Genetics of Complex Traits:Quantitative Genetics

Extra Credit Question Given in Email

Genetic Variation

Continuous Variation (height)

Discrete Variation (presence/absence of tail)

PolygenicEnvironmental influences

Have continuous (not discrete) distributions

HeightWeight

Athletic abilityRisk of heart disease

Risk of diabetesRisk of cancer

PolygenicEnvironmental influences

Have continuous (not discrete) distributions

Can be measured on a quantitative scale

Quantitative Traits

1

2

1

0

1

2

Genotype

Frequency

RR Rr rr

Discrete distribution

Partial dominanceIntermediate dominance= “additive” gene action

F2: AB Ab aB abAB AABB AABb AaBB AaBb

Ab AABb AAbb AaBb Aabb

aB AaBB AaBb aaBB aaBb

ab AaBb Aabb aaBb aabb

Red

Lt Red

Pink Lt Pink

Lt Red

PinkLt Red

Pink

Pink

Lt Pink

Lt Red

Pink

Pink

Lt Pink

Lt Pink

white

P: AABB red

x aabb white

F1: AaBb x AaBb All Pink

1 Red: 4 Lt Red: 6 Pink: 4 Lt Pink: 1 white

Two additive genes: discrete phenotypic distribution

1

4

6

4

1

0

1

2

3

4

5

6

Red Lt Red Pink Light Pink White

Color of wheat kernels: three additive genes

aabbcc AABBCC

AaBbCC

Several additive genes

Plus environmental “noise”

Additive Genes

# Additive genes # Phenotypes # Genotypes(n) (2n+1) (3n)

1 3 32 5 9 3 7 275 11 24310 21 59,049

20 41 3,486,784,401

Frequency Distribution of Height of the Band

mean=68 inches

Mean = = 68 inches

€

x =x i

i=1

n

∑n

Variance = = 9.5 in2

€

σ 2 =Var =x i − x( )

2

i=1

n

∑n −1( )

Properties of distributions

n=160

Types of Variance

Phenotypic variance: total variance of the population, includes variation from

genes and from the environment

Genetic variance: the variance that is due to variation among individuals in the

alleles that they have, excludes environmentally-caused variation

Phenotypic Variance

Var = 9.5 in2

Phenotypic variance = Genetic variance + Environ. variance VP = VG + VE

Mean = 68 in

Genetic variance = Additive variance + Dominance Variance VG = VA + VD

VP = VA + VD + VE

Phenotypic variance = Genetic variance + Environ. variance VP = VG + VE

Dominance effects Additive effectsAA Aa aa BB Bb bb+2 +2 +0 +2 +1 +0

P: AABB x aabb20cm 16 cm

F1: Aa Bb 19 cm

F2 Genotypes: AABB AABb AAbb AaBB AaBb Aabb aaBB aaBb aabbGenotypic

Effects +4 +3 +2 +4 +3 +2 +2 +1 +0

Phenotype(cm)

20 19 18 20 19 18 18 17 16

F2 proportions: 1/16 2/16 1/16 2/16 4/16 2/16 1/16 2/16 1/16

Additive and Dominance Effects (No Environmental Effects)

Dominance effects Additive effectsAA Aa aa BB Bb bb+2 +2 +0 +2 +1 +0

F1: Aa Bb x Aa Bb19 cm 19 cm

F2 Genotypes: AABB AABb AAbb AaBB AaBb Aabb aaBB aaBb aabbGenotypic

Effects +4 +3 +2 +4 +3 +2 +2 +1 +0

Phenotype(cm)

20 19 18 20 19 18 18 17 16

F2 proportions: 1/16 2/16 1/16 2/16 4/16 2/16 1/16 2/16 1/16

Mean = 18.5 cm Var = 1.333 cm2

Dominance effects Additive effectsAA Aa aa BB Bb bb+2 +2 +0 +2 +1 +0

F1: Aa Bb x Aa Bb19 cm 19 cm

F2 Genotypes: AABB AABb AAbb AaBB AaBb Aabb aaBB aaBb aabbGenotypic

Effects +4 +3 +2 +4 +3 +2 +2 +1 +0

Phenotype(cm)

20 19 18 20 19 18 18 17 16

F2 proportions: 1/16 2/16 1/16 2/16 4/16 2/16 1/16 2/16 1/16

VP = VA + VD + VE

Var = 1.333 cm2

1.333 = 1.0 + 0.333 + 0

Heritability

Broad-sense heritability H2 = VG/VP

Narrow-sense heritability h2 = VA/VP

VP = VA + VD + VE

1.333 = 1.0 + 0.333 + 0

= 1.0

= 0.75

Uses of heritability

• The degree to which offspring resemble their parents is determined by the narrow-sense heritability h2

• The efficacy of natural and artificial selection is also determined by h2

h2 = 1

h2 = 0

VA/VP = 1

VA/VP = 0

Efficacy of artificial selection: size of Labradors

Breeder’s Question

Q: A horse breeder wants to win the Kentucky Derby. If she breeds her mare to a really fast stallion, how likely is it that the colt will be faster than all the other three-year-olds when it runs in the Derby?

A: It depends on the heritability of running speed!

Breeder’s Equation

• R = h2 S• S = Selection differential difference between selected parents and the

population as a whole (within a generation)• R = response to selection difference between selected offspring and the

unselected population (across generations)

Breeder’s EquationR = h2 SA dog breeder chooses his largest dogs to

breed together. The average height of the breed is 60 cm (at the shoulder), and the dogs he chooses to breed average 70 cm tall.

He knows from previous work that the heritability of height is 0.5.

How big can he expect the offspring to be?

R = h2 S = 0.5 * 10cm = 5cm

Breeder’s Equation

R = h2 S = 0.5 * 10 cm = 5 cm

If the response to selection is 5 cm, he can expect his puppies to grow to be

60 cm + 5 cm = 65 cm tall

Exactly the same equation can be used to understand

natural selection!

Efficacy of natural selection:Darwin’s finches

If large bills are favored in drought years, what effect will

an El Nino year have on

the population?

h2 = 0.8

R = h2 S

Birds that survive the drought have bills that are 2 mm deeper (on average)

than the population mean.

Q: What will happen to the average bill depth in the next generation?