January 27, 2013

Regression toward the mean and IQ

A reader sends me an Excel file for calculating expected IQs of children based on their parents' IQs. 

As I've been pointing out for a long time, these questions are of particular interest to the infertile and to lesbians. (I coined the term "lesbian eugenics" to summarize the issues that lesbian would-be mothers confront in picking a sperm donor, but it hasn't caught on. After all, as we all know, lesbians are Good and eugenics is Bad, so ... Does Not Compute!)
I am an avid reader of your site for ~10 years (not even sure since when) and wanted to email you about a Steve Sailer / Steve Hsu inspired analysis I did over the weekend ... The topics are intelligence, heredity and mating (I am 32 year old single male considering the best course of action).

The best course of action is probably to find somebody you like talking to because you are going to be doing that for a long time. But, all this stuff is definitely interesting.
This is is based on a presentation by Steve Hsu entitled "Investigating the genetic basis for intelligence".

On slide 19 of the presentation, with the header "Your kids and regression" Steve writes "Assuming a parental midpoint of n standard deviations above the population average the kids' IQ will be normally distributed about a mean which is around +0.6n with residual standard deviation of about 12 points." He also gives a helpful example immediately below "So, e.g., for n=4 (parental midpoint of 160 - very smart parents!), the mean for the kids would be 136 with only a few percent chance of any kid to surpass 160 (requires +2 standard deviation fluctuation)."

I've seen estimates of the "narrow sense heritability" of IQ ranging from 0.34 to 0.86. At the lowest figure, the two 160 IQ parents' children would average 120 and at the highest, 152. But, as my reader points out, for most values in the middle of that range, the implications he draws are still more or less true.

Another thing to keep in mind is that this assumes that the IQs of grandparents and earlier ancestors are unknown. In contrast, the Darwin-Wedgwood-Galton-Keynes-Benn-Vaughan Williams extended family seems to regress toward a higher IQ than 100, as do the Huxley-Arnolds.

Here are some implications the reader draws, assuming a 0.6 figure.
1) Mating insight

Many nerdy or high achieving men bent on reproducing are troubled by the fact that most intelligent women want a career and likely do not want to have children (or want to adopt orphan baby at age 50, once they have “made it”). Women who are slightly less intelligent may want to have families and even to have bigger families. The above Excel file lets one see the impact of say a man with an IQ of 140 marrying a woman with an IQ of 140 and having only one child (whose expected IQ would be 124) vs. that same man marrying a woman with an IQ of 120 and having three children. The second man's highest IQ child will have an expected mean IQ of 128 which is higher than the man who married the smarter woman but had only one child. Even if the smarter woman chooses to have two children the two smartest children out of the three children that the less intelligent woman had will have approximately the same expected IQ as the two children of the high IQ woman.

Takeaway - twenty IQ points is a lot: 120 vs. 140 is a big difference and it will be by definition much harder to find a woman with an IQ of 140+ (one in 261) vs. one with an IQ of 120+ (one in 11) and it will be much more difficult to persuade your wife to give up IQ 140-career track (Fortune 500 CEO, Ivey League tenured professorship etc.) than IQ 120-career track (nurse, high school teacher etc.) for changing diapers in the middle of the night. If one is concerned about having one or two competent kids to whom one can leave the family business to one might consider finding a slightly less intelligent woman who is willing to have a few kids. Of course there are other factors. Having more children means giving each child less attention but spacing births helps mitigate this and we know that nature dominates over nurture in this matter anyhow. Not to mention that having only one child can result in tragedy if god forbid something was to happen to it.

2) The speed of the regression to the mean.

If one starts with two parents whose IQs are 160 and looks at the average IQs across generations the speed of the regression to the mean is quite fast.

Parents 160, 160
Children average 136 (assume these mate with a 136)
Grandchildren average 122 (assume these mate with a 122)
Greatgrandchildren average 113 (assume these mate with a 113)

There is already a huge drop between the grandparents and the grandchildren. So in just 4 generations the regression to the mean has brought down the Nobel-prize-level grandparents to the pretty much average intelligence. (all this is of course "on average")

This might be a reason why the intellectual elite might want to pay more attention to making America a country where those with IQs of 110-115 can still live satisfying lives with good middle class jobs and publicly funded services. Chances are that most of their descendants will need those jobs and services only century from now; after all “fool and his money are soon parted” – even if dimmer kids inherit billions chances are that they will not have what it takes to keep the wealth in the long run.  

