Strains of petunias come in four pure-breeding colors: white, blue, red, and purple. White petunias are produced when plants synthesize no flower pigment. Blue petunias and red petunias are produced when plants synthesize blue or red pigment only. Purple petunias are produced in plants that synthesize both red and blue pigment (the mixture of red and blue makes purple). Flower-color pigments are synthesized by gene action in two separate pigment-producing biochemical pathways. Pathway I contains gene A that produces an enzyme to catalyze conversion of a colorless pigment designated to blue pigment. In Pathway II, the enzymatic product of gene B converts the colorless pigment designated to red pigment. The two genes assort independently.
True-breeding red petunias are crossed to pure-breeding blue petunias, and all the F₁ progeny have purple flowers. If the F₁ are allowed to self-fertilize and produce the F₂, what is the expected phenotypic distribution of the F₂ progeny? Show your work.

Verified step by step guidance

1. Step 1: Understand the genetic basis of the problem. Gene A is responsible for producing the enzyme that converts a colorless pigment to blue pigment (Pathway I), and Gene B is responsible for producing the enzyme that converts a colorless pigment to red pigment (Pathway II). Both genes assort independently, meaning they follow Mendel's law of independent assortment.
2. Step 2: Analyze the parental cross. True-breeding red petunias (genotype aaBB, where 'aa' means no blue pigment and 'BB' means red pigment is produced) are crossed with true-breeding blue petunias (genotype AAbb, where 'AA' means blue pigment is produced and 'bb' means no red pigment). The F₁ progeny will inherit one 'A' allele from the blue parent and one 'B' allele from the red parent, resulting in the genotype AaBb. Since both pathways are functional in the F₁ (AaBb), the flowers will be purple (a mixture of blue and red pigments).
3. Step 3: Determine the genotypes of the F₂ generation. When the F₁ plants (AaBb) self-fertilize, the offspring will follow a dihybrid cross pattern. Use a Punnett square to determine the genotypic combinations of the F₂ generation. The possible alleles for each gene are A or a (from Gene A) and B or b (from Gene B). The Punnett square will have 16 cells, representing all possible combinations of these alleles.
4. Step 4: Determine the phenotypes based on the genotypes. For each genotype, determine whether the plant produces blue pigment (requires at least one 'A' allele) and/or red pigment (requires at least one 'B' allele): - Purple flowers: At least one 'A' and one 'B' allele (e.g., AaBb, AABb, AaBB, AABB). - Blue flowers: At least one 'A' allele but no 'B' allele (e.g., Aabb, AAbb). - Red flowers: At least one 'B' allele but no 'A' allele (e.g., aaBb, aaBB). - White flowers: No 'A' or 'B' alleles (e.g., aabb).
5. Step 5: Calculate the phenotypic ratios. Count the number of genotypes corresponding to each phenotype from the Punnett square. Since this is a dihybrid cross, the expected phenotypic ratio for the F₂ generation is typically 9:3:3:1 (9 purple: 3 blue: 3 red: 1 white), assuming no epistasis or other genetic interactions. Verify this ratio by summing the genotypes for each phenotype.

Key Concepts

Mendelian Genetics

Mendelian genetics is the study of how traits are inherited through generations based on the principles established by Gregor Mendel. It includes concepts such as dominant and recessive alleles, segregation, and independent assortment. In this scenario, the inheritance of flower color in petunias follows Mendelian principles, where the alleles for blue and red pigments interact to produce the purple phenotype in the F₁ generation.

Phenotypic Ratios

Phenotypic ratios describe the relative frequencies of different phenotypes in the offspring of a genetic cross. In this case, the F₂ generation's phenotypic distribution can be predicted using a Punnett square, which illustrates the combinations of alleles from the parental generation. The expected ratio of flower colors in the F₂ generation will reflect the interactions of the alleles from the F₁ generation, typically resulting in a 9:3:3:1 ratio for a dihybrid cross.

Independent Assortment

Independent assortment is a principle stating that alleles for different traits segregate independently during gamete formation. In the context of the petunia flower color, genes A and B assort independently, meaning the inheritance of one color trait does not affect the inheritance of the other. This concept is crucial for predicting the phenotypic ratios in the F₂ generation, as it allows for the combination of different alleles from both pathways.