## The breeder’s equation

R = h2 S.

R is the response to selection, S is the selection differential, and h2 is the narrow-sense heritability. This is the workhorse equation for quantitative genetics. The selective differential S, is the difference between the population mean and the mean of the parental population (some subset of the total population).

For example, imagine a set of parents with IQs of 120, drawn from a population with an average IQ of 100. Suppose that the narrow-sense heritability (in that population, in that environment) is 0.5 . The average IQ of their children will be 110. That’s what is usually called regression to the mean.

Do the same thing with a population whose average IQ is 85. We again choose parents with IQs of 120, and the narrow-sense heritability is still 0.5. The average IQ of their children will be 102.5 – they regress to a lower mean.

You can think of it this way. In the first case, the parents have 20 extra IQ points. On average, 50% of those points are due to additive genetic factors, while the other 50% is is the product of good environmental luck. By the way, when we say ‘environmental” we mean “something other than additive genetics”. It doesn’t look as if the usual suspects – the way in which you raise your kids – contributes much to this ‘environmental’ variance, at least for adult IQ. In fact we know what it’s not, but not much about what it is, although it must include factors like test error and being hit on the head.

The kids get the good additive genes, but have average ‘environmental’ luck – so their average IQ is 110. The luck (10 pts worth) goes away

The 120-IQ parents drawn from the IQ-85 population have 35 extra IQ points, half of which are from good additive genes and half from good environmental luck. But in the next generation, the luck goes away… so they drop 17.5 points.

The next point is that the luck only goes away once. If you took those kids from the first group, with average IQs of 110, and dropped them on an uninhabited but friendly island, they would presumably get around to mating eventually – and the next generation would also have an IQ of 110. With tougher selection, say by kidnapping a year’s worth of National Merit Finalists, you could create a new ethny with far higher average intelligence than any existing. Eugenics is not only possible, it’s trivial.

So what can you explain with the breeder’s equation? Natural selection, for one thing. We think that you can explain the Ashkenazi Jews – it looks as if there was an unusual reproductive advantage for people who were good at certain kinds of white collar jobs, along with a high degree of reproductive isolation.

But it also explains why the professors’ kids are a disproportionate fraction of the National Merit Finalists in a college town – their folks, particularly their fathers, are smarter than average – and so are they. Reminds me of the fact that Los Alamos High School has the highest scores in New Mexico. Our local high school tried copying their schedule, in search of the secret. Didn’t work. I know of an approach that would, but it takes about 15 years.

But those kids, although smarter than average, usually aren’t as smart as their fathers: partly because their mothers typically aren’t theoretical physicists, partly because of regression towards the mean. The luck goes away. Henry used to teach here at UNM: he remembers the “Los Alamos kids”.

There are reasons that that families have trouble running the corporation Daddy founded: regression to the mean, not just in IQ. Dynasties have a similar problem: the Ottoman Turks may have avoided it for a number of generations, partly by a form of delayed embryo screening.

And of course the breeder’s equation explains how average IQ is declining today, because of low fertility among highly educated women. It also tells you what hasn’t happened, like a 1-std drop since the Victorian era.

I’m trying to make clear that the breeder’s equation is immensely useful in understanding evolution, history, contemporary society, and your own family.

And hardly anyone has heard of it. I checked on Google Ngram Viewer: zip. “Muon-catalyzed fusion”, “Korteweg-De Vries equation” and totient show up, but not “breeder’s equation”. It doesn’t even have its own Wiki page – sheesh, I have a Wiki page. “breeder’s equation” has not been used by the New York Times in the last hundred and sixty years. There’s not a single mention in S.J. Gould’s bloated, necrotic opus, “The Structure of Evolutionary Theory”. Aren’t we all surprised?

I have long wished that people had a little LED in their forehead that would indicate just how full their intellectual tank was, for a given subject. Seeing a steady yellow light, particularly one that lights up the entire room, like that of Malcolm Gladwell, would save valuable time.

When it comes to the most basic understanding of practical genetics, the talking classes are running on empty. Running wild.

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### 122 Responses to The breeder’s equation

1. misdreavus says:

It also tells you what hasn’t happened, like a 1-std drop since the Victorian era.

Bruce Charlton still can’t understand this. And I doubt he ever will.

2. misdreavus says:

R = (h^2)*S showed up in my genetics textbooks, which is where I first learned it. But I’ve never heard it referred to as the “breeder’s equation”.

• gcochran9 says:

I thought it was called the “breeder’s equation” more often than not, but I must be wrong. I still think that almost no one is familiar with the idea (by any name), except for ag geneticists and evolutionary biologists, but maybe I’m wrong about that, too.

Something as simple as kids of professional types scoring higher because of heredity – very few people seem to know that. I can’t believe that they’re all secret devotees of quantitative genetics.

• misdreavus says:

Undergraduate genetics courses at most universities are nothing but dressed-up molecular biology. Of course, they gloss over it. So do the genomics and bioinformatics courses. Many a student will earn a diploma in the field without ever learning the difference between broad narrow-sense heritability. Or even what heritability means.

On occasion, you might encounter the concept in a population genetics course, which is typically available only through the evo. bio/ecology department (who needs math, anyway?) — and nobody who is interested in the human body takes those courses, if they can help it.

• A Erickson Cornish says:

When I took Genetics in college 7 years ago, the book we used (the current version is here: http://bcs.whfreeman.com/pierce4e/#t_646189____) included chapters on quantitative, population, and evolutionary genetics, and the quant. genetics chapter included a decent discussion of broad and narrow sense heritability as well as the Breeder’s Equation, referred to as “response to selection,” which I think is common. The course itself, like most introductory genetics courses, was taught by a molecular geneticist, with the focus naturally being on molecular genetics; I don’t think we spent more than a day or two on quant./pop./evo. genetics. This is certainly the norm for undergrad genetics instruction, and since most students don’t remember much of what they learn in class for more than a week after the test anyway, close to nobody with a degree in biology, much less other subjects, is going to be familiar with the Breeder’s Equation or its broad usefulness. In Bio. I courses Hardy-Weinberg Equilibrium is generally covered (and it periodically shows up on the MCAT, which is presumably why it is covered), which is all fine and good, but if we are going to teach bio. majors just one equation from basic pop./quant. genetics, the Breeder’s Equation would seem to be a better choice. I think Greg has a post or two on how frequently various people make claims about recent evolution that are easily falsifiable by the Breeder’s Equation, or at least would require exceptionally strong selection (I remember one example being Roland Fryer’s argument that the Middle Passage selected for high salt retention in slaves, enough so that it shifted the mean for the trait amongst their descendants a large fraction of a standard deviation in one effective generation, which sure does not seem likely when you start plugging in values to the Breeder’s Equation). Since it only requires arithmetic, you would think this would be a good candidate for introducing some quantitative sense to people (public intellectuals, say), but just about nobody in public life understands heritability, so I am not optimistic about progress in this area.

