Tuesday, 8 October 2013

Loci and genetic groups: The Keyhole Problem


It may be to belabour a point, but some errors take on a life of their own, and are resistant to disproof. Presumably they meet some need, personal or social. We all have favourite arguments and treasured ideas. We tend to abandon such positions reluctantly. It takes an open mind to go with the evidence, particularly as it sways to and fro. The scientific ideal of enthusiastic open-mindedness to new ideas and then the dispassionate evaluation of those notions is hard for all of us to achieve. In my case I am reluctant to abandon any position which I have depicted in a complicated slide and lectured on more than three times. Call it the Powerpoint Theory of Perverse Persistence.

At present people still argue that there cannot be real genetic groups similar to traditional races, because there is more variance within races (85%) than there is between races (15%). This is an argument put forward by Lewontin in 1972 so the fact that is is being discussed shows it has stayed in popular consciousness for 41 years. I should like to believe that some of my arguments might remain interesting for 41 weeks but Lewontin’s is a meme which has survived with a vengeance.

Let us try to understand this statement by considering the traditional racial classifications of Black Pigmies and White European. If the statement about variation is to be taken seriously, it means that there is more variability within Black Pigmies then there is between Black Pigmies and White Europeans. This is an odd assertion. Both groups have things in common which make it easy to distinguish one from another. Skin colour, for one thing. This is why we refer to “white” Europeans and “black” Pigmies. So, is there more variation in skin pigmentation within whites than between Europeans and Pigmies? No. This simple point was raised by G. Cochran, and should have been enough to dispose of the matter. However, it is possible that followers of Lewontin might argue that skin is a special case, and they are referring to other human characteristics. This is a significant concession. Presumably it means that skin must be considered part of the 15% which varies between groups more than it varies within groups. Perhaps the 15% contains most of the socially significant traits such as personality and intelligence.

However, Cochran goes on to wonder whether Lewontin’s argument might apply to height, which is brought about by very many small genetic effects, rather than just a few genes as in the case of pigmentation. Not so. Pigmies are all short, and neighbouring Bantus are as tall as Europeans.  In a mixed population, part Bantu part Pigmy, height is determined by the proportion of Bantu ancestry. The Lewontin variance approach is found wanting.

In some exasperation Cochran writes: “So Lewontin’s argument does not work.  You can’t predict group differences in trait values from the distribution of genetic variation – except in the limiting case where all of the variation is within-group, which means that the two populations are genetically identical.  You know you can’t apply it to other traits, whether they are influenced by a few genes or by many.  It’s not essential to know _why_ it doesn’t work – the mere fact that its predictions don’t come true is reason enough to discard it.”

So, why don’t people discard the “more variation within races” argument? Why don’t all commentators discard it? Cochran continues:

“We do know why, though. Selection generates correlated genetic differences. Selection for increased height causes changes in the frequency of many alleles, in principle at all loci that influence height, although that is still a small subset of the genome.   What matter is the difference in that subset: the overall distribution of genetic variation tells you nothing.  Moreover, imagine that in the ancestral population, there were two alleles for each of those loci – a short allele with a frequency of 0.7 and a tall allele with a frequency of 0.3. Suppose that after selection for height, the frequency of each short allele was 0.3 and the frequency of the tall allele was 0.7.   This could significantly increase height. In that subset of the genome, about 85% of the variation between those two population is within-group  while 15% is between-group.”


In the words of the song, not the technical terminology of geneticists, it is a case of “You got the Right Key, but the wrong Key Hole”. By a process of selection the frequency distribution of Long Keys has changed, but the overall number of keys and locks has not changed. The change has come about because there are now more functional links between Long Keys and Key Holes, resulting in generations getting taller and taller.

Evidently, since the 85-15 variance argument persists, this explanation needs to be given several times in different forms. Imagine you are in charge of a jail, and hold the key to each cell. You are told that the inmates are of different races, or different religions, or have different view on the relative contributions of nature and nurture, or just vary considerably in height. Whatever the reason, they tend to assault each other during exercise periods. Your task is to let the inmates get exercise without rioting. Using one selection of keys you release only one set of prisoners. Perhaps it is the short prisoners. They exercise, in their short way. Once they are back in their cells you release the tall ones, and they exercise in their lofty way. Neither the number of keys nor the number of locks has altered, but anyone closely observing the exercise yard would notice a significant difference in the two sets of prisoners. It is the subset of activated key/lock combinations which has caused the changes in the prison population.

Can you please find someone who still believes the Lewontin argument, and try my version out on them?  I may need to find yet further ways to explain it.

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