A polygenic trait usually demonstrates a great deal of phenotypic variability in a population. Some of this variation is genetic, VG, due to the different genotypic classes in the population and to dominance and epistatic effects. Some of the variation is environmental influence on the genes, VE. (There may also be gene-environemntal interaction variance; we will, for now, assume this to be 0). Thus, there are two major components of the total phenotypic variability observed in a sample, and they are additive:

VP (total phenotypic variance) = VG (genetic variance)+ VE(environmental variance)

Scientists and others have long been interested in methods to measure these quantities. VP is the total statisitcal variance for the trait in the population and can be statistically calculated from population data. However, it is not easy to determine VG and VE; even when estimated values are obtained, their accuracy is in doubt and they pertain only to the population at that one time, in that one environemnt. The values would likely change if the environment changed or if a different sample (from a different population) were to be measured for that trait. Since one can't partition an individual into genetic versus environmental components of a trait, measures of variability in samples of populations are used, even though these measures need to be treated with a great deal of caution.

The heritiability of a trait, H, is defined as the fraction of the total variance for that trait that is genetic.

Notice that H is the fraction of the variability that is genetic; it is not the fraction of the trait that is genetically determined. (That cannot be measured). Notice that if there were no genetic variation (all individuals having the same genotype), then VG = 0, and H = 0. Conversely, if there were no environmental variability (each individual subject to identical environmental influences), then VE = 0 and H = 1. These are the theoretical limits for the H value. Of course, there always is some VG and some VE for any polygenic trait, so H would lie somewhere between 0 and 1.

It is extremely important to interpret the H value correctly. An H value of 0.5 or greater is considered a trait with high heritability -- most of the variance for the trait is genetic. This is not the same as saying that the trait is mostly genetically determined; the trait may, in fact, not be influenced much by the genes at all, but still happen to have a diversity of genotypes in the population and not much environmental variation. Consequently, VG comes out higher than VE, giving a high H value. Conversely, an H value of less than 0.2 is considered a low heritability value, meaning that most of the variance for the trait is environmental. Again, it is the variability that is being judged, not necessarily the trait itself. It could be that the environment does not influence the trait all that much, but if there is almost no genetic variation in the population for this trait, then what little VE there is still accounts for most of the variation, giving a low H value.

Because the environmental influences are so diverse from one population to another, H values apply only to the population on which they are measured at the time of the measurement. They should never be extended to a comparison of populations, unless the environments of the populations are identical. With humans, for example, this is impossible to claim. When someone says that H = 0.8 for human IQ and, therefore, IQ is mostly genetically determined, and, therefore, any differences between populations (races) in IQ are genetically based, this person is making at least three errors by making this claim:

1) H = 0.8 is the value obtained for samples of Caucasian populations; it applies only to the specific population (s) sampled in the test. African Americans have not been as extensively tested as Caucasians. If one were to compare them, one would have to assume identical environmental influences on IQ for African Americans as for Caucasians. Obviously, African Americans and U.S. Caucasians have different cultural and socio-economic realities in the U.S. The issue, then, is whether cultural and socio-economic differences between African Americans and Caucasians are inconsequential insofar as affecting IQ scores -- probably not.

2) H = 0.8 is indeed a high value, but it means only that there is extensive genetic variability (as compared to environmental variability). This should never be interpreted as necessarily meaning that there is a large genetic component to IQ determination itself.

3) There are indeed differences in average IQ between African americans and Caucasians. To say that these differences are genetic is, however, scientifically invalid. One cannot use the H value of one population sample and compare it to another population sample unless that other population is under identical environmental influences.

Scientifically, there are insufficient data and knowledge of what determines IQ to make any definitive conclusions. There probably is a significant VGE term -- interaction between genes and environment -- so that in reality VP = VG + VE + VGE. The VGE may be bigger that either VG or VE alone -- who knows?

The genetic view on IQ determination would be something as follows: Each individual's genes set a range of possible IQ values, but where within that range (upper and lower limits) the IQ is realized depends on environmental factors. Thus, the genetic view is that (1) people differ in their genetic basis for IQ -- everyone isn't created equal -- because no two people are genetically identical, (2) environment sets IQ within each person's range potential, and (3) different genotypes (individuals) probably respond to different environments --there is no single best environment for all genotypes (the VGE).

One can get a rough idea of the extent of genetic involvement in a trait by comparing concordance values for that trait between MZ and DZ twins. Consider, for example, diabetes mellitus. MZ twin concordancy is 47% versus 9.7% for DZ twins. The comparison of MZ twins with DZ shows a genetic basis, but it also shows an environmental role, since 47% is less than 100%. In contrast, MZ and DZ twins have the same concordance value for death from acute infection; if MZ = DZ concordance, then there is little if any genetic basis for the trait.

To get an H value we need V (variance) values to plug into H = VG/VE. Consider the trait "height". Measure the V in height for MZ twins. Since these are genetically identical, VMZ = VE = all environmental variance. If we use DZ twins of like sex, then we can (maybe) assume that they have the same VE as MZ twins, so we have a value for VE.

The variability value for DZ twins underestimates the overall population VG, because DZ twins have half their genes in common and, therefore, aren't as variable genetically as other members of the population. So, double the variabilty of DZ twins to extend it to the population as a whole. Also notice that VDZ = 1/2VG + VE, so VDZ - VE = 1/2 VG, or VG = 2(VDZ - VE).

Now our assumption that we can use VMZ as VE comes into play, and we get VG = 2(VDZ - VMZ). Thus, the value of H is calculated from measured VDZ and VMZ values as H = 2(VDZ - VMZ)/VP.

H values so calculated are subject to many errors, especially because of the VMZ = VE assumption: VE for DZ may, in fact, be higher than VE for MZ.

Going back to IQ, researchers have, in this manner, calculated H to be somewhere around 0.6 - 0.8. Other studies using correlation coefficients also suggest large H values. MZ twins reared together show a correlation coefficient of 0.85 (expect 1.00 if totally genetically determined). MZ twins reared apart give a value of 0.65 (less than 0.85), showing environmental component. Sibs reared apart give a value of 0.25, showing a genetic component. The data, therefore, show both genetic and environmental components involved in the determination of IQ.