Machine learning swallowing population genetics = understanding patterns in population genomics

Dan Schrider and Andy Kern have a new review preprint out, Machine Learning for Population Genetics: A New Paradigm. On Twitter there has already been a little snark to the effect of “oh, you mean regression?” That’s fair enough, and the preprint would probably benefit from a lower key title, though that’s really the sort of titles journals seem to love.

I would recommend this preprint to two large groups of my readers. There are those with strong computational skills who are curious about biology. It makes it clear why population genomics benefits from machine learning methods. Second, those who are interested or trained in genetics with less of a computational and pop gen background.

Yes, all models are wrong. But some give insight, and some are just not salvageable. In population genomics some of the model-building is obviously starting to yield really fragile results.

Carving nature at its joints more realistically

If you are working on phylogenetic questions on a coarse evolutionary scale (that is, “macroevolutionary,” though I know some evolutionary geneticists will shoot me the evil eye for using that word) generating a tree of relationships is quite informative and relatively straightforward, since it has a comprehensible mapping onto to what really occurred in nature. When your samples are different enough that the biological species concept works well and gene flow doesn’t occur between node, then a tree is a tree (one reason Y and mtDNA results are so easy to communicate to the general public in personal genomics).

Everything becomes more problematic when you are working on a finer phylogenetic scale (or in taxa where inter-species gene flow is common, as is often the case with plants). And I’m using problematic here in the way that denotes a genuine substantive analytic issue, as opposed to connoting something that one has moral or ethical objections to.

It is intuitively clear that there is often genetic population structure within species, but how to summarize and represent that variant is not a straightforward task.

In 2000 the paper Inference of Population Structure Using Multilocus Genotype Data in Genetics introduced the sort of model-based clustering most famously implemented with Structure. The paper illustrates limitations with the neighbor-joining tree methods which were in vogue at the time, and contrasts them with a method which defines a finite set of populations and assigns proportions of each putative group to various individuals.

The model-based methods were implemented in numerous packages over the 2000s, and today they’re pretty standard parts of the phylogenetic and population genetic toolkits. The reason for their popularity is obvious: they are quite often clear and unambiguous in their results. This may be one reason that they emerged to complement more visualization methods like PCA and MDS with fewer a priori assumptions.

But of course, crisp clarity is not always reality. Sometimes nature is fuzzy and messy. The model-based methods take inputs and will produce crisp results, even if those results are not biologically realistic. They can’t be utilized in a robotic manner without attention to the assumptions and limitations (see A tutorial on how (not) to over-interpret STRUCTURE/ADMIXTURE bar plots).

This is why it is exciting to see a new preprint which addresses many of these issues, Inferring Continuous and Discrete Population Genetic Structure Across Space*:

A classic problem in population genetics is the characterization of discrete population structure in the presence of continuous patterns of genetic differentiation. Especially when sampling is discontinuous, the use of clustering or assignment methods may incorrectly ascribe differentiation due to continuous processes (e.g., geographic isolation by distance) to discrete processes, such as geographic, ecological, or reproductive barriers between populations. This reflects a shortcoming of current methods for inferring and visualizing population structure when applied to genetic data deriving from geographically distributed populations. Here, we present a statistical framework for the simultaneous inference of continuous and discrete patterns of population structure….

The whole preprint should be read for anyone interested in phylogenomic inference, as there is extensive discussion and attention to many problems and missteps that occur when researchers attempt to analyze variation and relationships across a species’ range. Basically, the sort of thing that might be mentioned in peer review feedback, but isn’t likely to be included in any final write-ups.

As noted in the abstract the major issue being addressed here is the problem that many clustering methods do not include within their model the reality that genetic variation within a species may be present due to continuous gene flow defined by isolation by distance dynamics. This goes back to the old “clines vs. clusters” debates. Many of the model-based methods assume pulse admixtures between population clusters which are random mating. This is not a terrible assumption when you consider perhaps what occurred in the New World when Europeans came in contact with the native populations and introduced Africans. But it is not so realistic when it comes to the North European plain, which seems to have become genetically differentiated only within the last ~5,000 years, and likely seen extensive gene flow.

The figure below shows the results from the conStruct method (left), and the more traditional fastStructure (right):

There are limitations to the spatial model they use (e.g., ring species), but that’s true of any model. The key is that it’s a good first step to account for continuous gene flow, and not shoehorning all variation into pulse admixtures.

Though in beta, the R package is already available on github (easy enough to download and install). I’ll probably have more comment when I test drive it myself….

* I am friendly with the authors of this paper, so I am also aware of their long-held concerns about the limitations and/or abuses of some phylogenetic methods. These concerns are broadly shared within the field.

After agriculture, before bronze

 

The above plot shows genetic distance/variation between highland and lowland populations in Papa New Guinea (PNG). It is from a paper in Science that I have been anticipating for a few months (I talked to the first author at SMBE), A Neolithic expansion, but strong genetic structure, in the independent history of New Guinea.

What does “strong genetic structure” mean? Basically Fst is showing the proportion of genetic variation which is partitioned between groups. Intuitively it is easy to understand, in that if ~1% of the genetic variation is partitioned between groups in one case, and ~10% in another, then it is reasonable to suppose that the genetic distance between groups in the second case is larger than in the first case. On a continental scale Fst between populations is often on the order of ~0.10. That is the value for example when you pool the variation amongst Northern Europeans and Chinese, and assess how much of it can be apportioned in a manner which differentiates populations (so it’s about ~10% of the variation).

