Biology 20

Hardy-Weinberg problems: Answers in bold

1. We have always thought that Rudolph the red-nosed reindeer was a one of a kind. However in the remote reaches of Scandinavia, there has been numerous citings of red-nosed reindeer. A recent study by population genetics reviled that red-nosed reindeers occur 3 out every 100 reindeer. Further DNA analysis has shown that the red-nosed gene is recessively inherited.

• What is the frequency of the recessive allele? Dominant allele?

q² = 3/100 = .03 à q = à q = .17 frequency of the recessive allele

p + q =1 à p = 1 – q à p = 1 - .17 = .83 frequency of the dominant allele

• What is the percentage of the population that does not have red-noses, but could pass on this gene to its offspring?

p² + 2pq + q² =1 2pq à 2(.83)(.17) = .28 or 28% of population that’s heterozygous

• What’s the probability that two non-red nosed reindeer may meet and have red-nosed offspring?

Aa x Aa à (2pq) (2pq) à (.28)(.28) = .078 or 7.8%

2. During the holiday season the dominantly inherited gene for overspending often times kicks into high gear. Roughly 80% of shoppers in The Shops at Mission Viejo have the overspending gene.

• What percentage of the population is recessive for the overspending gene?

20% of the population is recessive for the overspending gene

1. What is the frequency of both the dominant and recessive alleles?

NOTE: you’ll need to always start by determining the recessive allele, NOT the dominant one

q² = 20% or .20 à q = à q = .45 frequency of the recessive allele

p + q =1 à p = 1 – q à p = 1 - .45 = .55 frequency of the dominant allele

• What percentage of the shoppers at The Shops at Mission Viejo are homozygous dominant for this overspending gene?

p² + 2pq + q² =1 AA = p² à .55² = .30 or 30% are homozygous dominant

• What percentage is heterozygous for this overspending gene?

p² + 2pq + q² =1 Aa = 2pq à 2(.55)(.45) = .495 or 49.5% are heterozygous

3. Elf is one of the taller elves, but he’s not alone. The allele for increased height is recessively inherited and actually occurs in about 5% of the elf population working in Santa’s workshop.

• What is the frequency of this recessive allele?

q² = 5% or .05 à q = à q = .22 or 22% frequency of the recessive allele