1. Genesis 25:24-26
24 And when her days to be delivered were fulfilled, behold, there were twins in her womb.
25 And the first came out red, all over like an hairy garment; and they called his name Esau.
26 And after that came his brother out, and his hand took hold on Esau's heel; and his name was called Jacob . . .

2. Quantitative Genetics
Timothy G. Standish, Ph. D.

3. How Could Noah Have Done It?
The diversity of appearance in humans and other animals is immense
How could Adam and Eve or Noah and his family have held in their genomes genes for all that we see today?
At least one explanation, that the dark-skinned races descended from Cain who was marked with dark pigment (the mark of Cain mentioned in Gen. 4:15) or Ham as a result of the curse mentioned in Gen. 9:22-27
Quantitative or polygenic inheritance offers much more satisfying answer to this quandary

4. Definitions
Traits examined so far have resulted in discontinuous phenotypic traits
Tall or dwarf
Round or wrinkled
Red, pink or white
Quantitative inheritance deals with genetic control of phenotypic traits that vary on a continuous basis:
Height
Weight
Skin color
Many quantitative traits are also influenced by the environment

5. Nature Vs Nurture
Quantitative genes’ influence on phenotype are at the crux of the nature/nurture debate
Socialism emphasizes the environment
Fascism emphasizes genetics
Understanding quantitative genetics helps us to understand the degree to which genetics and the environment impact phenotype
Aside from political considerations, quantitative genetics helps us to understand the potential for selection to impact productivity in crops and livestock

6. Additive Alleles
Additive alleles are alleles that change the phenotype in an additive way
Example - The more copies of tall alleles a person has, the greater their potential for growing tall
Additive alleles behave something like alleles that result in incomplete dominance
More CR alleles results in redder flowers
CRCW
CRCR
CWCW
F2 Generation 2: 1 1:
CRCR
CRCW
CWCW CR CW

7. Additive Alleles
If more than one gene with two alleles that behave as incompletely dominant alleles are involved, variability occurs over more of a continuum
If two genes with two alleles are involved, X phenotypes can result
Additive
alleles 4 3 2 1
1/16
6/16 = 3/8
4/16 = 1/4 F2
1/4 AA
1/2 Aa
1/4 aa
1/4 BB -- 1/16 AABB
1/2 Bb -- 2/16 AABb
1/4 bb /16 AAbb
1/4 BB -- 2/16 AaBB
1/2 Bb -- 4/16 AaBb
1/4 bb /16 Aabb
1/4 BB -- 1/16 aaBB
1/2 Bb -- 2/16 aaBb
1/4 bb /16 aabb

8. Additive Alleles
Graphed as a frequency diagram, these results look like this:

9. Estimating Gene Numbers
The more genes involved in producing a trait, the more gradations will be observed in that trait
If two examples of extremes of variation for a trait are crossed and the F2 progeny are examined, the proportion exhibiting the extreme variations can be used to calculate the number of genes involved: 4n 1
= F2 extreme phenotypes in total offspring
If 1/64th of the offspring of an F2 cross of the kind described above are the same as the parents, then 64 1 43 1 =
N = 3 so there are probably about 3 genes involved

10. Economic Implications
Environment or genetics?

11. Describing Quantitative Traits: The Mean
Two statistics are commonly used to describe variation of a quantitative trait in a population
The Mean - For a trait that forms a bell-shaped curve (normal distribution) when a frequency diagram is plotted, the mean is the most common size, shape, or whatever is being measured
Sum of individual values X
D Frequency
D Trait = n
SXi X
Number of individual values

12. Describing Quantitative Traits: Standard Deviation
Standard Deviation - Describes the amount of variation from the mean in units of the trait
Large SD indicates great variability
68 % of individuals exhibiting the trait will fall within ±1 SD of the mean, 95.5 % ±2, 99.7 % ±3 SD
95 % fall within 1.96 SD -1 +1
Number of individuals in each unit measured
Total number of individuals in sample X
D Frequency
D Trait
68.3% =
n(n - 1)
nSf(x2) - (Sfx2)
Gradations of units of measurement s

13. Heritability
Heritability is a measure of how much quantitative genes influence phenotype
Two types of heritability can be calculated:
Broad-Sense Heritability:
H2 - Expresses the proportion of phenotypic variance seen in a sample that is the result of genetic as opposed to environmental influences
Narrow-Sense Heritability:
h2 - Assesses the potential of selection to change a specific continuously varying phenotypic trait in a randomly breeding population

14. 1 Broad-Sense Heritability
Proportion of phenotypic variance resulting from genetic rather than environmental influences
Components contributing to phenotypic variation (VP) can be summarized as follows:
Genetic and Environmental interactions
VP = VE + VG + VGE
Environment
Genetics
VGE is typically negligible so this formula can be simplified to:
VP = VE + VG
As long as this is the case, broad heritability can be expressed as the ratio of environmental to genetic components in phenotypic variation = VP VG H2

15. 2 Narrow-Sense Heritability
Potential of selection to change a specific continuously varying phenotypic trait
Narrow-sense heritability concentrates on VG which can be subdivided as follows:
Interactive or epistatic variance
VG = VA + VD + VI
Additive
Dominance
VA is typically negligible so this formula can be simplified to:
VP = VE + VG
As long as this is the case, narrow-sense heritability can be expressed as the ratio as follows: = VP VA h2

16. The
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