A moth's color is controlled by two alleles, G and g, at a single locus. G (gray) is dominant to g (white). A large population of moths was studied, and the frequency of the G allele in the population over time was documented, as shown in the figure below. In 1980 a random sample of 2,000 pupae was collected and moths were allowed to emerge. Assuming that the population was in Hardy-Weinberg equilibrium for the G locus, what percentage of the gray moths that emerged in 1980 was heterozygous? (The Answer is 67%, can you please explain why it's 67%? thank you!!)
Answers
Answer:
67%
Explanation:
When taking random samples from a population, the observed numbers are not always as the expected ones. The difference is by chance, instead of 50% heter0zyg0us, the sample included 67%.
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Available data:
- Moths' color ⇒ diallelic gene
G allele → dominant → Codes for greyg allele → recessive → Codes for white- f(G) 1960 = 0.8
- f(G) 1965 = 0.7
- f(G) 1970 = 0.6
- f(G) 1975 and 1980 = 0.5
- 1980 ⇒ N = 2000 pupae
- Population in H-W equilibrium
Hardy-Weinberr equilibrium,
Assuming a diallelic gene, p and q are the allelic frequencies in a locus and represent the allelic d0minant or recessive forms. The gen0typic frequencies after one generation are p² (H0m0zyg0us d0minant), 2pq (Heter0zyg0us), q² (H0m0zyg0us recessive). Populations in H-W equilibrium will get the same allelic frequencies generation after generation.When adding the allelic frequencies of a population in H-W equilibrium, the result should be 1, this is p + q = 1.In the same way, when adding the genotypic frequencies, the result should also equal 1, this is p²+ 2pq + q² = 1In this problem we assume that the population is under H-W equilibrium, and we know that p = 0.5.
Considering that p + q = 1, then by clearing the equation, we get the value of q = 0.5
Finally, we know that the genotypic frequency of the heter0zygous genotype is 2pq, so,
F(Gg) = 2pq = 2 x 0.5 x 0.5 = 0.5 = 50%
Now, among the options in the problem, there is not 50% but others. One of them, and the closest to 50%, is 67%.
The chart reflects that through the years, the moth's populations stabilized. Both alleles were favored, and their frequencies got to be equal to each other -0.5-. So there is a high probability of getting heter0zyg0us individuals in the population -50%-, more than any of the h0mzyg0us ones -25%-.
However, in a natural population, the amount of h0m0zyg0us and heter0zygous individuals observed is not always the same as the expected ones. This fact happens especially when there are random samples.
In this experiment, the researcher took 2000 pupae, but they did not know their genotype. They just took them randomly. Even though the population is in H-W equilibrium, when sampling, the researcher took more heter0zyg0us individuals than the expected ones. It does not mean that the population is not under H-W equilibrium. It just means that by chance, more heter0zyg0us were selected.
So what you need to do in these situations, is to analyze your problem and the provided information, and think about the most feasible answer.
In this case, the expected number is 50% heter0zyg0us. The closest option is 67% and the most feasible. So that would be the answer.
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