Students taking a genetics exam were expected to answer the following question by converting data to a 'meaningful ratio' and then solving the problem. The instructor assumed that the final ratio would reflect two gene pairs, and most correct answers did. Here is the exam question:
'Flowers may be white, orange, or brown. When plants with white flowers are crossed with plants with brown flowers, all the F₁ flowers are white. For F₂ flowers, the following data were obtained:
48 white
12 orange
4 brown
Convert the F₂ data to a meaningful ratio that allows you to explain the inheritance of color. Determine the number of genes involved and the genotypes that yield each phenotype.'
Solve the problem for two gene pairs. What is the final F₂ ratio?

Verified step by step guidance

1. Step 1: Begin by analyzing the F₁ generation. The fact that all F₁ flowers are white suggests that white is the dominant phenotype. This indicates that the parental genotypes for white and brown flowers likely involve dominant and recessive alleles, respectively.
2. Step 2: Examine the F₂ generation data: 48 white, 12 orange, and 4 brown flowers. Calculate the total number of flowers in the F₂ generation by summing these values: 48 + 12 + 4 = 64. This will help determine the proportions of each phenotype.
3. Step 3: Convert the F₂ data into a ratio. Divide each phenotype count by the greatest common divisor to simplify the numbers. For example, divide 48, 12, and 4 by their GCD to find the simplest ratio.
4. Step 4: Interpret the simplified ratio in terms of genetic inheritance. Since the instructor assumed two gene pairs, consider how combinations of dominant and recessive alleles across two loci could produce the observed phenotypes. For example, white flowers might result from dominant alleles at both loci, orange flowers from one dominant and one recessive allele, and brown flowers from recessive alleles at both loci.
5. Step 5: Assign genotypes to each phenotype based on the two-gene model. For instance, white flowers could correspond to genotypes such as A_B_, orange flowers to A_bb or aaB_, and brown flowers to aabb. Verify that the ratio aligns with Mendelian inheritance patterns for two gene pairs.

Key Concepts

Mendelian Inheritance

Mendelian inheritance refers to the principles of heredity established by Gregor Mendel, which describe how traits are passed from parents to offspring through dominant and recessive alleles. In this context, the inheritance of flower color can be explained by Mendel's laws, particularly the law of segregation and the law of independent assortment, which govern how alleles segregate during gamete formation and combine in offspring.

Phenotypic Ratios

Phenotypic ratios represent the relative frequencies of different phenotypes in the offspring resulting from a genetic cross. In the given problem, the F₂ generation's flower color data (48 white, 12 orange, 4 brown) can be converted into a ratio that reflects the underlying genetic mechanisms. Understanding how to derive these ratios is crucial for interpreting the inheritance patterns of the traits involved.

Dihybrid Cross

A dihybrid cross involves examining the inheritance of two different traits, each controlled by two gene pairs. In this scenario, the flower color is influenced by two genes, which can exhibit various combinations of dominant and recessive alleles. The expected phenotypic ratio for a dihybrid cross, when both traits assort independently, is typically 9:3:3:1, which helps in determining the genotypes responsible for each phenotype observed in the F₂ generation.