Quantitative Genetics of Natural Variation: some questions
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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 effectat many (innumerable) loci, and no single substitution constitutes a majorportion 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 locusone locus + environment
two loci + environment
four loci + environment
many loci + environment
– a d + agenotypic value 0
A2A2 A1A2 A1A1genotype
Phenotypic Value and Population Means (Falconer and Mackay Ch. 7)
Phenotypic value = Genotypic value + Environmental Deviation
P = G + E
Genotype Freq Value Freq x ValA1A1 p2 +a p2aA1A2 2pq d 2pqdA2A2 q2 -a -q2a
Sum = Pop Mean = a(p-q) + 2dpq
PredictableLarval Habitat
PredictableEphemeral Pond
Time
Hatching Metamorphosis
Timing of Metamorphosis
The majority of organisms on planet earth have complex life cycles
T3
Hypothalamus
TRH
TSH
TRs
transcription
Target cells
TH
Pituitary
Thyroid
T4deiodionation
Thyroid Hormone Receptors as Candidate Genes forVariation in Metamorphic Timing
An extreme difference in metamorphic timing
Thyroid Hormone ReceptorAlpha Genotype
Timing ofMetamorphosis
(Days)
A1A1 A1A2 A2A2
200 160 150
a -a
d
0Homozygote
Midpoint(175)
-15
-2525
Thyroid Hormone Receptors : A Hypothetical Example
p = f(A1) q = f(A2)
0.0
0.3
0.5
0.7
1.0
1.0
0.7
0.5
0.3
0.0
A1A1 A1A2 A2A2
Genotype Freq Value Freq x ValA1A1 p2 25 p2(25)A1A2 2pq -15 2pq(-15)A2A2 q2 -25 -q2(25)
Sum = Pop Mean = 25(p-q) + 2(-15)pq
0 0 -25
2.25 -6.3 -12.25
6.25 -7.5 -6.25
12.25 -6.3 -2.25
25 0 0
Mean
-25 (150)
-16.3 (158.7)
-7.5 (167.5)
3.7 (178.7)
25 (200)
(reduces time)(adds time)
Let’s Consider a Second Locus
Thyroid Hormone ReceptorAlpha Genotype
Timing ofMetamorphosis
(Days)
A1A1 A1A2 A2A2
200 160 150
a -a0
HomozygoteMidpoint
(170)
-3030
A1A1 A1A2 A2A2
200 140
Thyroid Hormone ReceptorBeta Genotype
Timing ofMetamorphosis
(Days)
0
P = f(A1) Q = f(A2)
0.0
0.3
0.5
0.7
1.0
1.0
0.7
0.5
0.3
0.0
A1A1 A1A2 A2A2
0 0 -30
2.7 0 -14.7
0 0 0
14.7 0 -2.7
30 0 0
Mean
-30 (140)
-12 (158)
0 (170)
12 (182)
30 (200)
(reduces time)(adds time)
Genotype Freq Value Freq x ValA1A1 p2 30 p2(30)A1A2 2pq 0 2pq(0)A2A2 q2 -30 -q2(30)
Sum = Pop Mean = 30(p-q) + 2(0)pq
a -a0
AverageHomozygote
Midpoint(172.5)
5555
227.5 117.5
Timing ofMetamorphosis
(Days)
Total Range = a=110
Consider the joint effect of both TH Loci
Th A1A1Th A1A1
Th A2A2Th A2A2
Overall Mean
= a(p-q) + 2dpq
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
Empirically: An individual’s value based on the mean deviation of its progenyfrom the population mean.
Theoretically: An individual’s value based on the sum of the average effectsof the alleles/genes it carries.
Breeding Value
average effect of An:
n = mean deviation from the population mean of individuals that received An from one parent, if the other parent’s allele chosen randomly
1 = q [ a + d (q – p)]
2 = –p [ a + d (q – p)]
1 = pa + qd - [ a (p – q) + 2dpq ]
population mean
.
f (A1) f (A2)
Average Effect of an Allele
Type of Values and Freq Mean value Population Average gamete of gametes of genotypes mean effect of
geneA1A1 A1A2 A2A2
a d -a
A1 p q pa + qd -a(p-q) + 2dpq q[a+d(q-p)] A2 p q -qa + pd -a(p-q) + 2dpq -p[a+d(q-p)]
When there are only two alleles at a locus
A1A1 A1A2
+a d
A2A2-a
Average effect of a gene substitution
(a - d) (d + a)
p(a - d) + q(d + a)
= a + d(q - p)
p