1. Quantitative traits

2. Quantitative Traits
Mendel worked with traits that were all discrete, either/or traits: yellow or green, round or wrinkled, etc. Different alleles gave clearly distinguishable phenotypes.
Many traits don’t fall into discrete categories: height, for example, or yield of corn per acre. These are “quantitative traits”.
The manipulation of quantitative traits has allowed major increases in crop yield during the past 80 years. This is an important part of why today famine is rare. Until very recently, crop improvement through quantitative genetics was the most profitable aspect of genetics.
Early in the history of genetics was argued that quantitative traits worked through a genetic system quite different from Mendelian genetics. This idea has been disproved, and the theory of quantitative genetics is based on Mendelian principles.

3. Qualitative versus quantitative traits
Qualitative traits
Quantitative traits
1-Few genes
Low environmental influence
Distinct offspring classes
Many genes
Strong environmental influence
Continous segregation

4. Quantitative trait Qualitative traits: Discontinuous variation:
Quantitative trait: Continuous variation:
The observed phenotype is the result of the genotype, the environment and the genotype x environment interactions.

5. Examples: height, intelligence & hair color.
Quantitative Traits
Traits that are genetically influenced but do not show single gene (Mendelian) patterns of inheraitance
Phenotypes (characteristics) that vary in degree and can be attributed to polygenic effects, i.e., product of two or more genes, and their environment.
They are influenced by the combined action of many genes and are characterized by continuous variation. .
Examples: height, intelligence & hair color.

6. Types of Quantitative Trait
1. continuous trait: can take on any value: height, for example.
2. countable (meristic) can take on integer values only: number of bristles, for example.
3. threshold trait: has an underlying quantitative distribution, but the trait only appears only if a threshold is crossed.

7. Quantitative Traits are Caused by Mendelian Genes
In 1909 Herman Nilsson-Ehle from Sweden did a series of experiments with kernel color in wheat.
Wheat is a hexaploid, the result of 3 different species producing a stable hybrid. There are thus 3 similar but slightly different genomes contained in the wheat genome, called A, B, and D.
Each genome has a single gene that affects kernel color, and each of these loci has a red allele and a white allele. We will call the red alleles A, B, and D, and the white alleles a, b, and d.
Inheritance of these alleles is partially dominant, or “additive”. The amount of red pigment in the kernel is proportional to the number of red alleles present, from 0 to 6.

8. Wheat Kernel Color The cross: AA BB DD x aa bb dd. Red x white.
F1: Aa Bb Dd phenotype: pink, intermediate between the parents. Now self these.
F2: alleles follow a binomial distribution:
1/64 have all 6 red alleles = red
6/64 have 5 red + 1 white = light red
10/64 have 4 red + 2 white = dark pink
15/64 have 3 red + 3 white = pink
10/64 have 2 red + 4 white = light pink
6/64 have 1 red + 5 white = very pale pink
1/64 have all 6 white = white
Add a bit of environmental variation and human inability to distinguish similar shades: you get a quantitative distribution.
This demonstrates that a simple Mendelian system: 3 genes, 2 alleles each, partial dominance--can lead to a quantitative trait.

9. More Wheat Kernel Color

10. Quantitative Traits
Quantitative traits = complex traits = Multifactorial
Multifactorial traits are determined by multiple genetic and environmental factors acting together
Most traits that vary in the population are complex traits
Genetic architecture of a complex trait = specific effects and combined interactions of all genetic and environmental factors

11. Principles of Quantitative Trait Inheritance
Quantitative traits are influenced by the combined effects of numerous genes. These are called polygenic or multifactorial traits.
The genes follow Mendelian laws of inheritance; however, multifactorial traits have numerous possible phenotypic categories.
Environmental influences the phenotypic differences between adjacent genotypes.

12. Statistics of Quantitative Traits
Quantitative traits exhibit a continuous distribution of phenotypes, thus, they cannot be analyzed in the same manner as traits controlled by a few genes.
Rather, quantitative traits are described
in terms of statistical parameters.

13. Statistics of Quantitative Traits
The two primary statistics used are the mean and the variance.

14. Statistics of Quantitative Traits
An associated statistic that is also relevant is the standard deviation, because it is in the same units as the mean.

15. Statistics of Quantitative Traits
The mean is the average value of the distribution. The graph on the right demonstrates two distributions with the same mean but different variances.
Two distribution can have the same mean, but widely different shapes.
A wide distribution suggests a large range of values, whereas, a narrow distribution occurs when the range of observed values is small.
The variance is a measure of the variability of the distribution.

