# When little differences matter a great deal

Gene Expression
Apr 1, 2012 8:37 AMNov 20, 2019 4:52 AM

In the comment below Clark alludes to the fact that Jonathan Haidt kept reiterating that even if there were differences between populations due to recent evolution, if it was due to selection on standing variation upon quantitative traits then the between group variation would be dwarfed by within group variation. He didn't quite say it like that, but I'm sure that's what he meant. For example, there is now evidence that alleles which can explain the small height difference between Northern and Southern Europeans have been subject to natural selection. Most of the variation obviously remains within the groups; you can't guess that someone is Italian or Dutch just based on their height. There are many tall Italians, and many short Dutch. But on average there are differences between the groups which can be attributed to genes, and those genes seem to have been targets of selection. This is good as fair as it goes...but small average differences may not necessarily be marginal. That is because sometimes you select from the tails of a distribution. For example, if you want to ascertain which population will produce more N.B.A. players, it is less important that there is a small average differences, so the populations mostly overlap, than that that average difference can result in a large disproportion at the tails of the distributions. In the context of Jonathan Haidt's argument, let's talk about altriusm. Imagine that there is an altruism scale from 0 to 200, with a mean about 100. The standard deviation is 25, which implies that only ~2 percent of the population will be more than 150 in altruism, or less 50 in altruism (good in the latter case). Now let's call this population A. Imagine a population B, which differs only in that the mean altruism is 10 instead of 0. This is not that large of a difference, less than half a standard deviation. But what's the difference at 2 standard deviations? Below is a plot of the two putative populations, with a line at the 2 standard deviation mark for population A:

As you can see population A and B overlap a great deal. But at 150 altruism 2.2 percent of population A is above that threshold, while 5.5 percent of population B is above it. A factor of 2 difference. At three standard deviations the difference becomes a factor of 3.5. Why does this matter? Because there are some models of social change which are predicated upon small exceptional minorities. Haidt seems to be minimizing inter-group differences by emphasizing their small aggregate difference. But for many traits the exceptional few matter much more than the banal and pedestrian many. Small differences in distribution might be the difference between the existence or non-existence of these marginal slivers of the distribution. So, for example, many would suggest that Mother Theresa was a representative of extreme sot of altruism (yes, I am aware of Christopher Hitchens' book on this subject, I am referring here to the public perception). She was an ethnic Albanian. One might explain the fact that she was Albanian by supposing that this population is ever so slightly more altruistic than the norm! Where, after all, are the Mother Theresa's of the Kalahari Bushmen?* * For the literal minded (e.g., Onur) I am joking here.

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