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April 19, 2005

A golden error?

In the comment board Theresa asserted: "Another side note, lots of ethnic Norwegians have dark hair and dark eyes -- the blonde, blue-eyed folks are mainly in the inner valleys -- and over there in Sweden." I don't know if this is true, but, it did make me wonder.

My post Why evolution doesn't make sense ruminated over the difficulties that lay people have when they think about evolution. The macroevolutionary realities tend to overshadow the more operationally relevant microevolutionary details.

Let us assume that Norwegians of the inland valleys do tend to be blonder than coastal Norwegians. Why could this be?

Here are some quick answers people might come up with.

Migration-clinal admixture: In her comment Theresa alluded to the fact that Swedes tend to be blonde. When physical anthropologists had a great concern about such topics a common data point brought up was that southern Sweden represented the modal frequency of the "blue eyed blonded" "Nordic" type. In fact, some texts asserted that only in southern Sweden did the intersection of blue eyes and blonde hair characterize the majority of the population. From this it is common sense to assume that blondism decreases as a function of distance from southern Sweden.

Modern paternal and maternal DNA markers suggest that it is possible that northern Europe was "repopulated" after the Last Glacial Maximimum by disparate populations that have been driven south into "refuges." Iberia, the eastern European borderlands and the Balkans are the primary candidates for the nodes from which the demographic expansion repopulated Europe. Luigi Cavalli-Sforza's magmum opus The History and Geography of Genes prefigured the findings of the later geneticists as he transformed various principal components of variation in his data sets into rich maps that illustrated clinal transitions issuing out of the southeast, southwest and east.

The details of this model are not relevant, rather, I would like to point out physical anthropologists have observed an increase in the frequency of dark hair as one moves to the west in the British Isles, the Welsh being darker than the English and the western Irish being less blonde than the eastern Irish. All this is to flesh out the possibilities that admixture and various migrational movements (blondes from the east intermarrying with dark haired people migrating up from Iberia) might account for the local phenomenon of inland folk being blonder in Norway.

Selection: Another hypothesis is that microevolutionary selective pressures have resulted in the differences between inlanders and costal dwellers. If one opens the can of worms that is social and sexual selection the possibilities are endless, rather, I will point to the more prosaic option: coastal dwellers did not need to synthesize as much Vitamin D because they could acquire that nutrient through fish oil. Therefore, the blondeness of the highlanders is a correlated response to the selection for fair skin, which facilitates endogenous synthesis of Viatmin D.

But these aren't the only options. #1 is something that the typical person might offer without any prompting or recourse to research. The exact details of #2 are more difficult to intuit from common sense, while the various possible epicycles that sexual and social selection imply are not even on the table in conventional disource.

And yet, as the title suggests, there is another option: Random Genetic Drift might be the cause of the higher frequency blondeness among the highland population. And this "Random Genetic Drift" might not be happenstance, that is, the highland populations simply random walked into a higher frequency of the blonde phenotype, rather, it might be an inevitable consequence of particular tendencies toward population substructure.

The thought is triggered by my reading of some of Cavalli-Sforza's original work in Italy. He foud that people who lived in the mountainous regions and away from the coasts had far more constricted marital networks. They were more inbred because their operational "deme," the rough & ready breeding population, was far smaller, and not only did they share many coancestors but they were subject to greater forces of drift. In fact, the correlation between topography and the average distance of birth between the spouses was larger striking. Lowland people were aided by good roads, gentle grades as well as the supplement of water transportation. Though the lowlanders (at this time) might not have been economically that much more advanced than their highland neighbors, they were part of a much more tightly integrated wider social and populational network. The marital connections and gene flow between the lowland villages was far greater than what one found among the highland villages.

Which brings us back to Norway. Qualitatively the model can be described as thus: lowland Norway is a large deme where Random Genetic Drift has had less power because of the high effective population size. In contrast, the highland demes are rather small, and so each has been buffeted by sampling error, Random Genetic Drift, to a far greater extent than the lowlanders. A crucial point is that the swings should cancel out so that the frequencies of alleles might not differ very much between the lowland deme and "the highlands," but because of the high degree of population substructure there are many populations where alternative alleles have been fixed. This is where blondeness comes it: it is traditionally characterized as a phenotype that is expressed when the alleles are present as homozygous. So, while in the lowland deme 50% of the alleles might be for "blondeness," only about 1/4 of the population is blonde because only 1/4 is homozygous for blonde alleles. In contrast, though the highlanders as an aggregate might be characterized by the same allelic frequencies as the lowerlands, say a 50-50 split between "blonde" and "brunette" alleles, the frequency of heterozygotes where the blonde allele is masked by a brunette allele is far lower, so the number of blondes is far higher because of the rise in homozygosity due to Random Genetic Drift.

I don't know if this story is true, I don't know if the highlanders are blonder or more inbred than the lowlanders. Rather, I simply wanted to offer it as an explication of the power of simple genetic logic.

Addendum: My source for the clarification is Genetics of Populations by Philip Hedrick. I have made a few minor changes because of the limitations of HTML.

Kimur and Ohta's diffusion aproximation for a continous-time model for the mean time until fixation of allele A2 (in this case "blondeness") with an initial frequency q:

(1) - T(q) = - [4N(1-q) ln(1-q)]/q

As you can see, time until fixation is a function of population size, N, and the initial frequency. Let us assume that All-Father Odin created 200,000 Norwegians in Valhalla. Their frequency of alleles was A1 = 0.5 and A2 = 0.5. He divided them into two groups, the "lowland population" (L) and the "highland population" (H) of equal numbers, 100,000 each. Then, he settled the L group on the coasts. These villages and towns and farmsteads were connected by coastal roads and long-boats. They were functionally one population, one deme. In contrast, the H population was diffused amongst 100 valleys in equal portions, so you have H1...H100, each with an effective population of 1,000.1

Loki, trickster than he is, decides to put up walls between the L deme and all the H demes, as well as partitions between the H demes themselves. In other words, no migration. Also, Loki get's everyone drunk so that everyone mates with whoever they bump into at the local dance in a random fashion, so, no selection. Frey, feeling bad for them due to his Vanir soft heart decrees that they shall all birth perfect children, so, no mutation.

For population L, equation 1 suggests that the "mean time to fixation" for either allele will be about 280,000 generations. This doesn't mean it will necessarily take 280,000 generations, and offers no clue as to which one will really fix, but if you were All-Father Odin and turned time back and allowed the Norns to work their dice 280,000 would be the average time of fixation among the repeated iterations.

For the various H populations equation 1 suggests that fixation is going to happen on average in each population in about 2,800 generations. This makes sense, the N was 1/100th the size of L for each of them.

The probability of fixation for each allele is their initial frequency. In this case both have an equal shot, but, the substructure implies something special: after a long enough period L might fix, but "H" will likely not fix for a particular allele (it is not really one population aside from the ecological commonality), rather, each of the various H demes will fix, and the expected ratio A1 homozygotic demes to A2 homozygotic demes ratio should be 1:1.

Update: On second thought, I want to reiterate that I present the above argument for illustration's purpose primarily. If I was serious I suppose I would look to some sort of island model, but my interest in highlighting the topic was mostly to spur readers to explore the simple but often counter-intuitive concepts and algebra of population genetics. A high degree of fluency with the material requires good working knowledge of differential equations and linear algebra, but the basics are pretty accessible if you have high school algebra.

1 - Gods have perfect sampling sight, even with one eye. There isn't any "founder effect" at work here.

Posted by razib at 06:27 PM