This is why ancient DNA results which reported that Mesolithic hunter-gatherers and Neolithic farmers in Central Europe who coexisted in rough proximity for thousands of years exhibited differences on the order of ~0.10 elicited surprise. These are values we are now expecting from continental-scale comparisons. Perhaps an appropriate analogy might be the coexistence of Pygmy groups and Bantu agriculturalists? Though there is some gene flow, the two populations exist in symbiosis and exhibit local ecological segregation.

In PNG continental scale Fst values are also seen among indigenous people. The differences between the peoples who live in the highlands and lowlands of PNG are equivalent to those between huge regions of Eurasia. This is not entirely surprising because there has been non-trivial gene flow into lowland populations from Austronesian groups, such as the Lapita culture. Many lowland groups even speak Austronesian languages today.

Using standard ADMIXTURE analysis the paper shows that many lowland groups have significant East Asian ancestry (red), while none of the highland groups do (some individuals with East Asian admixture seem to be due to very recent gene flow). But even within the highlands the genetic differences are striking. The  Fst values between Finns and Southern European groups such as Spaniards are very high in a European context (due to Finnish Siberian ancestry as well as drift through a bottleneck), but most comparisons within the highland groups in PNG still exceeds this.

The paper also argues that genetic differences between Papuans and the natives of Australia pre-date the rising sea levels at the beginning of the Holocene, when Sahul divided between its various constituents. This is not entirely surprising considering that the ecology of the highlands during the Pleistocene would have been considerably different from Australia to the south, resulting in sharp differences in the hunter-gatherer lifestyles. Additionally, there does not seem to have been a genetic cline. Papuans are symmetrically related to all Australian groups they had samples from.

Using coalescence-based genomic methods they inferred that separation between highlands and some lowland groups occurred ~10-20,000 years ago. That is, after the Last Glacial Maximum. For the highlands, the differences seem to date to within the last 10,000 years. The Holocene. Additionally, they see population increases in the highlands, correlating with the shift to agriculture (cultivation of taro).

None of the above is entirely surprising, though I would take the date inferences with a grain of salt. The key is to observe that large genetic differences, as well as cultural differences, accrued in the highlands of PNG during the Holocene. In the paper they have a social and cultural explanation for what’s going on:

  Fst values in PNG fall between those of hunter-gatherers and present-day populations of west Eurasia, suggesting that a transition to cultivation alone does not necessarily lead to genetic homogenization.

A key difference might be that PNG had no Bronze Age, which in west Eurasia was driven by an expansion of herders and led to massive population replacement, admixture, and cultural and linguistic change (7, 8), or Iron Age such as that linked to the expansion of Bantu-speaking
farmers in Africa (24). Such cultural events have resulted in rapid Y-chromosome lineage expansions due to increased male reproductive variance (25), but we consistently find no evidence for this in PNG (fig. S13). Thus, in PNG, wemay be seeing the genetic, linguistic, and cultural diversity that sedentary human societies can achieve in the absence of massive technology-driven expansions.

Peter Turchin in books like Ultrasociety has aruged that one of the theses in Steven Pinker’s The Better Angels of Our Nature is incorrect: that violence has not decreased monotonically, but peaked in less complex agricultural societies. PNG is clearly a case of this, as endemic warfare was a feature of highland societies when they encountered Europeans. Lawrence Keeley’s War Before Civilization: The Myth of the Peaceful Savage gives so much attention to highland PNG because it is a contemporary illustration of a Neolithic society which until recently had not developed state-level institutions.

What papers like these are showing is that cultural and anthropological dynamics strongly shape the nature of genetic variation among humans. Simple models which assume as a null hypothesis that gene flow occurs through diffusion processes across a landscape where only geographic obstacles are relevant simply do not capture enough of the dynamic. Human cultures strongly shape the nature of interactions, and therefore the genetic variation we see around us.

Why you should learn some population genetics

From reader surveys I know a substantial portion of the people who will see this post are financially well off (of those who aren’t, a large number are students). Therefore, you can invest in some books.

Often people ask me questions related to population genetics in the comments (sometimes I get emails). That is all well and good. But it is always better to be able to fish than have to ask for fish. Additionally, learning some population and quantitative genetics allows you to develop some tacit schemas through which you can process information coming at you, and through with you can develop some general intuition.

If you have a modest level of mathematical fluency and and the disposable income, here are three indispensable books which are like the keys to the kingdom:

* Elements of Evolutionary Genetics
* Principles of Population Genetics
* Introduction to Quantitative Genetics.

If you don’t have the cash to spare, there are online notes which are pretty good:

* Graham Coop’s Population Genetics notes
* Joe Felsenstein’s Theoretical Evolutionary Genetics

There are others online resources, but they are not as comprehensive. John Gillespie’s Population Genetics: A Concise Guide is good as very gentle introductions go, but if you are going to spend money, I think just plumping down for a more comprehensive textbook (which will have more genomics in it) is better over the long run.

The goal of getting these books isn’t to make you a population geneticist, but, if you are interested in evolutionary questions it gives you a powerful toolkit. Really nothing in evolutionary process makes sense except in the light of population genetics.