Step 1: Understanding the Concept:
In diploid genetics, an offspring inherits one allele for each gene locus from each of its two parents.
For an offspring to display a homozygous recessive genotype at multiple loci (e.g., \(ppqqrr\)), both parents must possess at least one copy of the recessive allele (\(p\), \(q\), and \(r\)) for each of those genes.
Step 2: Detailed Explanation:
The target genotype of the offspring is \(ppqqrr\), which represents a triple homozygous recessive condition.
For the offspring to inherit the \(p\) allele from both the maternal and paternal parents, both parents must possess at least one copy of the recessive allele \(p\) in their genotype.
Similarly, both parents must possess at least one copy of the recessive allele \(q\) and at least one copy of the recessive allele \(r\).
Let us analyze the given potential parental genotypes:
- PPQQRR (Option A): Contains only dominant alleles. It cannot produce any gametes carrying the recessive alleles \(p\), \(q\), or \(r\).
- PPQqRr (Option B): This genotype lacks the recessive allele \(p\) entirely. It can only produce gametes containing the dominant allele \(P\).
- PpQqRr (Option C): This is a trihybrid heterozygous genotype. It contains at least one copy of all three recessive alleles (\(p\), \(q\), and \(r\)) and can successfully produce a gamete with the \(pqr\) genotype.
- PpQQRr (Option D): This genotype lacks the recessive allele \(q\) completely. It cannot produce gametes carrying the \(q\) allele.
Therefore, only the genotype \(PpQqRr\) satisfies the genetic requirements to be a parent of a \(ppqqrr\) offspring.
Step 3: Final Answer:
Thus, the genotype of either of the parents can be PpQqRr.