genetics of quantitative traits. quantitative trait any trait that demonstrates a range of...
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Genetics of Quantitative Traits
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Quantitative Trait
• Any trait that demonstrates a range of phenotypes that can be quantified
• Height
• Weight
• Coloration
• Size
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Continuous Variation vs Discrete Phenotypic Classes
• Continuous variation– Offspring show a range of phenotypes of
intermediate range relative to the parental phenotype extremes
• Discrete classes– Offspring show phenotype exactly like either parent
(dominance/recessiveness) – or in a single intermediate class (incomplete
dominance)– or have a combinatorial phenotype (co-dominance)
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Example of Continuous Variation
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Demonstrating Genetic Control of Variation
• Individually cross F2 at phenotypic extremes
• Subsequent ranges of progeny are centered on F2 phenotype
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Polygenic Inheritance
• A trait controlled by multiple genes with additive and non-additive allele types
• Additive allele (Uppercase)– an allele which contributes to the observe
phenotype• causes more color, height, weight, etc..
• Non-additive allele (lowercase)– an allele which does not contribute to observed
phenotype• causes less color, height, weight, etc…
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Polygenic Control of Wheat Color
P
F1
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Wheat Color Defined by Two Genes
• A and B are additive alleles of two genes• a and b are non-additive alleles of the same two
genes• The number of additive and non-additive alleles
in each genotype defines a distinct phenotype– 4 additive alleles ------ AABB – 3 additive alleles ------ AaBB, AABb, – 2 additive alleles ------ aaBB, AAbb, AaBb– 1 additive allele ------- Aabb, aaBb– 0 additive alleles ------ aabb
• Give 5 phenotype classes
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How Many Genes Control a Trait? &
How Many Phenotypes are
Possible?
Genes (n)
Genotypic Classes
Phenotypic Classes
Fraction like either parent
1 3 3 1/4
2 9 5 1/16
3 27 7 1/64
4 81 9 1/256
5 243 11 1/1024
6 729 13 1/4096
n 3n 2n+1 (1/4)n
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Statistics
Range of the phenotype being measured
Num
bers
of
indi
vidu
als
wit
h th
at p
heno
type
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Mean (aka Average) and Variance
• These two populations have a mean height that is the same• The range of heights in each population is quite different
Height of Population 1
Height of Population 2
1ft 10ft2.5ft 7.5ft
(Height)
Num
ber
of I
ndiv
idua
ls w
ith
Indi
cate
d H
eigh
t
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Measuring the Variance
• Sample variance s2
• Standard deviation = square root of variance
• Standard error
s = s2
s
nSX =
n = # of individuals for which trait has been quantified
s2 = (Xi - X)2
n-1
i=1
n
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Weight Distribution of F1 & F2 Tomato Progeny
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Example Statistics Problem
Weight6 7 8 9 10 11 12 13 14 15 16 17 18
Number of Individuals
F1 4 14 16 12 6
F2 1 1 2 0 9 13 17 14 7 4 3 0 1
Mean: XF1 = 12.04
Variance: s2F1 = 1.29
Stnd Dev: sF1 = 1.13
Mean: XF2 = 12.11
Variance: s2F2 = 4.27
Stnd Dev: sF2 = 2.06
12.04 ± 1.13 12.11 ± 2.06
See table 6.4 (4th ed) or table 5.4 (3rd ed)
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Nature or Nurture
• Phenotypic variation due to genetic factors
• Phenotypic variation due to environmental factors
• Heritability– Broad-sense
• Measure of variance due to genetics vs environment
– Narrow-sense• Measure of selectability
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Identifying Environmental vs Genetic Factors Influencing Variability
• Inbred strains– an inbred population is highly homozygous– lethal recessives are lost– allele frequencies are stabilized
• Variation in inbred populations in differing environments is due to environmental factors – VE
• Variation in inbred population in same environment is due to genetic differences - VG
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• If extreme phenotypes of highly inbred line are selected, do F1 show deviation from P mean?– yes – variance is genetic
– no – variance is environmental
Environmental vs Genetic Factor Measurement
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Broad-sense Heritability
• Heritability index – H2
Proportion of variance due to genetic factors
• VP = phenotypic variance (ie s2 for a measured trait in a population)
• VP = VE + VG
• VG = genetic variance• VE = environmental variance
VG
VP
H2 =
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Narrow-sense Heritability
R
Sh2 =
• S = deviation of selected population mean from whole population mean
• R = deviation of offspring mean from whole parental population mean
• ratio of R to S describes narrow-sense heritability – ie how selectable is the trait
h2 near 1 means trait could be altered by artificial selection
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