Hardy-Weinberg Calculations

Question 1

Hardy-Weinberg Law

Answer 1

genotypes are distributed in proportion to frequencies of individual alleles in a population and remain constant from generation to generation so long as the population is in equilibrium

Question 2

Allele frequencies

2, 3, and 4 alleles

Answer 2

2: p + q = 1
3: p + q + r = 1
4: p + q + r + s = 1

Question 3

Genotype frequencies (2, 3, and 4 alleles)

Answer 3

2: p^2 + 2pq + q^2 = 1
3: p^2 + q^2 + r^2 + 2pq + 2pr + 2qr = 1
4: p^2 + q^2 + r^2 + s^2 + 2pq + 2pr + 2ps + 2qr + 2qs + 2rs = 1

Question 4

HW in AD conditions

Answer 4

• frequency of mutant gene (q) = 1/2 incidence of disease (2pq)
• p^2 often lethal, so p approximates 0
• if incidence of disease is 1 in 10,000 (2pq), frequency of disease allele is 1 in 20,000

Question 5

HW in AR conditions

Answer 5

• frequency of disease allele (q) is the square root of disease incidence (q^2)
• p approximates 1
• carrier frequency = 2q
• if incidence of disease is 1 in 2500, q = 1 in 50 and 2pq = 1 in 25

Question 6

HW in XLR conditions

Answer 6

• because males are hemizygous, incidence of disease = q
• p approximates 1
• because females have two X’s, p^2 + 2pq + q^2 can be used
• if incidence of disease in 1 in 40, q = 1 in 40; carrier frequency in females is 1 in 20 and expected number of affected females is 1 in 160

Question 7

Fitness (f)

Answer 7

probability of transmitting one’s genes to the next generation compared to the average probability for the population

Question 8

Coefficient of selection (s)

Answer 8

measure of the loss of fitness

s = 1 - f

Question 9

Mu

Answer 9

• frequency of an allele in a population represents balance between mutation rate of gene (mu) and effects of selection against allele; as selection changes, allele frequency changes
• Mu = q * s, where s = 1 - f and q calculated based on inheritance pattern of condition
• Mu can be calculated by counting cases due to new mutations directly
• Mu = (# cases with new mutations)/(2 x total sample size)

Question 10

Assumptions of HW

Answer 10

• random mating
• no selection
• no new mutations
• no migration
• population infinitely large

Question 11

Exceptions to the Assumptions

Answer 11

• non-random mating (assortative mating, population stratification, consanguinity)
• selection does happen (heterozygote advantage/disadvantage)
• new mutations do happen, but they are rare
• gene flow/population admixture
• genetic drift (founder effect, population bottleneck)