The synthesis of flower pigments is known to be dependent on enzymatically controlled biosynthetic pathways. For the crosses shown here, postulate the role of mutant genes and their products in producing the observed phenotypes:
P₁: white × pink
F₁: all purple
F₂: 9/16 purple: 3/16 pink: 4/16 white

Verified step by step guidance

1. Step 1: Recognize that the problem involves a dihybrid cross, as evidenced by the phenotypic ratio in the F₂ generation (9:3:4). This ratio suggests epistasis, where one gene's expression affects or masks the expression of another gene.
2. Step 2: Define the roles of the genes involved. Assume two genes (let's call them Gene A and Gene B) are responsible for pigment synthesis. Gene A might produce an enzyme that synthesizes a precursor pigment, while Gene B might convert the precursor into the final pigment. Mutations in either gene could disrupt pigment production.
3. Step 3: Analyze the parental generation (P₁). The cross between white and pink flowers suggests that the white phenotype lacks functional enzymes from both genes, while the pink phenotype has partial functionality (e.g., one functional gene but not the other). This sets the stage for complementation in the F₁ generation.
4. Step 4: Examine the F₁ generation. All flowers are purple, indicating that the offspring inherit functional alleles for both genes (heterozygous for Gene A and Gene B), allowing full pigment synthesis.
5. Step 5: Interpret the F₂ generation phenotypic ratio. The 9:3:4 ratio suggests that: (a) 9/16 have functional alleles for both genes (purple), (b) 3/16 have one functional gene (pink), and (c) 4/16 lack functional alleles for one or both genes (white). Use a Punnett square to confirm this distribution based on the genotypes of the F₁ generation.

Key Concepts

Biosynthetic Pathways

Biosynthetic pathways are series of enzymatic reactions that lead to the production of complex molecules from simpler ones. In the context of flower pigments, these pathways involve specific enzymes that catalyze the conversion of precursor compounds into pigments, influencing the color of the flowers. Understanding these pathways is crucial for analyzing how mutations in genes can affect pigment production and, consequently, flower color.

Genetic Inheritance Patterns

Genetic inheritance patterns describe how traits are passed from parents to offspring, often illustrated through Mendelian ratios. In this case, the observed phenotypic ratios in the F₂ generation (9:3:4) suggest a dihybrid cross involving two genes, where one gene may exhibit incomplete dominance or epistasis. Recognizing these patterns helps in predicting the outcomes of genetic crosses and understanding the role of mutant genes.

Mutant Genes and Phenotypes

Mutant genes are altered versions of normal genes that can lead to changes in phenotype, the observable characteristics of an organism. In the context of the flower color experiment, mutations in specific genes involved in pigment biosynthesis can result in the production of different pigment types, leading to the observed white, pink, and purple flowers. Analyzing how these mutations affect enzymatic activity is key to understanding the resulting phenotypic ratios.