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.'
A number of students failed to reduce the ratio for two gene pairs as described above and solved the problem using three gene pairs. When examined carefully, their solution was deemed a valid response by the instructor. Solve the problem using three gene pairs

Verified step by step guidance

1. Step 1: Begin by analyzing the F₂ data provided: 48 white, 12 orange, and 4 brown flowers. Calculate the total number of flowers by summing these values: 48 + 12 + 4 = 64. This total will help you determine the proportions of each phenotype.
2. Step 2: Convert the observed numbers into a ratio by dividing each phenotype count by the greatest common divisor (GCD) of the counts. For example, divide 48, 12, and 4 by their GCD to simplify the ratio.
3. Step 3: Interpret the simplified ratio in terms of inheritance patterns. Since the problem specifies solving with three gene pairs, consider how combinations of dominant and recessive alleles across three loci could produce the observed phenotypes. For example, white flowers might result from dominant alleles at all loci, orange flowers from a mix of dominant and recessive alleles, and brown flowers from recessive alleles at all loci.
4. Step 4: Assign genotypes to each phenotype based on the three-gene model. For instance, white flowers could correspond to genotypes like AABBCC, orange flowers to genotypes like AaBbCc, and brown flowers to genotypes like aabbcc. Ensure the genotypes align with the observed phenotypic ratios.
5. Step 5: Verify the inheritance pattern by considering Mendelian ratios for three gene pairs. For example, calculate the expected phenotypic ratios for a cross involving three heterozygous gene pairs (AaBbCc x AaBbCc) and compare them to the observed data. This will confirm whether the three-gene model fits the inheritance pattern.

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 discrete units called genes. In this context, the inheritance of flower color in plants can be analyzed using Mendel's laws, particularly the law of segregation and the law of independent assortment, which help predict the ratios of different phenotypes in offspring.

Phenotypic Ratios

Phenotypic ratios represent the relative frequencies of different observable traits (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, which helps in understanding the underlying genetic mechanisms and the number of gene pairs involved in determining the flower color.

Gene Interaction

Gene interaction occurs when two or more genes influence a single trait, leading to a more complex inheritance pattern than simple Mendelian ratios. In this case, the students' consideration of three gene pairs suggests that multiple genes may contribute to flower color, resulting in a phenotypic ratio that reflects the combined effects of these genes, rather than a straightforward dominant-recessive relationship.