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).

Key concepts

Incomplete Dominance

Understanding incomplete dominance is essential to grasping some unique genetic outcomes. Incomplete dominance occurs when neither allele in a gene pair completely dominates the other, resulting in a blending of traits. This happens notably in flower color, where a mix creates a new phenotype.
For example, if a plant with red flowers (\( R_1R_1 \)) is crossed with one that has white flowers (\( R_2R_2 \)), their offspring will be pink (\( R_1R_2 \)).
Here, pink is the intermediate trait because neither the red nor the white allele is completely dominant.

• Red Allele (\( R_1 \)): Produces red pigment.
• White Allele (\( R_2 \)): Results in no pigment.

This partial dominance becomes evident in the heterozygous condition (\( R_1R_2 \)), producing pink flowers. Such outcomes highlight how incomplete dominance allows us to see a spectrum of traits in offspring, rather than just the traits of the dominant allele.

Genotype and Phenotype

Genotype and phenotype are foundational concepts in genetics. A genotype is the actual genetic makeup of an organism, consisting of various alleles received from its parents. In this context, genotypes dictate the potential physical traits an organism can express.
Phenotypes, on the other hand, are the visible or expressible attributes that are manifested. For instance, the flower color genotype (\( R_1R_2 \)) results in the phenotype of pink flowers.
It's important to connect genotype with the way traits are expressed in an organism:

• Genotype Example: \( R_1R_2P_1P_2T_1T_2 \) indicates pink, personate, and tall traits.
• Phenotype Example: Pink flowers (result of \( R_1R_2 \)), personate shape (due to dominant \( P_1 \)), and tall height (from dominant \( T_1 \)).

Ultimately, understanding the distinction between genotype and phenotype is crucial in decoding the organism's physical expression and is a fundamental concept in predicting genetic cross outcomes.

Genetic Cross

Performing a genetic cross involves breeding individuals to study how traits pass from one generation to the next. For plants, a genetic cross helps understand inheritance patterns by combining characteristics from different genotypes.
Consider a genetic cross between a red, personate, tall plant (\( R_1R_1P_1P_1T_1T_1 \)) and a white, peloric, dwarf plant (\( R_2R_2P_2P_2T_2T_2 \)). Their \( F_1 \) offspring would inherit alleles for each trait, forming a new combination (\( R_1R_2P_1P_2T_1T_2 \)), expressed as pink, personate, and tall.
Studying such genetic crosses involves using:

• Punnett Squares: Visualize all possible allele combinations.
• Probability Calculations: Determine the likelihood of specific traits appearing in offspring.

By examining these crosses, we can discern not only the possible genotypes but also predict the appearance and behavior of future generations. Genetic crosses are vital for breeders and botanists to determine trait distribution and inheritance in hybrid populations.