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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
Qualitative traits
Quantitative traits
1-Few genes
Low environmental
influence
Distinct offspring classes
Many genes
Strong environmental
influence
Continous segregation
Quantitative trait
 Qualitative traits: Discontinuous variation:
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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.
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.
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.
Quantitative genetics of ear length in corn
Generation
Tom Thumb (P1)
BMS (P2)
F1
F2
Mean
(cm)
16.80
6.63
12.12
12.89
Standard
deviation (cm)
0.816
1.887
1.519
2.252
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 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
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
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).
1.
2.
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
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
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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 / 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
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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.
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 100 moles/g
1983 : Darmor 25 moles/g
1989 : Samouraï 12 moles/g
2) Yield of irrigated rice in the Philippines
1920: Peta
1.5 t/ha
1962: IR8
5.0 t/ha
1998: IR72
10.0 t/ha
2001: New plant type 12.0 t/ha
(This increase is not exclusively due to genetic progress)