Lactase Persistence and Understanding History

I threw together some simulations a while ago for a lecture on selection. As usual they led to thinking about some of the implications of selection that I knew but that I had never really internalized.

Here, for example is a simulation of 100 histories, i.e. parallel worlds, in which a single mutation causing lactase persistence appears in an adequately mixed population of 50,000 reproducing adults who are dairying people. The mutation is dominant, so both carriers and homozygotes enjoy a 5% fitness advantage due to the ability to digest lactose and hence obtain 40% more calories from the same diet as people without the mutation: see here for the details. We don’t imagine this advantage to be important every year, but in times of stress lactase persistents (LPs) would have been more likely to survive and, perhaps, avoid slaughtering their herds to eat them.

Evolution of Advantageous Mutant in 100 Worlds

In twelve (the expected number is ten) of the one hundred worlds the mutant persisted long enough that deterministic forces took over and it increased in frequency just as theory predicts. In the other 88 worlds the mutation may have hung around a while at low frequency but was eventually lost to drift. Since the time until determinism takes over is random, even where the mutant eventually won the time is highly variable. In the green world it took about four thousand years to reach a frequency of one half while in the tardy red and dark blue worlds it took about six thousand years.

This may provide some quantitative understanding of history. A figure tossed about for the age of the west Eurasian mutation is eight thousand years. With a five percent advantage it only reaches a frequency of seventy to eighty percent in that time while the frequency in northern Europe today approaches fixation. The advantage must have been greater than five percent.

On the other hand there are grounds for sorry pessimism here. I have the naive human idea that history makes sense while this exercise shows that it is worse than a crapshoot. An extremely rare random accident, the mutation, caused one of the greatest population blooms we know about, if our theory of the Indo-European tie in with LP is correct.

When we teach population genetics we study gene frequency change, usually with the assumption that population size is held constant. In this case we can’t defend such an assumption since the 5% advantage of LP is huge. In this Malthusian dairying environment the advantage would lead immediately to explosive population growth, which is almost certainly what did happen.

This figure is from the same simulation program as the figure above but the outcome is slightly different (randomness). Only five of the one hundred mutations persisted and the simulation only goes to five thousand rather than ten thousand years (drawing a million binomial samples of size two slows my poor desktop to a crawl so I stop things early).

LP causes population growth

In the five rare cases where the new mutant persists it leads to population growth, but how much? In one history, the right red one, the population has risen to about seventy thousand people, while at the other extreme it has risen to nearly eight hundred thousand people because it happened to become common faster. With the more realistic advantage of ten percent these number would be much higher. The full figure is not shown because my poor desktop begged me to give it a rest.

Are these simulated population numbers implausible? I think not, recalling that the Indo-European expansion is like the explosion of a huge inkball in western Eurasia from the perspective of history. Toward the end of the five thousand year interval people at the center must have been moving away as fast as they could to avoid being trampled.

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24 Responses to Lactase Persistence and Understanding History

  1. Doug1 says:

    Great stuff.

  2. j says:

    Nice stuff and thanks for sharing with aficionados like me.

    I think the model would resemble real life more if you add a recurring “Ethiopian famine” event. During this famine event, say seven year drought and failure of agriculture and disappearance of wild animals, people (specially children) die in mass. Among the say 20% of the children who survive the drought a large percentage will be from milk-drinking families. Such events which in Ethiopia seem to occur every generation, will accelerate the process.

    • harpend says:

      In most human populations with decent data mortality gradually declines with age to a minimum just before adolescence. In West Africa a different pattern appears in which there is a big mortality spike around the time of weaning. If early folks on the Eurasian plains suffered a similar pattern then LP could have been advantageous even in “regular” years.

  3. TWS says:

    Good explanation of the situation. I can see why Europe became the preserve of dairy farming folk but how come it did not spread the other way? Instead of LT Caucasians pushing east we have intolerant Asian types pushing west. They butt up against the Asian populations at about the border of China then just fade out of history. Did they just run into an area that was not conducive to dairy farming environmentally or what?

    • dave chamberlin says:

      good question. my best guess is the asian populations had pathogen fitness advantages that stopped the European LT fitness expansion. certainly that is the case in sub saharan africa.

    • j says:

      You just touched the tabuest tabu of all, TWS. There is a sewsaw movement of peoples in the midle of the vas Eurasian plain, one Asians occupying half Europe, once Europeans pushing into West China. Which race will win? The Chinese seem to have done quite well without any lactase persistance gen.

      • billswift says:

        The Chinese have the advantage of a much more benign climate than most of Europe. That makes a difference, too.

      • Matt says:

        In China proper, benign as in more optimal for more nutritionally productive pure agriculture without a mixed pastoral component (both legume crops that substitutes for both nitrogen fixation and protein provision from large mammals and a higher agricultural yield potential from greater seasonal heat and moisture), yes.

