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 (review)
mean  standard deviation:
variance: 2

Variation follows "normal distribution" (bell-curve) iff
Multiple loci are involved  (quantitative)
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
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
Correlation
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:
Hamer
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)

```All text material ©2016 by Steven M. Carr