Introduction to Quantitative Genetics

In principle:

Extend single-locus  multi-locus  quantitative models

1AA : 2Aa : 1 aa (1AnAn : 2Anan : 1anan)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): genetic variation  can be correlated with phenotypic variation

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 is minimal)
              Ex.: Suppose a trait is influenced by 5 loci, each with two alleles A & a
                         35 = 243 genotype classes in 11 phenotype classes variation continuous

Phenotypic variance ( 2P ) has two sources: genetic (2G) & environmental (2E) variance
       Variance is additive:       
2A+B  =  2A  +  2B

       phenotypic variance      2P  =  2G  +  2E2GxE

             where 2GxE is interaction variance, if 2G  and  2E are not independent

              If  2G  and  2E  independent (or assumed so),  2Gx ~ 0

      additive variance            2A  =  2G  +  2E  

      Heritability                          h2   =  2G  /  2A   =  2G / (2G  +  2E)

          "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  2GxE

                       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           
shows association between variables
(cf. regression analysis)
                    Mid-parent value
Offspring / mid-parent correlation estimates heritability

                    Limits of prediction from correlation & regression

            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'?

Quantitative Trait Loci (QTL) analysis:
et al. (1993) shows nature of experimental design and analysis
             LOD analysis; a Poker example.   

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 rrww 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.: Parental x Offspring differences in height
                    Ex.: Predisposition to obesity within families.

Myth 3: Heritability is a measure of 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
                     h2     2Genotype   /  2Phenotype  not including 2E  & 2GxE
                     the assumption that h2  2P   =  2G   ignores   2E  & 2GxE

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 2GxE is large

               Ex.: Heritability of Myopia (National Public Radio, 2015 Mar 24)

See also:
         Gray & Thompson (2004) [Fig. 3]. Neurobiology of intelligence: ethics and science, Nature Revs Neurosci 5: 471-482.
         American Eugenics Archive for a survey of past excesses through ignorance
         Wray & Visscher (2008) Estimating trait heritability. Nature Education 1: 29

All text material ©2016 by Steven M. Carr