Parent Child
          Adoptive correlation

Heritability as a Phenotype x Genotype correlation

    Consider a set  on 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" educational environment. Upon testing, they achieve the same average score (115) as their adoptive parents.

    What does this tell us about the heritability of scores? Note that 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 h2) between them is therefore rBxC = 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
rCxA ~ -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)

Numerical example after Griffiths et al. (2002); All text material ©2016 by Steven M. Carr