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Fst

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Sewall Wright
Credit: University of Wisconsin, Madison

You have probably heard or read that most genetic variation is within races, not between races. This assertion has led, in my opinion, to unwarranted inferences. Often bracketed under “Lewontin’s Fallacy”, the basic intuition is that if most variation is within races, then races as a taxonomic unit are without utility or substantive basis. This is disputable. In plain English, though most genetic variation may be within races (i.e., not diagnostic of racial identity), the variation across races is quite systematic because that variation reflects deep population history. In this way of thinking population or racial substructure are simply reflections of the tips of the tree which has been shaped by history.

But these discussions are ultimately predicated upon a statistic, F ST. F ST is generally considered one of the fixation indices pioneered by the American evolutionary geneticist Sewall Wright. What Wright’s F ST aims to capture is the relative amount of genetic variance which is due population substructure. In regards to human races out of the total genetic variation ~15% of it can be inferred simply by looking at population substructure (F ST ~0.15), with the balance not being due to population structure. But this is an average value. At rs1426654 in SLC24A5 when comparing Europeans and Africans almost all of the variation is between the populations, because the allele frequencies are disjoint. But what if I told you that Wright’s F ST is quite a bit woollier than you might think?

Citation: Patterson, Nick, Alkes L. Price, and David Reich. “Population structure and eigenanalysis.” PLoS genetics 2.12 (2006): e190.

The issue here is that measuring genetic distance is not like measuring acceleration or length. Acceleration is a clearly defined phenomena with a first order relationship to material entities, while length is a physical property of concrete objects. What population genetics is attempting to do is formalize and render abstract phenomena whose ultimate basis are not constrained by human preconceptions or easily amenable to intuitions, and may be nested within other abstruse constructions. In most cases what “genetic distance” really is is a way for humans to be able to conceptualize easily patterns of variation which are the outcome of complex historical processes. Often the interest of population geneticists is not in taxonomy as such, but the historical events which can be inferred by the classifications.

Wright’s F ST is useful because it gives you a number. And, due to its age it is also easy to compute using single marker data, as was prevalent before the molecular revolution of the 1960s. Today I much prefer visualizations of genetic relationships such as can be found in principal component analysis, or the ubiquitous bar plots of explicit population model clustering (e.g., Admixture or Structure). But if you are submitting a paper for peer review you may still be asked to provide F ST, meaning that this is still a relevant statistic.*

This is why a new preprint in Genome Research is very important for scientists working in this area, Estimating and interpreting F ST : the impact of rare variants. I had a short conversation with Gaurav Bhatia, the first author, at ASHG 2012, so I was waiting for this preprint to come out. In the text the authors provide explicit guidelines for ‘best practices’ on using and computing F ST. This is needed. I myself have shied away from using F ST much because I have seen that different methods give different results. Yes, qualitatively coherent, but it is not reassuring as F ST purports to a precise quantity.

The problem seems to be that F ST emerged in an earlier pre-genomic era, and with genome-wide dense SNP data biases, distortions, and inconsistencies across different F ST frameworks are starting to emerge. As an empirical result the authors point out that a recent paper has claimed that F ST < 0.10 for human populations using 1000 Genomes data. This is lower than the values inferred from HapMap3. Why? One possibility is that the 1000Genomes data is enriched for rare variants, which are likely to have emerged after the divergence of the populations from a common ancestor. This is problematic because many variants of F ST are predicated on a divergence from a common ancestor, and so should be evaluating shared variation (the authors observe that highly heterozygous alleles with a bias toward private alleles can paradoxically result in very low F ST). Because of the importance of taking into account shared and diverged population history the authors recommend ascertaining the SNPs in an outgroup, if possible (if not, then make the ascertainment strategy explicit and sample different genomics regions to get a sense of possible biases or distortions).

Additionally, there are problems with unequal sample sizes, as well as using pooled SNPs so as to compute individual distance values and taking the average of the results. They term the latter “average of ratios” (the ratio between the variance components), and conclude that this will underestimate the F ST, and that that is what occurred in the 1000 Genomes paper above. Rather, they recommend that taking the ratio of the average variances across the SNPs are less biased. This is where the pre-genomic origins of F ST show, as this would not be an issue in an age of few markers. But with the copious data from the 1000 Genomes these distortions can be amplified and result in genuine confusions about the biological history of a population.

