Re: Does 'regression to the mean' apply to the genetics of IQ?

Before I answer your question, I'm going to address some of the implicit
assumptions contained within it, so that my biases are clearly stated
before I proceed.

Okay, the first assumption is that races are discrete.  Race is an
invention of society, and is not a particularly meaningful or useful term
in the context of genetics.  For example, in the U.S. we have historically
identified three major races, corresponding to the three old world
continents: Africa, Asia and Europe.  However, closer inspection reveals a
great deal of variation within each "race" for virtually every trait
examined, and this variation overlaps between "races".  For example, in
caucasians skin color ranges from pale in Scandinavians to tan in Southern
Europe to very dark in some regions of India.  The same is true of each of
the other "races".  That is, for each trait used to distinguish groups from
one another there are no clear boundaries between groups, only a continuous
gradient.  

So the boundaries between "races" in the U.S. really are simply arbitrary
boundaries between continental populations.  What is more important is how
much variation exists within each population.  Let's use height as an
example.  Are African Americans significantly taller than European
Americans?  Possibly, if we used membership in the NBA as a metric, but
that's beside the point.  So are Africans really taller than Europeans? 
The answer is that it depends on which Africans and which Europeans we look
at.  If we look at the Masai, who live on the savannah, the answer is yes,
the Masai are pretty much taller on average than any European group. 
However, if we look at the bushmen they are shorter than most European
groups (possibly excluding the Finns), and the pygmies of Africa are
shorter on average than any other population on earth.  So comparisons of
Africa vs. the rest of the world don't really make sense, given that there
is more variation within Africa than in the rest of the world combined. 
Putting it another way, there are African populations which are more
different from one another than from any non-African population.

This distinction holds at the molecular level.  In DNA it is possible to
assess the fraction of all variation which is shared between populations,
and the fraction of variation which is private to a single population. 
Over 80% of all variation is shared between populations, leaving less than
20% as restricted within populations.  The greatest amount of variation
restricted to a single continent exists within Africa, so at the DNA level
as well, Africans are more diverse than the rest of the planet. 

Okay, the second assumption I want to address is the measurement of IQ. 
Herrnstein and Murray ignited quite a controversy with their book "The Bell
Curve", which asserts that African Americans have significantly lower IQ
than European Americans, even after correcting for other factors like socio
economic status.  An excellent counterpoint to this book is Stephen Jay
Gould's "The Mismeasure of Man", which is one of my favorites.  Anyhow, my
gut feeling is that Herrnstein and Murray are fine statisticians, but need
a primer in history. 

At the beginning of the 20th century there was a movement to limit
immigration by South and Eastern Europeans.  This was justified by
arguments that they were mentally inferior (the term back then was "feeble
minded").  This coincided with the development of some of the earliest IQ
tests, including the Stanford Binet test, and such tests were rapidly
applied and used to "prove" that South and Eastern Europeans have inferior
intelligence compared to Northern Europeans.  Of course, the fact is that
SE Europeans didn't speak English too well and the tests had questions
including knowledge of how many cylinders a specific make of automobile
had, so we look back on the analyses and recognize that the flaw was not in
the SE Europeans, but in the test.  My point is that not many Americans
honestly believe that Greeks, Italians and Russians are inferior today, so
I doubt that the supposedly lower average IQ of African Americans will hold
up either.

So now let's almost get back to your question.  Before we talk IQ, let's
talk about height.  Regression to the mean is an old concept, first
introduced by Francis Galton in a study of hieght.  He found that the
height of children tended to be between the population average and the
average of their parents' heights corrected for sex (the mid-parent
height).  Translation, children of tall parents tend to be taller than
average, but shorter than their parents.  Two points need to be addressed
here: first, regression to the mean is a group phenomenon.  Any individual
child of tall parents may be even taller than their parents.  It's just
that the average child of tall parents tends to be shorter than the
parents.  Second, regression to the mean is more dramatic for more extreme
observations.  That is, the average child of modestly tall parents will be
a little bit shorter, while the average child of extremely tall parents
will be much shorter than the parents.  

Ignoring environmental effects, it has been proposed that height is a
multigene trait, and therefore regression to the mean reflects multigenic
inheritance.  Let's assume there are a number of genes which determine
height, and each gene has both "tall" (t) and "short" (s) alleles.  Thus,
tall individuals carry a preponderance of "tall" alleles at height
determining genes.  Let's say there are ten height genes.  If we had two
tall parents, each carrying 75% "tall" alleles, what fraction of the
alleles transmitted to the kid will be "tall" alleles?  Well, if sampling
is random, we'd expect to see the kid get 75% "tall" from each parent and
to be the same height.  So something else causes regression to the mean. 
The most plausible explanations are allelic interaction (dominance) and
locus interaction (epistasis).  Dominance means that the contribution of a
"tall" allele to height at a given gene depends on the genotype: the effect
of a "tall" allele depends on whether the other allele at the same gene is
"tall" or "short".  Epistasis is the same notion except involving multiple
genes: the contribution of "tall" alleles at gene A is dependent on
genotype at locus B.  

Returning to our example, the parents are probably tall not only due to
carrying 75% "tall" alleles each, but also because they carry them in the
right combinations.  Even though the kid will get 75% "tall" alleles, the
kid is unlikely to have them in the right combinations, and will therefore
tend to be shorter on average, even if occasionally the kid will get just
the right combination and will be taller than either parent.

So now let's get back to IQ.  If we assume that IQ is as easy to measure as
height (it isn't), that there are no environmental effects (there are),
that the amount of variation in the African American population is the same
as in the European American population (it is not), and that on average
African Americans have significantly lower IQ than European Americans
(depends on who you ask), then your son would be right: 140 IQ parents from
the less IQ endowed population would be more extreme relative to the
average, and their children would therefore tend to have lower IQ than
children of parents with a 140 IQ from the more IQ endowed population.  

As you can see, if his assumptions were correct, your son would be right. 
However, I think there are enough flawed assumptions that you needn't worry
that he's correct.

   Chris

A good review of regression to the mean is available at http://trochim.human.cornell.edu/kb/regrmean.htm 

Galton's original regression data is available at http://www.stat.ucla.edu/history/regression.gif