1. Genetics: Analysis and Principles
Robert J. Brooker
CHAPTER 25
QUANTITATIVE GENETICS

2. 25.1 QUANTITATIVE TRAITS
A quantitative trait is any trait that varies measurably in a given species

3. Quantitative Traits Exhibit a Continuum of Phenotypic Variation
Quantitative traits show a continuum of variation within a group of individuals
Quantitative traits do not naturally fall into a small number of discrete categories

4. Quantitative traits can be described by using a frequency distribution The trait is divided arbitrarily into a number of discrete phenotypic categories

5. Figure 25.1 Normal distribution of a quantitative trait

6. 25.2 POLYGENIC INHERITANCE
Most quantitative traits are polygenic and exhibit a continuum of phenotypic variation
Polygenic inheritance refers to the transmission of traits that are governed by two or more genes
The locations on chromosomes that affect the outcome of quantitative traits are called quantitative trait loci (QTLs)
QTLs may contain many genes
Some or all of which may affect quantitative traits

7. Polygenic Inheritance and Environmental Factors
The first demonstration that continuous variation is related to polygenic inheritance occurred in 1909
The Swedish geneticist Herman Nilsson-Ehle studied the inheritance of red pigment in the hull of wheat Triticum aestivum

8. Nilsson-Ehle performed the following cross
P True-breeding red X true-breeding white
F1 Intermediate red
F2 Great variation in redness:
White, light red, intermediate red, medium red, dark red
As shown in Figure 24.3b, Nilsson-Ehle discovered that the colors fell into a 1:4:6:4:1 ratio
He concluded that this species is diploid for two different genes that control hull color
Each gene exists in two alleles: red or white
He hypothesized that these two loci must contribute additively to the color of hull

9. Figure 25.3

10. This is especially true when
Many polygenic traits are difficult or impossible to categorize into several discrete genotypic categories
This is especially true when
1. The number of genes controlling the trait increases
2. The influence of the environment increases

11. Effect of # of genes
If there is no environmental effect, the number of contributing genes can be estimated by either:
the number of phenotypic classes or
by the fraction of the total population of an extreme phenotype class
Figure 24-3 The results of crossing two heterozygotes when polygenic inheritance is in operation with 1–5 gene pairs. Each histogram bar indicates a distinct F2 phenotypic class from one extreme (left end) to the other extreme (right end). Each phenotype results from a different number of additive alleles.

12. The basic model for quantitative traits
P = G + E
P = phenotypic value for the trait of one individual (plant or animal).
G = the effect of the genes carried by the individual (genotypic value).
E = the effect of the environmental factors on the phenotype of the animal.

13. Genotypic Value G = A + D + I P = A+ D + I + E
Genotypic value is the overall effect of all the genes carried by the individual on its phenotype. It includes:
Additive effects of genes (A): the sum of individual effects (average effects) of alleles.
Dominance effects of genes (D): interaction between alleles at the same gene
Epistatic effects (I): interaction between alleles on different genes
G = A + D + I P = A+ D + I + E

15. Heritability
Heritability in the broad sense (H2): is the proportion of the phenotypic variance that is due to all genetic effects ( additive, dominance and epistasis):
It measures the strength of the relationship between the phenotypic values of the individuals and their genotypic values.

16. It measures two things:
Heritability in the narrow sense (h2): is the proportion of the phenotypic variance that is due to additive genetic effects only.
It measures two things:
The degree to which the offspring resemble their parents in the phenotype for a trait.
The strength of the relationship between the phenotypic values and the additive genetic effects (the relationship between P and A).

17. Notes:
Heritability is a measure on a population of individuals in a given environment for a given character. It is NOT measured on one individual.
Heritability can be estimated for each quantitative trait.
It varies from population to another and from environment to another for the same traits.

18. Importance of heritability
Heritability is very important in selection (in genetic improvement)
It determines if phenotypic selection would be efficient or not:
Small heritability: phenotypic selection is not efficient (low accuracy of selection).
High heritability: phenotypic selection is efficient (high accuracy of selection)

19. Realized heritability
The most common way to estimate narrow sense heritability in a starting population
Where
R is the response in the offspring
S is the selection differential in the parents = R S
hN2
Where
Here
is the mean of the starting population X XO R = – X
is the mean of the offspring XO XP S = – X
is the mean of the parents XP So =
hN2 XO – X XP

20. Thus, 48% of the phenotypic variation is due to additive alleles
Example:
An experiment is begun with a population of fruit flies in which the average bristle number for both genders is 37.5.
The parents chosen from this population had an average bristle number of 40
The offspring of the next generation had an average bristle number of 38.7 =
hN2 XO – X XP
Thus, 48% of the phenotypic variation is due to additive alleles =
hN2 –
38.7
37.5 40 =
1.2
2.5
= 0.48

21. Example 1
The narrow-sense heritability for potato weight in a starting population of potatoes is 0.42, and the mean weight is 1.4 lb. If a breeder crosses two strains with average potato weights of 1.9 and 2.1 lb, respectively, what is the predicted average weight of potatoes in the offspring?

23. Example 2. A farmer wants to increase the average body weight in a herd of cattle. She begins with a herd having a mean weight of 595 kg and chooses individuals to breed that have a mean weight of 625 kg. Twenty offspring were obtained, having the following weights in kilograms: 612, 587, 604, 589, 615, 641, 575, 611, 610, 598, 589, 620, 617, 577, 609, 633, 588, 599, 601, and 611. Calculate the realized heritability for body weight in this herd.