From looking at the responses to recent articles on the science of race by Massimo Pigliucci and Michael White, it is clear that a lot of people are coming poorly equipped to the quantitative genetics party. A great deal of fuss was made over the heritability of IQ. What does heritability mean?

RED FLAG: If someone says the heritability of X is Y, then they probably don't know what they are talking about.

Folks in the know, know that there are two kinds of heritability, broad sense and narrow sense. Those knowledgeable folks in the know are aware that it is extremely important to clearly state which heritability one is using, as the interpretation of each is different.

To understand broad sense heritability (traditionally symbolized as H^2), one needs to consider the following equation:
Var(P) = Var(G) +Var(E)+2*Cov(G,E)
where Var(P) is the phenotypic variance, Var(G) is genetic variance, Var(E) is the environmental variance, and Cov(G,E) is the genotype-environment covariance, which is generally 0 is experiments. Broad sense heritability is defined as Var(G)/Var(P), essentially the proportion of the total phenotypic variance that is due to all possiblegenetic effects (includes additive, dominance, epistatic, maternal, and paternal effects. For experimental purposes, it is frequently more practical to think of it as [Var(P)-Var(E)]/Var(P), because it is frequently much simpler to measure Var(P) and Var(E) than Var(G). In many cases it is formally appropriate to change our interpretation to the proportion of the total phenotypic variance that is not due to observed environmental variance.

Broad sense heritability tells us what proportion of the phenotypic variation is due to the genotypes of the individuals of the population. It tells us nothing about how similar the phenotype of a child will be to its parent. For that, we need the narrow sense heritability.

For the narrow sense heritability (traditionally symbolized h^2), we need to add some detail to our equation above by considering that:
Var(G)=Var(A)+Var(D)+. . .
where Var(G) is the genetic variance, Var(A) is the additive genetic variance, and the rest of the equation includes non-additive sources of variation, such as dominance effects [Var(D)]. The narrow sense heritability is defined as Var(A)/Var(P), essentially the proportion of the total phenotypic variance that is due to the additive genetic component. This measure allows one to know how well to the parent's phenotypic value of a character will predict the child's value. One can easily imagine how knowing the narrow sense heritability for traits like body size, milk production, and litter size would be very important for domestic animal breeders.

But, can we really interpret this as the proportion of phenotypic variation explained by additive genetic variation? That depends. Lets look at our equation for phenotypic variance again.
Var(P) = Var(G) +Var(E)+2*Cov(G,E)
If your experimental system is amenable and the experiments well designed, one can control the environmental variance and be sure that Cov(G,E)=0. These are key considerations in my own thesis project.

Human behavioral studies, such as on IQ, have it much more difficult. Environmental variance is very difficult to control experimentally. Statistical methods can be used to correct for the effects of known environmental variables, but one cannot be certain that all variables have been accounted for. Without knowledge of the environmental variance, one cannot determine the value of Cov(G,E). Underestimating environmental variance and assuming, without evidence, that Cov(G,E)=0, will lead to an overestimation of Var(G), Var(A), and both broad and narrow sense heritability.

In this context, it becomes impossible to interpret either broad sense or narrow sense heritability rigorously. It is even questionable whether these metrics have any validity at all.

For a more thorough examination of the issue of heritability of IQ along these lines, I recommend dusting off a Science paper from 1974 by Layzer entitled "Heritability analyses of IQ scores: science or numerology?". The Wikipedia page for "heritability" seems to be of high quality, if unreasonably dense (like many Wikipedia entries dealing with statistics), and generally recommendable. The "heritability of IQ" page, however, seems to be bit of an ideological battleground filled with poorly referenced claims. Therefore, I do not feel comfortable recommending it at this time.