Interaction of Heritability & Environment

Variation can be quantified

       mean  standard deviation:  σ
       variance: σ2

Variation has two sources: genetic (σ2G) & environmental (σ2E ) variance

      phenotypic variance     σ2P = σ2G + σ2E + σ2GxE
      additive variance           σ2A = σ2G + σ2E
      heritability                      h2  = σ2G  / σ2A  = σ2G / (σ2G + σ2E)

          "Heritability in the narrow sense" ignores interaction variance (σ2GxE)
           Identical genotypes produce different phenotypes in different environments.

           Ex.: Hypothetical IQ test scores change according to adoptive environment

Heritability calculation

Mean IQ score of Children is 20 pts higher than midpoint of Biological Parents;
     Each child's IQ score has been raised by modified adoptive environment.
     IQ scores of Biological Parents and their Children remain perfectly correlated (BxC): h2 = 1.0

Mean IQ score of Children is identical to that of Adoptive Parents (115)
    AND scores of Children and Adoptive parents are uncorrelated: r = h2 < 0.13

HOMEWORK:  Is it possible that Adoptive Parents have been matched with Biological Parents with proportionately higher or lower IQ scores?
                           Calculate the correlation between the Biological and Adoptive Parents.

All text material ©2019 by Steven M. Carr