3) "Geniuses belong to the people"

Imagine that with two parents with IQs of 160 set out to produce one child with the same IQ. How many kids we can expect them to have before they succeed? They would have to have 44 kids to have one kid whose IQ would be 160 or higher on average! This is clearly impossible. And if they set standard to IQ 170 - they would require 434 kids!!! Thus geniuses are really borne out of a people and not out of any two particular parents. Having smart parents helps, a lot, but even then, the chances that your little one is going to be the next Newton are small. Very, very small. On the other hand, according to historians none of Newton’s paternal kinsfolk were able to even sign their names. 
4) "The advantage of the rich - buying IQ points through marriage?"

Say you have a family scion with an IQ of 160 who marries a woman with an IQ of 132 (so top 2%). And then their kid perhaps regresses but he leverages family fortune and name to marry a woman with an IQ of 132 and so on and so on. (Sure he might not be the smartest but he's rich so why not marry him). Assume other generations repeat the same trick. What happens?

In just three generations the IQ falls to 114 and stays there. The 132 woman helps keep it at 114 vs. falling back down but it doesn't go up.

Thus another conclusion, being multi-generational rich helps, you can buy intelligence and ensure that your kids are one standard deviation higher than the average. That is a lot, but it also allows for a lot of overlap between the populations. (Especially because never dipping under the IQ 132 threshold is an optimistic assumption - it assumes multi-generational saintly resistance to blonde bimbo's charms). Thus, richer kids are on average smarter but plenty of them are dumber than the average Joe. 

213 comments:

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Anonymous said...

@ James B. Shearer

All right. This sounds like a Bayesian problem with assumed distributions. I have not looked at this stuff for a while. I will try to build a simple model and get some approximate probabilities.

Neil Templeton

Anonymous said...

Sure, it could. And the average intelligence of gypsies 250 years ago could have been very high. But there's no actual evidence to support either hypothesis.

Nor do you have any evidence that average Jewish intelligence was low 250 years ago. It is implausible to me that the whole set of mutations responsible for the increase in Jewish intelligence arose within that timeframe.

Anonymous said...

"But unless you're from Africa and barring cases of incest in your family, you certainly do have 1024 ancestors from ten generations ago."

Most of the world practises or recently practised cousin marriage as a preference so it's not just Africa.

The norm changed in Europe but in very small rural communities - which is where 90% of Europeans were 10 generations ago - even if you're trying to marry as exogamously as possible you're still all going to end up cousins - just not as close cousins as you would otherwise.

The icelanders have a giant book to keep track of who's related to who for this very reason.

So i don't think it's likely that europeans from even the most assiduous non cousin marrying regions have 1024 *distinct* ancestors.

They may have far *more* distinct ancestors than people with other histories and that may have interesting consequences but i don't believe 1024 distinct ancestors is likely to be very common.

Anonymous said...

"Nor do you have any evidence that average Jewish intelligence was low 250 years ago. It is implausible to me that the whole set of mutations responsible for the increase in Jewish intelligence arose within that timeframe."

There is a second possibility.

1) Direct selection for higher IQ during the banking monopoly phase c. 400 to 1300.

2) Burial of (1) under build up of genetic load in little rural villages in eastern europe.

3) Shedding of the genetic load in the driftback to western europe via adopting the north euro marriage model which unburies the effects from (1).

Anonymous said...

Nor do you have any evidence that average Jewish intelligence was low 250 years ago. It is implausible to me that the whole set of mutations responsible for the increase in Jewish intelligence arose within that timeframe.


The "whole set"? Nobody has any idea which genes are responsible for intelligence. Why are you pretending otherwise? And absent such knowledge you cannot speak about what is or is not plausible within a certain time frame.

Historically speaking it does appear that the prevalence of genius within a particular population does rise (and fall) relatively quickly. Ancient Greece, for example.

Anonymous said...

This sort of calculation is temptingly simple, but questionable. The truth is, we don't know *how* intelligence is heritable, only that it is (to a greater or lesser extent: this is still debatable). For example, it's entirely possible that some very intelligent people shouldn't breed with each other, as their cluster of characteristics wouldn't be compatible. It is almost certainly true that some degree of inbreeding might be required. That's how they do it with dog breeds. It might turn out that, say, a very high IQ Frenchman and a very high IQ Chinese woman will produce ... a perfectly average, or even below average set of children, with high probability.
On the other hand, a high-IQ man with a hot tomato might actually produce very high IQ offspring, with high probability. Lord knows I've met a few of those among the old elites, and also among my circle of /com and hedge fund types. Most of them did not marry women who overtly display high intelligence, yet their kids are doing things like quadratic equations at 8, and C++ at 10. Millions of years worth of evolutionary instincts cause me to abhor the idea of sticking my genetic code into someone that looks like Emmy Noether, despite the fact that she was a mathematical genius. I find that more compelling than bad gaussian models.

