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.'
We now have a dilemma. The data are consistent with two alternative mechanisms of inheritance. Propose an experiment that executes crosses involving the original parents that would distinguish between the two solutions proposed by the students. Explain how this experiment would resolve the dilemma.

Verified step by step guidance

1. Step 1: Analyze the F₁ generation data. The fact that all F₁ flowers are white suggests that white is dominant over both orange and brown. This indicates that the inheritance pattern involves dominance relationships.
2. Step 2: Examine the F₂ generation data. The phenotypic distribution is 48 white, 12 orange, and 4 brown. Convert these numbers into a ratio by dividing each count by the smallest number (4). This yields a ratio of 12:3:1, which suggests the involvement of two gene pairs.
3. Step 3: Determine the genotypes for each phenotype. Based on the ratio, propose that one gene controls the presence of color (dominant allele leads to white flowers), and the second gene modifies the color (orange or brown). For example, white flowers could be dominant (A_), orange could result from a specific combination (aaB_), and brown could result from another combination (aabb).
4. Step 4: Propose an experiment to distinguish between the two mechanisms of inheritance. Perform test crosses using the original parents (white and brown flowers). Specifically, cross F₁ individuals (white flowers) with the brown parent to observe the segregation of phenotypes in the offspring.
5. Step 5: Explain how the experiment resolves the dilemma. If the offspring phenotypes match the expected ratios for one proposed mechanism (e.g., 1:1:1:1 for a dihybrid test cross), it confirms that mechanism. If the ratios differ, it supports the alternative mechanism. This experiment clarifies the genetic basis of flower color inheritance.

Key Concepts

Mendelian Inheritance

Mendelian inheritance refers to the principles of heredity established by Gregor Mendel, which include the concepts of dominant and recessive traits. In this context, the inheritance of flower color can be explained through Mendel's laws, particularly the law of segregation, which states that alleles segregate during gamete formation. Understanding these principles is crucial for interpreting the F₂ ratios and determining the genotypes responsible for each phenotype.

Phenotypic Ratios

Phenotypic ratios are the relative frequencies of different phenotypes in the offspring resulting from a genetic cross. In the given problem, the F₂ generation produced a ratio of 48 white, 12 orange, and 4 brown flowers, which simplifies to a 12:3:1 ratio. This ratio can indicate the involvement of multiple alleles or gene interactions, and analyzing these ratios helps in understanding the genetic mechanisms behind the observed traits.

Experimental Design for Genetic Crosses

Experimental design in genetics involves planning crosses to test hypotheses about inheritance patterns. To distinguish between the two proposed mechanisms of inheritance, one could perform test crosses using the F₁ generation and the original parent plants. By analyzing the offspring ratios from these crosses, one can determine whether the inheritance follows a simple Mendelian pattern or involves more complex interactions, thus resolving the dilemma presented in the question.