Luca Cavalli-Sforza's work in population genetics has been fundamental to the field, and we have the utmost respect for his many pioneering contributions. It is with some regret, then, that we must disagree with some of his comments on our 2008 paper in the interview published in the June 2010 issue of Human Biology. Here we attempt to clarify some particular points of contention that arose during the interview, referring the reader to the original paper (Novembre and Stephens 2008) and related recent work (e.g., François et al. 2010; McVean 2009) for a fuller treatment.
First, we emphasize that our paper was not intended to condemn the use of principal components analysis. Indeed, principal components analysis has proved itself an incredibly useful and powerful technique across a wide range of disciplines, including population genetics. Instead, our paper aimed to draw attention to results that affect how the results of a principal components analysis should be interpreted. In particular, we noted how principal components analysis tends to produce sinusoidal patterns, such as gradients and waves, when applied to data that exhibit a spatial dependence structure. These patterns occur quite generally and have a fundamental mathematical basis related to Fourier series. Indeed, the phenomenon has been noted previously in several different scientific fields [see citations in Novembre and Stephens (2008)], and our primary goal was to draw these results to the attention of the population genetics community. We agree with Cavalli-Sforza that many of our simulations were simple—indeed, they were deliberately designed this way to emphasize that wavelike patterns arise under extremely simplistic scenarios as a result of intrinsic mathematical properties of spatial data. This does not mean that we believe human demographic history to be simple or that human populations have not engaged in expansions and large-scale migrations at various points in history. However, it does mean that a gradient or wave in a principal components analysis should not be regarded as a footprint specific to such events.
In our experience, much of the controversy regarding inferences of population expansions centers around the inference of a Neolithic expansion in Europe. It seems worth emphasizing, then, that our work does not imply that no Neolithic expansion took place. A thorough examination of this issue requires, as Cavalli-Sforza strongly championed, a synthesis of different types of data from multiple sources. One major interest of ours in writing the paper, and an ongoing interest, is how spatial patterns in genetic variation can best serve as one such source of historical insight.
On a personal note, we regret that our response to Cavalli-Sforza's review of our paper was not shared with him [by the editors of Nature Genetics—Editor] [End Page 469] and that he did not appreciate the various changes and improvements to our paper that took place in response to his review.