Question

A strain of plants has a mean height of \(24 \mathrm{cm} .\) A second strain of the same species from a different geographical region also has a mean height of \(24 \mathrm{cm}\). When plants from the two strains are crossed together, the \(F_{1}\) plants are the same height as the parent plants. However, the \(\mathrm{F}_{2}\) generation shows a wide range of heights; the majority are like the \(P_{1}\) and \(F_{1}\) plants, but approximately 4 of 1000 are only $12 \mathrm{cm}\( high, and about 4 of 1000 are \)36 \mathrm{cm}$ high. (a) What mode of inheritance is occurring here? (b) How many gene pairs are involved? (c) How much does each gene contribute to plant height? (d) Indicate one possible set of genotypes for the original \(\mathrm{P}_{1}\) parents and the \(\mathrm{F}_{1}\) plants that could account for these results. (e) Indicate three possible genotypes that could account for \(\mathrm{F}_{2}\) plants that are \(18 \mathrm{cm}\) high and three that account for \(\mathrm{F}_{2}\) plants that are \(33 \mathrm{cm}\) high.

Short answer

Answer: The mode of inheritance is quantitative or polygenic inheritance, with three gene pairs (A, B, and C) involved. Each gene pair contributes 8 cm to the plant height. Possible genotypes for P1 parents and F1 plants include AABBCC (24 cm) x aabbcc (24 cm) and F1: AaBbCc (24 cm). Possible genotypes for F2 plants with height 18 cm are AABbcc, AaBBCc, and aaBbCC, and for F2 plants with height 33 cm are AabBCC, aaBBCC, and AABBCc.

Step-by-step solution

Determine the mode of inheritance

Based on the fact that F1 plants are the same height as the parent plants and F2 generation shows a wide range of heights, we can conclude that the mode of inheritance is quantitative, or polygenic inheritance.

Identify the number of gene pairs involved

Considering the range of heights found in the F2 generation, and the fact that approximately 4 of 1000 plants are either 12 cm or 36 cm tall, we can infer that there are three gene pairs (A, B, and C) that are likely involved, giving rise to multiple gene combinations that affect height.

Calculate the contribution of each gene to plant height

If we consider that the heights range from 12 cm to 36 cm (extremes) in the F2 generation, and that three genes pairs (A, B, and C) are involved, we can assume that each gene pair contributes equally to the plant height. Therefore, each gene pair contributes (36 - 12)/3 = 8 cm to the plant height.

List possible genotypes for P1 parents and F1 plants

One possible set of genotypes for the original P1 parents and the F1 plants accounting for these results could be as follows: P1 parents: AABBCC (24 cm) x aabbcc (24 cm) F1: AaBbCc (24 cm)

List possible genotypes for F2 plants with height 18 cm and 33 cm

Three possible genotypes that could account for F2 plants that are 18 cm high: 1. AABbcc (18 cm) 2. AaBBCc (18 cm) 3. aaBbCC (18 cm) Three possible genotypes that could account for F2 plants that are 33 cm high: 1. AabBCC (33 cm) 2. aaBBCC (33 cm) 3. AABBCc (33 cm)