A fair eyed lass!

Click for larger version
Click for larger version
Every now and then a bizarre character named Alistair Moffat comes on my radar. I presume he’s famous in Britain, but I don’t know much about him. Except that is he is keen on making the most bizarre pronouncements. A lot of the Debunking Genetic Astrology website is devoted to tackling Moffat’s mischief. There’s an unfortunate aspect here in that Jim Wilson, a scientist who I respect, seems to have gotten involved with Moffat’s ventures. If you don’t follow the scientific literature you wouldn’t know that Wilson is a respected scholar after listening to Moffat’s garbling of his science. In any case the latest Moffat gem is pretty amusing. The British tabloids are reporting on a Map of blue-eyed Britain: As scientists suggest colour is more attractive, study shows it is most common in Ireland and Scotland, but least likely in the south. If you click through you’ll see a map, derived from data compiled by Moffat’s firm. They report that in Ireland and in Scotland the frequency of blue eyes is on the order of 50 percent or more, while it drops to 35 percent in Cornwall, and 41 percent in East Anglia. The always factually innocent Moffat declares “…he was surprised at the findings. He told The Times: ‘A lot of people think blue eyes are much rarer than they are.’” I don’t know. Perhaps Moffat spends a lot of time in East London in the Tower Hamlets, because the little time I’ve spent in England didn’t suggest to me the British were a dark eyed folk, at least compared to Italians. Mind you, that doesn’t compare to the time in Tampere, Finland, where I counted to 30 before I saw someone with brown eyes step off a boat. The range in frequency is actually somewhat smaller than I would have expected (note that “not blue” does not mean brown, as many of the rest would have green or hazel eyes). It seems what Moffat’s firm is doing here is just repeating the sort of anthropometric observations which were reported by John Beddoe, most famously in his index of negrescence. Beddoe found that darker hair predominated among the people of the Celtic Fringe, and linked it to various theories of the inferiority of these aboriginal peoples.

I actually think attempts to map and catalog phenotypic variation are interesting and worthwhile. It just bothers me when people turn it into a veritable carny-show. Here’s what I mean:

He [Moffat] said the colour may be more dominant because it is regarded as attractive, adding: ‘It may be that blue eyes are like the peacock’s tail. It doesn’t confer any evolutionary advantage … except that it gets him more mates.’

Blue-eyed Hollywood stars Angelina Jolie, Daniel Craig, Nicole Kidman, Hugh Grant, Kate Winslet and Paul Newman all support the theory that blue eyes add to a person’s sexual appeal.

Mr Moffat added: ‘All of them have inherited their eye colour …  through their DNA, and because of the way that blue eyes deal with light, they also appear to have inherited a natural sparkle.

The idea that light eyes rose in frequency because of sexual attractiveness has scholarly support (e.g., Peter Frost). But this is a very frontier zone of science, and not everyone believes that this is the most likely explanation (I myself would put my money on it being a side effect of selection for something else, but my confidence is low). It shouldn’t be that hard to judge whether blue eyed individuals have more sexual partners, or are more fertile, than their co-ethnics. Eye color segregates within families, and as suggested in the article we know where most of the genomic variation is resident (in the HERC2-OCA2 region). If it was strongly correlated with fertility I presume it would have showed up in GWAS earlier.

All I can say is that in the interests of his personal gain Moffat is making a potential area of scientific inquiry as to the genetics of the British peoples into a farce.

Open Thread, 8/31/2014

Happy Labor Day! (to Americans)

A few days ago someone asked about books on genetics. More specifically, textbooks. I didn’t know what to say really, because “genetics” is a big field. Genetics on the evolutionary/population scale is a rather abstract field of analysis. Genetics in the molecular sense is a concrete physical science. For my qualifying exam I went with . Though the title emphasizes the classical genetic analytic framework (i.e., Mendelism as formulated in the early 20th century), there is coverage of fields as diverse as quantitative genetics and genomics. I particularly liked the deep treatment of meiosis, in both its biophysical and analytic dimension. For molecular genetics, I can’t complain about , though people who actually do molecular biology would have an opinion you might want to listen to. At the other end of the spectrum is the easy choice. Though I really like , at least the parts I’ve had time to work through.

