Unveiling the genealogical lattice

To understand nature in all its complexity we have to cut down the riotous variety down to size. For ease of comprehension we formalize with math, verbalize with analogies, and visualize with representations. These approximations of reality are not reality, but when we look through the glass darkly they give us filaments of essential insight. Dalton’s model of the atom is false in important details (e.g., fundamental particles turn out to be divisible into quarks), but it still has conceptual utility.

Likewise, the phylogenetic trees popularized by L. L. Cavalli-Sforza in The History and Geography of Human Genes are still useful in understanding the shape of the human demographic past. But it seems that the bifurcating model of the tree must now be strongly tinted by the shades of reticulation. In a stylized sense inter-specific phylogenies, which assume the approximate truth of the biological species concept (i.e., little gene flow across lineages), mislead us when we think of the phylogeny of species on the microevolutionary scale of population genetics. On an intra-specific scale gene flow is not just a nuisance parameter in the model, it is an essential phenomenon which must be accommodated into the framework.

This is on my mind because of the emergence of packages such as TreeMix and AdmixTools. Using software such as these on the numerous public data sets allows one to perceive the reality of admixture, and overlay lateral gene flow upon the tree as a natural expectation. But perhaps a deeper result is the character of the tree itself is torn asunder. The figure above is from a new paper, Efficient moment-based inference of admixture parameters and sources of gene flow, which debuts MixMapper. The authors bring a lot of mathematical heft to their exposition, and I can’t say I follow all of it (though some of the details are very similar to Pickrell et al.’s). But in short it seems that in comparison to TreeMix MixMapper allows for more powerful inference of a narrower set of populations, selected for exploring very specific questions. In contrast, TreeMix explores the whole landscape with minimal supervision. Having used the latter I can testify that that is true.

The big result from MixMapper is that it extends the result of Patterson et al., and confirms that modern Europeans seem to be an admixture between a “north Eurasian” population, and a vague “west Eurasian” population. Importantly, they find evidence of admixture in Sardinians, which implies that Patterson et al.’s original were not sensitive to admixture in putative reference populations (note that Patterson is a coauthor on this paper as well). The rub, as noted in the paper, is that it is difficult to estimate admixture when you don’t have “pure” ancestral reference populations. And yet here the takeaway for me is that we may need to rethink our whole conception of pure ancestral populations, and imagine a human phylogenetic tree as a series of lattices in eternal flux, with admixed nodes periodically expanding so as to generate the artifice of a diversifying tree. The closer we look, the more likely that it seems that most of the populations which have undergone demographic expansion in the past 10,000 years are also the products of admixture. Any story of the past 10,000 years, and likely the past 100,000 years, must give space at the center of the narrative arc lateral gene flow across populations.