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Quantitative Genetics of Natural Variation:
some questions
Do most adaptations involve the fixation of major genes?
micromutationist view: adaptations arise by allelic substitution of slight effect
at many (innumerable) loci, and no single substitution constitutes a major
portion of an adaptation (Darwin, Fisher)
macromutationist views:
1. single “systemic” mutations produce
complex adaptations in essentially
perfect form (Goldschmidt)
2. adaptation often involves one or a few
alleles having large effects
• Of 8 studies, only 3 consistent with
changes involving > 5 loci (Orr and Coyne 1992)
Quantitative Genetics of Natural Variation:
some questions
• How many loci contribute to naturally occurring phenotypic
variation, and what are the magnitudes of their effects?
• What sorts of genes —and changes in these genes—are
responsible for trait variation within populations
(e.g., transcription factors, structural genes, metabolic genes)
• Do the same genes that contribute to variation within species also
contribute to variation between species?
• What genes underlie evolutionary novelties?
• What are the genetic bases for evolutionary novelties?
• How do pleiotropic effects of genes evolve?
Answers require a mechanistic approach towards identifying the
relevant loci and how genetic differences are translated into
phenotypic differences
Quantitative traits depend on multiple
underlying loci
one locus +
environment
one locus
four loci +
environment
two loci +
environment
many loci +
environment
Phenotypic Value
and Population Means
P=G+E
Phenotypic value = Genotypic value + Environmental Deviation
genotype
genotypic value
A2A2
–a
Genotype
A1A1
A1A2
A2A2
0
Freq
p2
2pq
q2
Value
+a
d
-a
A1A2
A1A1
d
+a
Freq x Val
p2a
2pqd
-q2a
Sum = Pop Mean = a(p-q) + 2dpq
Timing of Metamorphosis
The majority of organisms on planet earth have complex life cycles
Predictable
Larval Habitat
Hatching
Metamorphosis
Predictable
Ephemeral Pond
Time
Thyroid Hormone Receptors as Candidate Genes for
Variation in Metamorphic Timing
Hypothalamus
TRH
Pituitary
TSH
Thyroid
TH
An extreme difference in
metamorphic timing
Target cells
T4
deiodionation
T3
TRs
transcription
Thyroid Hormone Receptors : A Hypothetical Example
Thyroid Hormone Receptor
Alpha Genotype
Timing of
Metamorphosis
(Days)
A1A1
A1A2
A2A2
200
160
150
d
-15
a
-25
25
0
Homozygote
Midpoint
(175)
-a
Genotype
A1A1
A1A2
A2A2
Freq
p2
2pq
q2
Value
25
-15
-25
Freq x Val
p2(25)
2pq(-15)
-q2(25)
Sum = Pop Mean = 25(p-q) + 2(-15)pq
(adds time)
(reduces time)
p = f(A1)
q = f(A2)
A1A1
A1A2
A2A2
0.0
1.0
0
0
-25
0.3
0.7
2.25
-6.3
-12.25
-16.3 (158.7)
0.5
0.5
6.25
-7.5
-6.25
-7.5 (167.5)
0.7
0.3
12.25
-6.3
-2.25
3.7 (178.7)
1.0
0.0
25
0
0
Mean
-25 (150)
25 (200)
Let’s Consider a Second Locus
Thyroid Hormone Receptor
Alpha Genotype
Timing of
Metamorphosis
(Days)
A1A1
200
0
A1A2
A2A2
160
150
Thyroid Hormone Receptor
Beta Genotype
Timing of
Metamorphosis
(Days)
A1A1
A1A2
A2A2
200
a
0
140
-a
-30
30
Homozygote
Midpoint
(170)
Genotype
A1A1
A1A2
A2A2
Freq
p2
2pq
q2
Value
30
0
-30
Freq x Val
p2(30)
2pq(0)
-q2(30)
Sum = Pop Mean = 30(p-q) + 2(0)pq
(adds time)
(reduces time)
P = f(A1)
Q = f(A2)
A1A1
A1A2
A2A2
0.0
1.0
0
0
-30
-30 (140)
0.3
0.7
2.7
0
-14.7
-12 (158)
0.5
0.5
0
0
0
0.7
0.3
14.7
0
-2.7
12 (182)
1.0
0.0
30
0
0
30 (200)
Mean
0 (170)
Consider the joint effect of both TH Loci
Total Range = 2Sa=110
Tha A1A1
Thb A1A1
Timing of
Metamorphosis
(Days)
Tha A2A2
Thb A2A2
227.5
a
0
55
55
Average
Homozygote
Midpoint
(172.5)
Overall
Mean
=
S a(p-q) + S 2dpq
117.5
-a
Genotypic value is not transferred from parent to
offspring; genes are.