The land of no fiction

On Facebook challenged me to name 10 books that have stuck with me. Many of you have probably been tagged on this challenge. For what it’s worth, here’s the list:

* (Hartl & Clark)
* (Jacques Barzun)
* (Steven Pinker)
* (L. L. Cavalli-Sforza)
* (Isaac Asimov)
(Scott Atran)
(Colleen McCullough)
(Matt Ridley)
(Peter Brown)
(Richard Elliott Friedman)

The challenge stipulated that you not think too long, and I came up with the list in less than two minutes. But the first five, which I’ve placed asterisks next to, came to mind within 10 seconds. I’m rather sure that these five would be on any list of 10 books of note from my own perspective.  and  probably explain to some extent why I’m where I am professionally.  is a testament to the continuity of the life of mind of a sort which I aspire to attain (though I doubt I will). Steven Pinker’s  opened up for me a window to a world where disciplinary boundaries are violated for both fun and profit. The last five took me longer because there are many books which have stuck with me with at the next tier of salience. These might change from instance to instance, though the set isn’t that large.

Which brings me to . Why is it in the top five? It’s not even the best of the Foundation novels (I would probably go with for that). As Nathan pointed out my list leaned toward non-fiction. is on this list because it is the first fiction book I proactively selected at the library at the age of 13. The main reason I picked it is because I’d read some of the author’s non-fiction works for children when I was younger, and was curious that he’d written science fiction (only later did I find out that he was originally known as a science fiction author). But I have to be specific here. After responding to Nathan I realized that I’d read two works of fiction before , , when I was 12, and , when I was 9. My reading was something of a mistake. I was sleeping over at a friend’s house, and he had a copy of the book, which I mistook for a work of paleontology. I began reading it sometime around 9-10 PM, and kept going until the sun came up, when I was done. I read over an extremely boring Christmas vacation where my parents visited old friends for a week, and I forgot to bring any books and had to find something to read in the house we were staying at.

This is autobiographical trivia, but I thought I’d submit it into the record because as you can tell by the precision of my recollections I had very little interest in fiction when I was younger. To some extent this remains true, when I have little marginal time I continue to read non-fiction and basically cut out fiction totally. From interacting with people as I grew older I began to realize this was a little strange. I wonder how many other children are the same as me? I’m also curious how my children will turn out.

Addendum: To be clear, I was a huge reader of non-fiction from about the age of 7 onward.

No two look-alikes

Credit: Segal, Nancy L., Jamie L. Graham, and Ulrich Ettinger. "Unrelated look-alikes: Replicated study of personality similarity and qualitative findings on social relatedness." Personality and Individual Differences 55.2 (2013): 169-174.
Credit: Segal, Nancy L., Jamie L. Graham, and Ulrich Ettinger. “Unrelated look-alikes: Replicated study of personality similarity and qualitative findings on social relatedness.” Personality and Individual Differences 55.2 (2013): 169-174.

The New York Times summarizes some new research in behavior and personality, Holding a Mirror to Their Natures: Looking at Twin Personality Through Look-alikes:

As she expected, the unrelated look-alikes showed little similarity in either personality or self-esteem. By contrast, twins — especially identical twins — score similarly on both scales, suggesting that the likeness is largely because of genetics. Her results were published in the journal Personality and Individual Differences.

For a second study, she teamed with a skeptic, Ulrich Ettinger, a psychologist at the University of Bonn in Germany who had heard about the look-alike project during a postdoctorate at the University of Montreal.

“I thought that if two people looked alike, they would have similar personality traits because people would treat them the same,” he said. “For example, I thought men who looked alike and were tall and handsome would probably be extroverts.”

