Gaussian curves are specified by just two parameters, the mean and the variance (or the standard deviation, which is the square root of the variance). Variances have the useful property of being additive when they are due to independent causes. Thus, the overall variance of the phenotype VP is the sum of the variances due to the individual causes of variation—the genetic variance VG and the environmental variance VE :
VP = VG + VE
VG can in turn be broken down to a variance VA, which is due to simply additive genetic effects, and two extra terms. VD accounts for dominance effects: because of dominance, the effect of a certain combination of alleles at a locus may not be simply the sum of their individual effects. VI is an interaction variance: the overall effect of genes at several loci may not be simply the sum of the effects that each would have if present alone:
VG = VA + VD + VI
Therefore:
VP = VA + VD + VI + VE
The heritability (h2) of a trait is the proportion of the total variance that is genetic (the h2 notation reflects the fact that heritability is a correlation coefficient). The broad heritability is defined as:
h2 = VG / VP
The narrow heritability, VA /VP , governs the response to selection. For animal breeders interested in breeding cows with higher milk yields, this is an important measure of how far a breeding program can create a herd in which the average animal resembles today’s best.
For humans, heritability figures require very careful interpretation. For many human traits, especially behavioral traits, the simple partitioning of variance into genetic and environmental components is not applicable. We give our children both their genes and their environment. Genetic disadvantage and social disadvantage often go together, so genetic and environmental factors are not independent. Moreover, different genotypes are likely to respond differently to different environments. A much-quoted study of the effects of poor upbringing on a person’s behavior in adult life (Caspi et al. [2002]; PMID 12161658; see Further Reading) illustrated this. In a sample of 1037 individuals in Dunedin, New Zealand, followed to age 26, these authors showed that, as expected, those who had suffered maltreatment in childhood were more likely to commit antisocial acts later on. However, the tendency was much stronger among those who had a certain common variant in the MAOA gene that encodes monoamine oxidase. A variable tandem repeat polymorphism present in 35% of the group caused low expression of the enzyme, which is important in regulating turnover of the neurotransmitter serotonin. Individuals with low expression of MAOA were much more prone to respond to child hood abuse by developing antisocial behavior.
If genetic and environmental factors are not independent, we need to introduce additional variances to account for the correlations or interactions between specific genotypes and specific environments. A proliferation of variances can rapidly reduce the explanatory power of the models, and in general this has been a difficult area in which to work.
Misunderstanding heritability
The term “heritability” is often misunderstood. Heritability is quite different from the mode of inheritance. The mode of inheritance (autosomal dominant, polygenic, and so on) is a fixed property of a trait, but heritability is not. Heritability of IQ is shorthand for heritability of variations in IQ. Contrast the following two questions:
• To what extent is IQ genetic? This is a meaningless question. Somebody’s ability and willingness to sit down and fill in an IQ test paper depend on innumerable factors in both their genetics and their upbringing;
• How much of the differences in IQ between people in a particular country at a particular time is caused by their genetic differences, and how much by their different environments and life histories? This is a meaningful question (in so far as IQ is a meaningful concept), even if difficult to answer.
In different social circumstances, the heritability of IQ will differ. The more equal a society is, the higher the heritability of IQ should be. If everybody has equal opportunities, several of the environmental differences between people have been removed. Therefore more of the remaining differences in IQ will be due to the genetic differences between people.
