You are researching a population of 100 cows, where 91 of them are grey and 9 are black. You know that black colour is a recessive trait for this type of cow. Using the Hardy-Weinberg Equilibrium equation (p2 + 2pq + q2 = 1), what number would be heterozygous?

Question

BlackTom AI · Accepted Answer

In this population genetics problem, we start from the phenotype data: 9% black cows, which are recessive, meaning aa. Therefore q^2 = 0.09, so q = sqrt(0.09) = 0.3. The proportion of the other allele, p, is 1 - q = 0.7. The heterozygous genotype frequency is 2pq = 2 × 0.7 × 0.3 = 0.42.

Option by option analysis:
- Option 42: This matches the calculated heterozygote frequency of 0.42. Since there are 100 cows, 0.42 × 100 = 42 individuals would be heterozygous (Aa). This aligns with Hardy-Weinberg expectations given q = 0.3 and p = 0.7.
- Option 80: If 80 individuals were heterozygous, that would correspond to a frequency of 0.80 for Aa. That would imply p and q values that do not satisfy p^2 + 2pq + q^2 = 1 with q^2 = 0.09; it would require an unrealistically high 2pq value, inconsistent with the observed recessive phenotype frequency.
- Option 70: A heterozygote frequency of 0.70 would also imply 2pq = 0.70, which would force p and q to values that do not produce q^2 = 0.09 when used in p^2 + 2pq + q^2 = 1; this is not mathematically compatible with the given recessive phenotype proportion.
- Option 32: 32 heterozygotes would correspond to a frequency of 0.32, which is lower than the calculated 0.42 from p = 0.7 and q = 0.3, indicating a mismatch with the Hardy-Weinberg proportions based on the observed data.

In summary, the 0.42 heterozygote frequency derived from p = 0.7 and q = 0.3 best fits the given data and the Hardy-Weinberg framework, leading to 42 individuals being heterozygous in a population of 100.

You are researching a population of 100 cows, where 91 of them are grey and 9 are black. You know that black colour is a recessive trait for this type of cow. Using the Hardy-Weinberg Equilibrium equation (p2 + 2pq + q2 = 1), what number would be heterozygous?Single choice

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