Their analysis was consistent with the findings of Dr. Segal’s first study: Personality traits do not appear to be influenced by the way people are treated because of appearance. Moreover, they found, there appears to be no special bond between look-alikes.

Segal, Nancy L., Jamie L. Graham, and Ulrich Ettinger. "Unrelated look-alikes: Replicated study of personality similarity and qualitative findings on social relatedness." Personality and Individual Differences 55.2 (2013): 169-174.
Segal, Nancy L., Jamie L. Graham, and Ulrich Ettinger. “Unrelated look-alikes: Replicated study of personality similarity and qualitative findings on social relatedness.” Personality and Individual Differences 55.2 (2013): 169-174.

The original study, Unrelated look-alikes: Replicated study of personality similarity and qualitative findings on social relatedness, is quite modest in scope. You can see the sample sizes are not large in the table to the left. With that said, I think this is adding to a growing body of results that validate the soundness of the original work on twins in behavior genetics. For many reasons this research program has come under sharp critiques over the past 50 years, but it seems to me that the big picture findings of modest heritabilities for most behavioral phenotypes is holding up. For a complementary tack I suggest Whole genome approaches to quantitative genetics, which uses different methods to explore some of the same class of
traits. Relying on the body of twin research alone as a foundation might be a shaky basis for conjecture, but now this area is going multi-disciplinary,
allowing for a stool with multiple legs. Of course all it is doing is confirming modest heritabilities for behavioral phenotypes. But one needs to remember that a lot of the environmental component is not amenable to control, whether by parents or society (i.e., it is “non-shared environment”).

God does play dice.

A 1 million genotype project?

Recently in Washington D.C. at the International Conference for Genetic Genealogy Spencer Wells ran through a survey of personal genomics, and asserted that over the past year we’ve nearly doubled the number of genotypes on dense marker arrays, from ~1 million to nearly ~2 million. Talking to people that seems about right, 23andMe is approaching the million mark itself alone. Combined with the databases of National Geographic, Ancestry and Family Tree DNA the 2 million mark is surely approaching us. But the presentation wasn’t simply about personal genomics today. He integrated the modern changes to events which occurred over the past generation to bring genetics to the people, and allow its widespread utilization among researchers to explore historical questions. Coming out of the Human Population Genetics Lab at Stanford in the 1990s Wells pointed out that the constituent populations of the HGDP were selected by L. L. Cavalli-Sforza consciously to be biased toward those which were more isolated and genetically less subject to globalization. The theory was to pick up stronger signals of ancient population structure which might be obscured by more recent movements of peoples across the earth.

MDS representation of Europeans, with a focus on Germans. Click to englage. Credit: Family Tree DNA
MDS representation of Europeans, with a focus on Germans. Click to englage. Credit: Family Tree DNA

By and large Cavalli-Sforza’s intuition has been validated. The HGDP data set has yielded enormous insight, first with classical markers (see ), then during the Y and mtDNA era around 2000, as well as microsatellites and dense SNP arrays in the aughts. I’ve heard that the Sardinian samples that Cavalli-Sforza selected were somewhat less cosmopolitan than other Sardinians that have been collected later, indicative of his personal knowledge of Italian genetic variation on a personal level. But he also had the area knowledge to sample both the western and eastern Pygmy populations of the Congo. The evolutionary history separating these two groups is likely on the order of that dividing inter-continental populations outside of Africa, and the eastern Pygmies in particular are an invaluable reservoir of human genetic variation. To answer a few big questions a data set of 1,000 specially selected humans from across the world turns out to have been sufficient. 

But there is a flip side. The answers to the many small questions are going to require much more sample coverage. Wells himself illustrates this reality, as he recounted a story from his Geno 2.0 database where a few percent of ethnic Hungarians exhibit Central Asian uniparental haplotypes. He points out that standard analyses don’t show anything special about Hungarians, but then again you are likely to miss admixtures on the order of a few percent here and there if you are working with sample sizes of less than 100, which is still typical for European nations. Even a large data set, such as the POPRES, is dwarfed by those of commercial firms and National Geographic.

