Step 1: Understanding the Concept:
The Hardy-Weinberg Principle states that in a large, random-mating population, allele (gene) and genotype frequencies remain constant from generation to generation in the absence of evolutionary influences.
Step 2: Key Formula or Approach:
If \(p\) and \(q\) represent the gene (allele) frequencies of two alleles at a locus in the parental generation:
The genotype frequencies in the progeny generation are given by the binomial expansion of:
\[ (p + q)^2 = p^2 + 2pq + q^2 \]
Step 3: Detailed Explanation:
Under the assumption of random mating, male and female gametes pair up purely based on their relative allele frequencies in the parental gene pool.
Therefore, the proportion of offspring genotypes (\(p^2\) for AA, \(2pq\) for Aa, and \(q^2\) for aa) depends entirely on the allele (gene) frequencies (\(p\) and \(q\)) of the parents, rather than their parental genotype distribution.
Step 4: Final Answer
The genotype frequencies in the progeny depend only on the gene frequencies in the parents.