The wing color of a certain species of moth is controlled by alleles at a single locus. Gray (G) is dominant to white (g). A scientist studied a large population of these moths, tracking the frequency of the G allele over time, as shown in the figure below:
Assuming that the population was in Hardy-Weinberg equilibrium for this gene, what percentage of the moth population was heterozygous in 1960?
20%
32%
40%
64%

Question

The wing color of a certain species of moth is controlled by alleles at a single locus. Gray (G) is dominant to white (g). A scientist studied a large population of these moths, tracking the frequency of the G allele over time, as shown in the figure below: 
Assuming that the population was in Hardy-Weinberg equilibrium for this gene, what percentage of the moth population was heterozygous in 1960?
20%
32%
40%
64%

anonymous · Answer

attachment

anonymous · Answer

@BadgerBoy HW: $$p^2+2pq+q^2=1$$where "p" and "q" are the frequencies of the two alleles in the system. Does that help?

anonymous · Answer

yes thank you

anonymous · Answer

You're welcome.

anonymous · Answer

What should I use as the two frequencies. I have an idea but I am not sure.

anonymous · Answer

@BadgerBoy In your question you have two alleles ("G" and "g").  Here, the term "frequency" could be replaced by the phrase "proportion of 'G' allele of gene X in a population with two alleles ('G' and 'g') for gene X, expressed in non-percentage terms."

Frequency can go from 0 to 1, the frequency of the two alleles should add to 1 or something has gone wrong. Once you know the frequency of an allele you can find proportion of each genotype (replace 'p' and 'q' with freqG and freqg):$$(freq G)^2+2(freqG)(freqg)+(freqg)^2=1$$so, proportions of each genotype in a population can be calculated by solving for the appropriate term.

anonymous · Answer

Because this is the first kind of problem that I have seen like this, could you show me how to get the answer so I can use it as an example for my notebook?

anonymous · Answer

@BadgerBoy Okay. The graph gives you the frequency of the G allele over time.  If we know the frequency of the G allele (freq.G) you can find the frequency of the g allele (freq.g). $$1-freq.G=freq.g$$. I'm sure you can find the frequency of G at 1960 yourself.  Once you do, find the frequency of g in the population by the above formula.  Now look back at my previous post with the HW equation.  We map the genotypes to the terms in that equation.  Recall p is for G and q is for g, so $$p^2\ =\ GG$$$$q^2\ =\ gg$$ and$$2pq\ =\ Gg$$All you need to do is pick the heterozygote, fill in the appropriate frequencies and do the simple math. Remember "hetero" means different, as in not having same .