Germany population density
Germany population density

Last week I reported that Afrikaners do seem admixed using the Family Tree DNA database. But that’s not the first strange thing that I saw. When devising myOrigins I had to attempt to tackle the problem of German ancestry and assigning individuals to a particular cluster. I was skeptical for a simple reason: the historical literature was clear that substantial numbers of Germans from the eastern zones of habitation were acculturated Slavs. But I was met with a surprise. Yes, the genetic variation showed substantial amount of admixture with Slavs. Using MDS/PCA you can see that there is an admixture cline with a Polish reference population for individuals who state that both their parents were born in Germany. But there is a second distinct cluster among Germans which overlaps with that of northern France. I don’t have data on the scale of specific geographic points, but my suspicion is that the region around Cologne is genetically distinct because of long-term gene flow with northern France. The scale of Hugenot migration to Germany in the 18th century seems unlikely to explain this.

On the scale of the “big questions” this is trivial and of minor note. But, to answer this sort of question about genetically close populations you need dense geographic coverage and large population sizes. Currently only the personal genomics firms have this, to my knowledge. POPRES and Framingham Heart Study both have sample sizes in the ~5,000 range total. 1000 Genomes is an improvement, but even its sample sizes and coverage is not sufficient. Where are we going? Spencer Wells talks a lot about citizen science. Many of the enthusiasts for scientific genealogy have done very deep analyses of their own genotypes. They certainly have skills to analyze bigger datasets. If computing power is needed then an Amazon cloud server could provide that. The problem though is that customer data can’t just be shared by the big companies themselves. In the short term the ultimate solution is to scale up projects, like Harappa DNA, and formalize their structure so that those who submit their genotype data are protected in some fashion (e.g., exposure of identity). Academic scholars are going to be focusing on whole genomes, more subtle methods, as well as exotic and obscure populations which can get at the big questions.  To really see my point, see what Google Scholar returns when you type “genetic population structure germany”.

Juggling 300 million variables

My post The Islamic State Is Right About Some Things was a “success” as far these things go. It was noted in a column in The New York Times, and highlighted issues which you can see being emphasized in pieces in Slate and The Spectator. But obviously in a single post there is a lot of nuance which I had to elide for reasons of space. Though I may be a population genomicist by day, I do think that in certain domains outside of my bread & butter I bring insights which you can’t find elsewhere, so I try to inject it into the broader discussion. But I’m limited in what I can do in a single post. One of the things I noticed as my post was circulating is that many people asserted that I was suggesting you can understand the actions of the Islamic State by the nature of its theology. Long time readers (I’ve been writing for 12 years on these sorts of issues) might be surprised by this, as was I, because actually I think that is one of the major problems that people have when attempting to understand the nature of religious phenomena. Theology is an abstruse field which is the purview of religious professionals of a particular sort. The vast majority of humans today are marginally literate at best, and for most of human history have been illiterate. To put it succinctly and semi-accurately I think our interpretations of theology are actually effects of prior beliefs, which are due to non-theological parameters. For example, I suspect most Christians would assert that their theology is such that slavery is anathema to their moral system with a proper understanding of God (i.e., theology). Obviously this was not so for the whole of Christian history up until 1800.  One conclusion I derive from these sorts of facts is that theology derives its content from the subjective preferences of its practitioners. It is not like mathematics, an objective sequence of inferences and derivations from axioms. Nor is it like the natural sciences, extending itself step by step along a scaffold defined by the world around us. Rather, it starts from a presupposition, that God, with particular semantically distinct characteristics, exists, and then proceeds to enter into complex and subtle interpretations of that fact.

