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 \(\mathrm{F}_{1}\) flow ers are white. For \(\mathrm{F}_{2}\) flowers, the following data were obtained: 48 white 12 orange 4 brown Convert the \(\mathrm{F}_{2}\) 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) Solve the problem for two gene pairs. What is the final \(\mathrm{F}_{2}\) ratio? (b) 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.

Step by step solution

01

Convert the F2 data to a meaningful ratio

The F2 data obtained are 48 white, 12 orange, and 4 brown flowers. We can simplify this data to a ratio by dividing each number by the lowest value, which is 4: $$ \frac{48}{4}:\frac{12}{4}:\frac{4}{4}=12:3:1 $$

02

Determine the number of genes involved

When analyzing the problem for two gene pairs, the ratio 12:3:1 suggests that there are two gene pairs involved in determining flower color.

03

Find the genotypes that yield each phenotype

For two gene pairs, we can use the ratio to find the genotypes that yield each phenotype. The dominant alleles are represented by A and B, and the recessive alleles are represented by a and b. 1. White flowers (12): AAB_, A_B_, or AABB 2. Orange flowers (3): Aabb 3. Brown flowers (1): aabb From the given data, the final F2 ratio for two gene pairs is 12:3:1. This implies that the inheritance of the color in the flowers is based on two gene pairs, with a dominance interaction between the genes. #b. Three Gene Pairs#

04

Consider a valid response with three gene pairs

If the problem were to be solved using three gene pairs instead of two, the students may have interpreted the data and found a different ratio that would also be considered valid. In this scenario, we will see if there is an F2 ratio that works with three gene pairs.

05

Find a ratio for three gene pairs

There are several possible ratios that could be derived from the data for three gene pairs. One such possibility is that the data doesn't simplify to a basic ratio like in the two gene pair case, we can leave the initial data as it is: 48:12:4.

06

Determine the genotypes for three gene pairs

For three gene pairs, we can represent the dominant alleles with A, B, and C, and the recessive alleles with a, b, and c. 1. White flowers (48): AABBCc, AAbbCC, or AABBcc 2. Orange flowers (12): AabbC_ 3. Brown flowers (4): aabbc_ For this scenario, we would have a ratio of 48:12:4 for the F2 generation. While the dominant and recessive genes interact differently compared to the two gene pairs scenario, this is still a valid solution to the problem using three gene pairs. In conclusion, the most correct answer is to consider two gene pairs involved in the determination of the flower color, with a final F2 ratio of 12:3:1. However, considering three gene pairs and finding a valid response is also possible, with a ratio of 48:12:4.

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