In the comments below there was a question as to why outcomes for offspring from parents can vary a great deal even without regression toward the mean. First, about regression. It’s a confusing and misunderstood concept. There is a general statistical phenomenon here, but let’s focus on genetics. Often in the comments of this weblog I’ll get the rhetorical question which has the general form of “but what about regression toward the mean?” Usually this is a good clue that the person has no idea what they are talking about. What about regression toward the mean? It’s not a magical force which shifts populations back toward a set point in an orthogenetic fashion. Basically when you select an individual based on their traits, and infer about the likely character of their offspring, you can predict the expected impact of genes on the outcome. The phenotype is an intelligible signal of the nature of genes in a heritable trait, and genes are predictably transmitted to offspring. In contrast there is an “environmental”* component which you don’t understand, can’t control, and can’t account for. This component is often not transmitted across the generations, so fluke contingencies which lead to individuals who are sharply deviated from the average of a population are not replicated in subsequent generations, and individuals are expected to be more typical. A perfectly heritable trait would not regress at all on the population level.

But you can predict only so much from heritability. The above plot is from John Hawks’ anthropology class. You see that the regression line is 0.72, so the heritability as inferred from these data is such. That means that 72% of the variance in the phenotype, height, can be accounted for by variance in genes. That’s a population wide statistic. That doesn’t mean that height is “72% genetic” on the individual level. That’s not even wrong. Since heritability is a population wide measure, so you need to be judicious when inferring toward individuals.

Yet still tall parents tend to have tall children. If two tall parents had hundreds of children, then you could make some inferences about the average height of the children using the breeder’s equation. But observe that there’s still noise in the prediction. There’s going to be a distribution of outcomes. Height in the developed world is 80 to 90 percent heritable, but the correlation in heights between siblings is on the order of 0.5. Similarly, IQ is on the order of 50 percent heritable, but the correlation between siblings is on the order of 0.5. Presumably segregation and recombination are working in a fashion to mix and match the genomes of individuals so that even heritable polygenic traits aren’t quite as predictable as you’d think.

* Before someone points it out, I am aware this component often collapses non-additive genetic variance, such as epistasis.