I have come to this state of affairs over time through reading. Though I was raised in a religious (Muslim) environment, it was not exceedingly devout or observant, and my personal beliefs were rather devoid of much interest or consideration of supernatural entities. For some people God is an intuitive and intoxicating concept, which draws them in a magnetic fashion. For me a lack of belief is, and was, the natural state. Atheism bubbled up naturally, unbidden, at the age of eight when I decided to look within. When I considered God’s existence seriously, I couldn’t help but reject it. This meant that my understanding of religion has always been as an outsider, and I tended to take religious people at their word when it came to what they believed and how they believed. Religious people of the sort I interacted with explained that their faith was revealed in a set of scriptures, and from those scriptures one could derive the nature of religion. Even religions, such as Roman Catholicism, where scripture is not emphasized generally accept that the foundational texts are necessary and essential in truly comprehending the faith in a deep way with mind (as opposed to just receiving sacraments through liturgy). This was congenial to my mind, as it rationalized religion, turning into a system of propositions from a set of axioms. My scientific bent meant that I naturally understood this sort of mentality.

Therefore, to understand something like Islamic violence, one only need to look at the foundational texts. But though this seems like a fruitful way to go I no longer believe it describes the structure of reality because on an individual level religious belief and practice does not seem rooted at all in texts. Though one can make broad correspondences and draw arrows of causality, with an understanding at a lower and more fine-grained scale this model has as much validity as Galenic medicine. It captures fragments of reality and presents it before us in a persuasive fashion, but at a deeper level of inspection it fails to explain the basic mechanics of religious belief. To understand how I came to this position one has to know that I have long been interested in evolutionary psychology, and therefore cognitive science. After 9/11 I decided to read books on religion besides the basic scriptures, and I stumbled upon the field of evolutionary cognitive anthropology, and in particular the scientific study of religion in the naturalistic paradigm. Two of the primary sources in this domain are Scott Atran’s and Pascal Boyer’s . In these dense works they illustrate the cognitive foundations of religious belief and practice, and exposed me to the reality that despite what many religious believers might tell you religious scripture is actually a sideshow to the richness of the phenomenon. Like the coffee table book that one proudly displays, the value of scriptures is that is a visible marker and a common point of reference, as opposed to an instruction manual. In the author explores the reality that religious people don’t even seem to believe what they say they believe on a deep level. For example, monotheists and polytheists seem to have the same internal model of the supernatural world, despite their explicit verbal scripts being very different. To put this in another context, many people who espouse views which deny the existence of the supernatural still get “spooked” in a dark cemetery. Why? They are sincere in their belief that there are no ghosts and demons in the dark, but in the deep recesses of their minds reflexive intuitions honed over evolutionary time remain at the ready, alert for any sign of danger in the darkness. Similarly, most religious people may believe sincerely in a glorious afterlife, but when there is a gun to their head they may soil themselves nonetheless.

Belief matters, but it seems likely that it matters at the margins. For whatever reason we humans tend to believe that we have explicit control over our beliefs and actions, and our decisions are due to conscious reflection. This is just often not so, and it has been scientifically validated to my satisfaction. On a personal level I think it is possible that in a different social milieu I would have “rediscovered” my faith in God at some point because of constant feedback from my peers. Though the United States is often depicted, correctly, as a particularly pious developed nation, it is not difficult to seal oneself in a secular bubble. Very few of my friends are religious, despite most Americans being religious. So my atheism is nicely insulated from countervailing pressures. My beliefs, my understanding of reality, is the outcome of a complex interaction between my dispositions and my social-cultural environment. So it is for us all.

But I don’t want to imply from this that if you understand the cognitive science of religion you understand religion. Rather, it is the basic general chemistry of the understanding of the religious phenomenon. In David Sloan Wilson outlines a theory of religion which explains the patterns around us in functional terms; i.e., religions as forms of cultural adaptations. Though I’m sceptical of religious models predicated on rational choice theory, that also has its utility in particular contexts. Religion in a socially corporate context such as India is far different from that in the United States, where religion is understood in more individual terms (e.g., defection from a mainstream religion to another mainstream religion does not necessarily entail a massive rupture in your social ties to friends and family in the United States, so churn is common).

