In principle:

We can extend single-locus  multilocus  quantitative models

1AA : 2Aa : 1 aa (1A_nA_n : 2A_na_n : 1a_na_n)ⁿ normal distribution

Genotype / Phenotype correlation Heritability
    Genotypic expression depends on environment
    Heritability (h²) estimates proportion of phenotypic variation due to genetic variation  

"Is It Genetic?" : Genotype / Environmental interaction is variable (& unpredictable)
       The Norm of Reaction describes this

Heritability is not inevitability;
    Genetics is not destiny

Variation can be quantified (review)

      mean  standard deviation: 
      variance: ²

Variation follows "normal distribution" (bell-curve) iff
              Multiple loci are involved  (quantitative)
              Each locus has about equal effect (additive)
              Each locus acts independently
                    [interaction variance (see below) is minimal]
              Ex.: Suppose a trait is influenced by 5 loci, each with two alleles A & a
                      A contributes 2 units to phenotype, a contributes 1 unit
                      Range of contributions = (2u aa : 3u Aa: 4u AA)⁵
                         mean = 15 units , range 10 ~ 20 units
                               (Aa Bb Cc Dd Ee) vs (aa bb cc dd ee ff ~ AA BB CC DD EE FF)
                         3⁵ = 243 genotype classes in 11 phenotype classes => variation continuous

Variation has two sources: genetic (²_G) & environmental (²_E) variance
       Variance is additive:        ²_A+B  =  ²A  +  ²B

      phenotypic variance      ²_P  =  ²G  +  ²_E +  ²_GxE

             where ²_GxE is the interaction variance, if ²G  and  ²_{E are not independent}

              If  ²G  and  ²_E  are assumed to be additive, then the interaction variance  ²_{GxE  ~ 0}

      additive variance            ²_A  =  ²G  +  ²_E  

      Heritability                          h²   =  ²G  /  ²_A   =  ²G / (²G  +  ²_E)

          "heritability in the narrow sense" genetic component of the additive variance
           heritability h² is the fraction of the (additive) phenotypic variance due to genotypic variance
                  assuming genotype / phenotype relationship is independent of environment

                  ignoring interaction variance  ²_GxE
                       genotype / phenotype relationship differs  in different environments.
                       Ex.: same strain of corn produces different yields in different fields

       Artificial breeding indicates that phenotypic variation is highly heritable
             Artificial selection on agricultural species
                  Commercially useful traits can be improved by selective breeding
             Common Garden experiments           
             Correlation shows association between variables (cf. regression analysis)
                    Mid-parent value
                    Offspring / midparent correlation estimates heritability

            For many quantitative traits in many organisms:  h² = 0.5 ~ 0.9

Heritability is typically calculated in a single environment.

The Norm of Reaction mediates genotype through environment to produce phenotype
             Variation within groups: Is variation 'genetic' ?
             Variation among groups: Are differences 'genetic'?
                  

Genetics, Heritability, & Society

"Is it Genetic?"
       Myth 1: That which is heritable is purely genetic
                   phenotypic variance       ²_P  = ²_G   [ignore   ²_E  & ²_GxE]

       Myth 2: That which is genetic is fixed & unchangeable

All text material © 2012 by Steven M. Carr