Finally, they make explicit recommendations as to the form of F ST to use:

Hudson estimator > Weir and Cockerham > Nei

All this goes to show that even in established science it is important check your premises. Too often F ST is simply a black-box, one of the elements which you have to check off. But it is a tool which should be used with subtle understanding.

Addendum: Alkes Prices’ software page has some great resoruces. And there’s a new version of Eigensoft! I know what I’m going to do this weekend….

Citation: Genome Research, Estimating and Interpreting FST: the Impact of Rare
Variants, Gaurav Bhatia1, Nick Patterson2, Sriram Sankararaman, Alkes L. Price. doi:10.1101/gr.154831.113
* In F ST is still useful in many cases as part of a broader population genetic toolkit.

(Republished from Discover/GNXP by permission of author or representative)
 
• Category: Science • Tags: Fst, Population Genetics 
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Since we’ve been talking about Fst a fair amount, I thought it might be nice to put it in some concrete graphical perspective. First, to review Fst in the genetic context measures the proportion of genetic variation which can be attributed to between population differences. To give a “toy” example if you randomly divided the population of a large Swedish village into two groups, and calculated their Fst, it should be ~ 0, because if you randomly select from an unstructured population by definition there shouldn’t be noticeable between population differences. In contrast, if you compare a Swedish village to a Japanese village, a large fraction of the genetic variation is going to be distinct to each population. Around ~10% of the genetic variation in fact will be between the two groups. Many of the genes will be extremely informative, so that if you know the allelic state from a given individual you can predict with a high degree of certitude which population that individual was from (e.g., SLC24A5 and EDAR). A small set of ancestrally informative alleles would produce a sequence of conditional probabilities of extremely high certitude (on the order of 10 genes for these two populations should suffice, perhaps three for “government work”).

But to put this in perspective, and show how genetic variation differs from locale to locale, I though I would compare continental-scale Fst values with that in a small region, southern Africa. The Fst values for the first I obtained from Investigation of the fine structure of European populations with applications to disease association studies, and the second, Complete Khoisan and Bantu genomes from southern Africa. The Bantu in this case is Desmond Tutu, who is from the Xhosa tribe, and has substantial admixture from the non-Bantu populations which were resident in South Africa prior to the arrival of the Bantus.

First, in tabular format:

Spain Sweden Russia Japan
France 0.0008 0.0023 0.0037 0.1116
Spain 0.0047 0.0059 0.1118
Sweden 0.0025 0.1095
Russia 0.1057
Japan
KB1 NB1 TK1 MD8 Desmond Tutu
KB1 0.021 0.024 0.022 0.08
NB1 -0.007 0.006 0.091
TK1 0.016 0.088
MD8 0.061

Second, two adjacent bar graphs. In the foreground I’ve simply take the Spain vs. other Eurasian population comparisons, while in the background Desmond Tutu is the reference for the four Bushmen.

FinalscreenbushFinal

In some ways this comparison is an exaggeration of the variation in African genes. The Bushmen and Bantu populations are of very distinct origins, as the latter spread over eastern and southern Africa only in the last 2,000 years. The Bushmen-Bantu cultural gap is one of sharp discontinuity, and despite gene flow it is still to some extent a genetic one as well. But there are other factors dampening Fst in this case. First, Tutu is himself of partial Khoisan ancestry (of whom there are other groups besides the Bushmen), so his genetic distance is likely to be smaller than someone from the Zulu tribe, which has presumably had less admixture with the indigenous populations, being a bit farther from the edge of the demographic “wave of advance.” Second, the gene chips are geared toward Eurasian populations, and presumably missed African, and particularly Bushmen, specific variants because they didn’t go looking.

My own confusion on these issues the past week illustrates I suppose the difficulty in mapping these abstruse and yet materially concrete patterns onto human categories. But quite often wrestling with the difficulties in the surest path to illumination.

(Republished from Discover/GNXP by permission of author or representative)
 
• Category: Science • Tags: African Genetics, Bushmen, Fst, Genetics, Genomics 
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Razib Khan
About Razib Khan

"I have degrees in biology and biochemistry, a passion for genetics, history, and philosophy, and shrimp is my favorite food. If you want to know more, see the links at http://www.razib.com"