So where does this leave us in relation to the Islamic State? Does genocide history and scriptures of Islamic explain its atavistic savagery? I think not. Unlike most Muslim spokespersons I don’t think the behaviour of the Islamic State is “un-Islamic.” Religion is to my mind a made-up affair, and people can remake it in its own image however they want. And, as a point of fact the early Wahabbi movement in the 18th century exhibited many of the same ticks as the Islamic State, down to genocide treatment of those who avowed wrong belief. What I found particularly interesting in a detached manner about the Islamic State is how well versed many of its proponents are in a particular streak of the history of Islam. Watching the Vice documentary of the Islamic State I can pick up terms and concepts from my rudimentary religious education, as well as references to “the Romans,” which in that case refers to the Byzantines under the Heraclian dynasty. Rather than theology I suspect history is a better guide as to what’s going on, and why, from the violent exclusive strain of Islam which periodically emerges from the Kharijites down to the Wahabbis, to early modern period and post-colonial conflicts, as well as the ethnography of political radicalism among small motivated groups such as the anarchists. Most proximately the Islamic State clearly draws energy and strength from Sunni resentment toward Alawite hegemony in Syria and Shia dominance in Iraq. Over time this may evolve into something else, as a generation grows up under the influence of the message of the Islamic State and its broader Weltanschauung. It is essential to keep in mind both the generalities (e.g., it is a Sunni movement) and particularities (e.g., it is global in its imagination and aspiration, at least notionally) when attempting to gauge the possible arcs of the future.

Addendum: And in the interest of frankness, I will also admit that though comments can be highly informative, I don’t listen closely when someone decides to lecture me on the nature of religion because it is rare than I encounter anyone with as much breadth of knowledge as me in this domain (i.e., I have read economic, sociobiological, cognitive, and historical models of religion). If I seem to dismiss your opinion, that’s probably because I don’t think much of your ideas because you likely know far less than I do.

European Muslims, a problem that won’t go away

Woman_in_niqab,_Aleppo_(2010)USA Today is blasting a headline, More British Muslims fight for Islamic State than Britain, based on the fact that a conservative estimate suggests that 800 fighters for the Islamic State hold British Passports. It turns out that 600 Muslims serve in the British armed forces, which number 200,000. A separate article in The New York Times gives ballpark figures of 10 to 20 thousand as the number of fighters for the Islamic State overall. That means that 5 to 10 percent of the forces of the Islamic State are British.

There are about 2.7 million Muslims in the United Kingdom. There are 1.6 billion Muslims in the world. That means 0.17% of the world’s Muslims are British. About 1 out of 600. Let’s say that 5% of the fighters for the Islamic State are British. 1 out of 20. British Muslims are represented at a 30-fold greater rate in the Islamic State than their world-wide representation among Muslims. Overall about 2,000 Europeans are believed to be serving in the forces of the Islamic State. About 20 to 45 million Muslims live in Europe (this is dependent on whether you’re talking about the European Union only, or include Russia). So at most 3% of the world’s Muslims are European nationals. But they make up 10 to 20 percent of the fighting forces of the Islamic State, depending on how you gauge the figures.

I review these numbers because I believe they are a place where we can start to grapple with the facts that confront us. It is easy to say “Islam is the problem,” but that is as informative as saying that all phenomena can be reduced to physics. That is true on some level, but it is useless in a practical sense. The gross over-representation of European Muslims is of interest, because if it was simply Islam then there wouldn’t be an over-representation. On flip side it seems hard to deny that Left multiculturalism which presupposes that accommodation and acceptance will serve as a balm against all separatist inclinations among Muslims simply is hard to support. Britain arguably is the most accommodating of European nations to Islam and the Muslim community, but it is contributing far greater than its quota to the forces of the Islamic State. These issues are complex, but they need to be confronted without qualms. The chickens are going to come home to roost soon.

Addendum: “European Muslims” includes a diverse array of individuals and populations. There are European ethnic groups which are historically majority Muslim, such as Albanians and Bosnians. Then there are the immigrant communities. And finally there are the converts.

