In the Hardy-Weinberg formula for determining a population's genotype frequencies, the 2 in the term 2pq is necessary because.....

Question

BlackTom AI · Accepted Answer

In Hardy-Weinberg equilibrium, genotype frequencies are given by p^2 + 2pq + q^2 = 1, where p and q are the frequencies of the two alleles. The middle term 2pq specifically represents the frequency of heterozygotes.

1) Relevant knowledge points and concepts
- Allele frequency: p and q sum to 1 (p + q = 1).
- Random mating: gametes combine at probabilities equal to allele frequencies.
- Genotype formation: probabilities for genotypes are products of gamete allele probabilities: AA = p·p, aa = q·q, and Aa = p·q or q·p.

2) Step-by-step reasoning
- The probability a gamete contributes allele A is p; the probability the other gamete contributes a is q.
- One heterozygote combination is A from parent 1 and a from parent 2: probability p × q = pq.
- The other distinct combination is a from parent 1 and A from parent 2: probability q × p = qp = pq.
- Sum these two mutually exclusive possibilities: pq + pq = 2pq.

3) Intermediate calculation example
- If p = 0.7 and q = 0.3:
  - p·q = 0.7 × 0.3 = 0.21
  - q·p = 0.3 × 0.7 = 0.21
  - Total heterozygote frequency = 0.21 + 0.21 = 0.42 = 2pq

4) Why the correct answer is correct
- The factor 2 accounts for the two distinct parental-origin orders that produce a heterozygote (A from one parent and a from the other, in either order). Each order has probability pq, so both together give 2pq.

5) Why the other options are incorrect
- A: Diploidy (two sets of chromosomes) does not by itself create the numerical 2 in the heterozygote term; the factor arises from two gamete-order combinations.
- C: Population growth or doubling of individuals is irrelevant to the algebraic derivation.
- D: All individuals (including homozygotes) have two alleles at a locus in diploids, so this statement is false.
- E: The heterozygote frequency is not generally “twice the sum of the homozygous ones”; 2pq is not 2(p^2 + q^2).

6) Conclusion
The correct answer is B) Heterozygotes can come about in two ways. This matches the provided answer.

In the Hardy-Weinberg formula for determining a population's genotype frequencies, the 2 in the term 2pq is necessary because.....Single choice

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