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In a previous post, I discussed the opinions of “Duke of Leinster” as he now prefers to be known, who who has stated that he had an astonishing score of 1560 on the old much harder version of the SAT; a score that would be high enough to qualify for the Prometheus society which only accepts those who have intelligence tested at or above the one in 30,000 level. He has also stated that he is part of the prestigious BGI study which analyzes the genes of the super intelligent and that he has ancestors who have attended Ivy League schools and at least one who very famously survived the Titanic (or at least married someone who did). Obviously I have no way of verifying all these astonishing claims, but it’s clear just from reading his posts that he is very worldly, cultured and intelligent (despite his occasionally belligerent tone).

“Duke of Leinster” feels that the behavioral genetics community does not understand heritability. I’m not sure I do because I very ignorantly avoided science in school, but I have read a lot about IQ (especially Jensen’s work) and the topic comes up there, so I’m going to share my understanding.

Identical twins raised apart

In statistics there is a concept called correlation. For example, if you took many pairs of identical twins (separated since birth) and tested their IQ’s in later adulthood, you could plot the scores of each twin pair on a graph. The X access would record the IQ of one twin and the Y access would record the IQ of her co-twin. If there were a perfect correlation between the IQ’s of the twins, your graph would produce a perfect straight line when you connected all the dots, because an increase along the X access would be perfectly matched by an increase on the Y access.

However in real social science research, perfect correlations are virtually never observed, so your graph would look quite messy; however you could draw what’s called a line of best fit through the dots, and because both the X access and the Y access are using the same unit of measurement (IQ), the slope of that line (rise/run) would equal the IQ correlation between the identical twins reared apart. Identical twins reared apart have historically been studied because they’re assumed to have perfectly correlated geneotypes, but perfectly uncorrelated environments, though both those assumptions are oversimplifications.

Confusing part (you may want to skip this section)

Now here’s where things get confusing. When you square a correlation, you get the percentage of variability in X explained by Y (and vice versa). Heritability (symbolized H2) is defined as the percentage of a measured trait (i.e. IQ) explained by genes, which means it’s not a correlation, but rather a correlation squared. Does this mean we square the IQ correlation between the identical twins reared apart to estimate the heritability of IQ? No, we actually leave it alone because the correlation between the twins raised apart actually is the square of the correlation between the genotype and the phenotype. This is because when the correlation between one variable (IQ’s of identical twins) with another variable (IQ’s of their separated co-twins) is entirely mediated by both variables’ correlation with a third variable (IQ genotype), then the first correlation is the square of the second correlation.

So if the heritability of IQ is 0.8 by later adulthood (as scholar Arthur Jensen stated), then that would imply that identical twins raised apart correlate 0.8 in IQ by later adulthood, and that there’s a near perfect correlation of 0.89 between IQ and genes by later adulthood.

Broad vs narrow heritability

Now the 0.8 heritability refers to what’s known as “broad heritability” which means it includes gene-environment interactions. “Narrow heritability” is more meaningful because it excludes these. If I understand these concepts correctly, a person’s weight would be influenced by gene-environment interactions because people who are naturally quite muscular might be motivated to lift a lot of weights (because they know they have the genetic potential). So genes for a lot of muscle weight inspire one to engage in behaviors that create even more muscle weight (gene-environment interaction). By contrast, height would have narrow heritability because there are no exercises you can do to significantly increase your height.

It’s unclear whether IQ is more like height or like weight. If I had to guess I would say that crystallized IQ tests (i.e. tests that measure how much you have learned) are more like weight and have huge gene-environment interactions, but fluid IQ tests (i.e. tests that attempt to directly measure your ability to learn) would have narrow heritability (by later adulthood). However “Duke of Leinster” feels the entire fluid-crystallized dichotomy is silly because he feels that all IQ tests are measuring learned knowledge. He has cited evidence showing that crystallized IQ is actually more heritable than fluid IQ, however I don’t know if anyone has compared these abilities on narrow heritability.

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