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• 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

Udny Yule (1871 – 1951)

• Scottish statistician

• Recognized that Mendelism

and biometics were compatible

• Mistakenly believed that

dominant traits naturally spread

over populations

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

George Shull (1874 – 1954)

• American plant geneticist

• Came from a poor family

• Worked with inbred and

hybrid plants

• Founding editor of the

journal “Genetics”

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

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

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

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

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

Additional requirements

• No selection

• No mutations

• No migration/gene flow

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

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.