        Generically more benign for anything other than agricultural food production, no. For one, the extremes of heat and cold are much higher while mean temperature is only slightly higher.

  4. bill says:

    Well doesn’t this assume that there is just one advantageous mutation? What happens when there are multiples, so that if one dies out there are others waiting to show up?

  5. dave chamberlin says:

    If I remember correctly a large fitness advantage grows slowly in a population to 20% and then moves rapidly to 80% and then slows down again, your graph bears this out.

  6. dearieme says:

    What happens if you bring in a positive feedback of the milk-drinkers breeding cattle with higher milk yields? Say you wrote a model with three differential equations, one for cattle numbers, one for human numbers and one for yields. Allow the yields to increase proportional to human numbers (more herders to experiment with breeding) and cattle numbers (more cattle to experiment on).

    • harpend says:

      Yes, you are certainly on our wavelength. Please have at it. BTW if you or anyone wants the code that generated these simulations please let me know. It is written in the language python with the inclusion of two modules, scipy and pylab. Every linux distribution includes these and they can be had for Macs with with no effort. Windows I have no idea about, and please excuse the grammar.

  7. Greying Wanderer says:

    “I think the model would resemble real life more if you add a recurring “Ethiopian famine” event”


    Just for example an estimated neolithic population timeline


    so you can get some pretty major population crashs. If the LP percentage survived better then there’d be a founder effect as the population regrew and possibly a cultural effect also?

    “Did they just run into an area that was not conducive to dairy farming environmentally or what?”

    The terrain *most* suited to (cows) milk production is very wet and flat pasture land – steep slopes suit sheep better and less wet flatland suits crops better. In Europe the most suitable regions are the Atlantic coast and some of the inland mountainous bits like the alps and dinaric alps.

    The rain pattern fits the distribution of LP quite well.

    The other side to this is a very wet climate might not be as good for crops so in specifc regions the total advantage might be a lot bigger i.e. say an acre of land near neolithic Paris could produce 2x calories in crops or x calories in milk but on the Atlantic coast it was the other way round where an acre could produce x calories in crops or 2x calories in milk.

    • j says:

      Wanderer, dont forget that dairy farming was not developed in Europe, but in what now is Turkey.

      • Greying Wanderer says:

        Sure but dairying isn’t the point as you don’t need to be LP to eat cheese etc. It’s being able to drink milk on its own that makes the big difference imo.

  8. Greying Wanderer says:

    Another point is, if you have a population with say 5% LP (or whatever the average outside Europe is) then you’re not going to have many whole families who are all that way and if the whole family isn’t LP then the culture is unlikely to shift to prioritize milk production.

    Now assume some kind of starvation event where the LP people survived better so the regrowing population had a high enough percentage of LP such that there were now some families who were all LP. In that case it might pay to switch some of the family’s land to extra milk production. But what if you were in Greece and most of your flat land wasn’t suitable for pasture or could produce more calories as crop land? On the other hand if the same thing happened along the Atlantic coast where there was a lot of land that was good for pasture and not that good for crops then it would make sense for the family to switch some of their crop production to raising more cattle and producing more milk as milk is basically free food if you can drink it.

    So maybe you need a combination of two things: some event(s) that produces a potential takeoff percentage of LP such that you start to get all LP families *and* land / climate that allows the switch to producing more milk.

  9. Sean says:

    “{I]f our theory of the Indo-European tie in with LP is correct […] In this Malthusian dairying environment the advantage would lead immediately to explosive population growth, which is almost certainly what did happen.”

    But wouldn’t that mean that the Indo-European would have supplanted the original inhabitants. ‘Elite dominance’ of by Indo-Europeans of the aboriginal Europeans which in my reading of 10,000 YE, is what you suggested in the book, does not seem to square with a Indo-European population explosion.

    • harpend says:

      I hope that we didn’t push the elite dominance theory of the IE expansion. From the scraps of ancient DNA data that we have near-replacement is looking better and better. Elite dominance does describe the invasion of Britain in 1066 but the IE expansion looks not to be that.

      • Sean says:

        If that is true all I can say is – the women the wolf packs of young IE warriors found in Europe must have been truly hideous. Considering that you’re proposing extremely derived west European Neanderthals interbred with humans, it seems a little far fetched that the IE didn’t exercise their prerogatives. And as the mutation is dominant …

        • saintonge235 says:

          You raise this point a lot. It’s wrong.

          If the Indo-Europeans had genetic advantages that allowed them to achieve a higher population density, then they tend to push out the existing population without ‘Kill all the men and rape all the women.’ The indigenes aren’t replaced by conquest, they’re just outcompeted.

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  11. Greying Wanderer says:

    If the LP part of the population grew taller – from gaining more calories from the same quantity of food – and there was sexual selection in the culture then the fitness advantage may have had two components.

    Also the height which may have been an advantage in regions particularly suited to cattle-raising may have become a disadvantage in regions less suited to cattle and more suited to grains.

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