Question

Height in a certain plant species is controlled by two pairs of independently assorting alleles, with each participating allele A or B adding \(5 \mathrm{~cm}\) to a base height of \(5 \mathrm{~cm} .\) A cross is made between parents with genotype \(\mathrm{AABB}\) and aabb. Disregarding environmental influences, (a) What are the heights of each parent? (b) What is the expected height of the members of the \(\mathrm{F}_{1}\) generation? (c) What are the expected phenotypic ratios in the \(\mathrm{F}_{2}\) generation?

Short answer

The heights of the parents are 25 cm (AABB) and 5 cm (aabb). The expected height of the F1 generation is 15 cm. The expected phenotypic ratios in the F2 generation are 1 (25cm) : 2 (20cm) : 4 (15cm) : 2 (10cm) : 2 (5cm).

Step-by-step solution

Calculate the heights of each parent

For parent with genotype AABB (A homozygous dominant and B homozygous dominant), we can calculate the height as follows: - Base height: 5 cm - Two A alleles contribute: 2 * 5 cm = 10 cm - Two B alleles contribute: 2 * 5 cm = 10 cm Total height = 5 cm + 10 cm + 10 cm = 25 cm For parent with genotype aabb (A homozygous recessive and B homozygous recessive), there are no dominant alleles to contribute to height, so the plant will have the base height of 5 cm. Answer (a): Heights of each parent are 25 cm (AABB) and 5 cm (aabb).

Calculate the expected height of F1 generation

Since we are given that both pairs are assorting independently, the cross between the AABB and aabb genotypes would produce heterozygous offspring with genotype AaBb. The height for the AaBb offspring can be calculated as follows: - Base height: 5 cm - One A allele contributes: 1 * 5 cm = 5 cm - One B allele contributes: 1 * 5 cm = 5 cm Total height = 5 cm + 5 cm + 5 cm = 15 cm Answer (b): The expected height of the members of the F1 generation is 15 cm.

Calculate the expected phenotypic ratios in the F2 generation

To find the phenotypic ratios in the F2 generation, we can set up a dihybrid cross between two heterozygous plants (AaBb x AaBb). For simplicity, we will consider each pair separately and then combine the results. Punnett square for Aa x Aa, ignoring the B alleles: ``` A a A AA Aa a Aa aa ``` Therefore, the genotype ratios for A/a are: 1 AA: 2 Aa: 1 aa And, for Bb x Bb, ignoring the A alleles: ``` B b B BB Bb b Bb bb ``` The genotype ratios for B/b are: 1 BB: 2 Bb: 1 bb Now, we combine the ratios by multiplying the probabilities: 1 AABB (25cm): 2 AABb (20cm): 2 AaBB (20cm): 4 AaBb (15cm): 2 Aabb (10cm): 2 aaBB (10cm): 1 aaBb (5cm): 1 aabb (5cm) Phenotypic ratios (heights in cm): 1 (25cm) : 2 (20cm) : 4 (15cm) : 2 (10cm) : 2 (5cm) Answer (c): The expected phenotypic ratios in the F2 generation are 1 (25cm) : 2 (20cm) : 4 (15cm) : 2 (10cm) : 2 (5cm).

Key concepts

Dihybrid Cross

A dihybrid cross involves studying two different traits that are controlled by different pairs of alleles. In genetics, this is an important concept because it helps in understanding how traits are passed from parents to offspring. In our exercise, the traits are controlled by pairs of alleles for each characteristic, which participate in enhancing the height of the plants. When you perform a dihybrid cross, you are essentially looking at how these pairs of alleles segregate and combine during the formation of gametes and during fertilization.

For the plant height problem, the parents with genotypes \( AABB \) and \( aabb \) are crossed. This produces offspring in the \( F_1 \) generation with the genotype \( AaBb \). Each of these alleles contributes to the trait in a simple manner, adding a consistent value to the base trait, which in this case culminates in the height of the plant.

By setting up and analyzing a dihybrid cross (in this case from \( AaBb \) x \( AaBb \)), we can see the different possible combinations of alleles in the \( F_2 \) generation. This process involves creating a Punnett square, which helps to visualize and calculate the probabilities of obtaining each genotype and phenotype.

Phenotypic Ratio

The phenotypic ratio is a way of showcasing the different outcomes of traits you can expect among offspring, based on a genetic cross. In our case, the phenotypic ratio is concerned with the height of the plants in the \( F_2 \) generation resulting from the cross between \( AaBb \) individuals.

The phenotypic ratio describes the relative numbers of offspring with certain observable traits (phenotypes). From our exercise, we calculated the expected heights, which are evidence of phenotypic traits based on the distribution of alleles. The phenotypic ratio tells us about the frequency of each phenotype, making predictions about how common each form of the trait will be.

In the \( F_2 \) offspring, the phenotypic ratios are given as 1 (25cm): 2 (20cm): 4 (15cm): 2 (10cm): 2 (5cm). These numbers imply that out of the total offspring, a single part will be 25 cm tall, two parts will be 20 cm tall, and so on, providing a clear picture of what heights can be expected in the population.

Independently Assorting Alleles

Independently assorting alleles are a fundamental concept in genetics, first proposed by Gregor Mendel. This principle states that alleles for different traits are distributed to gametes independently. It means that the segregation of alleles for one gene does not affect the segregation of alleles for another gene.

In our plant height exercise, this concept applies to the alleles \( A/a \) and \( B/b \). When crossing two heterozygous plants \( (AaBb) \), the alleles \( A \) or \( a \) will sort independently of \( B \) or \( b \). This independent assortment during gamete formation results in the various combinations of genotypes as seen in our dihybrid cross.

This notion is crucial to grasp because it explains the observed phenotypic ratios and the diversity of the offspring in terms of genetic makeup. Here, each allele contributes to the final trait (height, in this case) adding to the variation seen in the F2 generation when recombined during fertilization.