3. misdreavus says:
4. B.B. says:

Wider public exposure of what James Flynn has referred to as “shorthand abstractions” encapsulated in a simple phrases could immeasurably improve public dialog on a number of pertinent issues. One useful addition to the publics cognitive toolkit would be what Arthur Jensen has referred to as the sociologist’s fallacy. A common understanding of this basic concept would quickly put a stop to a lot of woolly thinking that is currently common in the prestige press.

5. B.B. says:

Using Google Ngram, it seems to be a bit finicky when it comes to apostrophes. Searching books for breeder’s equation, it gives me zero results and I see it stated in the yellow box Replaced breeder’s equation with breeder ‘s equation to match how we processed the books. You may of noticed that for some reason a space has been automatically inserted behind the apostrophe. It didn’t just do this with breeder’s equation, it seems to do this with anything with an apostrophe in it. If I search Google Books for “breeder’s equation”, I get 375 results with no problems. I’m not very familiar with Ngram, so maybe someone else can fill me in on if I’m doing something wrong and why it’s doing this.

• gcochran9 says:

I tried using ‘response to selection’ in Ngram – that works. For comparison Black-Scholes outcompetes ‘response to selection’ by quite a bit, while ‘stereotype threat’ is a late starter but is now ahead of “response to selection’.

• gcochran9 says:

Both ‘stereotype threat’ and ‘epigenetics’ are now ahead of “response to selection” (which occurs mostly in technical genetics books, I think). Both are now ahead of ‘heritability of IQ’.

6. georgesdelatour says:
• misdreavus says:

Of course, three loci would explain a trivial amount of the total viariation in anything. In fact, the authors of the paper admit as much. It’s there in the last few paragraphs. Clowns.

Some days, I find it very amusing that the vast majority of science reporters take after John Horgan and Sharon Begley. Today, not so much.

• gcochran9 says:

There is a 1-std difference in white blood count between African-Americans and Europeans, and it’s explained by one (1) locus.

• misdreavus says:

I have heard of chromosome locus 1q. Single genes of large effect can explain much of the interdemic variation in a species, but what about social classes within the same ethnic group, which are of comparatively recent origin, and are blurred by intermittent gene flow between classes?

I thought under any given regime of selection, any gene that altered a phenotype in a big way would either rise to fixation within a population, or be eliminated from the genome entirely, arising here and then only through spontaneous mutation. (There is yet another possibility involving balancing selection. Or it could be neutral, which is rare for any gene that heavily alters anything. Etc.) Either way, there should be few loci of large effect that explain much of the variation for things like IQ within a single population, not unless it is subdivided into reproductively closed castes that are under different degrees of selection. Which is why the GWAS studies routinely turn out zilch.

West Africans and Europeans have lived in very different environments for essentially forever, and there hasn’t been anywhere enough gene flow since then to blur most differences resulting from selection. Not so for social classes in the UK.

• 420blazeitfgt says:

Ignore this part, it’s wrong:
“Earlier studies focusing on twins have suggested that 75% of the variance in children’s reading skills is down to genetic factors, but this new research appears to challenge such claims.”

Remember this part:
“Dr Jerriam added: “It is a very small difference and it may come back to the fact that we can only look at these three genes.

“Many more more genes maybe implicated in the reading process – possibly hundreds, each with small independent effects.”

• They need to understand that many, many genes of small effect are involved in intelligent behaviour. To be able to explain 2% of the variance in reading with just a few genes is brilliant, suspiciously brilliant, in fact. The report is a mess.

7. misdreavus says:

I think I can count on one hand the number of students I have met who are aware of at least two of the following: 1) virtually all human behavioral phenotypes, however poorly defined, have a heritability above zero; 2) narrow-sense heritability tells you the extent to which a phenotype can evolve over time, given a selection differential; and 3) a couple thousand years is more than enough time for average differences to evolve between human populations that are under different regimes of selection. It’s all common sense, really. #3 follows deductively from #1 and #2, although most people never even get that far.

It’s kind of cute when undergraduate students in the life sciences haven’t got a single clue. Not so much, when we’ve got public intellectuals [sic] actively defrauding the public.

Psychology majors are by far the most ignorant about this (and not just this, but everything else about the human mind!) — and they rarely grasp it, even when I am forced to explain it to them. Anthropology students are a close second. Looks like four years of undergraduate tuition have amounted to zilch — at this rate, they might as well have wasted all that money on booze and ramen noodles. Now there’s a good way to feed yourself on the public dole.

8. @GC

“And of course the breeder’s equation explains how average IQ is declining today, because of low fertility among highly educated women. It also tells you what hasn’t happened, like a 1-std drop since the Victorian era.”

Except, of course, that is not true.

What the breeder’s equation explains is that differential reproductive success is *not sufficient* to explain a 1-std drop in IQ since the Victorian era.

The breeders equation does not “tell you” that a 1-std drop has not happened.

Indeed how could it possibly do anything of the sort!

Neither I, nor Woodley at al, have at any point claimed that differential reproductive success was *sufficient* to explain the observed (reaction-time-based) 1-std drop in g since Victorian times.

It is becoming annoying that you persist in misrepresenting this fact.

This mechanism of differential reproductive success seems to explain *about* half an SD decline – but the rest of the decline must be accounted for by one – or probably more than one – further mechanisms; of which there are several plausible possibilities – as I am sure you can work-out for yourself.

• misdreavus says:

Judging from the comments you have left on this blog, among several others, you appear resolute in your conviction that a 1 stdv decline in genotypic IQ has occurred since the Victorian era, and that none of this may be attributed to environmental factors. (Please correct me if I am wrong.) Without asking you in advance, I venture to guess that you’re thinking of a decline in childhood and infant mortality as a partial mechanism for the relaxation in selection for “g”.

