Understanding Flower Color Inheritance

This problem involves basic Mendelian genetics, specifically focusing on incomplete dominance.

Defining Alleles and Parental Cross

Let the allele for red flowers be represented by $R$ and the allele for white flowers by $W$. Since the plants are pure-bred, their genotypes are:

• Pure-bred red plant: $RR$
• Pure-bred white plant: $WW$

The initial cross is between these two pure-bred plants:

$ RR \textit{ (Red)} \times WW \textit{ (White)} $

F1 Generation Analysis

All offspring in the F1 generation inherit one allele from each parent. Therefore, the genotype of all F1 plants is $RW$.

Due to incomplete dominance, the heterozygous genotype $RW$ results in a blended phenotype, which is pink flowers.

F1 Genotype: $RW$ (all plants)

F1 Phenotype: Pink Flowers

F2 Generation from Selfing F1

The F1 plants ( $RW$ ) are selfed, meaning they are crossed with themselves:

$ RW \textit{ (Pink)} \times RW \textit{ (Pink)} $

The possible genotypes in the F2 generation can be determined using a Punnett square:

• $RR$: Inheriting $R$ from both parents.
• $RW$: Inheriting $R$ from one parent and $W$ from the other.
• $WW$: Inheriting $W$ from both parents.

The resulting genotypic ratio is:

$ 1 RR : 2 RW : 1 WW $

F2 Phenotypic Ratio Calculation

Based on incomplete dominance:

• $RR$ genotype results in Red flowers.
• $RW$ genotype results in Pink flowers.
• $WW$ genotype results in White flowers.

Therefore, the phenotypic ratio in the F2 generation is:

$ 1 \textit{ Red} : 2 \textit{ Pink} : 1 \textit{ White} $

Final Proportion Calculation

The question asks for the proportion of white : pink : red flowers.

Based on the F2 phenotypic ratio, the proportion is:

$ 1 \textit{ (White)} : 2 \textit{ (Pink)} : 1 \textit{ (Red)} $

This corresponds to the ratio 1:2:1.