Genetics of Complex Traits:
Quantitative Genetics
Genetic Variation
Discrete Variation
(presence/absence of tail)
Continuous Variation (height)
Quantitative Genetics
Polygenic
Environmental influences
Have continuous (not discrete) distributions
Can be measured on a quantitative scale
Height
Weight
Athletic ability
Risk of heart disease
Risk of diabetes
Risk of cancer
Intermediate dominance
= “additive” gene action
Partial dominance
2
2
Frequency
Discrete distribution
1
1
1
0
RR
Rr
Genotype
rr
P:
AABB
red
AaBb
F1:
x
x
aabb
white
AaBb All Pink
F2:
AB
AB
AABB
Red
Ab
AABb
Lt Red
aB
AaBB
Lt Red
ab
AaBb
Pink
Ab
AABb
Lt Red
AAbb
Pink
AaBb
Pink
Aabb
Lt Pink
aB
AaBB
Lt Red
AaBb
Pink
AaBb
Pink
aaBB
Pink
aaBb
Lt Pink
Aabb
Lt Pink
aaBb
Lt Pink
aabb
white
ab
1 Red: 4 Lt Red: 6 Pink: 4 Lt Pink: 1 white
Two additive genes: discrete
phenotypic distribution
6
6
5
4
4
4
3
2
1
1
1
0
Red
Lt Red
Pink
Light Pink
White
Color of wheat kernels: three
additive genes
aabbcc
AABBCC
AaBbCC
Frequency Distribution of Height of
the Band
mean=68 inches
n =160
Properties of
distributions
n
Mean = x 
x
i1
n
i
= 68 inches

Variance =
n
 2  Var 
 x
i1
i
x

n 1
2
= 9.5 in2
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
Mean = 68
in
Phenotypic
Variance
Var = 9.5 in2
Phenotypic variance = Genetic variance + Environ. variance
VP
=
VG
+
VE
Phenotypic variance = Genetic variance + Environ. variance
VP
=
VG
+
VE
Genetic variance = Additive variance + Dominance Variance
VG
VP
=
VA
=
VA +
+
VD
VD
+
VE
Additive and Dominance Effects
(No Environmental Effects)
P:
Dominance effects
AA
Aa
aa
+2
+2
+0
AABB
20cm
F1:
F2 Genotypes:
Genotypic
Effects
Additive effects
BB
Bb
bb
+2
+1
+0
aabb
16 cm
x
Aa Bb
19 cm
AABB AABb AAbb AaBB
AaBb
Aabb
aaBB
aaBb
aabb
+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
Dominance effects
AA
Aa
aa
+2
+2
+0
F1:
F2 Genotypes:
Genotypic
Effects
Additive effects
BB
Bb
bb
+2
+1
+0
Aa Bb
19 cm
x
AABB AABb AAbb AaBB AaBb
Aa Bb
19 cm
Aabb
aaBB
aaBb
aabb
+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
VP
=
1.333 =
VA +
VD
+
1.0 + 0.333 +
VE
0
Frequency in
population
VP
VA
VD
VE
=
=
=
=
1.333 cm2
1.0
0.333
0
0.4
0.3
0.2
0.1
0
16
17
18
19
Length in inches
20
Heritability
VP
=
1.333 =
VA +
+
VE
1.0 + 0.333 +
0
Broad-sense heritability
VD
H2 = VG/VP = 1.0
Narrow-sense heritability h2 = VA/VP = 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 Equation
R = h2 S
A 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
h2
= 0.8
If large bills
are favored in
drought years,
what effect will
an El Nino
year have on
the
population?
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?