A cross between a spicy variety of Capsicum annum pepper and a sweet (nonspicy) variety produces F₁ progeny plants that all have spicy peppers. The F₁ are crossed, and among the F₂ plants are 56 that produce spicy peppers and 20 that produce sweet peppers. Dr. Ara B. Dopsis, an expert on pepper plants, discovers a gene he designates Pun1 that he believes is responsible for spicy versus sweet flavor of peppers. Dr. Dopsis proposes that a dominant allele P produces spicy peppers and that a recessive mutant allele p results in sweet peppers.
Assuming the proposal is correct, what proportion of the spicy F₂ pepper plants do you expect will be pure-breeding? Explain your answer.

Verified step by step guidance

1. Start by identifying the genetic basis of the problem. The spicy flavor is controlled by a dominant allele (P), while the sweet flavor is controlled by a recessive allele (p). This means that plants with genotypes PP or Pp will produce spicy peppers, and plants with genotype pp will produce sweet peppers.
2. Determine the expected genotypic ratio in the F₂ generation. Since the F₁ generation is heterozygous (Pp) for all plants, a cross between two heterozygous plants (Pp × Pp) will produce offspring in the ratio 1:2:1 (PP:Pp:pp).
3. Calculate the phenotypic ratio in the F₂ generation. Based on the genotypic ratio, the phenotypes will be 3 spicy (PP and Pp) to 1 sweet (pp). This matches the observed data of 56 spicy and 20 sweet plants, as the ratio 56:20 simplifies approximately to 3:1.
4. Focus on the spicy plants (PP and Pp) and determine the proportion that are pure-breeding. Pure-breeding spicy plants have the genotype PP. From the genotypic ratio (1:2:1), the proportion of PP among the spicy plants (PP and Pp) is 1/(1+2) = 1/3.
5. Conclude that 1/3 of the spicy F₂ pepper plants are expected to be pure-breeding (PP). This is because the genotypic ratio of PP:Pp among spicy plants is 1:2, and only the PP plants are pure-breeding.

Key Concepts

Dominant and Recessive Alleles

In genetics, alleles are different forms of a gene that can exist at a specific locus on a chromosome. A dominant allele, represented by a capital letter (e.g., P), masks the effect of a recessive allele (e.g., p) when both are present in a heterozygous individual. This means that if at least one dominant allele is present, the dominant trait will be expressed in the phenotype, while the recessive trait will only be expressed if two recessive alleles are present.

Punnett Square

A Punnett square is a diagram used to predict the genotypes of offspring from a genetic cross. It allows for the visualization of how alleles from each parent combine to form the possible genotypes of the progeny. By filling in the squares based on the alleles contributed by each parent, one can determine the expected ratios of dominant and recessive traits in the offspring, which is crucial for understanding inheritance patterns.

Pure-Breeding

Pure-breeding refers to organisms that consistently produce offspring with the same phenotype when crossed with each other. In the context of the pepper plants, a pure-breeding spicy pepper plant would have the genotype PP, while a pure-breeding sweet pepper plant would have the genotype pp. Understanding the concept of pure-breeding is essential for predicting the proportion of offspring that will exhibit a specific trait, especially when considering the F2 generation resulting from a cross between heterozygous parents.