Question

Three gene pairs located on separate autosomes determine flower color and shape as well as plant height. The first pair exhibits incomplete dominance, where color can be red, pink (the heterozygote), or white, The second pair leads to the dominant personate or recessive peloric flower shape, while the third gene pair produces either the dominant tall trait or the recessive dwarf trait. Homozygous plants that are red, personate, and tall are crossed with those that are white, peloric, and dwarf. Determine the \(P_{1}\) genotype(s) and phenotype(s). If the \(F_{1}\) plants are interbred, what proportion of the offspring will exhibit the same phenotype as the \(F_{1}\) plants?

Short answer

Answer: 9/32

Step-by-step solution

Define genotype and phenotype symbols

Let's assign symbols to each gene and phenotype: Flower color: Incomplete dominance - Red (R₁R₁) - Pink (R₁R₂) - White (R₂R₂) Flower shape: Dominant personate and recessive peloric - Personate (P₁) - Peloric (P₂) Plant height: Dominant tall and recessive dwarf - Tall (T₁) - Dwarf (T₂)

Identify the P₁ genotypes and phenotypes

The problem states that the two parent plants have the following phenotypes: - Red, personate, and tall - White, peloric, and dwarf Using the symbols we defined earlier for genotypes and phenotypes, the \(P_{1}\) genotypes and phenotypes will be: Red, personate, and tall plant: R₁R₁P₁P₁T₁T₁ White, peloric, and dwarf plant: R₂R₂P₂P₂T₂T₂

Find F₁ genotypes after the cross

To find the genotypes of the \(F_{1}\) generation after the cross, we will perform a cross-pollination between the two \(P_{1}\) plants: R₁R₁P₁P₁T₁T₁ x R₂R₂P₂P₂T₂T₂ For each gene pair, the \(F_{1}\) offspring will inherit one allele from each parent, so the \(F_{1}\) genotype will be: Flower color: R₁R₂ (Pink) Flower shape: P₁P₂ (Personate) Plant height: T₁T₂ (Tall) The \(F_{1}\) genotype is: R₁R₂P₁P₂T₁T₂ The \(F_{1}\) phenotype is: Pink, personate, and tall

Interbreed F₁ plants and find proportions

When we interbreed the \(F_{1}\) plants, we will be performing the following genetic cross: R₁R₂P₁P₂T₁T₂ x R₁R₂P₁P₂T₁T₂ To find the proportion of offspring that have the same phenotype as the \(F_{1}\) plants (Pink, personate, and tall), we need to consider each gene pair separately: - Flower color: R₁R₂ x R₁R₂ Proportion of offspring with pink flowers: 2/4 (Only heterozygotes will be pink) - Flower shape: P₁P₂ x P₁P₂ Proportion of offspring with personate shape: 3/4 (Personate is the dominant trait) - Plant height: T₁T₂ x T₁T₂ Proportion of offspring with tall height: 3/4 (Tall is the dominant trait)

Determine the overall proportion

Now, we need to find the proportion of offspring that have all three required traits: pink flower color, personate flower shape, and tall height. We can find this by multiplying the proportions for each trait together: \(Proportion = \frac{2}{4} \times \frac{3}{4} \times \frac{3}{4} = \frac{9}{32}\) Thus, \(9/32\) of the offspring of the \(F_{1}\) plants will exhibit the same phenotypes as the \(F_{1}\) plants (Pink, personate, and tall).