Hardy-Weinberg

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Hardy-Weinberg

• Daniel Chu

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Geoffrey Hardy (1877 1947)

• British Mathematician
• Not a biologist
• Disliked applied mathematics
• Pacifist
• Wrote A Mathematician's Apology

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Wilhelm Weinberg (1862 1937)

• German physician
• Strong moral sense
• Delivered 3500 babies
• Studied heredity
• Worked alone
• Published over 160 papers
• First to understand ascertainment bias
• Explained anticipation
• Found a higher incidence of like sexed
• twins, deduced that they were of a 1 egg
• (monozygotic) and 2 egg (dizygotic) origin,
• and was able to calculate the frequency of
• the two types of twins
• Found a relationship between achondroplasia and
  last born children

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Udny Yule (1871 1951)

• Scottish statistician
• Recognized that Mendelism
• and biometics were compatible
• Mistakenly believed that
• dominant traits naturally spread
• over populations

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Ronald Fisher (1890 1962)

• English statistician and geneticist
• Showed that biometrics and
• mendelian could be reconciled
• Developed statistical methods for research
• Submitted The correlation between relatives on
  the supposition of Mendelian inheritance (1916)
  which was rejected by Punnett and Pearson

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George Shull (1874 1954)

• American plant geneticist
• Came from a poor family
• Worked with inbred and
• hybrid plants
• Founding editor of the
• journal Genetics

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Background of the letter

• Response to Yules comment of, in the course of
  time one would expect, in the absence of
  counteracting factors, to get three
  brachydactylous to one normal.
• Yules comment was an attack on Mendelian
  genetics
• Punnett introduced Hardy to the problem

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Hardys Letter

• Conditions large population, random mating, the
  genotypes are equally distributed among the
  sexes, all equally fertile
• Genotypes have no tendency to increase or
  decrease in frequency over time after the first
  generation

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Hardys proof

• If the ratios between AA, Aa, and aa are p2rq
  respectively
• The next generation gives frequencies of
• (pq)2 2(pq)(qr) (qr)2
• Under the condition of q2 pr, the distribution
  will not change over time
• If there is a population that has 1 that is AA, 0
  that are Aa, and 10,000 who are aa, and everyone
  mates and selfs
• The second generation will have 1 that is AA,
  10,000 that are Aa, and 100,000,000 that are aa
• Since 10,0002 100,000,0001, the population is
  stable

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Naming Hardy-Weinberg

• Initially called Hardys law
• Stern brought attention to Wienbergs paper
  changing the name to Hardy-Wienbergs law, 35
  years after it was published
• Wienbergs paper went largely unnoticed because
  genetics at the time was made up of English
  speakers
• Pearson and Castle also came up with the
  principle but the name would be too long
• Several other unnamed people independently came
  up with the principle

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Using allele frequencies

• Assuming there are two alleles for a single gene
  with p representing the frequency of A and q
  representing the frequency of a

• p q 1
• f(AA) f(Aa) f(aa) 1
• In order for AA to appear two As need to
• selected with the probability being p X p
  or p2
• The same holds true for aa to appear
• except with q
• In order for Aa to appear A and a need to
• be selected however Aa can also exist as
• aA so the probability of Aa or aA appearing
  
• is pq qp 2pq
• So f(AA) p2, f(Aa) 2pq, f(aa) q2
• p2 2pq q2 1
• Knowing the allele frequencies allows us to
• know the genotype frequency under Hardy-
• Weinberg conditions

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Additional requirements

• No selection
• No mutations
• No migration/gene flow

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Hybrid Maize

• Maize bred from inbred lines showed decreased
  vigor
• In 1908 Shull showed hybrid
• maize bred from two inbred
• lines often showed increased
• yields
• Producing inbred lines to make hybrids
• was impractical
• Double cross solves this
• In 1935 only 10 of the corn grown in
• Iowa was hybrid, four years later 90
• was hybrid corn
• By the 50s most of the corn grown in the US was
  hybrid corn
• Eventually lines for single crosses were
  developed
• The dominance hypothesis in which dominant
  alleles suppress deleterious recessive alleles in
  hybrids is currently favored

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Discussion

• Since no real populations meet the requirements
  of the Hardy-Weinberg law, how useful is it?
• Considering maize yields have increased linearly
  over the past 50 years, would you expect this to
  continue or plateau.