That’s also silly. Think of what was responsible for the vast majority of early childhood deaths throughout human history, well into the Victorian era. I’ll give you a hint — it rhymes with “sleaze”, and even identical twins reared in the same household will suffer highly discordant outcomes. Certain “high IQ genes” might help you survive, to the extent that they have pleiotropic effects on health, but collectively, they wouldn’t be much of an advantage at all. Not even close.

If you are seriously suggesting that this purported decline (for which I see little compelling evidence) is entirely the result of selection, then it would require a selection differential far greater than the impact of the Black Plague on medieval Europe. …Just what the hell? Nobody could have possibly missed anything this big.

• “Nobody could have possibly missed anything this big.”

No they didn’t miss it – the combination of possible plausible mechanisms is well known, at least to those in the fields with which I am somewhat familiar – but maybe you don’t know about them?

I got the specific idea that accumulation of deleterious mutations from the abolition of very high chidlhood mortality rates might have large and rapid dysgenic effects (which is a different mechanism from differential reproductive success, because it results in a different range of intelligence for each successive cohort) from a guy called WD Hamilton (Narrow roads of Gene Land – volume 2) – maybe you’ve heard of him?

But – either way – none of this justifies GC *persistently* *misrepresenting* my explanation of the observed (and unrefuted, at present) rapid 1 SD decline in g as being due entirely to differential RS – which I not only never said, but have specifically argued-against (as has Woodley at al) including on this blog and in links given from this blog.

• misdreavus says:

That’s absolute hogwash.

And of course I’ve heard of W.D. Hamilton.

• harpend says:

Would you and Greg have a look at what Bruce actually says please. He is not claiming that gene frequency changes account for the purported difference.

• misdreavus says:

He claims that there has been a 1 stdv decline in IQ, and that it is entirely hereditary.

Is there another mechanism of genetic inheritance I am unaware of that has nothing to do with genes?

• gcochran9 says:

I’m not annoyed at you, Yet. So calm down.

I don’t have much confidence in those Victorian studies and I see no practical way of ever increasing my level of confidence. I don’t think the data on differential fertility supports even a half-std drop since then. I know about overall mutational accumulation due to relaxed selection, but I doubt that it plus dysgenic selection would account for a 1-std drop. I doubt it a WHOLE LOT.

Next, if there had been a 1-std drop in genotypic intelligence, I figure that the highest levels of the most demanding intellectual subjects would have collapsed – since a drop in the average drastically decreases the fraction that exceeds a high threshold.

By the most demanding subjects, I mean math and physics.

That has not happened.

• @GC”Next, if there had been a 1-std drop in genotypic intelligence, I figure that the highest levels of the most demanding intellectual subjects would have collapsed – since a drop in the average drastically decreases the fraction that exceeds a high threshold. By the most demanding subjects, I mean math and physics. That has not happened.”

I suppose this is hard to settle – but to an outsider, a collapse in the highest levels of physics has very obviously happened, since the quality of the best modern physicists seems qualitatively *much* inferior to those of, say, 100 years ago – or, to put it another way, the supply of geniuses has almost completely dried-up. Maths looks much the same – but I don’t know so much about it.

That’s how it looks from outside physics, although perhaps modern physicists think they are as good as those of four generations ago – but I know of at least a couple of very eminent physicists who agree with me.

Either way, I would not regard your point concerning the non-collapse of phsyics as anything like decisive.

• gcochran9 says:

I would. I know something about it, you don’t.

• dearieme says:

I dunno. Some cynics might claim that physics since the quantum revolution has largely just been dotting the “i”s and crossing the “t”s.

• @GC – Just so as you know that my remarks on the collapse of top level physics are not an ad hoc defense of the 1 SD decline idea – I wrote about about this in 2008 en route to predicting the collapse for medical research

http://qjmed.oxfordjournals.org/content/98/1/53.full.pdf+html

In fact I got this wrong: medical research did collapse – or rather went into rapid reverse (see David Healy’s Pharmageddon) – but medical research funding did not collapse but instead continued to grow.

• gcochran9 says:

There has been no such collapse in physics or mathematics. There, I’ve said it again.

• syon says:

dearieme:”I dunno. Some cynics might claim that physics since the quantum revolution has largely just been dotting the “i”s and crossing the “t”s.”

Yeah, Murray advances a rather similar argument in HUMAN ACCOMPLISHMENT (438-440). As much as we would like to deny it, fields have limits. Take chemistry, for example, Murray notes how the goal of chemistry (” understand[ing] the principles that govern the behavior of molecules during reactions”) was effectively reached in 1931 when Linus Pauling published “The Nature of the Chemical Bond.” Work still remains to be done in chemistry, but it is more a matter of filling in details than making grand breakthroughs.Hence, it would be wrong to think that the dearth of names to equal Lavoisier or Priestly or Berzelius indicates a decline in intellect. Instead, it simply indicates that the field has been thoroughly mapped, with no hidden continents left to discover.

• Next, if there had been a 1-std drop in genotypic intelligence, I figure that the highest levels of the most demanding intellectual subjects would have collapsed – since a drop in the average drastically decreases the fraction that exceeds a high threshold.

This isn’t completely convincing. The normal distribution of intelligence is more of a convention than a precise law of nature. If the average is dropping because of low IQ subpopulations are growing while high IQ subpopulations are just remaining stable in numbers but there isn’t much mixing between the populations then you wouldn’t expect a drop in the absolute number of very talented individuals. Especially in the short run.

And if the sources of environmental luck are poorly understood it is hard to be confident that such luck hasn’t become more likely in recent years.

Although I agree that a 1-std drop in genotypic seems unlikely and that a single reaction time study doesn’t seem like a lot of evidence.

• Anon says:

I have no dog in brucecharlton vs. gcochran9 fight, but BC’s argument sounds more convincing. Can you elaborate on “There has been no such collapse in physics or mathematics.” GC?

• There’s been a 2 SD increase in non-verbal phenotypic IQ since the Victorians. If there’s been a 1 SD decrease in genotypic IQ, that would imply that nutrition has increased non-verbal IQ by 3 SD in a century. Implausible.

