1. Spring 2009: Section 5 – Lecture 1
Quantitative genetics
Reading: Chapter 25
3rd Writing Assignment due May 1st

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3. Quantitative Genetics
Traits whose phenotypes vary continuously from one extreme to the other such that no distinct phenotypic classes can be distinguished are said to be under quantitative genetic control.

4. The individual contribution or affect of an allele or gene in a quantitative trait is small compared to qualitative genes.
polygenic trait - a trait that is controlled by many genes each contributing a small affect on the phenotype.

5. With a quantitative trait the gene action can be either additive, non-additive, or a combination of the two.
Additive gene action - The number of genes or alleles control the degree of expression.
This is sometimes considered a dose effect.

6. Example: seed color in wheat
There are 3 genes in wheat that control seed color. Each dominant allele gives one dose of color.
white seed X dark red seed
aabbcc AABBCC 
F1 medium red seed
AaBbCc

7. F1 medium red seed
AaBbCc

9. An interesting result of additive genetic control is transgressive segregation. Here the extremes in an F2 population can exceed the expression in the parents.
Hamburgh X Sebright Bantam
(large) (small) 
F1 (medium size)

10. F1 medium size X F1 medium size

11. F1 medium size X F1 medium size

12. Hamburgh X Sebright Bantam
AABBCCdd aabbccDD
(6 doses)  (2 doses) F1
AaBbCcDd (4 doses) 
aabbccdd AABBCCDD
(0 doses) (8 doses)

13. Non-additive gene action - Where the expression of an allele can express like a homozygous individual (dominance) or a gene can mask the expression of another gene (epistasis).

14. example: hybrid vigor in crops
homozygous X homozygous
inbred line inbred line
(small-weak) (small-weak) 
F1 heterozygous at
many alleles
(large-vigorous)

15. By crossing two homozygous individuals that differ in genetic makeup you can maximize the non-additive gene action in the F1. This results in a very vigorous individual because for most of the genes there will be at least one dominant or functional allele at every gene loci

16. The term for this is heterosis
The term for this is heterosis. This could also explain what is actually being observed with over-dominance.

17. If you can identify the completely homozygous genotype in a population, you can estimate the number of genes and genotypes involved in the quantitative trait.

18. Number of genes
Look at the fraction of the population showing the extreme expression of the trait.
If 2 genes involved = 1/16
If 3 genes involved = 1/64

19. So you can develop a formula to determine the number of genes
(1/2)2N where N = number of genes
So if you solve for N you can determine the number of genes involved.

20. Number of genotypes
If 1 gene = 3 genotypes
2 genes = 9 genotypes
3 genes = 27 genotypes
Then a formula of (3)N where N = number of genes can be used to determine the approximate number of genotypes.

21. When the quantitative trait is controlled by many genes then it may be difficult to identify the extreme genotype

22. In traits under quantitative genetic control the F2 segregating population shows a wide range of phenotypes that can not be divided into distinct classes.

23. What causes the phenotypic variability?
genetic variability
additive
non-additive
environmental variability
causes modifications in genetic expression

24. So phenotypic = genetic + environmental
variability variab. Variability or
VP = VG + VE

25. When working with quantitative traits it is difficult to work with gene expression in individuals and expect to see much change.

26. To observe changes in quantitative traits it is better to work with populations. You can estimate the phenotypic variation in a population for a trait by the amount of variation for the trait from the mean (average) of the population.

27. What you need to know with a quantitative trait is how much of the variation you observe for a trait is genetic in nature.
The more the variation is under genetic control the easier it is to modify expression of the trait in the population.

28. You can estimate the genetic variation by manipulating the equation:
VP = VG + VE to
VP - VE = VG

29. To estimate the environmental variance you can use uniform genetic controls (individuals that do not vary genetically in your population).
examples:

30. If all the variation observed was genetic then a graph of individuals with the same genotype would look like this:

31. Any deviation or variation from the expected appearance would be caused by the environment.

32. Example: height in corn
Tall parent x short parent
VP1 = VE VP2 = VE F1
VF1 = VE

33. F1 F2
VF2 = VG + VE

34. What good is knowing the genetic variation (VG)?
You can use the estimate of genetic variation to determine how heritable a trait is and how fast improvement or change can be made in a trait.

35. Heritability
heritability (h2) is an indication of how much of the variation observed for a trait is under genetic control.
formula: h2 = VG/VP
This is called broad-sense heritability

36. A better estimate of the genetic variation that can be manipulated is to work with just the additive genetic variation. The overall genetic variation (VG) can be partitioned into an additive (VA) component and a non-additive (VD) component. So VG = VA + VD.

37. So for the narrow-sense heritability where only the additive genetic variation is taken into account the formula changes to:
h2 = VA/VP

38. example of estimating broad-sense heritability:
If the VP is 150 and VG is 75 then
h2 = 75/150 = .50
so 50 % of the variation observed is under genetic control.

39. Estimating heritability: height in corn
Gen. mean + s s2 = variance
F VF1 = 16 = VE
F VF2 = 100 = VG + VE
VG = VF2 - VF1 = = 84
h2 = VG/VP= (VF2 - VF1)/VF2 = 84/100 = .84

40. The closer h2 is to 1 the more the trait is under genetic control and the more heritable the trait.
example:
Cattle h2
birth weight
milk yield
white spotting .95

41. Genetic Gain
You can also use h2 to estimate the genetic gain in breeding to improve a trait.
So the question that can be asked is how much will the population mean change if only the selected individuals are allowed to mate.

42. example: height in humans
If the population mean is 5’ 7’’ or 67’’
and the selected population mean is 6’ 2’’ or 74’’ and h2 = .3
What would be the genetic gain after one year?

43. The genetic gain can be calculated by the following equation:
genetic = (sel. pop. mean - pop. mean) x h2
gain
= (74’’ - 67’’) x .3
= 7’’ x .3
= 2.1’’
so population mean height should change approximately 2 inches in the next generation, 5’7’’ to 5’9’’.

44. To continue realizing a 2’’ gain in height every generation you would need to continue increasing the selected population mean each generation (6’2’’ to 6’4’’ etc.)