Saturday, September 22, 2007

Heterosis and the Flynn Effect   posted by DavidB @ 9/22/2007 06:21:00 AM

I posted recently on the Flynn Effect, and some interesting papers on the subject came to my attention afterwards.

First, there is a review of Flynn's recent book by Richard Lynn in Intelligence, 2007, (35), 515-16. Lynn defends his own nutritional explanation of the Flynn Effect against various criticisms. He points out that it is one of the few theories that can explain an increase in IQ among young children.

A more substantial piece was mentioned in comments on my post. For several years M. Mingroni has been arguing that heterosis ('hybrid vigor') has played a major part in the Flynn Effect. This makes him unusual in proposing a mainly genetic, rather than environmental, explanation. His latest paper is in Psychological Review, 2007, 114(3), 806-29. An abstract is available here.

The first part of the paper criticises existing explanations such as nutrition, schooling, etc. Mingroni makes some good points, but I think that he and some others make the mistake of assuming that there has to be a single, or at least a main, explanation of the Flynn Effect. If the Flynn Effect were substantially uniform across all tests, all age groups, all countries, etc, this would be a reasonable assumption, but it isn't that uniform. There is no more reason to expect to find a single explanation of rising IQ scores than of rising life expectancy. The Flynn Effect might be due to a bit of nutrition, a bit of schooling, a bit of heterosis, a bit of audiovisual stimulation, and other factors, in various proportions in different times, places, and age groups. I'm all in favour of simple explanations where they work, but we should not always expect them to.

[Added on 24 September: Of course, all the various suggested factors - nutrition, schooling, heterosis, etc - are ultimately due to economic growth, but it would not be helpful to identify 'economic growth' as the 'cause' of the Flynn Effect, any more than of increasing life expectancy. We want something more specific. ]

The second part of Mingroni's paper is more constructive, and sets out a model for examining the effects of heterosis. I discuss it further below the fold, but I should stress now that Mingroni does not prove (or even claim to prove) that heterosis accounts for a large part of the Flynn Effect. Using plausible parameters his model only accounts for an increase of 2 to 5 points in mean IQ, which is less than a quarter of the cumulative Flynn Effect.

The possibility of heterosis increasing IQ scores is not controversial. Close inbreeding (e.g. cousin marriage) usually reduces the IQ of the offspring. This suggests that some genes for low IQ are recessive. Conversely, genes for higher IQ are probably often dominant. If so, then for any given set of underlying gene frequencies in the population, the mean IQ will be higher when the proportion of heterozygotes is higher. Random mating will therefore produce higher mean IQ than inbreeding, which for this purpose includes not only inbreeding in the traditional sense, but also breeding confined within subpopulations. If gene frequencies within such subpopulations vary, then the proportion of homozygotes will on average be higher than if the subpopulations were merged together in a random-mating total population.

If subpopulations are geographically or otherwise isolated from each other, they will evolve differing gene frequencies as a result of genetic drift or differential selective pressures. Over the last few centuries the population structure in many countries has changed in such a way as to break down such isolation. Small communities have been absorbed into larger towns, much of the rural population has migrated into cities, and improved transport has mixed up populations within the same countries and even internationally.

It is therefore reasonable to hypothesise that heterosis has made some contribution to the Flynn Effect. The question is how much. Mingroni's paper develops a model to explore this question. I can only give a rough outline here. It is assumed that a large number of loci affect IQ, with two alleles at each locus. The population is assumed to be initially subdivided and then merged into a single random-mating population. The variable quantities are the number of loci, the degree of dominance, the frequency of each allele in the total population, and the amount of increase in heterozygosity assumed to take place as a result of changing population structure. Values are assigned to genotypes in accordance with the degree of dominance, and gene frequencies for each allele are assigned stochastically to each locus within the subpopulations. The initial mean and standard deviation of IQ in the population resulting from the model is calculated and scaled to have a mean of 100 and s.d. of 15. The effect of the postulated change in heterozygosity on the mean and s.d. of IQ is then derived for a range of values for the key variables.

The choice of values is determined in part by plausibility and in part by empirical data. It is assumed that the number of relevant loci is either 50, 75 or 100. The dominant homozygote has the value 1, the recessive homozygote has the value 0, and the heterozygote has the value .6, .8 or 1 according to the degree of dominance. The population frequency of the recessive allele at each locus is either .4, .5, or .6. The increase in heterozygosity resulting from merging the subpopulations is either .02, .03, or .04; that is, between 2 and 4 percent. (These figures are based largely on Cavalli-Sforza's classic studies on isolated Italian villages in the late 1950s.)

