Quantitative and Polygenic Traits

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Quantitative and PolygenicTraits
http//biolmolgen.slam.katowice.pl/

• Aleksander L. Sieron
• Department of General and Molecular Biology and
  Genetics

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Description All traits fall into a few distinct
classes. These classes can be used to predict
the genotypes of the individuals. For example,
if we cross a tall and short pea plant and look
at F2 plants, we know the genotype of short
plants, and we can give a generalized genotype
for the tall plant phenotype. Furthermore, if we
know the genotype we could predict the phenotype
of the plant. These type of phenotypes are
called discontinuous traits. Other traits do
not fall into discrete classes. Rather, when a
segregating population is analyzed, a continuous
distribution of phenotypes is found. An example,
is ear length in corn. Black Mexican Sweet corn
has short ears, whereas Tom Thumb popcorn has
long ears. When these two inbred lines are
crossed, the length of the F1 ears are
intermediate to the two parents. Furthermore,
when the F1 plants are intermated, the
distribution of ear length in the F2 ranges from
the short ear Black Mexican Sweet size to the Tom
Thumb popcorn size. The distribution resembles
the bell-shaped curve for a normal distribution.
These are Polygenic Traits
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Description (cont.) Traits that are determined
by more than one gene are called continuous
traits and cannot be analyzed in the same manner
as discontinuous traits. Continuous traits are
often measured and given a quantitative value,
thus, they are often referred to as quantitative
traits. The area of genetics that studies their
mode of inheritance is called quantitative
genetics.
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• Description (cont.)
• Many important agricultural traits such as
• crop yield,
• weight gain in animals,
• fat content of meat
• are quantitative traits.
• Much of the pioneering research into the modes of
  inheritance of quantitative traits was performed
  by agricultural geneticists.

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• Quantitative traits are controlled by multiple
  genes.
• Each of these genes segregates according to
  Mendel's laws.
• Quantitative traits can also be affected by the
  environment to varying degrees.
• e.g.
• Crop Yield
• Some Plant Disease Resistances
• Weight Gain in Animals
• Fat Content of Meat
• IQ
• Learning Ability
• Blood Pressure

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Images of quantitative traits in plants
The image demonstrates variation of flower
diameter, number of flower parts and the color of
the flower Gaillaridia pilchella. Each trait is
controlled by a number of genes, therefore it is
a quantitative trait.
The photographs demonstrate color variability for
Indian Paintbrush flower. The parents in the
left photo are either yellow or reddish orange.
The F2 individuals though show a distribution of
colors from yellow to reddish orange. This range
of phenotypes is typical of quantitative traits.
(This should be compared to flower color of
Mendel's peas where the F2 individuals were
either purple or white, the two parental
phenotypes.)
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Genetic and Environmental Effects on Quantitative
Traits

• If the allelic interactions are known for a
  particular gene the genotype can be used to
  predict the phenotype.
• With one gene controlling a trait there are three
  possible genotypes,
• AA, Aa and aa and depending on the allelic
  interactions (dominance or incomplete dominance)
  we can have two or three phenotypes.
• As more and more genes control a trait, a greater
  number of genotypes are possible.
• The formula that predicts the number of
  genotypes from the number of genes is 3 to the
  power n. (n is the number of genes.)
• The following is the number of genotypes for a
  selected number (n) of genes which control an
  arbitrary trait.

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Genetic and Environmental Effects on Quantitative
Traits

• The number of genotypes for a selected number (n)
  of genes which control an arbitrary trait is as
  follow.
• of Genes of Genotypes
• 1 3 2 9
• 5 243
• 10 59,049

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Genetic and Environmental Effects on Quantitative
Traits (an example)

• An example with two genes, A and B.
• When assigned are metric values to each of the
  alleles. The A allele will give 4 units while the
  a allele will provide 2 units.
• At the other locus, the B allele will contribute
  2 units while the b allele will provide 1 units.
• With two genes controlling that trait, nine
  different genotypes are possible.

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Genetic and Environmental Effects on Quantitative
Traits (an example cont.)