Anonymous said...

The norm changed in Europe but in very small rural communities - which is where 90% of Europeans were 10 generations ago - even if you're trying to marry as exogamously as possible you're still all going to end up cousins - just not as close cousins as you would otherwise.


Yeah, at the level of "forty-second cousins" it is probable that virtually all Englishmen share ancestors, as do virtually all Germans and so so. At a sufficiently large value of "n" all human beings are nth-cousins.

But if some hypothetical man and woman who became husband and wife in 1763 were third cousins, and are also in my own family tree, that does not mean that I do not have 1024 distinct ancestors ten generations back. The third cousins would have to marry each other six (or fewer) generations ago from my standpoint. That is, they would have to have married in the 1860's. (Because the common ancestor of third cousins is four generations prior to those third cousins)

And since I know that my own ancestors of the 1860's generation came from completely different European countries and not from the same "very small rural community", I can say with near perfect certainty that none of them were third cousins to one another. QED, I have 1024 ancestors ten generations ago

Your general principle is correct (there obviously was a great deal of cousin marriage going on for most of human history) but your practical application of it is off.

Cail Corishev said...

"And since I know that my own ancestors of the 1860's generation came from completely different European countries and not from the same "very small rural community", I can say with near perfect certainty that none of them were third cousins to one another."

So you not only know all 64 of your ancestors at six generations back, but you know enough about them to be certain that none were third cousins? That's some impressive genealogical knowledge. My grandmother's been studying our family for quite a few years and tracing it back to various parts of Europe, but I doubt she's come anywhere close to that. I didn't know anyone had. I'd think most people would have gaps in a family tree that tall where the records simply didn't exist.

Anonymous said...

Nobody has any idea which genes are responsible for intelligence. Why are you pretending otherwise? And absent such knowledge you cannot speak about what is or is not plausible within a certain time frame.

But most scientists in the field currently think that the hereditary component of intelligence is the product of many genes of small effect. Under this model, in order to achieve a significantly higher average population intelligence, many genes would have to be involved. That increases the likelihood that the process extends farther back in time, but it is admittedly very circumstantial evidence.

Anonymous said...

I come from an Ashkenazi family, very intelligent and creative on both sides. Just an anecdote obviously but we have seen no regression over 4 generations in the United States. In the 3rd and 4th generation we have those that surpass the very first highly intelligent generation. The family is increasing in wealth and not from inheritance. I have told my children - and yes this is admittedly terribly racist - if they want smart children, they will marry Ashkenazi Jews. It seems to work.

Unknown said...

Does this mean we should expect the South Asian and Southeast Asian populations within the USA, Canada, Singapore, Australia, and other Western countries to continue to drop as time goes by?

Right now, Indians, Filipinos, Vietnamese etc. tend to do really well and are net contributors to their new countries in almost every way. Should we expect them to go the way of the South/SE Asian populations at home throughout the generations?

Is there any data on this? And if so, how long before they end up falling below the White mean IQ?

Thanks

Anonymous said...

Well I think it is like this. Children's IQ's regress to the mean. But having a child with a high IQ, is a higher probability with two high IQ parents, because they have a greater chance of hitting that standard deviation.

Like two very tall parents. Not every kid they have will be that tall. They will probably be taller than average, but shorter than the parents. But SOME of their kids, MAY be that tall, or taller.

And if this tall kid meets a very tall wife later, SOME of HIS kids will be that tall. But not all of them. And on average, their heights will all go down more towards average

So I think as a class, higher class people are more likely to have some very smart kids included in there, but the effect can be very uneven. Most of the high class kids will not be that smart. And the average intelligence in each family goes down slowly to average with time.

But on the other hand, the IQ of the total population may go up too. Like height.

But I think there is a lot of variability, so don't count on your kids being that smart.




Anonymous said...

I am just not familiar with the scientific research you are implying when you say that two parents with an IQ of 160 will produce a child with a lower IQ. It just doesn't make sense to me, and goes against my observations. And then you have the news headlines of the past couple of years that say intelligence is a hundred per cent inherited from the mother, not the father, which I don't believe either. I think intelligence, like other heritable qualities, can skip generations, you get throwbacks to many generations back.

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