1. Genetics of Quantitative Traits

2. Quantitative Trait
Any trait that demonstrates a range of phenotypes that can be quantified
Height
Weight
Coloration
Size

3. Continuous Variation vs Discrete Phenotypic Classes
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)

4. Example of Continuous Variation
Figure: 06-01C
Caption:
Kolreuter's cross btw dwarf & tall tobacco plants carried to the F2 generation.

5. Demonstrating Genetic Control of Variation
Individually cross F2 at phenotypic extremes
Subsequent ranges of progeny are centered on F2 phenotype
Figure: 06-02C
Caption:
Results of East's cross btw 2 strains of Nicotiana w/different corolla lengths.

6. Polygenic Inheritance
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…

7. Polygenic Control of Wheat Color
Figure: 06-03
Caption:
How the multiple-factor hypothesis accounts for the 1:4:6:4:1 phenotypic ratio of grain color when all alleles designated by uppercase letters are additive and contribute an equal amount of pigment to the phenotype.

8. 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

9. How Many Genes Control a Trait? & How Many Phenotypes are Possible?
Genes (n)
Genotypic Classes
Phenotypic Classes
Fraction like either parent 1 3
1/4 2 9 5
1/16 27 7
1/64 4 81
1/256
243 11
1/1024 6
729 13
1/4096 n 3n
2n+1
(1/4)n
Figure: 06-04
Caption:
The results of crossing two heterozygotes when polygenic inheritance is operative with 1–5 gene pairs. Each histogram bar indicates a distinct phenotypic class from one extreme (left end) to the other extreme (right end). Each phenotype results from a different number of additive alleles.

10. Weight Weight Number of individuals Number of individuals
Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display.
Low environmental effect
High environmental effect
Number of individuals
Number of individuals aa Aa AA aa Aa AA 1 2 1 1 2 1
Weight
Weight
Ww x Ww

11. Number of individuals Weight Number of individuals Weight
Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display.
Low environmental effect
Number of individuals
aabbcc 1
Aabbcc 6
AAbbcc 15
AaBbCc 20
AABbCc 15
AABBCc 6
AABBCC 1
Weight
High environmental effect
Number of individuals
aabbcc 1
Aabbcc 6
AAbbcc 15
AaBbCc 20
AABbCc 15
AABBCc 6
AABBCC 1
Weight
WWW www x WWW www

12. Statistics Numbers of individuals with that phenotype
Figure: 06-05
Caption:
A normal frequency distribution characterized by a bell-shaped curve.
Numbers of individuals with that phenotype
Range of the phenotype being measured

13. Mean (aka Average) and Variance
Height of Population 2
Number of Individuals with Indicated Height
Figure: 06-06
Caption:
Two normal frequency distributions with the same mean but different amounts of variation.
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

14. Measuring the Variance
Sample variance s2
Standard deviation = square root of variance
Standard error
s2 =
(Xi - X)2
n-1
i=1 n
n = # of individuals for which trait has been quantified
s = s2 s
 n SX =

15. Weight Distribution of F1 & F2 Tomato Progeny

16. Example Statistics Problem
Weight 6 7 8 9 10 11 12 13 14 15 16 17 18
Number of Individuals F1 4 F2 1 2 3
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

17. 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

18. 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

19. 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

20. 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 =

21. 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 S
h2 =
h2 near 1 means trait could be altered by artificial selection

22. Long term breeding study for corn oil content
Figure 21.16A 22

23. Figure: 06-08
Caption:
Survival rates of Drosophila carrying combinations of chromosomes from DDT-resistant and DDT-sensitive (control) strains when exposed to DDT. The results indicate that DDT resistance is polygenic, with genes on each of the major chromosomes making a major contribution. Chromosome 4 carries only a few Drosophila genes and was omitted from this analysis.

24. Figure: UN
Caption:
Different combos of chromosomes from control strain & resistant strain.