Evolution at Multiple Loci:
Quantitative Genetics
I. Rediscovery of Mendel and
Challenges to Natural Selection
• Do traits that exhibit continuous variation
have a genetic basis?
• If the only traits which have genetic variation
are controlled by one or two loci then natural
selection not as important as mutation
• Darwin envisioned evolution to be a
continuous process of selection acting on
limitless genetic variation, with small changes
occurring in any one generation, but large
changes occurring over long periods.
Why the normal distribution: Central Limit Theorem
Mendelian genetics can explain quantitative traits
Ex. 1: NILSSON-EHLE: Red and White Kernel Color in Wheat
(red dominant, white recessive)
Ex. 2:
East’s work
with tobacco
Quantitative traits are influenced by the environment as well as genotype
Yarrow plant
1. Fisher’s prediction
Probability of Fixation
II. Neo Darwinian Synthesis
Theoretical models that support vs. contend the Darwinian model
2. Kimura’s
modification
Mutation Effect
3. Orr’s modification
Typical results
Testing the Models:
M. micranthus
M. guttatus
F1
F1
F2
BC
F2
Fenster & Ritland 1994
Corolla Width (mm)
No filter
Filtered image—
“bumblevision”
Segregation
Of floral types
Demonstrate
Genetic basis
Of trait
Differences
Convergent evolution??
Yosemite Sam thinks so
in the F2 generation
MC Qc
ML QL
x
MC Qc
ML QL
MC Qc
ML QL
If the map distance is 5 cm then there is a 95% chance that
the marker will be associated with the QTL in the F2:
1- r(MQ)
MC1 Qc
MC2
ML1 QL
ML2
x
MC1 Qc MC2
ML1 QL ML2
MC1 Qc
x
MC2
x
ML1 QL ML2
If the map distance between markers and QTL are 5 cm then
there is a 99.5% chance that one of the markers will be associated
with the QTL in the F2:
1-2 r(M1Q)(QM2)
1. Fisher’s prediction
Probability of Fixation
Theoretical models that support or contend with the Darwinian model
2. Kimura’s
modification
Mutation Effect
3. Orr’s modification
Alleles with a distribution of effect sizes
contribute to adaptations
III. Measuring Selection and Response to Selection
on Continuous Traits
A. Heritability
Song sparrows
Galapagos finches
Class
Data
D
Female Wt
0.015
e
n
s
0.01
i
t
y
0.005
0
90
105
120
135
150
165
180
195
210
F e ma l e Wt
D
e
Female HT
0.1
n
s
i
t
0.05
y
0
58
60
62
64
66
F e ma l e Ht
68
70
72
74
D
Male Wt
0.015
e
n
s
0.01
i
t
y
0.005
0
100
125
150
175
200
225
250
275
Ma l e Wt
0.15
Male Ht
D
e
n
0.1
s
i
t
0.05
y
0
62.5
65.0
67.5
70.0
Ma l e Ht
72.5
75.0
77.5
Heritability of Female Wt
Mo d e l
F e ma l e Wt
=
91. 1457
Eq u a t i o n
+
0. 2807
Mo t h e r Wt
200
F
e
m
a
150
l
e
W
t
100
100
150
200
Mo t h e r Wt
250
Heritability of Female Wt
Mo d e l
F e ma l e Wt
=
75. 0179
Eq u a t i o n
+
0. 3094
F a t h e r Wt
200
F
e
m
a
150
l
e
W
t
100
150
200
F a t h e r Wt
250
300
Heritability of Female Wt
Mo d e l
F e ma l e Wt
=
57. 2357
Eq u a t i o n
+
0. 4499
Mi d P a r e n t Wt
200
F
e
m
a
150
l
e
W
t
100
150
200
Mi d P a r e n t Wt
250
Heritability of Female Ht
Mo d e l
F e ma l e Ht
F
=
Eq u a t i o n
48. 4108
+
0. 2592
Mo t h e r Ht
70
e
m
a
l
65
e
H
t
60
55
60
65
Mo t h e r Ht
70
75
Heritability of Female Ht
Mo d e l
F e ma l e Ht
F
=
26. 1514
Eq u a t i o n
+
0. 5575
F a t h e r Ht
70
e
m
a
l
65
e
H
t
60
65
70
F a t h e r Ht
75
Heritability of Female Ht
Mo d e l
F e ma l e Ht
F
=
23. 3220
Eq u a t i o n
+
0. 6198
Mi d p a r e n t Ht
70
e
m
a
l
65
e
H
t
60
62
64
66
68
Mi d p a r e n t Ht
70
72
Heritability of Male Wt
Mo d e l
Ma l e Wt
=
137. 452
Eq u a t i o n
+
0. 1867
Mo t h e r Wt
250
M
a
l
200
e
W
t
150
100
150
Mo t h e r Wt
200
Heritability of Male Wt
Mo d e l
Ma l e Wt
=
107. 950
Eq u a t i o n
+
0. 2951
F a t h e r Wt
250
M
a
l
200
e
W
t
150
150
200
250
F a t h e r Wt
300
Heritability of Male Wt
Mo d e l
Ma l e Wt
=
99. 5721
Eq u a t i o n
+
0. 3870
Mi d P a r e n t Wt
250
M
a
l
200
e
W
t
150
150
200
Mi d P a r e n t Wt
250
Heritability of Male Ht
Mo d e l
Ma l e Ht
=
29. 1168
Eq u a t i o n
+
0. 6420
Mo t h e r Ht
75
M
a
l
e
70
H
t
65
60
65
Mo t h e r Ht
70
Heritability of Male Ht
Mo d e l
Ma l e Ht
=
31. 2457
Eq u a t i o n
+
0. 5623
F a t h e r Ht
75
M
a
l
e
70
H
t
65
65
70
F a t h e r Ht
75
Heritability of Male Ht
Mo d e l
Ma l e Ht
=
14. 7069
Eq u a t i o n
+
0. 8275
Mi d p a r e n t Ht
75
M
a
l
e
70
H
t
65
62
64
66
68
Mi d p a r e n t Ht
70
72
Conclusions from class data:
Distributions of Wts and Hts are roughly normal
Distribution indicates that Wts and Hts are likely controlled
by many loci, = many loci are segregating alleles that
contribute to wt and ht differences among individuals
Heritabilities for Ht >> WT
50% >> 30%
Interpretation for other human traits??
Black
Red
Red
B. Selection
t
t*
S=
S= t* - t
Functional significance of trait
variation
C. Response to Selection
The “2” term is meaningless, just an historical artifact of the derivation
The slope of the best-fit line is 0.13
Stabilizing selection on a gall-making fly
Disruptive selection on bill size in the black-bellied seedcracker
IV. Phenotypic Plasticity
Inducible defenses in Daphnia
Genetic by
Environment
Interaction
in yarrow
Low Altitude Site (Stanford)
High Altitude Site, Mather California
Plasticity can evolve
Conclusion
• Continuous traits are common
• Continuous traits can be heritable
• Continuous traits can respond to
selection
• Darwin’s notion of natural selection
acting on continuous variation is
consistent with evidence
• Genetic x Environment interactions
may be important
• G x E is a trait that can evolve