• Douglas Knight says:

If you hold, as claimed by Woodley et al, that you can compare modern reaction time studies to Victorian reaction time studies, then you must also hold that you can compare modern reaction time studies to each other. So you must conclude that Finns and Australians are 2 sd smarter than Scots and Americans. Here is the scatterplot of the studies against time.

• gcochran9 says: June 7, 2013 at 5:11 pm There has been no such collapse in physics or mathematics. There, I’ve said it again.

I think you need to say it yet again.

“Just the place for a Snark! I have said it twice:
That alone should encourage the crew.
Just the place for a Snark! I have said it thrice:
What I tell you three times is true.”

Faraday, Maxwell, Thomson, Einstein, Rutherford, Bohr, Heisenberg and Dirac (a small sample) – but nowadays with a bigger population base and resources we have (…crickets.. – or maybe some ancients such as Wheeler and Hawking? But not really…).

Let me be plain: Leaving aside the cause of it (which is arguable and probably multiple), if modern physics is *not* a prime representative instance of what major intellectual decline looks-like, then I don’t know what does!

At any rate the state of modern physics cannot – surely! – be used as evidence *against* a major decline in ‘g’.

Even if you do go ahead and say it three times….

• gcochran9 says:

I guess you don’t have any idea of what major intellectual decline looks like. Nor do you know anything about theoretical physics or higher mathematics. I suggest reading The Princeton Companion to Mathematics.

All of it.

• Andrew Cornish says:

Along with research in math and physics, another way to gauge whether there has indeed been a 1 SD decline in mean intelligence would be to look at elite competitions in those subjects, like the Putnam. As essentially nobody with an IQ below 160 (on today’s scale) has a chance of succeeding in IMO, Putnam, and such competitions, and a 1 SD decline in IQ would reduce the number of people at this level by several orders of magnitude, we would expect such competitions to essentially cease to exist, on account of there being nobody available to compete in them. The Putnam did not exist in the Victorian era, but much of any change in mean IQ since 1938, when it was inaugurated, would drastically reduce the pool of capable competitors. Ditto with other competitions. This has not happened.

• This isn’t convincing. Tests like the Putnam are graded on the curve in that to win you just have to do better than the other competitors. You would need to somehow compare the difficulty of the questions on the test over time.

• Anonymous says:

They’re gettting harder over time. I can’t find information on scores going back far enough to tell if the top scores are staying the same though. Presumably the top scores aren’t changing too much. I do know that there have been only four perfect scores, and one of those was Richard Feynman, who wrote it very early on in its history.

9. johnfuerst says:

“On average, 50% of those points are due to additive genetic factors, while the other 50% is is the product of good environmental luck. By the way, when we say ‘environmental” we mean “something other than additive genetics”. It doesn’t look as if the usual suspects – the way in which you raise your kids – contributes much to this ‘environmental’ variance, at least for adult IQ.”

The luck component is everything but shared environment and additive genetics, this includes the non-additive genetic component. Equating non-additive genetics with environment is confusing. Shared environment isn’t typically included since this isn’t a large factor when it comes to most non human animals. Because R=(h^2+c^2)S, differential regression between populations only implies that differences are intergenerationally transmitted. I’m not certain that the c^2 for g by adulthood is 0. See here: http://humanvarietiesdotorg.files.wordpress.com/2013/05/the-effects-of-shared-environment-on-adult-intelligence-a-critical-review-of-adoption-twin-and-mza-studies.pdf

• JayMan says:

” I’m not certain that the c^2 for g by adulthood is 0.”

Here’s the problem with that:

There were studies that looked adopted children from advantaged homes compared to those from disadvantaged ones. Several of these were discussed by J. P. Rushton and Arthur Jensen. Those studies that note IQ gains from advantaged homes failed to note of those gains were on g itself. And predictably, Jensen found that such gains were only on the non-g aspects of the tests.

This is the likely explanation for Kaplan’s observation of big differences in reared-apart twins where one is raised in a more privileged environment. I’d like to see more tests like that done with a much more comprehensive battery of IQ tests (including reaction time) to see just how big of a real IQ impact these people received from their privileged upbringings.

Further, we do know that c2 is 0 for broad personality traits, as well as “meaningful” stuff life major adult life outcomes and average income.

Technically MZT-MZA is supposed to give you c2. Kaplan doesn’t discuss this.

It has been suggested (most clearly by Steve Sailer , also here) that perhaps there is a sort of parenting “floor”, that is, a minimum level of parental care beyond which differences matter little:

It may well be that, to paraphrase Garrison Keillor, everyone was above average, parenting-wise, in these populations. Which means that, within them, variations will tend to lose their predictive power.

All serious commenters on this topic make this point, but we generally tend to think of the bare basics like food, shelter, and normal human interaction. But adoptive homes and most subjects of behavioral genetic studies do tend to be White and middle-class – many from Scandinavian countries and their derivatives (e.g., Minnesota). There is a dearth of behavioral genetic studies from other groups. I have been trying to track down behavioral genetic studies done on non-Whites for this reason, to see if the pattern of c2 ~ 0 holds.

10. albatross says:

If I understand this correctly, one nice application is in personal selective breeding. The smart girl from a family of smart parents probably has better genes for intelligence than a smart girl from a dumb family. You’d like to know which mean her kids are going to regress to before you decide to have your kids with her.

I dated a girl in school who was the one diamond in a family full of trash–her parents and sisters were on public assistance, and she was in a PhD program in chemistry. It’s rather likely that her high IQ was mostly luck in developmental noise or environment or whatever, because the rest of her family gave no indication of much intelligence. I later married a differrent smart girl whose parents are also very smart. Her intelligence is likely to be more genetic and less luck.

is there a simple way to incorporate siblings into this calculation? It seems like I should start with a prior of the population genetic IQ distribution, and update it with each parent and sibling, but I haven’t thought this through yet.

• harpend says:

Check out what is called path analysis.

• Matt says:

Another, impersonal, implication of this would be that, so long as there is any random component involved, a pure form of meritocracy which functioned to assign the most offspring to the highest IQ per generation* would actually (perhaps slightly) under-perform one which took into account ancestry information to some degree.

In a population with 0.5 heritability, a person A with IQ 105 from a mean 110 IQ extended family, who is likely to have lost some genetic IQ, would, mating with another similar person, have offspring with the 107.5 IQ.