The Intel of sequencing

Credit: Forbes
Credit: Forbes

Matt Herper’s piece in Forbes, Flatley’s Law: How One Company Is Creating Medicine’s Genetic Revolution, is a must read. Here’s the conclusion:

It’s hard to disagree with him. The cost of sequencing a human being’s DNA is less than one-hundred-thousandth of what it was when Flatley started running Illumina 14 years ago. Illumina is hoping to lower the price further. Ronaghi, the CTO, says the market has been disrupted every time the cost of sequencing has dropped by five to ten times. He foresees DNA sequencers that might cost $10,000, as compared with $250,000 for Illumina’s midline models, opening up whole new markets–and cures. Says Flatley: “The road maps that we have are pretty breathtaking as far as where the technology can move in the next three to five years.”

As narrated in the piece competiters have tried to take Illumina down a notch since 2008, and failed. So you don’t want to bet against them. That being said its dominance is having an effect on the famous chart of “cost per genome” decline. With the stabilization of the monopoly prices haven’t really dropped much since 2012. It might take a full frontal assault by a credible competiter like Oxford Nanopore to induce more than incremental change on the margins.

Geneological descent and identity by descent

Credit: How much of your genome do you inherit from a particular ancestor?

In the post below I made an offhand comment that most Americans with colonial stock in their family could probably trace at least one genealogical line back to a Native American. To some extent this implies omniscience, as most people don’t have such a paper trail. But to give an example of what I’m talking about, a huge number of Americans can trace descent from Pocahontas, because her great-grandson John Bolling is an ancestor of the semi-endogamous gentry of Virginia, the First Families.

America before 1800 was one of the world’s highest fertility societies. The over 1 million people living in New England at the time of the American Revolution were almost totally descended from ~30,000 settlers who arrived in the 1630s from England. Because of this finite pool of ancestry the genealogies of people of Yankee stock often intersect, and the same individuals show up over and over. Just a few Native Americans in the genealogy of settler stock can quickly propogate, so that in the present day it is entirely likely that the majority of the population with settler ancestry would be able to trace a sequence of ancestors back to someone who was of Native American stock.

But, that doesn’t mean the vast majority of these individuals would exhibit evidence of ancestry on the genetic level. The reason is illustrated in the chart above, published in a blog post by Graham Coop’s lab, How much of your genome do you inherit from a particular ancestor? The answer is that for ancestors who lived in ~250 years ago, and don’t show up in your genealogy over and over (so they get more than one shot), you are unlikely to have inherited any distinctive genetic segments. That’s because aside from parent to child transmission there’s a random component around the expected value of how much ancestry you are going to inherit from an individual, due to segregation and recombination at the genomic level. The shuffling during meiosis usually skews the fraction transmitted from the maternal and paternal parents of the transmitter away from parity (50% each). As the expected fraction get’s smaller and smaller with each generation it is no surprise that there is a high probability that some segments of ancestry don’t get transmitted at all.

The above framework has interesting implications. One of the results of Afrikaner admixture is that it was relatively evenly distributed across the sample. Instead of one individual with 5-10% non-European ancestry, and the rest with ~0%, the range was closer to 3-7%. I’ve done some local ancestry inference with RFMix, and the segments are all over the genome, and not particularly long. Admixture on the order of 250 years ago seems plausible, in line with the historical evidence in regards to the ethnogenesis of the Boer/Afrikaner people. The people who moved into the Dutch settler population with large amounts of non-European ancestry were not isolated individuals, like Pocahontas. Almost certainly they were a substantial number in the original founding population of thousands. In contrast in a place like Canada a segment of Native American ancestry among Quebecois or old stock white Anglo-Canadians reflects the Pocahontas scenario. A few non-Europeans entered the genealogical tree of the compact and endogamous community, and so are direct ancestors of most or many, but their genetic segments are only found in a small fraction.