1. 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)

2. 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

3. Quantitative traits depend on multiple underlying loci
one locus +
environment
two loci +
environment
one locus
four loci +
environment
many loci +
environment

4. Phenotypic Value and Population Means
P = G + E
Phenotypic value = Genotypic value + Environmental Deviation
A2A2
A1A2
A1A1
genotype
– a d
+ a
genotypic value
Genotype Freq Value Freq x Val
A1A1 p2 +a p2a
A1A2 2pq d pqd
A2A2 q2 -a q2a
Sum = Pop Mean = a(p-q) + 2dpq

5. Timing of Metamorphosis
The majority of organisms on planet earth have complex life cycles
Predictable
Larval Habitat
Hatching
Metamorphosis
Predictable
Ephemeral Pond
Time

6. Thyroid Hormone Receptors as Candidate Genes for
Variation in Metamorphic Timing T3
Hypothalamus
TRH
TSH
TRs
transcription
Target cells TH
Pituitary
Thyroid T4
deiodionation
An extreme difference in
metamorphic timing

7. Thyroid Hormone Receptors : A Hypothetical Example
Alpha Genotype
A1A1
A1A2
A2A2
Timing of
Metamorphosis
(Days)
200
160
150 d
-15 a -a 25
-25
Homozygote
Midpoint
(175)

8. Genotype Freq Value Freq x Val A1A1 p2 25 p2(25) A1A2 2pq -15 2pq(-15)
A2A2 q q2(25)
Sum = Pop Mean = 25(p-q) + 2(-15)pq
(adds time)
(reduces time)
p = f(A1)
q = f(A2)
A1A1 A1A2 A2A2
Mean
0.0
0.3
0.5
0.7
1.0
1.0
0.7
0.5
0.3
0.0
25 0 0
-25 (150)
-16.3 (158.7)
-7.5 (167.5)
3.7 (178.7)
25 (200)

9. Thyroid Hormone Receptor Thyroid Hormone Receptor
Let’s Consider a Second Locus
Thyroid Hormone Receptor
Alpha Genotype
A1A1
A1A2
A2A2
Timing of
Metamorphosis
(Days)
200
160
150
Thyroid Hormone Receptor
Beta Genotype
A1A1
A1A2
A2A2
Timing of
Metamorphosis
(Days)
200
140 a -a 30
-30
Homozygote
Midpoint
(170)

10. Genotype Freq Value Freq x Val A1A1 p2 30 p2(30) A1A2 2pq 0 2pq(0)
A2A2 q q2(30)
Sum = Pop Mean = 30(p-q) + 2(0)pq
(adds time)
(reduces time)
P = f(A1)
Q = f(A2)
A1A1 A1A2 A2A2
Mean
0.0
0.3
0.5
0.7
1.0
1.0
0.7
0.5
0.3
0.0
0 0 0
30 0 0
-30 (140)
-12 (158)
0 (170)
12 (182)
30 (200)

11. Consider the joint effect of both TH Loci
Total Range = 2Sa=110
Tha A1A1
Thb A1A1
Tha A2A2
Thb A2A2
Timing of
Metamorphosis
(Days)
227.5
117.5 a -a 55 55
Average
Homozygote
Midpoint
(172.5)
Overall
Mean =
Sa(p-q) + S2dpq

12. 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.

13. Average Effect of an Allele
Type of Values and Freq Mean value Population Average
gamete of gametes of genotypes mean effect of
gene
A1A A1A A2A2
a d a
A p q pa + qd a(p-q) + 2dpq q[a+d(q-p)]
A p q qa + pd 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)]

14. Theoretically: An individual’s value based on the sum of the
average effects of the alleles/genes it carries.
Genotype
Breeding Value
A1A1
A1A2
A2A2
2a1
a1 + a2
2a2

15. Average Effects Frequency q (A2 orTHa2) 0.0 0.3 0.5 0.7 1.0
: THa
: THa
d = -15; a = 25

16. Breeding Values - THa example
A2 or Tha Pop Mean A1A1 A1A A2A2
q =
q =
q =
q =
q =

17. = = + (A) G = A + D Sum of average effects across loci +
Breeding Value
(A)
A1A A1A A2A2
2a1 a1 + a a2
B1B B1B B2B2
2a1 a1 + a a2 +
(breeding values)
(breeding values)
G = A + D = +
Genotypic
Value
Additive effects
of genes
Dominance
deviation

18. End Here: Continue Next Monday

19. Partitioning the phenotypic value
genotypic value
breeding
value
deviations from population mean
phenotypic value
of individual
genotypic value
G = A + D
breeding value
dominance
deviation
P = G
Pop
Mean
G = G1 + G2 + I12
interaction
two-locus:
P = A1 + D1 + A2 + D2 + I12
d=3/4a, q = 1/4

20. Environmental effects on phenotypes
P = A + D
One locus, two alleles
One locus, two alleles + environmental variation
environmental
deviation
P = A + D + E

21. Amount of genetic variation in a population depends on
# of genotypes, genotypic value, and gene frequencies.
More variation
Less variation
0.75
0.75
p = 0.5
p = 0.9
0.50
0.50
0.25
0.25 9 10 11 9 10 11
A1A1 A1A2 A2A2
A1A1 A1A2 A2A2
Mean
Mean

22. Components of phenotypic variation
f (A1)
a = d = 0.07
P = A + D + I + E
Variance partitioning:
VP = VG VE
VP = VA + VD + VI + VE .
total
phenotypic
variance
additive
genetic
dominance
interaction
(epistatic)
environmental
• Phenotypic variation can be decomposed into additive genetic and other variation
• Relative contributions of different sources depend on allele frequencies