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Hardy-Weinberg

Hardy-Weinberg. Daniel Chu. Geoffrey Hardy (1877 – 1947). British Mathematician Not a biologist Disliked applied mathematics Pacifist Wrote “A Mathematician's Apology”. Wilhelm Weinberg (1862 – 1937). German physician Strong moral sense Delivered 3500 babies Studied heredity

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Hardy-Weinberg

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  1. Hardy-Weinberg Daniel Chu

  2. Geoffrey Hardy (1877 – 1947) • British Mathematician • Not a biologist • Disliked applied mathematics • Pacifist • Wrote “A Mathematician's Apology”

  3. 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

  4. Udny Yule (1871 – 1951) • Scottish statistician • Recognized that Mendelism and biometics were compatible • Mistakenly believed that dominant traits naturally spread over populations

  5. 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

  6. George Shull (1874 – 1954) • American plant geneticist • Came from a poor family • Worked with inbred and hybrid plants • Founding editor of the journal “Genetics”

  7. Background of the letter • Response to Yule’s comment of, “in the course of time one would expect, in the absence of counteracting factors, to get three brachydactylous to one normal.” • Yule’s comment was an attack on Mendelian genetics • Punnett introduced Hardy to the problem

  8. Hardy’s 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

  9. Hardy’s proof • If the ratios between AA, Aa, and aa are p:2r:q respectively • The next generation gives frequencies of (p+q)2 : 2(p+q)(q+r) : (q+r)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 = 100,000,000*1, the population is stable

  10. Naming Hardy-Weinberg • Initially called Hardy’s law • Stern brought attention to Wienberg’s paper changing the name to Hardy-Wienberg’s law, 35 years after it was published • Wienberg’s 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

  11. 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 A’s 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

  12. Additional requirements • No selection • No mutations • No migration/gene flow

  13. 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 50’s 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

  14. 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.

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