Quantitative traits

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.

Qualitative versus quantitative traits

1-Few genesLow environmental influence Distinct offspring classes

Many genesStrong environmental influenceContinous segregation

Qualitative traits Quantitative traits

Quantitative trait

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Quantitative trait: Continuous variation:

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The observed phenotype is the result of the genotype, the environment and the genotype x environment interactions.

Qualitative traits: Discontinuous variation:

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.

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Examples: height, intelligence & hair color.

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.

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.

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.

More Wheat Kernel Color

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

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.

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.

Statistics of Quantitative Traits

The two primary statistics used are the mean and the variance.

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..

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.

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.

Generation Mean Standard (cm) deviation (cm)

Tom Thumb (P1) 16.80 0.816 BMS (P2) 6.63 1.887 F1 12.12 1.519 F2 12.89 2.252

Quantitative genetics of ear length in corn

Statistics of Quantitative Traits

Several observations can be made from the example.

1. 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.

2. 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.

3. 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.

4. The F2 population is more variable than the F1. 5. 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.

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.

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 populationVG = genetic variation that contributes to the total phenotypic

variationVE = environmental contribution to the total phenotypic variationVGE = variation associated with the genetic and environmental

factor interactions

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.

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).

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

Heritability

1. Broad-sense heritability proportion of phenotypic variance among individuals in a population that results from genetic differences.

2. Narrow-sense heritability proportion of phenotypic variance that results from additive genetic variance

The proportion of observed different on a trait among individuals of a population that are due to genetic

differencesA measure of variance and is only meaningful for characteristics of a population (not the individual).

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Broad-Sense Heritability

• Broad-sense heritability (H2) includes all genetic effects combined

H2 = sg2 / sp

2 = sg2 / sg

2 + 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

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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 / sp

2 = sg2 / sa

2 + sd2 + se

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• 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

Heritability

1. The heritability estimate is specific to the population and environment which is analyzed.

2. The estimate is a population, not an individual parameter.

3. 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.

It is a long and difficult process

Examples of efficient conventional selection 1) Reduction of glucosinolate rate of rapeseed grains

1977 : Jetneuf 100 moles/g1983 : Darmor 25 moles/g1989 : Samouraï 12 moles/g

2) Yield of irrigated rice in the Philippines 1920: Peta 1.5 t/ha1962: IR8 5.0 t/ha1998: IR72 10.0 t/ha2001: New plant type 12.0 t/ha

(This increase is not exclusively due to genetic progress)

The improvement of quantitative traits through conventional