Heritability as a Phenotype x Genotype correlation

Consider a
set of educational test
scores for six children (C) born to one set of
parents and adopted by another set. The mean score of the
birth parents (B)
(calculated as the
mid-parent value)
is 95. The
average score of the adoptive parents (A) is 115, 20 points higher
than that of the birth parents. After adoption, the
children are provided with an "enriched" environment. Upon testing,
they achieve the same average score (115) as their adoptive
parents.

What does this tell us about the heritability of test scores? Each of the children is exactly 20 points higher than the average of the birth parents: the correlation r (which is equivalent to the heritability, h^{2})
between them is therefore
r_{BxC} = 1.0. The adopted children
collectively achieve exactly the same mean score
as the adoptive parents.
However, the range of
the difference is scattered from -8 to +6 points: the *correlation
*between them is r_{CxA} ~ -0.09,
effectively zero.

That is, a trait that is perfectly heritable may also be perfectly changeable by modification of the environment. A modified environment increases the trait mean, but does not improve any particular individual in a specific way.

**HOMEWORK**: The
calculation of **heritability **as a **correlation
**is relatively straightforward, either as a spreadsheet
problem or from first statistical principles.**
In an enlarged data set**, (1) **repeat the
calculations** as a check of the results above. (2) It
might be the case that Adoptive parents are consciously or
unconsciously paired with children from Birth Parents of
similar socio-economic background.
Test this hypothesis by calculating the **correlation
**between Birth and Adoptive Parents (**B x A**)

What does this tell us about the heritability of test scores? Each of the children is exactly 20 points higher than the average of the birth parents: the correlation r (which is equivalent to the heritability, h

That is, a trait that is perfectly heritable may also be perfectly changeable by modification of the environment. A modified environment increases the trait mean, but does not improve any particular individual in a specific way.

Numerical
example after Griffiths et al. (2002); All text material
©2020 by Steven M. Carr