Whereas, person B with IQ 120 from a mean 90 IQ extended family, who is the beneficiary of luck and would, mating with another similar person, would have offspring with 105 IQ.

In this way, a pure meritocracy of reproduction would actually be slightly less perfectly eugenic than a less pure meritocracy (because it would assign lower reproduction priority to A than B, when it should do the reverse). This may be more extreme than in reality (i.e. the heritability is too low), but even with heritabilities of 0.8 (or anything less than 1.0), but it seems like there would be some return to reproductive privileging those from “good families”, individual ability being equal.

It kind of amuses me that the lower heritability of IQ becomes, the stronger an argument for reproduction based on extended family status, rather than individual status, becomes (I’m not sure that this qualifies to quite get into the territory of “must be true, yet can’t be”, but…)

*e.g. Ron Unz’s interpretation of Chinese history, for all that it probably never obtained exactly in China.

11. JayMan says:

“You can think of it this way. In the first case, the parents have 20 extra IQ points. On average, 50% of those points are due to additive genetic factors, while the other 50% is is the product of good environmental luck. By the way, when we say ‘environmental” we mean “something other than additive genetics”. It doesn’t look as if the usual suspects – the way in which you raise your kids – contributes much to this ‘environmental’ variance, at least for adult IQ. In fact we know what it’s not, but not much about what it is, although it must include factors like test error and being hit on the head.”

For readers who are wondering what Dr. Cochran is talking about, see these here:

12. not_my_subject says:

Odd. I was just this week thinking about coming here and asking about this very issue; about the regression towards the mean and if that would mean that the blacks would have an even harder time increasing their IQ than I thought would be possible, even if they could increase the reproductive rate of their smarter members.

Another question: can the said IQ mean of population vary inside, say, a country? Can academic families that have married mostly inside educated circles have a higher mean than the usual 100, which their offspring would regress towards? Is there some theoretical gene pattern that reveals this hidden value of a population mean inside each individual?

• albatross says:

You mean like Ashkenazi Jews living in the same country as blacks? Demonstrably, you can have persistent IQ differences and other differences within a country.

• not_my_subject says:

albatross: I guess I didn’t mean clearly genetically separate groups in a country like the blacks and Jewish – more like can the mean IQ be different for castes, families of one genetic group? Is it more likely that academic families regress towards a 100 IQ mean just like the rest of that ‘ethnicity’ (say white Norwegian), or could that number be higher for certain families, castes?

• Andrew Ryan says:

It is my understanding that the “mean” to which offspring will regress is the mean of their ancestors. Unrelated individuals obviously cannot impact the heritability of a given trait.

However, I am not sure how far back or distantly related an individual could be and still be included in the “mean”–obviously there is some degree of relatedness throughout all members, past and present, of a particular species. However, trying to determine regression to the mean for white Americans by including Aborigines for example, doesn’t make much sense.

• harpend says:

I worked some of that out and posted about it long long ago on this blog. See
https://westhunt.wordpress.com/2012/01/13/class-caste-and-genes/ . In brief, yes, absolutely. This very question was the central issue that Murray and Herrnstein were concerned with in The Bell Curve. Murray got whacked by the talkers about race but it is readily apparent reading the book that they had no interest at all in race and regarded it, for their purposes, as a nuisance.

• albatross says:

One place the insight of regression to the mean should be used (but I haven’t really seen it being used) is in SF, specifically space colonization. The original thousand people who are selected for the Mars colony, long trip in suspended animation to some other solar system, etc., will all be exceptional in most every way–a bunch of Heinleinian heroes, astronauts who have two PhDs and were also olympic athletes. The transition from them to their kids will be fucking brutal. All across the Mars colony, at about the same time, genius surgeons and engineers and botanists and such will be replaced with relatively smart and competent surgeons, engineers, and botanists. It will be like having a really tight, first-rate organization and then having all the top workers replaced with affirmative-action hires and nephews of the boss, or like what happens to the US as all the competent people go on strike in Atlas Shrugged. (The difference is, regression to the mean could actually happen.)

• melendwyr says:

“Can academic families that have married mostly inside educated circles have a higher mean than the usual 100, which their offspring would regress towards?”

Yes. You can think of it as regression to a weighted mean of the ancestors of the people involved, with more recent relatives having greater weight. If you don’t know anything about a person’s ancestors, or they’re randomly selected from the population at large, you might as well use the average of the population.

If I recall correctly, there are certain famous families that have produced intellectually extraordinary offspring for quite a long time. It’s hard to say how much of that is due to enriched environment (good health, good nutrition, stimulating surroundings, etc.) and careful mate choice on both sides, but the latter was probably significant. The Darwins were one of them, I think.

Yes, the mean iq can vary within a country. My own family is full of non colleged readers, intelligent skilled tradesmen. All of us. I think that my family has long had a preference for smart mates, for generations. No doubt, English farmers who had something on the ball tried to marry their daughters off to the sons of other farmers who had some smarts. Just as Mexican ranchers in Old California were willing to give their daughters away to smart Yankee newcomers rather than the local caballeros.

13. Robert King says:

Discover magazine did an ok piece a couple of years back
http://blogs.discovermagazine.com/gnxp/?p=947

14. Bill says:

Can someone, ideally our host, recommend to me a graduate-level textbook in quantitative genetics, on the assumption that the intended reader “gets math,” if you know what I mean.

• gcochran9 says:

Introduction to Quantitative Genetics, 4th ed, Falconer and MacKay

• Bill says:

Thanks!

15. My Dogma overran your Karma says:

Ye gawds, one can easily refute the entire hogwash of the Victorian Era loss of intelligence by simply looking at average height. As the average height has shot up, intelligence has also shot up. Gee, could it be better youth nutrition for all classes of people?

How many people fail to understand that when children are not starved, and are fed food with supplements http://en.wikipedia.org/wiki/Enriched_flour which we started before the second world war mind you, these circumstances will allow fuller expression of any genetic potential.

First problem with looking at history is the sheer number of effects overlaid in the last century, many of which do fully allow the genes to be used, and the people to be taller than ever.

And yes, I think height can be considered a proxy for health in this case, and that same increased level of health could easily be responsible for a significant part of the Flynn effect.

After all, how many kids have http://en.wikipedia.org/wiki/Rickets today, compared to a century ago?