• The genotypes and their associated metric values
• No. Genotype Ratio in F2 Metric value
• AABB 1 12
• AABb 2 11
• AAbb 1 10
• AaBB 2 10
• AaBb 4 9
• Aabb 2 8
• aaBB 1 8
• aaBb 2 7
• aabb 1 6

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The data distribution from table in previous
slide. The bell-shaped
curve that is indicative of the normal
distribution. This has important implications for
the manner in which quantitative traits are
analyzed.
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Genetic and Environmental Effects on Quantitative
Traits (an example explanation)

• The example demonstrates additive gene action.
• This means that each allele has a specific value
  that it contributes to the final phenotype.
• Therefore, each genotypes has a slightly
  different metric or quantitative value that
  results in a distribution (or curve) of metric
  values.

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Genetic and Environmental Effects on Quantitative
Traits

• Other genetic interactions such as dominance or
  epistasis also affect the phenotype.
• For example, if dominant gene action controls a
  trait, than the homozygous dominant and
  heterozygote will have the same phenotypic value.
  
• Therefore, the number of phenotypes is less than
  for additive gene action.
• Furthermore, the number of phenotypes that result
  from a specific genotype will be reduced further
  if epistatic interactions between several loci
  affects the phenotype.

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Genetic and Environmental Effects on Quantitative
Traits

• Additive, dominance, and epistatic effects
• can all contribute to the phenotype of a
  quantitative trait,
• but generally additive interactions are the most
  important.

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Genetic and Environmental Effects on Quantitative
Traits

• All of mentioned factors are genetic in nature,
  but the environment also affects quantitative
  traits.
• The primary affect of the environment is to
  change the value for a particular genotype.
• Using our previous example, the value for the
  genotype AaBb might vary from 8-10.
• This variation would be the result of the
  different environments in which the genotype was
  grown.
• The consequence of this environmental effect is
  that the distribution even more resembles a
  normal distribution.

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Genetic and Environmental Effects on Quantitative
Traits

• To illustrate the effect of environment on the
  expression of a genotype, the yields of winter
  wheat at one North Dakota location (Casselton,
  ND) during the last ten years are presented.
• Any year for year variation in yield for any one
  genotype is largely an effect of the environment.

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Genetic and Environmental Effects on Quantitative
Traits

• Yield (bushels/acre)
• Genotype
• Year Roughrider Seward Agassiz
• 1986 47.9 55.9 47.5
• 1987 63.8 72.5 59.5
• 1988 23.1 25.7 28.4
• 1989 61.6 66.5 60.5
• 1990 0.0 0.0 0.0
• 1991 60.3 71.0 55.4
• 1992 46.6 49.0 41.5
• 1993 58.2 62.9 48.8
• 1994 41.7 53.2 39.8
• 1995 53.1 65.1 53.5

Note All plants in 1990 experienced winter kill.
(The data from Dr. Jim Anderson, Dept of Plant
Sciences, North Dakota State University, Fargo,
ND.)
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Genetic and Environmental Effects on Quantitative
Traits

• Thus the phenotype is a sum of the environmental
  and the genetic effects.
• Stated in a mathematical format
• Phenotype Genetic Factors Environmental
  Factors

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Genetic and Environmental Effects on Quantitative
Traits

• One of the goals of quantitative genetics is to
  measure the contribution of genetic and
  environmental factors on a specific phenotype.
• However, the field of quantitative genetics also
  studies other aspects
• of quantitative traits.

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Genetic and Environmental Effects on Quantitative
Traits

• Questions Studied By Quantitative Geneticists
• What is the genetic and environmental
  contribution to the phenotype?
• How many genes influence the trait?
• Are the contributions of the genes equal?
• How do alleles at different loci interact
  additively? epistatically?
• How rapid will the trait change under selection?

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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.

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Statistics of Quantitative Traits

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

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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.

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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.

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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) 16.80 0.816 BMS (P2)
6.63 1.887 F1 12.12 1.519 F2
12.89 2.252
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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.

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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.

