Intelligence and assortive mating

Arnold Kling writes:

The story I tell for bimodalism is mating behavior. When high earners marry high earners, class divisions will emerge. But this has implications for the IQ distribution. One would expect bimodalism to appear in the IQ distribution, with the children of high-IQ parents tending centered around one mode and the children of low-IQ parents centered around another.

Kling’s expectation depends on our assumptions about the nature of the assortive mating.

Take an extreme example, where mating is perfectly assortive and everyone mates with someone of the same income and intelligence as themselves. If intelligence is perfectly heritable, their children’s intelligence will be the same. Intelligence in the next generation will only vary to the extent that people of different levels of intelligence have different levels of fertility. If there is no difference in fertility, the distribution of intelligence will be the same one generation to the next.

So how could we generate a bimodal distribution? One way would be if there is some threshold level of intelligence that acted as a barrier to mating. If, for example, those of below average intelligence only mated with people of below-average intelligence (although not necessarily the same intelligence as themselves), while those with above-average intelligence only mate with others in their group, the two populations’ intelligence will cluster around different means.

For this threshold to exist, there must be some non-linear returns to intelligence. There might be competition to live in certain suburbs or attend certain schools. Those that scrape into the high intelligence college get access to much larger rewards and access to significantly more intelligent mates than those that narrowly miss out.

As for what is actually occurring, I do not expect that the existing mating patterns in developed countries such as the United States will result in a bimodal distribution of intelligence. The focus on assortive mating masks the huge level of mixing that currently occurs. Consider the assortive mating that occurred as humans spread themselves across the globe and mated within their small bands. Populations were separated for millennia. Even in recent centuries, people largely mated within their small communities and class. Today’s population has a level of dynamism and mixture far beyond most of human history, regardless of what class divisions there now are.

13 comments

  1. I don’t know if you or Arnold realize this, because I only just recently learned myself, but the mother almost entirely decides her children’s IQ, in the same sense, but to a lesser degree, that the father decides what sex the child is.

    http://www.psychologytoday.com/articles/201109/the-incredible-expanding-adventures-the-x-chromosome

    What does this do for assortative mating? Maybe not much. But it does explain another phenomenon: asymmetric IQ variances across the sexes. Women have two X chromosomes which vie for expression. On the other hand, men only get one X chromosome, so whatever intelligence is (or isn’t) there is expressed at full strength, hence the higher variance in IQ among men.

    I’m not quite sure this changes the bimodalism story at all, but it’s an interesting tidbit, so I’ll leave it here. 😀

  2. Ah, I see one error. I should have said that this is only true for male children.

    Although, it would be nice to never claimed the article said what I said. It’s called paraphrasing, and this time I did it poorly. Communication takes two, and I acknowledged my error. No one likes a pedant.

    1. Thanks for the link to Badcock’s article – I’ve had this issue raised before in the comments, but was unsure where the argument was coming from, so that has helped.

      Badcock oversells his argument. The genes discovered thus far that are associated with intelligence and located on the X-chromosome account for a tiny fraction of the heritable variation in intelligence – as is the case for all of the genes that have ever been argued to be relevant to intelligence (hence the missing heritability debate). The empirics of father-child intelligence correlation don’t back Badcock’s argument up. Fathers have considerable influence on the intelligence of their children, which suggests that many of the relevant genes are located throughout the autosomal (non-sex linked) chromosomes.

      1. Thanks for the note on the broader literature. I hadn’t looked into it much, myself. I just had a passing interest since it sounded pretty neat, and did explain the variability difference quite neatly.

  3. Jason, let’s work through this more carefully.

    Suppose we have perfectly assortive mating. This could result in one population with a mean IQ of 110 and another population with a mean IQ of 90. A bimodal distribution.

    If behavior stays constant over generations, then the distribution will not change. Granted. But it still will be bimodal.

    Now, suppose that we start with a situation of non-assortive mating in the generation that marries before 1970. Then the mean is 100 and the distribution is unimodal. But starting in 1970, mating becomes increasingly assortive, until 1990 when it becomes perfectly assortive. By now, we see a young generation where the distribution is bimodal.

    1. If people with 90 IQ mate with 90 IQ people, 91 IQ with 91 IQ, etc, you could call the population bimodal by splitting it, but it is not bimodal due to the assortive mating. The distribution would have been the same in the generation before the assortive matings.

      Your 1970 to 1990 example is interesting. The question is then “what is the nature of the imperfectly assortive mating between 1970 and 1990?” A threshold type effect? Assortive mating between classes but random mating within?

      1. I wasn’t sure about this at first. The distributions and effects were a bit foggy, so I thought to write a simulation. I sat down to tackle the problem with some heroic assumptions:

        1) Perfect assortment
        2) IQ is 100% heritable and deterministic

        I got this:

        Male IQFemale IQChild IQ
        909090
        919191
        929292
        ………
        109109109
        110110110
        111111111

        Is this what you were saying, Jason? The child population matches the parent population with perfect assortment?

      2. Basically, that’s right. To get any interesting distributional effects you need to relax those heroic assumptions – which was the initial point of my post. The question is in what way do you relax them? My suggestion was assortment across two classes (above and below average intelligence) but no assortment within.

        The trigger for the post was my experience last year when I was drafting a working paper about the Galor-Moav growth model and considered experimenting with a degree of female choice. I quickly realised that if the quality-preferring only mate with quality-preferring (perfect assortment), their children are the same as in the asexual model. The assortive mating is irrelevant to the distribution of traits in the population. I would have needed something less than perfect assortment or heritability to get an interesting result.

  4. One comment said “Ironically then, mothers with children of “genius” sperm-bank fathers were probably laboring under something of a delusion. Any intellectual talent in their children was most likely predominantly attributable to them”

    This ignores several points. Firstly, if the father passes on his X-chromosome to a duaghter, then she will get some benefit (although perhaps not as much as a son) and also carry that “excellent X” into the future gene pool, perhaps to be expressed fully in one of her own sons. Still a good reason to have genuis sperm banks, just the results might not immediately show.

    Secondly, there are of course genes on other chromosomes – I understand that chromosome 2 is believed to be another important location of these genes.

    So don’t throw away the genius sperm just yet – it’d make an awful mess, for one thing.

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