Yes, the breeder’s equation more than shows the reversion to the mean in intelligence tends to happen, unless you keep breeding intelligence back into the gene pool, but the proof would be in examining how many outlier children are born to parents with lower intelligence.

Show me the numbers of children that violate the norm and that would be interesting.

• albatross says:

Is there any data on the height of the people who took the reaction-time tests in Victorian times that are the basis of the idea that IQ has fallen?

• Galtonian says:

There should be- this was at Galton’s science museum exhibit where people got measured in lots of different ways.

16. Matt says:

The next point is that the luck only goes away once. If you took those kids from the first group, with average IQs of 110, and dropped them on an uninhabited but friendly island, they would presumably get around to mating eventually – and the next generation would also have an IQ of 110.

Greg and Henry, regarding this and Ashkenazis, the theory you have tended to plump for, (unless I’ve misunderstood) is that the Ashkenazis probably started off as a reproductively isolated population of fairly ordinary IQ with some tradition of literacy, who just happened to be in a Christianising Roman Empire and thus sort of trapped in to the financier / lender niche, and then differential selection took place within that population.

Wouldn’t another theory though, be the migrating populations to Europe that went on to form the Ashkenazis were simply high IQ migrants, who migrated to Europe to fill a trade and banking niche and then sort of just stayed there due to reproductive isolation?

Or six of one and half a dozen of the other?

I mentioned this idea to Peter Frost at his blog and he seemed to feel the disease history of Ashkenazis made the first idea more likely. But it doesn’t seem straightforward to me that this is the case, i.e. if you took a group of IQ 130 or 120 gentiles and dumped them on an island, then I’m not sure that their kids would have a rate of neurological diseases lower than the Ashkenazi simply because the selection has all happened in one generation.

• melendwyr says:

What about regression to the mean? A group of 120-130 IQ people would have children with higher than average scores, but notably below their own. Also, I suspect that only the men would have had significantly higher intelligence – is there any particular reason to think that men capable of being traders and bankers would have had wives as bright as themselves? Especially given the time period. If not, then half the contribution to the next generation would be at the average of the originating population. The fathers’ IQs would have had to be extraordinarily high for the regression to have resulted in the current results.

I think the best way to explain the persistence of the elevation is selection across time. There’s only so much that can be done with a single selection.

• dearieme says:

“is there any particular reason to think that men capable of being traders and bankers would have had wives as bright as themselves?” Read Pride and Prejudice to see what happens when a bright man marries a dim wife, and then you’ll see why many bright men wouldn’t consider it.

• albatross says:

I don’t think the founder selection effect can work out with the existing numbers, though. If narrow-sense heritability of IQ is .5, and Ashkenazi Jews ended up with an average IQ of 115, they’d have to have had a founding population with an average IQ around 130–the top 2% of the original population, mothers and fathers. (And narrow-sense heritability was probably lower back then, since environmental conditions were so much more uneven, so you’d have needed to be even more selective.)

• Matt says:

Good response.

I would note though that, as I understand the maths, you don’t actually need truncation at IQ 130 to get a subset population with mean IQ 130 (a set of people with IQ higher than 130 is going to have an mean IQ higher than 130).

As I work it out, truncation at the top 20% (i.e. the bottom 80% are lost), in a population at IQ 100 yields a population with mean IQ 130 (or mean IQ 120 if we assume the population mean 90).

(https://westhunt.wordpress.com/2013/04/02/against-biology/#comment-11355 – Henry’s math on the kind of truncation selection that would take a pop of mean IQ 85 to 100 assuming heritability 0.8 basically seems to agree with this kind of “survivor fraction”).

And that said, there have been work indicating that the population was initially quite small at the founding of the Ashkenazi Jewish community – “400 families” as the founders for the Ashkenazi Jewish community and “For Ashkenazi Jews, the relatedness was similar to what one might observe for fifth cousins” have been reported. Even working from a population of say only 500,000 or less and mean IQ 90, there still seems like plenty of room for that to only be a subset of the top 20%.

I would not necessarily argue for total founder selection but some degree of founder selection intuitively feels likely to me because I have a hard time seeing a community of average intelligence and small in number being good enough at banking and lending in the first place to move into that niche and have it be stable enough as a niche for selection to take place. Even with religious prohibitions and all, which I am tempted to see as effect as well as cause. They’d just get eaten alive quickly by the more intelligent, numerous and ruthless nobles, and the usury prohibitions would be rationalized away more quickly.

• gcochran9 says:

You’d better try working it out again.

• Matt says:

OK, so I was wrong and having a bit of free time… I tried again by grabbing the software described in the link and following the method described by HH, so…

Boost mean IQ from 100 to 115, assuming heritability 0.5, a response of 15 points or 1 standard deviation, selective differential must be 30 IQ points, since 15/0.5 is 30 (2 standard deviations).

from scipy.stats import truncnorm
truncnorm.mean(1.6,Inf)
2.0241

from scipy.stats import norm
norm.sf(2.02)
0.0547

so survivor fraction of the top 5% (a lot lower than my wrongly worked out 20%, which doesn’t hold under this level of heritabilty)

If heritability is 0.65 then 16%ish survivor fraction, if heritability is 0.8 then 25% survivor fraction (as described by HH).

So a single “elite” founder generation having anything like an almost total impact seems pretty implausible unless heritability was / is quite high.

• gcochran9 says:

I wouldn’t say that an initial colonization by successful merchants couldn’t help a little , but as you have just seen, it can’t be the primary explanation. Nor would it explain the pattern of sphingolipid genetic diseases.

Charles Murray, in his Commentary article, argued for another one-generation effect (the Babylonian captivity) boosting the the IQ of Jews in general, not just the Ashkenazi Jews. That was of course wrong, because A. the exile involved a lot of the population (the army, for example) : it wasn’t the top 5% or anything like it, or is there any reason to think that those exiles even account for the preponderance of later Jewish ancestry B. Jews in Classical times never had a reputation for special smarts C. Most non-Ashkenazi Jewish groups don’t even have high average IQs to explain. I thought it was a ridiculous article, But then, I think that of so many things.

• Greying Wanderer says:

“Wouldn’t another theory though, be the migrating populations to Europe that went on to form the Ashkenazis were simply high IQ migrants”

High IQ relative to where though? Jews in one place might be high IQ relative to the population in that place but only average somewhere else.

