Quantitative InheritanceGenetics

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Quantitative Inheritance/Genetics
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Statistical Methods Evaluate A Frequency
Distribution

• Statistical tools are used to analyze a normal
  distribution in a number of ways
• One measure, the mean computed using the
  following formula

• where

• X is the sum of all values in the group

N is the number of individuals in the group
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• In genetics,interest exists in the amount of
  phenotypic variation that exists in a group
• A common way to evaluate variation within a
  population is a statistic called variance

where, VX is the variance
N is the number of observations
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• Variances are very important in the analysis of
  quantitative traits because they are additive
  under certain conditions
• The variances of genetic and environmental
  factors that contribute to a quantitative trait
  can be added to predict the total variance for
  that trait
• To gain an intuitive grasp of variation, we can
  take the square root of the variance
• The statistic is standard deviation

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Polygenic Inheritance
a situation in which _____ gene loci or multiple
gene loci contribute to a single phenotypic
trait.
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Polygenic Inheritance
To date, Traits discussed have clearly
identifiable phenotypes with limited
variability. eg., red / white hair color in
cattle, belting in swine.
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Traits discussed to date have been qualitative,

• phenotypes - easy to identify
• no need to measure
• the trait
• controlled by a few
• (1-2) loci

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Now quantitative traits,
the phenotype exhibits very small phenotypic
variations not readily distinguishable eg.,
phenotype - steer gaining 3.1 /day vs 3.2 is
real but difficult to identify
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First Demonstration of a Polygenic Trait-
Nilsson-Ehle Experiment Red and White wheat
pigment in wheat hulls
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First demonstration of continuous variation
related to polygenic inheritance, 1909

• Swedish geneticist, Herman Nilsson-Ehle - the
  inheritance of red pigment in the hull of wheat
  Triticum aestivum

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• - P True-breeding red X true- breeding
  white
• F1 Intermediate red
• F2 Great variation in redness
• White, light red, intermediate red, medium red,
  dark red
• Colors fell into a 14641 ratio
• Two different genes that control hull color
• Each gene exists in two alleles red or white
• Two loci contribute additively to the color of
  hull

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Phenotypic variation in quantitative traits is
continuous

• Quantitative traits controlled by many gene
  loci on numerous chromosomes.
• - Gene loci with small positive contributions
  (non-dominant) to the phenotype are additive
  genes and additive gene actions.
• - Loci that contribute to the phenotype but
  actions are dominance and epistasis, non-additive
  genes

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- Quantitative genes segregate separately from
each other and have specific effects.
- Dominance, epistasis, and linkage involving
both autosomes and sex-linked genes are
associated with polygenic /quantitative traits.
A hypothetical example of polygenic inheritance,
White Spotting in Cows.
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Inheritance of Hypothetical Spotting in Cattle
10 White 50 White 90 White
Ref J. Hered. 1999 (90)629-34.
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Inheritance of Hypothetical Spotting in Cattle

• Number of Possible
  Degree Nos. in
• Additive Genes Genotypes (9) of
  Spotting Phenotype
• 0 aaee
  10 white, 1
• 9 0 black
• 1 Aaee, aaEe
  30 white, 4
• 
  70 black
• 2 AAee, aaEE,
  50 white, 6
• AaEe
  50 black
• 3 AAEe, AaEE
  70 white, 4
• 
  30 black
• 4 AAEE
  90 white, 1
• 
  10 black

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• Dihybrid cross - 2 pairs of alleles A,a and
  E,e
• Let A, E more spotting a,e neutral, no
  spotting
• A and E contrib. same amt. of increasing wht.
  20 animals surface.

Assume
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Theoretical Expectations in F2 Populations with
Trait Controlled by Polygenic Inheritance

• Chance of
• Number of Pairs Size of F2 Necessary
  No. of Phenotype Obtain.
• of Alleles for All Combinations
  Classes Either Extreme
• 1 4
  3 1/4
• 2 16
  5
  1/16
• 3 64
  7
  1/64
• 4 256
  9
  1/256
• 5 1024
  11 1/1024
• 6 4096
  13 1/4096
• n 4 n
  2 n1 1/4 n

2 Pairs of alleles in F2 Dihybrid cross
various phenotypic ratios 9331 , 363121
, 934, now 14641 (prev. slide).
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Polygenic Inheritance of Mature Size in Chickens

• Number of Additive Number of
• Genes
  Phenotype Animals
  0 750
  g 1
• 1 825 g 8
• 2 900 g 28
• 3 975 g 56
• 4 1050 g 70
• 5 1125 g 56
• 6 1200 g 28
• 7 1275 g 8
• 8 1350 g 1

256

• Mature size controlled by 4 pairs of
  hypothetical genes
• Genes A,B,C,D contr. 75 g ea. genes a,b,c,d
  no contrib. aabbccdd 750 g bird

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Polygenic Inheritance of Mature Size in Chickens..

• Number of Additive Number of
• Genes
  Phenotype Animals
  0
  750 g 1
• 1 825 g 8
• 2 900 g 28
• 3 975 g 56
• 4 1050 g 70
• 5 1125 g 56
• 6 1200 g 28
• 7 1275 g 8
• 8 1350 g 1

256

• AaBbCcDd x AaBbCcDd 256 combinations, 9
  phenotypic. classes
• What are the genotypes of the 70 1050g
  birds?

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Histogram of Chicken Weights
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Apply a Normal
Distribution
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Curve
50
40
Number
30
20
10
0
750
825
900
975
1050
1125
1200
1275
1350
Weight in Grams
What happens to the phenotypic distinctions
between phenotypes if the no. of phenotypes
increases? Genotypes?
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Other Names (aka) for Quantitative Traits

• Polygenic
• Continuous
• Metric

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Examples of polygenic / quantitative traits (and
their unit of measure)
in Cattle ? Dogs ? Horses
? Chickens ? Big Horn Sheep ? Trout /
Salmon ? Wolves ?