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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
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)]
When there are only two alleles at a locus
Average effect of a gene substitution
A1A1
A1A2
+a
A2A2
d
-a
(a - d)
(d + a)
p(a - d)
+
q(d + a)
a = a + d(q - p)
a
a
ap a
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
a: THa2
-40
-21.7 -12.5
-5.7
0
19
10
aa
a
40
31
25
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 = 2qa
A1A2
a1 + a2 = (q - p)a
A2A2
2a2 = -2pa
Breeding Values - THa example
A2 or Tha2
Pop Mean
A1A1
A1A2
q = 1.0
150
20
20
q = 0.7
158.7
26.6
15.2
q = 0.5
167.5
25
q = 0.3
178.7
18.6
-24.8
-43.4
q = 0.0
200
0
-80
-80
0
A2A2
0
-11.4
-25
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
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
VA = 2pq[a + d (q - p)]2
VD = (2pqd)2
TH alpha Example
q = 0.3
q = 0.7
Genotypic, VG
443.31
191.24
Additive, VA
403.62
151.62
Dominance, VD
39.69
39.69
d = -15; a = 25
(178.7)
(158.7)
Environment and genotype can interact
Different environmental effects across genotypes result in
G x E interaction variance
VP = VA + VD + VI + VE
VP = VA + VD + VI + VE + VGxE
genetic x
environmental
interaction
variance
Heritability
h2 = VA/Vp
Proportion of total phenotypic variance attributed to
variation in breeding values.
Expresses the extent to which genes are transmitted
from parents to offspring
Detecting the genetic component
of phenotypic variation
Drosophila wing length
Resemblance between parents and
offspring indicates degree to which
a trait is inherited
h2
parental average (P)
offspring (O)
heritability (narrow sense):
VA
=
VP
h2 = bOP
bOP
Fraction of variation in parents that
is explained by variation in their genes (VA).
• heritability can also be estimated with offspring–midparent regression
Bill depth
in the
Ground Finch
1978
1976
h2 = 0.9
Heritability is often
measured in the lab;
estimates are higher
than would be
expected in nature.
Almost all characteristics
in almost all species are
genetically variable to
some extent.