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
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
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.
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
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)
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
Environmental effects on phenotypes
P = A + D
One locus, two alleles
One locus, two alleles + environmental variation
environmentaldeviation
P = A + D + E
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
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
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)
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
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
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).
19761978 h2 = 0.9
Bill depthin the
Ground Finch
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.