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 strain A × white strain B
F₁: all purple
F₂: 9/16purple: 7/16 white

Verified step by step guidance

1. Step 1: Recognize that the problem involves a dihybrid cross with a 9:7 phenotypic ratio in the F₂ generation. This ratio suggests complementary gene action, where two genes interact to produce the phenotype. Both genes must have at least one dominant allele to produce the purple pigment.
2. Step 2: Define the genes involved. Let Gene A and Gene B represent the two genes controlling pigment synthesis. The dominant alleles (A and B) are required for purple pigment production, while the recessive alleles (a and b) result in a lack of pigment (white phenotype).
3. Step 3: Analyze the P₁ generation. Both strains (A and B) are white, indicating they are homozygous recessive for one of the genes (e.g., strain A is aaBB and strain B is AAbb). When crossed, the F₁ generation inherits one dominant allele from each parent, resulting in all purple offspring (AaBb).
4. Step 4: Examine the F₂ generation. The F₁ individuals (AaBb) are self-crossed, producing offspring with a 9:7 phenotypic ratio. Use a Punnett square to determine the genotypes of the F₂ generation. Only individuals with at least one dominant allele for both genes (A_B_) will be purple, while all other combinations (aaB_, A_bb, aabb) will be white.
5. Step 5: Conclude that the observed phenotypes are due to complementary gene action. The mutant genes in the parental strains disrupt different steps in the biosynthetic pathway, and both dominant alleles are required to restore the pathway and produce the purple pigment.

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, such as anthocyanins, which give flowers their color. Understanding these pathways is crucial for analyzing how mutations in genes can affect pigment production and, consequently, flower color.

Genetic Mutations

Genetic mutations are changes in the DNA sequence of a gene that can alter the function of the gene's product, typically a protein. In this scenario, mutant genes may lead to the loss or gain of function in enzymes involved in pigment synthesis, resulting in the observed phenotypes. Identifying whether these mutations are dominant or recessive is essential for predicting the inheritance patterns seen in the F1 and F2 generations.

Phenotypic Ratios

Phenotypic ratios describe the relative frequencies of different observable traits in the offspring of a genetic cross. In this case, the F2 generation shows a 9:7 ratio of purple to white flowers, suggesting a complex inheritance pattern, possibly involving epistasis, where one gene's expression is affected by another. Analyzing these ratios helps in understanding the genetic interactions and the roles of the mutant genes in determining flower color.