NB Principle Components Analysis Patterns

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., Francois 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] and that he did not appreciate the various changes and improvements to our paper that took place in response to his review.

Literature Cited

Francois, O., M. Currat, N. Ray et al. 2010. Principal component analysis under population genetic models of range expansions and admixture. Mol. Biol. Evol. 27:1257-1268; doi:10.1093/ molbev/msq010.

McVean, G. 2009. A genealogical interpretation of principal components analysis. PLoS Genet. 5(10):e1000686; doi:10.1371/journal.pgen.1000686.

Novembre, J., and M. Stephens. 2008. Interpreting principal components analyses of spatial population genetic variation. Nat. Genet. 40:646-649.

Interview with Cavalli-Sforza

Selon Luca Cavalli-Sforza, généticien et, surtout, auteur de célèbres études sur la diffusion des langues et des techniques, l'évolution culturelle ne s'explique pas autrement que celle des organisme vivants. Mutation, dérive et sélection : telles sont les nouvelles clés de l'aventure des cultures humaines.

Dans l'introduction de votre livre, prenant le contre-pied des traditions scientifiques qui considèrent que l'évolution biologique et l'histoire culturelle sont indépendantes, vous avancez que la « théorie de l'évolution biologique peut être étendue à la culture ». Que voulez-vous dire par là ?
La théorie génétique de l'évolution biologique reconnaît quatre facteurs d'évolution biologique : la mutation, qui est la source de toutes les diversités entre individus et espèces et se transmet par hérédité ; la sélection naturelle, découverte simultanée de Charles Darwin et de Alfred Wallace, qui trie les mutations en fonction de leur succès reproductif ; la dérive génétique, ou hasard généralisé, qui est la conséquence de deux faits : d'abord, les mutations sont rares et apparaissent au hasard ; ensuite, le nombre d'enfants engendrés par chaque parent est très variable en raison d'une multitude de facteurs qui ne sont pas sous notre contrôle et ne peuvent être abordés que par des méthodes statistiques. Tout cela nous autorise à dire qu'une partie du changement évolutif est le produit du hasard. Enfin, le quatrième facteur est la migration des individus et des populations, qui opère des mélanges génétiques.

Ces phénomènes sont tous liés à une propriété centrale du vivant : les organismes sont capables de reproduire des individus extrêmement semblables à eux-mêmes, et c'est ce qu'on appelle aussi la capacité d'autoreproduction. Naturellement, tout cela est possible seulement dans un environnement qui offre tous les matériaux et les conditions physiques nécessaires pour la reproduction des êtres vivants.