Math/Chemistry Problems 

1) The allelic frequency of the recessive allele causing phenylketonuria is 0.008. Calculate the allelic frequency of the normal dominant allele. Then, calculate the amt. expressed as a decimal (2 places after the decimal) of the population that are homozygous dominant (p²), heterozygous (2pq) and homozygous recessive (q²).

q = 0.008

p = .992

p² = .98

2pq = 0.016

q² = 6.4 × 10^-5

2) In Drosophila the allele for normal-length wings is dominant over the allele for vestigial wings (vestigial wings are stubby little curls that cannot be used for flight). In a population of 1000 individuals, 37 have vestigial wings. What amt. expressed as a decimal (2 places after the decimal) would you expect to be homozygous dominant (p²) and heterozygous (2pq) for this trait? 

q = 0.2

p = 0.8

p² = 0.64

2pq = 0.32

q² = 0.04

3) A study on blood types in a population found the following genotypic distribution among the people sampled: 1101 were MM, 1496 were MN and 503 were NN. Calculate the allele frequencies of M and N, and the expected numbers of the three genotypic classes (expressed as whole numbers) assuming random mating has occurred.

1101 MM

1496 MN

503 NN
Total = 3100 Individuals

Total = 6200 Alleles

P=M and Q=N

P=0.35

Q= 1496 + 2(503) =2502 alleles/6200 alleles = 0.40

P = 2(1101) + 1496 = 3698 alleles/6200 alleles = 0.60

0.36 + 0.48 + 0.16 = 1

EXPECTED = p² (0.6)² x 3100 = 1116

EXPECTED = 2pq (0.48) x 3100 = 1488

EXPECTED = q² (0.4)² x 3100 = 496

4) Calculate X² (to 2 places after the decimal) and using p = 0.05 determine whether or not the population in question 3 is in Hardy-Weinberg equilibrium.

(1101-1116)²

5) Calculate the realized heritability to the nearest hundredth for plant height in Wisconsin Fast Plants if the original population had an average height of 23.8 cm, the selected subpopulation had a height of 25.2 cm, and their offspring had a height of 24.7 cm.

Heritability (h²) = (ave. population – ave. offspring)/(ave. population – ave. subpopulation)

6) Nickel-59 has a half-life of 76000 years. What percent of a sample of nickel-59 would remain

after 760000 years? 

7) Calculate the time since divergence (expressed as a whole number) for two groups differing

in 47 of 213 amino acids for a certain protein. Assume a divergence rate of 2% per million years.

8) Calculate the divergence rate to the nearest hundredth for two groups differing in 13 of 158 amino acids if radiometric evidence places their common ancestor 15 million years ago.