With these assumptions Mingroni obtains increases in mean IQ ranging between 1.2 and 5.1 IQ points, with most results falling between 2 and 4 points. These changes are much smaller than the observed cumulative Flynn Effect, but Mingroni argues that the total change in heterozygosity at a national level might be much larger than those suggested by the Italian data. Opinions will differ on the plausibility of this. Personally, I would be sceptical. Cavalli-Sforza chose his Italian villages to represent a relatively isolated pattern of settlement and marriage, in order to give genetic drift a chance to show itself. I doubt that the traditional degree of isolation would be as large as this in many parts of Europe. (The degree of inbreeding might be higher in some non-European societies, especially where cousin-marriage is common.)

It is possible to calculate the initial difference in allele frequencies needed to produce a given increase in heterozygosity when the subpopulations are merged. For two equal subpopulations, and two alleles at a locus, the increase in heterozygosity produced by merging the subpopulations, as a percentage of the population, is (D^2)/2, where D is the difference in allele frequencies between the subpopulations. [Note] To produce an increase greater than Mingroni's upper figure of 4 percent the differences between subpopulations have to be quite large, e.g. a difference of around 30 percent in allele frequencies. This is larger than the usual differences between European nations, let alone different parts of the same nation. If there are more than two alleles the differences in allele frequencies have to be even larger. For example, if the subpopulations have 3 alleles at a locus, with frequencies of .2, .4, .4 in one subpopulation, and .1, .6, and .3 in the other (an aggregate difference of 40 percent), the effect of merging the subpopulations would only be to increase heterozygosity at the locus from .59 to .605. (If there are more than two subpopulations, a multi-allele system would have more scope, as each allele might be concentrated in a different subpopulation, but the differences in frequency between subpopulations would still have to be large to make much impact.)

In Mingroni's simulations an increase of 1 percent in heterozygosity produces an increase of about 1.1 points in the mean IQ of the population. The increase seems to be linear, as it should be, since each substitution of heterozygotes for homozygotes adds a fixed amount to the total IQ 'score' of the population. A cumulative IQ increase of around 20 points therefore requires an increase in heterozygosity equivalent to around 18 percent of the population. This requires a huge initial difference in allele frequencies - around 60 percent - larger than the usual difference between continents.

I also see a problem with the timing of the changes. In the first countries to industrialise, much of the breakdown in traditional population structure occurred in the 18th and 19th centuries. To take the most obvious example, in Britain some 90% of the population already lived in large towns and cities by the end of the 19th century. The scope for further increases in heterozygosity during the 20th century (excluding interracial mating) must have been quite small. Yet the Flynn Effect has been much the same in Britain as elsewhere.

Then there are those populations founded by immigrants. The best example is perhaps Australia. From the beginning of white settlement around 1800, the population of Australia was drawn from all over the British Isles (and contrary to myth, only a small proportion were convicts). If Mingroni is right in believing that heterosis can account for the bulk of the Flynn Effect, we would expect Australia to have had a spectacular one-off increase in IQ compared with the parent population. I mean no disrespect to Australia if I say that this has not been observed. Much the same argument can be applied to New Zealand and Anglophone Canada. The United States is a more complex case, as settlement extended over a longer period, and involved a variety of European groups who settled to some extent in different areas (Germans in Pennsylvania, Scandinavians in Minnesota, etc.) There could be parts of the United States where populations were quite inbred and the scope for heterosis was correspondingly large. But there must also have been areas (e.g. California and other west coast states) where the white population was well-mixed from the beginning of settlement. This would leave little scope for further IQ gains from heterosis. These are fairly obvious difficulties, but I cannot see that Mingroni addresses them

Note: Suppose the frequency of one allele in the total population is M. The frequency of the other allele is therefore (1 - M). Under random mating in the total population the proportion of heterozygotes will be 1 - M^2 - (1 - M)^2 = 2(M - M^2). Now suppose the population is divided into two equal subpopulations, A and B. If the frequency of one allele in A is (M - d), the frequency of the other allele must be (1 - M + d), while the corresponding frequencies in B are (M + d) and (1 - M - d). Under random mating within each subpopulation the average proportion of heterozygotes will be [1 - (M - d)^2 - (1 - M + d)^2 + 1 - (M + d)^2 - (1 - M -d)^2]/2 = 2(M - M^2 - d^2). This is 2d^2 less than under random mating in the total population. The amount 'd' is here the difference between the frequencies of each allele in the subpopulations and the mean for the total population. The difference in frequency of the same allele between the two subpopulations is 2d. If we set D = 2d, then 2d^2 = (D^2)/2. So it is easy to calculate the increase of heterozygosity (measured as a proportion of the population) resulting from the merger of the subpopulations for a given difference in allele frequencies, and the associated increase of IQ e.g.:

D...........(D^2)/2..........IQ points gain

These figures are independent of the value of M, but there are constraints on the possible values of D. E.g. if M is .8, D cannot be greater than .4, since M + D/2 cannot be greater than 1. There are of course many simplifying assumptions, so the figures should not be taken too seriously.