.
“I’m not sure that their kids would have a rate of neurological diseases lower than the Ashkenazi simply because the selection has all happened in one generation.”

If you select mostly on IQ over generations then by definition you’re not selecting as strongly on other traits like health. It’s like pedigree dog-breeds developing various health problems.

17. Greying Wanderer says:

“And of course the breeder’s equation explains how average IQ is declining today, because of low fertility among highly educated women.”

Is this definitely the case? Given the perils of childbirth for most of history I find it hard to believe very high IQ women ever had lots of children. Also given the difference in total numbers wouldn’t lower fertilty among women who were just above average IQ be more critical i.e. women in the 100-115 range?

• gcochran9 says:

Childbirth wasn’t that dangerous. Not until doctors got involved.

Really? You mean they were lower before doctors and then when doctors finally learned some science they went back to where they were before doctors got involved?

• gcochran9 says:

Maternal mortality is a rare thing in hunter-gatherers. It wasn’t common in, say, 1600: I looked at the record of a midwife, who lost one mother in something like 350 births. But once the MDs got involved, maternal mortality shot up, much of it because of puerperal fever (childbed fever). The majority of cases were iatrogenic, a special medical word that means ” I fucked up but you don’t know Latin! HA!” In some wards, maternal mortality could be as high as 25%.
A number of people realized this: Alexander Gordon in 1796, Oliver Wendell Holmes in 1843, Ignaz Semmelweiss in 1847. It was repeatedly rediscovered because nobody listened.

Lots of people have the idea that birth was terribly risky for the mother – but most of the time that was not the case. I once had to explain this to some Nobel-prize-winning economist, whose name I forget.

Eventually, doctor-assisted birth became safer. It became a net plus, sometime after 1900: maybe by 1920, certainly by 1940. Today it is safer than than alternatives.

• Greying Wanderer says:

Fair enough. However I still wonder if very high IQ women might always have been a lot less keen on the whole process than the average woman. If so the main target might be in the 100-115 segment.

• P says:

It’s Greek, not Latin.

• Lesser Bull says:

It’s both. Iatro is Grecian, genic is Latinate.

18. Greying Wanderer says:

I don’t know enough about the details of the Victorian thing to have an opinion but the population was a lot lower back then (between 1/3 and a 1/4 according to Wiki) and the percentage of fully educated people within that population was probably lower as well so a drop in average IQ since then may have been partly compensated for by larger numbers of people maybe?

• ChrisB says:

About half, actually, in the late 1880s – c. 26m versus 53m in 2011.

19. My Dogma overran your Karma says:

I am going to follow up one more time to the moronic loss of IQ from victorian era until now:
http://community.seattletimes.nwsource.com/archive/?date=20040214&slug=korea14

Gee, look ma at how nutrition matters- we now have a perfect 50 year real time comparison between close populations of North Asian- lookie at the height differences- do you think there might be some problems with developing intelligence too because of starvation?

Here, read this and just throw the trash out, period: http://www.emeraldinsight.com/books.htm?chapterid=1756854&show=abstract

Money quote: The height gap between the rich and poor was the greatest in England, reaching 22cm at age 16. The poverty-stricken English teenagers were among the shortest for their age so far discovered in Europe or North America; in contrast, the English rich were the tallest in the world in their time: only 2.5cm shorter than today’s US standard. Height of the poor declined in the late 18th century, and again in the 1830s and 1840s conforming to the general European pattern, while the height of the wealthy tended rather to increase until the 1840s and then levelled off. The results support the pessimistic view of the course of living standards among the ultra-poor in the Industrial Revolution period.

If I see another comparison about Victorian Intelligence I am going to barf.

20. hbd chick says:

@greg – thank you!

21. The point of the “Victorians” study is to show that an objective, true-zero, ratio scale measure of a simple human response (with a reasonable correlation with IQ) shows results which run counter to the no-true-zero IQ scale data on which the “Flynn Effect” is based. The 12 papers in the special issue I am guest editing at “Intelligence” are almost all of them already online, so you can look at the scope of the studies. It is really hard to show that the Flynn effect indicates that intelligence is really rising. It is doubtful if the effect is on g (see te Nijenhuis’ paper). IQs are great for ranking within a contemporary population, and have excellent predictive value, but they are not all that good at comparing generations. They weren’t designed to do that, though one might achieve it by lengthening the Arithmetic part of the test. If you think the reaction time studies have a problem, take a closer look at the item analysis of IQ tests which show measurement invariance.

Finally, I prefer to take one step at a time. At the moment we don’t have a convincing refutation of the finding that the Victorians had fast reaction times. We can keep looking at that, and even rebuild the original apparatus. Then we can look at explanations for the effect, or some of the effect.

22. My Dogma overran your Karma says:

Which Victorians? The rich, or the slum dwellers? Further questions include why reaction time has fallen given better feed- or maybe it is just the mind numbing effect of TV on modern populations. The height paradox is also shown just as soon as you start feeding kids the enriched foods- the minute you get rid of it, you will have shorter children.

Or the fact we are missing that many of the games the Victorian kidz played were physical games requiring skill and speed, and many of the games played today involved video games…

• Are you claiming that reaction time is not exercised in modern games? What are you 80 or something?

• My Dogma overran your Karma says:

Just past half of that- modern youth ain’t what it was 40 years ago. How much reaction time outside of small finger movements is generated by modern games? Have you seen how uncoordinated many of today’s young children are playing sports?

The total alternative of electronic babysitting has yielded some very interesting changes in today’s youth- and physical reaction time is cultivated by practice, extensive practice in physical play that generates that reaction time- gross motor skills.

23. Jaim Jota says:

Since the comments focus on reaction times as measured by Galton (1899) on the instrument he invented, let me add that his figures were never replicated since then and may have resulted from simple experimental error. His instrument was based on an elastic thread, and elasticity is not linear. With better instruments, reaction times “appear” to slow down, for example, reaction times of NCAA football players averaged 0.203 sec when determined with a simple falling meter stick but 0.268 sec when measured with a computer (Clemson). Reaction times are hereditary (what is not?) but Galton’s measurements are irrelevant.