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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

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Variance Components of a Quantitative Trait

• The genetic variation can be further subdivided
  into three components.
• 1. Additive genetic variation.
• Some alleles may contribute a fixed value to the
  metric value of quantitative trait.
• For example, if genes A and B control corn yield
  (it is actually controlled by many genes), and
  each allele contributes differently to yield in
  the following manner

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Variance Components of a Quantitative Trait

• If genes A and B control corn yield (it is
  actually controlled by many genes), and each
  allele contributes differently to yield in the
  following manner
• A 4 bu/ac
• a 2 bu/ac
• B 6 bu/ac
• b 3 bu/ac

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Variance Components of a Quantitative Trait

• AABB genotype will have a yield
• of 20 (4466) bu/ac
• The AaBb genotype will yield
• 15 (4263) bu/ac.
• Genes that act in this manner are additive, and
  they contribute to the
• additive genetic variance (VA).

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Variance Components of a 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.
• If the two such genes exhibiting dominance the
  metric value of the AaBb heterozygote would be 20
  bu/ac.
• This value equals the homozygous dominant
  genotype in the example where the alleles were
  acting additively.
• This source of variability is attributed to the
• dominance genetic variance (VD).

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Variance Components of a Quantitative Trait

• 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).

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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 VGE VGE

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Variance Components of a Quantitative
TraitCONCLUDING

• By performing specific experiments, quantitative
  geneticists can estimate the proportion of the
  total variance that is attributable to the total
  genetic variance and the environmental genetic
  variance.
• If geneticists are trying to improve a specific
  quantitative trait (such as crop yield or weight
  gain of an animal), estimates of the proportion
  of these variances to the total variance provide
  direction to their research.
• If a large portion of the variance is genetic,
  then gains can be made from selecting individuals
  with the metric value you wish to obtain.
• On the other hand if the genetic variance is low,
  which implies that the environmental variance is
  high, more success would be obtained if the
  environmental conditions under which the
  individual will be grown are optimized.

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Heritability

• Broad-sense heritability
• It is the ratio of total genetic variance to
  total phenotypic variance.
• H2 VG/VP
• Narow-sense heritability
• It is the ratio of additive genetic variance to
  the total phenotypic variance.
• h2 VA/VP

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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.

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Estimating the Offspring Phenotype

• If the narrow sense heritability of a trait has
  been determined and several population values is
  known the phenotypic value for an offspring can
  be estimated.
• The following formula can be used for the
  prediction.
• To T h2(T-T)
• Where
• To predicted offspring phenotypeT population
  meanh2 narrow sense heritabilityT
  midparent value (Tf Tm)/2

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Estimating the Offspring Phenotype

• An Example
• T 80 seeds/plantTf 90 seeds/plantTm 120
  seeds/plantT (90 120)/2 105h2 0.5
• Then
• To 80 0.5 (105-80)To 80 12.5To 92.5
  seeds/plant

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Estimating the Offspring Phenotype

• The conclusion is not that each plant in the next
  generation will have 92.5 seeds/plant, but rather
  that on average the population derived from
  mating these two parents will have 92.5
  seeds/plant.
• IMPORTANT!
• The quantitative traits are affected by the
  environment, and the environment will be
  responsible for the deviations that one would see
  from the estimated phenotype.

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Predicting Response to Selection

• Another use of heritability is to determine how a
  population will respond to selection.
• Typically parents with the phenotypic value of
  interest are selected from a base population.
• These parents are crossed, and a new population
  is developed.

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Predicting Response to Selection

• The distributions shown on right illustrate this
  point.

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Predicting Response to Selection

• The selection differential is the difference of
  the base population mean and the mean of the
  selected parents.
• The selection response is how much gain one make
  when mating the selected parents.
• IMPORTANT!
• The narrow sense heritability is a measure of the
  genetic component that is contributed by the
  additive genetic variance.
• The response to selection can thus be derived by
  multiplying the heritability by the selection
  differential.

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Predicting Response to Selection

• EXAMPLE
• The base sunflower population has a mean of 100
  days to flowering.
• Two parents were selected that had a mean of 90
  days to flowering.
• The quantitative trait days to flowering has a
  heritability of 0.2.
• What would be the mean of a population derived
  from crossing these two parents?
• R h2SR 0.2(90 - 100) days to floweringR
  -2 days
• The new population mean would therefore be 98
  days to flowering (100 days - 2 days).

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