Determining mice numbers and alleles using hardy-weinberg's equilibrium

Question

White: AA

Gray: AB BB BC AC

Black: CC

using hardy-weinberg equilibrium to fill the question marks (all mice have equal fertility rates)

Year: 0 

White mice (#): 300

Gray mice (#): 0 

Black mice (#): 700 

Total number of mice: 1000

"A" alleles (#): ?

"B" alleles (#): ?

"C" alleles (#): ? 

Year: 10 

White mice (#): 180 

Gray mice (#): ? 

Black mice (#): ? 

Total number of mice: ?

"A" alleles (#): ?

"B" alleles (#): ?

"C" alleles (#): ? 

Year: 20 

White mice (#): ? 

Gray mice (#): 2100 

Black mice (#): ? 

Total number of mice: ?

"A" alleles (#): ?

"B" alleles (#): ?

"C" alleles (#): ?

Answer 1

Hi Joe! Hardy-Weinberg equilibrium allows us to predict allele frequencies in a population under certain conditions, assuming random mating, no selection, no mutation, no migration, and a large population. The allele frequencies remain constant over generations.

Let's denote the frequencies of the alleles A, B, and C as p, q, and r, respectively. The genotype frequencies can be calculated based on these allele frequencies.

At Year 0:

1. Total number of mice = 1000
2. White mice (#): 300 (AA genotype) Black mice (#): 700 (CC genotype)
3. Since the frequencies of A and C alleles are represented by p and r, respectively, and the total number of alleles is twice the total number of individuals:
4. p + r = 1 (allele frequencies sum up to 1)
5. We know the number of white mice with the AA genotype (300), so the frequency of A alleles (p) can be calculated:
6. p = (2 * number of AA individuals) / (2 * total number of individuals) = (2 * 300) / (2 * 1000) = 600 / 2000 = 0.3
7. Similarly, r (the frequency of the C allele) is:
8. r = (2 * number of CC individuals) / (2 * total number of individuals) = (2 * 700) / (2 * 1000) = 1400 / 2000 = 0.7

So, at Year 0:

1. "A" alleles (#): 0.3 * 1000 = 300
2. "B" alleles (#): 0 (not present)
3. "C" alleles (#): 0.7 * 1000 = 700

Now, let's apply these principles to Years 10 and 20:

At Year 10:

White mice (#): 180 (AA genotype) The number of "B" alleles can be determined by the number of AB and BB genotypes.

The frequency of B alleles (q) is:

q = (2 * number of AB individuals + 4 * number of BB individuals) / (2 * total number of individuals) = (2 * ? + 4 * ?) / (2 * ?)

Without more information about the genotypes of gray mice, we cannot determine the exact number of "B" alleles or the total number of mice.

At Year 20:

Gray mice (#): 2100 The number of "B" alleles can be determined by the number of AB and BB genotypes.

The frequency of B alleles (q) is:

q = (2 * number of AB individuals + 4 * number of BB individuals) / (2 * total number of individuals) = (2 * ? + 4 * ?) / (2 * ?)

Similarly, the frequency of A alleles (p) and C alleles (r) can be determined.

Without more information about the genotypes of white and black mice, we cannot determine the exact numbers of "A," "B," and "C" alleles or the total number of mice.

To fully determine the genotype frequencies and calculate the numbers of alleles, we need information on the genotypes of gray, white, and black mice in Years 10 and 20.