24. Many of these “Victorians” issues are covered in “Psychological Comments” where the authors have answered criticisms and also posted about a modern replication of Galton’s original study

25. Jaim Jota says:

No Sir. They have not answered the criticism. http://drjamesthompson.blogspot.co.il/2013/05/original-paper-high-quality-replication.html?showComment=1370706358767#c417339476873779242 At least not to my satisfaction. Galton was a genius but limited by the materials available to him. Measuring the universe with Galileo’s perspicillum generates different results than with, say,a gravitational wave detector.

• melendwyr says:

“Measuring the universe with Galileo’s perspicillum generates different results than with, say,a gravitational wave detector.”

Especially since no one’s ever detected gravity waves, and we’re not even sure if the instruments we’ve developed would detect them if they’re real.

26. Jaim Jota says:

BTW I share Cicero’s and the above commenters impression that our contemporaries are degenerate offspring of superior ancestors. Let’s thank Heaven that we have Greg to show that it is not so.

• Toddy Cat says:

There are plenty of other ways to degenerate, besides intellectually…

• gcochran9 says:

For instance, eyeball licking.

• JayMan says:

@gcochran9:
“For instance, eyeball licking.”
There is that…

27. mmolehill says:

Just for fun, I wonder how the characters from Big Bang Theory would do:
Sheldon has an IQ of 187, but he comes from a family of East Texas rednecks.
Leonard has no stated IQ, but he comes from a family of world class PhDs and is considered a bit dull by family members. So, maybe IQ 145 out of an average of 160.

By geometric mean:
Sheldon: (187 x 95)^1/2 = 133
Leonard: (145 x 160)^1/2 = 152

So, we can expect Leonard’s children to be smarter than Sheldon’s

• misdreavus says:

That’s the single most implausible thing about that mediocre show. Especially since Sheldon’s father was supposedly a “real life Homer Simpson”.

• stephen c says:

in defense of Big Bang writers and advisers, they try to make it clear that Sheldon is not as gifted as he thinks – he is overjoyed to meet George Smoot, rather than vice versa; he can’t wrangle an invitation on his own to CERN; and the whiteboards in his apartment are fashionably up to date but apparently not exceptionally insightful….

• melendwyr says:

There IS no defense for that show. It makes smart people the butt of every joke, parodying their behavior, culture, and attitude. Which is why it’s so successful – if it were made to be liked by the intelligent, instead of the masses, it would have been cancelled before being aired.

• barb says:

Except, assuming Sheldon breeds with Amy, and Leonard breeds with Penny:
Assume Amy is 145 and at the mean of her group: 133 (Sheldon’s contribution) + 145 (Amy) / 2 = 139 for Sheldon + Amy’s kid.
Assume Leonard breeds with Penny, and Penny is at the mean for her group of 100 : Leonard (152) + Penny (100) / 2 = 126.
Leonard’s kids WON’T be smarter than Sheldon’s.

28. Greying Wanderer says:

Matt
“I have a hard time seeing a community of average intelligence and small in number being good enough at banking and lending in the first place to move into that niche and have it be stable enough as a niche for selection to take place. Even with religious prohibitions and all, which I am tempted to see as effect as well as cause. They’d just get eaten alive quickly by the more intelligent, numerous and ruthless nobles, and the usury prohibitions would be rationalized away more quickly.”

If their average IQ was 100 at the time (as the long-term result of filling a merchant niche among a middle-eastern population) and the average IQ in Europe was 100 then that doesn’t apply. The usury prohibitions would then create a sealed ecosystem where the smartest Jews were only competing with other Jews creating a “Farewell to Alms” effect. By contrast selection for most other niches during that period – including and almost especially nobles – was for a mixture of brains and brawn not just brains.

• Greying Wanderer says:

As one of the few other cognitively selecting niches at the time i’d have thought something similar would have happened with priests if they’d married (and their children were only allowed to marry the children of other priests). Perhaps it did later on?

(I’m curious about the semi-recent ancestors of the great Victorian inventors and scientists. I wonder how many were from specific trades like preachers, stonemasons etc.)

29. stephen c says:

in 1890, opportunity cost and risk of trying to leverage a 3, 4 or 5 sigma non-verbal IQ advantage into a family friendly academic job in math or physics was probably pretty high (outside of England and similar countries, anyway); today a 3, 4 or 5 sigma advantage, absent mental illness, is a relatively golden ticket with little to no risk within a population of 2 to 3 billion people (as opposed to approximately twenty percent of that back then). For purposes of understanding rhetoric and perceived outcomes, this may have resulted in the 4-5 sigma guys born then being absolutely unapologetically proud of their genes (& work habits) – whereas, currently, the younger 4-5 sigma math crew (as far as I can tell from my recreational math background) are – different – for example, Terry Tao has ( if I read him right) disavowed the thought he has a unique IQ benefit, Perelman is a very humble guy, almost too humble, and possibly Witten is little different (I have no clear read on him, but he seems a little more flustered than the top physicists of the 1920s would have admitted to have been) – i.e,, this group is not very quick to acknowledge their genetic gifts . BTW, I got those sigma estimates (sorry if they are wrong) indirectly from Steve Hsu, who has written a lot on this topic.

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31. Robert King says:

The Jack and Oscar story is even more compelling than the Jim twins. Finally got around to uploading it

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36. Lesser Bull says:

@ Matt

“I have a hard time seeing a community of average intelligence and small in number being good enough at banking and lending in the first place to move into that niche and have it be stable enough as a niche for selection to take place. Even with religious prohibitions and all, which I am tempted to see as effect as well as cause. They’d just get eaten alive quickly by the more intelligent, numerous and ruthless nobles, and the usury prohibitions would be rationalized away more quickly.”

It could work, in two different ways. First, if the environment requires elites to strongly specialize in warmaking, or if the returns from fighting are greater than the returns from banking. Either way, it would encourage elite specialization in fighting, not banking. Which seems to be true of the Middle Ages. Is it a coincidence that as society and states became safer and more stable, the prohibitions on usury did get pushed aside and the elites did move into finance? Probably not.

Second, the Jewish specialization in usury served elite interests. It directed popular frustration at usury away from the elites towards the Jews, while still allowing the elites to get the financial rewards through high taxes on the jews, forced loans, unrepaid loans, and outright expropriation. So, best of both worlds. It isn’t until you have a long and sustained period of economic growth that it is particularly rewarding to be directly involved.;

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