In principle:

Extend single-locus  multi-locus  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 variance due to genetic variance

"Is It Genetic?" : Genotype / Environmental interaction is variable & unpredictable

Quantitative Trait Loci (QTL) associates genetic variation with phenotypic variation

Genome-Wide Association Study (GWAS) associates SNP variation with phenotype

Variation can be quantified (review)
      mean  standard deviation:  σ   
      variance: σ²

Variation follows "normal distribution" (bell-curve) iff
              Multiple loci are involved  (quantitative)
              Each locus has about equal effect (additive)
              Each locus acts independently (interaction is minimal)
              Ex.: Suppose trait influenced by 5 loci, each with two alleles A & B
                         3⁵ = 243 genotype classes in 11 phenotype classes variation continuous

Phenotypic variance (σ²_P ) has two sources: genetic (σ²_G) & environmental $σ$(σ²_E) variance
       Variance is additive:        σ²_A+B  =  σ²_A  +  σ²_B

       phenotypic variance       σ²_P  =  σ²_G  +  σ²_E +  σ²_GxE

             where σ²_GxE interaction variance, if σ²_G  and  σ²_E not independent

              If  σ²_G  and  σ²_E  independent (or assumed so),  σ²_{GxE  ~ 0}

      additive variance            σ²_A  =  σ²_G  +  σ²_E  

      Heritability                          h²   =  σ²_G  /  σ²_A   =  σ²_G / (σ²_G  + σ²_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
                  ignoring interaction variance  σ²_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 (often) 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 / mid-parent correlation estimates heritability

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

            Heritability typically estimated in a single environment.

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?" Common Myths about Genetics

Myth 1: Genetic diseases are determined by the presence or absence of a "gene for a trait"
                Everyone has the same set of genes: persons with alternative forms a "genetic trait" have different forms of the gene (alleles)
                        Ex.: Allelic variants of the PAH gene result in a non-functional enzyme unable to metabolize phenylalanine (Phe)
                                If not treated by reduction of dietary Phe, this results in the disease Phenylketonuria (PKU)
                                PAH is not a gene "for" PKU , rather a gene for an enzyme that prevents PKU
                        Ex.: The typical function of "cancer genes"  is to prevent cancer: some allelic variants fail to perform this function properly
                                "Removal" of these genes would not "cure cancer": removal of defective spark plugs does not allow a car to start

Myth 2: Genetic traits always follow the Mendelian Model
               Ex.: If rr ww peas are always green and wrinkled
                     Then persons with certain alleles "for" BRCA1 with always get breast cancer
               Many traits follow a Quantitative Model, with 10s ~ 100s of genes each contributing a small effect
                    Ex.: Mid-Parental x Offspring differences in height
                    Ex.: Predisposition to obesity within families.

Myth 3: Heritability is the same thing as Mendelian inheritance
                    Ex.: Traits with high "heritability" need not be genetically pre-determined
                         *** Heritability (h²) is a specific mathematical concept :
                                    the fraction of total measurable variation (variance) due to genetic variance  
                            h^{2     2}_Genotype   /  σ²_Phenotype  not including σ²_E  & σ²_GxE
                            the assumption that h²  =  σ²_P   =  σ²_G   ignores   σ²_E  & σ²_GxE

Myth 5: That which is "genetic" is fixed & unalterable
                Ex.: Phenylketonuria is perfectly "genetic" in the Mendelian manner AND perfectly treatable
                Ex.:Heritability, IQ, & Education
                      IQ test scores in Homo: h² = 0.7~0.8 within groups
                      Highly heritable traits can be highly modifiable by change of environment if σ²_GxE is large

All text material ©2019 by Steven M. Carr