Genotypic value is not transferred from parent to offspring; genes are.
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Transcript of Genotypic value is not transferred from parent to offspring; genes are.
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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
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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)]
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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
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Frequency q (A2 orTH2)
0.0 0.3 0.5 0.7 1.0
: TH1 0 9.3 12.5 13.3 10
:TH2 -40 -21.7 -12.5 -5.7 0
4031 251910d = -15; a = 25
Average Effects
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Genotype Breeding Value
A1A1
A1A2
A2A2
21 = 2q
1 + 2 = (q - p)
22 = -2p
Theoretically: An individual’s value based on the sum of the average effects of the alleles/genes it carries.
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Breeding Values - TH example
A2 or Th2 Pop Mean A1A1 A1A2 A2A2
q = 1.0 150 20 20 0
q = 0.7 158.7 26.6 15.2 -11.4
q = 0.5 167.5 25 0 -25
q = 0.3 178.7 18.6 -24.8 -43.4
q = 0.0 200 0 -80 -80
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Sum of average effects across loci
Breeding Value
(A)=
G = A + D
Genotypic Value = Additive effects
of genes + Dominancedeviation
A1A1 A1A2 A2A2
21 1 + 2 22(breeding values)
+B1B1 B1B2 B2B2
21 1 + 2 22(breeding values)
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Partitioning the phenotypic value
P = G
P = A1 + D1 + A2 + D2 + I12
phenotypic value of individual
genotypic value of individual
G = A + D
breeding value
dominancedeviation
G = G1 + G2 + I12
interaction
two-locus:
genotypic value
breedingvalue
geno
typi
c va
lue
deviations from population m
ean
d=3/4a, q = 1/4
Pop Mean
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Environmental effects on phenotypes
P = A + D
One locus, two alleles
One locus, two alleles + environmental variation
environmentaldeviation
P = A + D + E
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Amount of genetic variation in a population depends on# of genotypes, genotypic value, and gene frequencies.
p = 0.5 p = 0.9
A1A1 A1A2 A2A2 A1A1 A1A2 A2A2
0.75
0.50
0.25
0.75
0.50
0.25
Mean Mean
9 10 11 9 10 11
More variation Less variation
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Components of phenotypic variation
P = A + D + I + E
VP = VG + VE
Variance partitioning:
totalphenotypic
variance
additivegenetic
variance
dominancegenetic
variance
interaction(epistatic)
geneticvariance
environmentalvariance
VP = VA + VD + VI + VE
.
• Phenotypic variation can be decomposed into additive genetic and other variation• Relative contributions of different sources depend on allele frequencies
V
f (A1)
a = d = 0.07
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Genotypic, VG
Additive, VA
Dominance, VD
q = 0.3
443.31
403.62
39.69
q = 0.7
191.24
151.62
39.69
VA = 2pq[a + d (q - p)]2 VD = (2pqd)2
d = -15; a = 25
TH alpha Example
(178.7) (158.7)
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Environment and genotype can interact
VP = VA + VD + VI + VE
Different environmental effects across genotypes result in G x E interaction variance
VP = VA + VD + VI + VE + VGxE
genetic xenvironmental
interactionvariance
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h2 = VA/Vp
Expresses the extent to which genes are transmitted from parents to offspring
Proportion of total phenotypic variance attributed to variation in breeding values.
Heritability
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Resemblance between parents and offspring indicates degree to which a trait is inherited
heritability (narrow sense):
h2 = VA
VP
h2 = bOP
• heritability can also be estimated with offspring–midparent regression
Drosophila wing length
offs
prin
g (O
)
bOP
parental average (P)
Detecting the genetic componentof phenotypic variation
Fraction of variation in parents that is explained by variation in their genes (VA).
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19761978 h2 = 0.9
Bill depthin the
Ground Finch
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Almost all characteristics in almost all species are genetically variable to some extent.
Heritability is often measured in the lab; estimates are higher than would be expected in nature.