Need a value that reflects the genes that an
individual carries and passes on to it’s offspring
Breeding Value
Empirically: An individual’s value based on the mean deviation of its progeny
from the population mean.
Theoretically: An individual’s value based on the sum of the average effects
of the alleles/genes it carries.
Average Effect of an Allele
Type of
gamete
Values and Freq
of gametes
A1A1
A1
A1A2
A2A2
a
d
-a
p
q
A2
p
Mean value
of genotypes
pa + qd
q
-qa + pd
Population
mean
-a(p-q) + 2dpq
Average
effect of
gene
q[a+d(q-p)]
-a(p-q) + 2dpq -p[a+d(q-p)]
average effect of An:
an = mean deviation from the population mean of individuals that received An
from one parent, if the other parent’s allele chosen randomly
a1 = pa + qd - [ a (p – q) + 2dpq ]
.
population mean
f (A1)
f (A2)
a1 = q [ a + d (q – p)]
a2 = –p [ a + d (q – p)]
Average Effects
Frequency q (A2 orTHa2)
0.0
0.3
0.5
0.7
1.0
a: THa1
0
9.3
12.5
13.3
10
a2: THa2
-40
-21.7 -12.5
-5.7
0
d = -15; a = 25
Theoretically: An individual’s value based on the sum of the
average effects of the alleles/genes it carries.
Genotype
Breeding Value
A1A1
2a1
A1A2
a1 + a2
A2A2
2a2
Breeding Values - THa example
A2 or Tha2
Pop Mean
A1A1
A1A2
A2A2
q = 1.0
150
20
10
0
q = 0.7
158.7
26.6
7.6
-11.4
q = 0.5
167.5
25
0
-25
q = 0.3
178.7
18.6
-12.4
q = 0.0
200
0
-40
-43.4
-80
Sum of average effects
across loci
A1A1
A1A2
A2A2
2a1
a1 + a2
2a2
=
+
Breeding Value
(A)
B1B1
B1B2
B2B2
2a1
a1 + a2
2a2
(breeding values)
(breeding values)
G=A+D
Genotypic
Value
=
Additive effects
of genes
+
Dominance
deviation
End Here: Continue Next
Monday
Partitioning the phenotypic value
genotypic value
of individual
G=A+D
two-locus:
breeding
value
breeding value
dominance
deviation
G = G1 + G2 + I12
interaction
P = A1 + D1 + A2 + D2 + I12
genotypic value
P=G
Pop
Mean
genotypic value
d=3/4a, q = 1/4
deviations from population mean
phenotypic value
of individual
Environmental effects on phenotypes
One locus, two alleles
P=A+D
One locus, two alleles + environmental variation
P=A+D+E
environmental
deviation
Amount of genetic variation in a population depends on
# of genotypes, genotypic value, and gene frequencies.
More variation
0.75
Less variation
0.75
p = 0.5
p = 0.9
0.50
0.50
0.25
0.25
9
A1A1
10
A1A2
Mean
11
A2A2
9
10
11
A1A1
A1A2
A2A2
Mean
Components of phenotypic variation
a = d = 0.07
P=A+D+I+E
V
Variance partitioning:
VP =
VG
+
VE
.
VP = VA + VD + VI + VE
total
phenotypic
variance
additive
genetic
variance
dominance
genetic
variance
interaction
(epistatic)
genetic
variance
f (A1)
environmental
variance
• Phenotypic variation can be decomposed into additive genetic and other variation
• Relative contributions of different sources depend on allele frequencies