Genetics of Quantitative Traits
Quantitative Trait
• Any trait that demonstrates a range of
phenotypes that can be quantified
• Height
• Weight
• Coloration
• Size
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)
Example of Continuous
Variation
Demonstrating Genetic
Control of Variation
• Individually cross F2 at
phenotypic extremes
• Subsequent ranges of
progeny are centered on
F2 phenotype
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…
Polygenic Control of Wheat Color
P
F1
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
How Many Genes
Control a Trait? &
How Many
Phenotypes are
Possible?
Genes Genotypic Phenotypic Fraction like
(n)
Classes
Classes
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
Numbers of individuals with that phenotype
Statistics
Range of the phenotype being measured
Number of Individuals with Indicated Height
Mean (aka Average) and Variance
Height of Population 2
Height of Population 1
1ft
2.5ft
7.5ft
10ft
(Height)
• These two populations have a mean height that is the same
• The range of heights in each population is quite different
Measuring the Variance
• Sample variance s2
i=1
s2 =
2
(X
X)
i
n
n-1
n = # of individuals for which
trait has been quantified
• Standard deviation = square root of variance
s = s2
• Standard error
SX =
s
n
Num ber
Weight Distribution of F1 & F2 Tomato Progeny
18
16
18
14
F1
16
12
F2
14
10
F1
12
8
F2
6
10
48
26
04
6
2
7
8
9
10
0
11
Fruit Weight
6
7
8
9
10
12
13
14
15
F2
F1
16
17
18
Example Statistics Problem
Weight
6
Number of
Individuals
7
8
9
F1
F2
1
1
2
0
10
11
12
13
14
4
14
16
12
6
9
13
17
14
7
15
16
17
18
4
3
0
1
Mean: XF1 = 12.04
Mean: XF2 = 12.11
Variance: s2F1 = 1.29
Variance: s2F2 = 4.27
Stnd Dev: sF1 = 1.13
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)
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
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
Environmental vs Genetic
Factor Measurement
• If extreme phenotypes
of highly inbred line are
selected, do F1 show
deviation from P mean?
– yes – variance is genetic
– no – variance is
environmental
Broad-sense Heritability
• Heritability index – H2
H2 =
VG
VP
Proportion of variance due to
genetic factors
• VP = phenotypic variance (ie s2 for a measured
trait in a population)
• VP = V E + VG
• VG = genetic variance
• VE = environmental variance
Narrow-sense Heritability
• 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
R
2
h =
S
h2 near 1
means trait
could be
altered by
artificial
selection