Question

4. The Hardy-Weinberg Proof. Consider a gene that has only two alleles R (dominant) and r (recessive). The sum total of all R plus all r alleles equals all the alleles at this gene locus, or 100% of all the alleles for that gene. Let p = the percentage or probability of all R alleles in the population. Let q = the percentage or probability of all r alleles in the population. If all R + all r alleles = 100% of all alleles then p + q = 1 (or p = 1– q or q = 1 – p) Note: frequencies are stated as percentages (for example, 50%) and their associated probabilities are stated a decimal fractions (for example, 0.5). Assume that 50% of the alleles for fur color in a population of mice are R (black) and 50% are r (brown). The fur-color gene is autosomal. a. What percentage of the gametes in the females (alone) carry the R allele? _________ b. What percentage of the gametes in the females (alone) carry the r allele? _________ c. What percentage of the gametes in the males (alone) carry the R allele? _________ Female gametes (p) (q) Male gametes (p) ______ (p2) ______ (pq) (q) ______ (pq) ______ (q2) d. What percentage of the gametes in the males (alone) carry the r allele? _________ e. Given the preceding case and all the Hardy-Weinberg assumptions, calculate the probabilities of the three possible genotypes (RR, Rr, and rr) occurring in all possible combinations of eggs and sperm for the population. Hint: Fill in the allele frequencies from above and finish out the Punnet square.

Answer 1

As 50% of the alleles for fur color in a population of mice are R (black) and 50% are r (brown) and the fur-color gene is autosomal,

a. What percentage of the gametes in the females (alone) carry the R allele?

Ans: 50%

b. What percentage of the gametes in the females (alone) carry the r allele?

Ans: 50%

c. What percentage of the gametes in the males (alone) carry the R allele?

Ans: 50%

d. What percentage of the gametes in the males (alone) carry the r allele?

Ans: 50%

e. Given the preceding case and all the Hardy-Weinberg assumptions, calculate the probabilities of the three possible genotypes (RR, Rr, and rr) occurring in all possible combinations of eggs and sperm for the population.

	Male gametes
Female gametes		R (p)	r (q)
R (p)	RR (p2)	Rr (pq)
r (q)	Rr (pq)	rr (q2)

It follows that p² + 2pq + q² = 1 or 100%.

So, probabilities of the three possible genotypes (RR, Rr, and rr) occurring in all possible combinations of eggs and sperm for the population is 100%.