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Tuesday, August 09, 2011

Demography and fast evolution

In an earlier post I discussed the population history uncovered by Gregory Clark in his book A Farewell to Alms. By examining British wills, he showed that the rich literally replaced (outreproduced) the poor over a period of several centuries.

The excerpt below is from a review of Greg Clark's book. The review is mostly negative about Clark's big picture conclusions, but does provide some interesting historical information. Note, the reviewer does not seem to understand population genetics (see discussion further below).

The comparison of Beijing nobility and Liaoning peasants is drawn from Lee and Wang’s (1999) survey of Chinese demography, which, in turn, is based on a very detailed investigation of population in Liaoning by Lee and Campbell (1997). In Liaoning, all men had military obligations and were enumerated in the so-called banner roles, which described their families in detail. Individuals’ occupations were also noted, so that fertility can be compared across occupational groups. High status, high income occupations had the most surviving sons: for instance, soldiers aged 46–50 had on average 2.57 surviving sons, artisans had 2.42 sons, and officials had 2.17 sons. In contrast, men aged 46–50 who were commoners had only 1.55 sons on average.

The references cited are

Lee, James Z., and Cameron D. Campbell. 1997. Fate and Fortune in Rural China: Social Organization and Population Behavior in Liaoning 1774–1873. Cambridge and New York: Cambridge University Press.

Lee, James Z., and Feng Wang. 1999. One Quarter of Humanity: Malthusian Mythology and Chinese Realities, 1700–2000. Cambridge and London: Harvard University Press.

So we have at least two documented cases of the descendants of the rich replacing the poor over an extended period of time. My guess is that this kind of population dynamics was quite common in the past. (Today we see the opposite pattern!) Could this type of natural selection lead to changes in quantitative, heritable traits over a relatively short period of time?

Consider the following simple model, where X is a heritable trait such as intelligence or conscientiousness or even height. Suppose that X has narrow sense heritability of one half. Divide the population into 3 groups:

Group 1 bottom 1/6 in X; < 1 SD below average
Group 2 middle 2/3 in X; between -1 and +1 SD
Group 3 highest 1/6 in X; > 1 SD above average

Suppose that Group 3 has a reproductive rate which is 10% higher than Group 2, whereas Group 1 reproduces at a 10% lower rate than Group 2. A relatively weak correlation between X and material wealth could produce this effect, given the demographic data above (the rich outreproduced the poor almost 2 to 1!). Now we can calculate the change in population mean for X over a single generation. In units of SDs, the mean changes by roughly 1/6 ( .1 + .1) 1/2 or about .02 SD. (I assumed assortative mating by group.) Thus it would take roughly 50 generations, or 1k years, under such conditions for the population to experience a 1 SD shift in X.

If you weaken the correlation between X and reproduction rate, or relax the assortative mating assumption, you get a longer timescale. But it's certainly plausible that 10,000 years is more than enough for this kind of evolution. For example, we might expect that the advent of agriculture over such timescales changed humans significantly from their previous hunter gatherer ancestors.

This model is overly simple, and the assumptions are speculative. Nevertheless, it addresses some deep questions about human evolution: How fast did it happen? How different are we from humans who lived a few or ten thousand years ago? Did different populations experience different selection pressures? Amazingly, we may be able to answer some of these questions in the near future.

Thanks to Henry Harpending for reminding me about the Chinese data and about the question of fastest plausible evolution for a quantitative trait.

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