POLYGENES AND MULTIFACTORIAL INHERITANCE

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POLYGENES AND MULTIFACTORIAL INHERITANCE
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• BASIC PRINCIPLES
• Complex traits are determined by multiple genetic
  and environmental factors acting together.
• The relative contributions of genotype and
  environment to a trait are measured by the
  variance due to genotype (genotypic variance) and
  the variance due to environment (environmental
  variance).
• Correlations between relatives are used to
  estimate various components of variation, such as
  genotypic variance, additive variance, and
  dominance variance.

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• In considering the genetics of complex traits,
  an important objective is to assess the relative
  importance of genotype and environment.
• Multiple sources contribute to phenotypic
  variance
• Genotypic variance
• Environmental variation
• Variation due to genotype-environment interaction
• Variation due to genotype-environment association
• Variation due to gene-gene interaction

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The mean of a population is estimated from a
sample of individuals from the population, as
follows
In this table, the mean height in the sample of
women is 63.1 inches.
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The variance is a measure of the spread of the
distribution and is estimated in terms of the
squared deviation (difference) of each
observation from the mean.
In this table, the variance of the population
of British women is estimated as s 2 7.24 in2.
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The variation in phenotype caused by differences
in genotype among individuals is termed genotypic
variance. The variation in phenotype caused by
differences in environment among individuals is
termed environmental variance.
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A) Genotypic variance sg2 2.0
B) Environmental variance se2 1.0
Distribution of phenotypes when there is no
variation in the environment genotypic variance
sg2 2.0
Distribution of phenotypes when there is no
variation in genotype environmental variance se2
1.0
C) Phenotypic variance sp2 sg2 se2 3.0
Distribution of phenotypes when there is
variation in both genotype and environment
Phenotypic variance sp2 3.0
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When genetic and environmental effects contribute
separate and independent effects on the
phenotype, the total variance equals the sum of
the genotypic variance and the environmental
variance.
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Genotype-Environment Interaction and
Association In the simplest cases, environmental
effects on phenotype are additive, and each
environment adds (or detracts) the same amount to
(or from ) the phenotype, independent of the
genotype. When this is not true, environmental
effects on phenotype differ according to
genotype, and a genotype-environment interaction
(G-E Interaction) is said to be present.
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An adaptation of Wotererks (1909) original
demonstation of a reaction norm
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Genotype-environment interaction in maize.
Strain A is superior when environmental quality
is low (negative numbers), but strain B is
superior when environmental quality is high.
B
In rich (positive) environments, B out-performs A
In poor (negative) environments, A out-performs B
110 100 90 80 70 60 50
A
Yield (110 kg/hectare)
-20 -10 0 10
20 Environmental quality
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When the different genotypes are not distributed
at random in all the possible environments, there
is genotype-environment association (G-E
Association).
E1
E2
AA
Aa
aa
C 2 p-value
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• Polygenic Inheritance of Complex Traits
• Polygenes A concept developed by R.A. Fisher to
  describe the genetics of continually distributed
  traits
• Denotes many genetic variations with small,
  inter-changeable, additive effects.
• In the limit, an infinite number of genetic
  variations with infinitely small effects.

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Polygenes For example, suppose that a trait
(like weight) is controlled by 8 genes that are
biallelic (e.g. A, a). If having an A makes
you 1 unit heavier than the a allele, then
having 8 genes gives rise to a wide variety of
weights in the population.
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Correlation Between Relatives
Studies of complex inheritance rely extensively
on similarity among relatives to assess the
importance of genetic factors. Covariance and
Correlation Genetic data about families are
frequently pairs of relatives pairs of parents,
pairs of twins, or pairs consisting of a single
parent and a single offspring. An important
issue in quantitative genetics is the degree to
which the phenotypes of each pair are associated.
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Correlation Between Relatives
Calculation of the covariance is similar to
calculation of variance, except that the squared
deviation term (xi x )2 is replaced with the
product of the deviations of the pairs of
measurements from their respective means that
is, (xi x) (yi y).
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The estimated covariance (Cov) of the trait among
relatives is Where N is the total number of
pairs of relatives studied.
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Estimation of Heritability
The table below give the theoretical values of
the correlation coefficient for various pairs of
relatives h2 represents the narrow-sense
heritability and H 2 the broad-sense heritability.
Contributions from interactions among alleles of
different genes have been ignored. For this and
other reasons, H 2 correlations are approximate.
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The broad-sense heritability is often calculated
using twins
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Twin Studies
Twin studies are subject to several important
sources of error, most of which increase the
similarity of identical twins. Therefore, the
numbers in this table should be considered very
approximate and probably too high.
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Twin Studies

• Four potential sources of error in Twin Studies
  are
• Genotype-environment interaction, which increases
  the variance in fraternal twins but not in
  identical twins.
• Frequent sharing of embryonic membranes between
  identical twins, resulting in more similar
  intra-uterine environments than those of
  fraternal twins.
• Greater similarity in the treatment of identical
  twins by parents, teachers, and peers, resulting
  in a decreased environmental variance in
  identical twins.
• Different sexes in half of the pairs of paternal
  twins, in contrast with the same sex of identical
  twins.

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Additive and Dominance Variance
Suppose two alleles, a and A, segregate at a
locus influencing height. In the environments
encountered by the population, the mean
phenotypes (heights) and frequencies of the three
genotypes might be There is genetic variance
in the population the phenotypic means of the
three phenotype classes are different. Some of
the variance arises because there is an average
effect on phenotype of substituting an allele A
for and allele a.
a/a A/a A/A Phenotype 10 18 20 Frequency 0.36 0.
48 0.16
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By defining the average effect of an allele as
the average phenotype of all individuals that
carry it, we necessarily make the average effect
of the allele depend on the frequencies of the
genotypes. Thus, the average effect of all the a
alleles is and, by a similar argument,
This average difference in effect between A and a
alleles of 5.60 cm accounts for some of the
variance in phenotype but not all of it. The
heterozygote is not exactly intermediate between
the homozygotes there is some dominance
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We partition the total genetic variance in a
population into additive genetic variation (s
2a), the variance that arises because there is an
average difference between the carriers of a
alleles and the carriers of A alleles, and a
component called the dominance variance (s 2d),
which results from the fact that heterozygotes
are not exactly intermediate between the
homozygotes. Thus
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The components of the variance in our example,
where a/a 10, A/a 18, and A/A 20, can be
calculated by using the definitions of mean and
variance. The mean phenotype can be calculated
thus The total genetic variance that arise
from the variation among the mean phenotypes of
the three genotypes is
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The frequency of allele a is (by counting
alleles) And the frequency of the A allele
is
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The variance of allelic means is then And
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The total phenotypic variance can now be written
as We define a new kind of heritability, the
heritability in the narrow sense (h 2), as
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ADDITIONAL PRINCIPLES 1. Additive variance
accounts for the parent-offspring correlation
dominance variance accounts for the sib-sib
correlation over and above that expected from the
additive variance. 2. Narrow-sense heritability
is the ratio of additive (transmissable)
variance it is widely used in plant and animal
breeding to predict the response to artificial
selection. 3. Genes that affect quantitative
traits can be identified by genetic mapping using
highly polymorphic DNA markers, or by specifying
candidate genes on the basis of knowledge of the
physiology and development of the trait.
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Application of these Principles to Common
Complex Traits