16. Statistics of Quantitative Traits
A simple way to describe a distribution is in terms of its mean and its standard deviation.
The mean ± one standard deviation encompasses ~66% of the distribution. Thus a larger standard deviation suggests that the distribution is wider than one with a smaller standard deviation.
Furthermore, ~95% of the distribution is found within ± two standard deviations of the mean and ~99% of the distribution is found within ± three standard deviations.
Quantitative genetics of ear length in corn
Generation Mean Standard
(cm) deviation (cm)
Tom Thumb (P1)
BMS (P2) F F

17. Statistics of Quantitative Traits
Several observations can be made from the example.
Even though the mean ear length of the BMS is smaller, the standard deviation is larger. This suggests that it is more variable than the long ear line.
Because the F1 population is derived from two pure lines, it should be entirely homogeneous (all are heterozygotes). Thus all the variance associated with that population is environmental variance.
The mean of a quantitative trait in a F1 population is intermediate to the two parents, and the mean of the F2 is approximately equal to that of the F1.
The F2 population is more variable than the F1.
The extreme values of the distribution should be equivalent to the two parents used in the cross because this small portion of the population will have the same genotypes as the parents. If two genes control the trait 1/16 of the F2 populations will equal either of the two parents. If five genes control the trait then 1/243 of the F2 populations will equal either parent.

18. Variance Components of a Quantitative Trait
The metric value (or phenotypic value) for a specific individual, is the result of genetic factors, environmental factors, and the environmental factors that interact with the genetic factors.
The sum of these factors in a population of individuals segregating for a quantitative trait contributes to the variance of that population.

19. Variance Components of a Quantitative Trait
The total variance can be partitioned in the following manner.
VP = VG + VE + VGE
Where,
VP = total phenotypic variation of the segregating population VG = genetic variation that contributes to the total phenotypic
variation VE = environmental contribution to the total phenotypic variation VGE = variation associated with the genetic and environmental
factor interactions

20. Variance Components of a Quantitative Trait
The genetic variation can be further subdivided into three components.
1. Additive genetic variation (VA)
Some alleles may contribute a fixed value to the metric value of quantitative trait.
2. Dominant genetic variance (VD).
In addition to genes which have an additive effect on the quantitative trait, other genes may exhibit a dominant gene action which will mask the contribution of the recessive alleles at the locus.

21. Variance Components of a Quantitative Trait
3. Interaction genetic variance (VI).
This final type of genetic variance is associated with the interactions between genes.
The genetic basis of this variance is epistasis, and it is called the interaction genetic variance (VI).

22. Variance Components of a Quantitative Trait
The total genetic variance can be partitioned into the three forms of variance
VG = VA + VD + VI
The total phenotypic variance can be rewritten as
VP = VA + VD + VI + VE + VGE

23. Heritability
The proportion of observed different on a trait among individuals of a population that are due to genetic differences
A measure of variance and is only meaningful for characteristics of a population (not the individual).
Broad-sense heritability
proportion of phenotypic variance among individuals in a population that results from genetic differences.
Narrow-sense heritability
proportion of phenotypic variance that results from additive genetic variance

24. Broad-Sense Heritability
Broad-sense heritability (H2) includes all genetic effects combined
H2 = sg2 / sp2 = sg2 / sg2 + se2
Knowledge of heritability is useful in plant and animal breeding because it can be used to predict the magnitude and speed of population improvement

25. Narrow-Sense Heritability
Narrow-sense heritability (h2) = proportion of the variance in phenotype that is transmissible from parents to offspring. The genetic variance can be split into both additive and dominant alleles.
h2 = sg2 / sp2 = sg2 / sa2 + sd2 + se2
Narrow-sense heritability can be used to predict changes in the population mean in with individual selection
h2 = (M’ - M)/(M* - M)
In general, h2 < H2 . They are equal only when the alleles affecting the trait are additive in their effects = heterozygous phenotype is exactly intermediate between homozygous dominant and recessive

26. Heritability
The heritability estimate is specific to the population and environment which is analyzed.
The estimate is a population, not an individual parameter.
Heritability does not indicate the degree to which a trait is genetic, it measures the proportion of the phenotypic variance that is the result of genetic factors.

27. The improvement of quantitative traits through conventional
It is a long and difficult process
Examples of efficient conventional selection
1) Reduction of glucosinolate rate of rapeseed grains 
1977 : Jetneuf  moles/g
1983 : Darmor  moles/g
1989 : Samouraï moles/g
2) Yield of irrigated rice in the Philippines 
1920: Peta t/ha
1962: IR t/ha
1998: IR t/ha
2001: New plant type t/ha 
(This increase is not exclusively due to genetic progress)