7. Pyrethrums are chemicals used to kill insects. In bed bugs, the mutant-type allele, r, confers resistance, but only in homozygous individuals. Assume the populations are in Hardy-Weinberg proportions before pyrethrum is sprayed and that there are two alleles at this gene. a. In 1955, pyrethrum was sprayed and killed 99% of the bed bug population. What were the genotype frequencies and allele frequencies in 1955 immediately before the spraying occurred

Allele frequency

Normal allele  

Mutant r allele

Genotype frequency

Homozygous normal bugs

Homozygous mutant bug

Heterozygous normal bug with one mutant r allele and one normal allele

Explanation:

It is given that 99% of the bugs were killed after the spray of  pyrethrum. This suggests that 1% of the bugs that were not killed must be homozygous for the mutant type allele "r"

Thus, the frequency of homozygous "rr" species i.e

From this we can evaluate the frequency of mutant "r" allele.

Thus,

As per Hardy-Weinberg first equilibrium equation,

Substituting the value of q in above equation, we get

Thus, the frequency of homozygous normal bug is equal to

As per Hardy-Weinberg second equilibrium equation-

Substituting all the available values we get -

Allele frequency

Normal allele  

Mutant r allele

Genotype frequency

Homozygous normal bugs

Homozygous mutant bug

Heterozygous normal bug with one mutant r allele and one normal allele

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