Question

You have discovered that a single gene controls the date when monarch butterflies break diapause (=become reproductively active) in Mexico. You were extremely busy this spring, and extensively sampled one overwintering site to find that 1751 monarchs broke diapause in early February, 424 broke diapause in late February, and 710 broke diapause in early March. You know there are two alleles for this gene (D, d), and that heterozygotes (Dd) break diapause in late February, Monarch butterfly while DD break diapause in early February. Showing your work, answer the following questions: a. What is the observed frequency of the allele coding for early emergence (early February)? b. Does this gene appear to be in Hardy-Weinberg equilibrium in this population?

Answer 1

The observed frequency of allele i.e. D coding for early emergence is 0.69 and is calculated as shown below:-

Total no of copies of allele D(x)= (1751×2)+424/2= 3741

Total no of copies of all alleles of gene(y)= (1751×2) +424+(710×2)=5346

Therefore, frequency of allele D= x/y= 3741/5346= 0.69

Now if the frequency of allele D is known, frequency of allele d can be calculated by the formula p+q=1 so,

D+d=1

d= 1-0.69= 0.31

Now expected genotype frequencies should be

Genotype DD= p^2= 0.69×0.69= 0.47

Genotype Dd= 2pq= 2×0.69×0.31= 0.42

Genotype dd= q^2= 0.31×0.31= 0.09

According to the question, observed genotype frequencies are as calculated:-

Genotype DD= 1751/2885= 0.60

Genotype Dd= 424/2885=0.14

Genotype DD= 710/2885= 0.24

As we can see that the observed frequency of genotypes do not match the expected frequency of genotypes. Thus this gene does not appear to be in Hardy-Weinberg equilibrium in this population.