Question

In the common garden pea, Pisum sativuum, the alleles for tall plants, yellow seeds and round seeds \(-\mathrm{D}, \mathrm{G}\), and \(\mathrm{W}\). respectively-are all dominant over the alleles for dwarf plants, green seeds, and wrinkled seeds \(-d, g\), and \(\mathrm{w}\). (a) A homozygous tall, yellow round plant and a dwarf. green, wrinkled plant are mated. Show all possible gametes from each parent and the \(\mathrm{F}_{1}\) generation. (b) Using the forked line method, show a cross between two \(\mathrm{F}_{1}\) plants (c) Show the results of a cross between an \(\mathrm{F}_{1}\) plant and a dwarf, green, wrinkled parent by using the forked line method again. Give results for the phenotypes, the genotypes, the genotypic frequency, and the phenotypic ratio.

Short answer

(a) The gametes of the parents are \(\mathrm{DWG}\) and \(\mathrm{dwg}\), and the F1 generation will have the genotype \(\mathrm{DdWwGg}\). (b) Crossing two F1 plants results in the following phenotypic ratios: Tall, Yellow, Round (9/64), Tall, Yellow, Wrinkled (3/64), Tall, Green, Round (3/64), Tall, Green, Wrinkled (1/64), Dwarf, Yellow, Round (3/64), Dwarf, Yellow, Wrinkled (1/64), Dwarf, Green, Round (1/64), and Dwarf, Green, Wrinkled (1/64). (c) Crossing an F1 plant with a dwarf, green, wrinkled parent results in a phenotypic ratio of 1:1:1:1:1:1:1:1 and a genotypic frequency of 1/8 for each offspring genotype.

Step-by-step solution

Identify the genotypes of the parents

In the given exercise, we have a homozygous tall, yellow, and round plant (which means it has dominant alleles for all three traits) and a dwarf, green, and wrinkled plant (having recessive alleles for all three traits). The genotypes are as follows: Tall plant: \(\mathrm{DDWWGG}\) and Dwarf plant: \(\mathrm{ddwwgg}\).

Find the gametes for each parent

As both the parents have homozygous genotypes for all traits, their gametes will contain only one type of allele for each trait. So, the Tall plant will produce a gamete with \(\mathrm{DWG}\) and the Dwarf plant will produce a gamete with \(\mathrm{dwg}\).

Determine the F1 generation

Cross the gametes from Step 2: Tall plant's gamete (\(\mathrm{DWG}\)) and Dwarf plant's gamete (\(\mathrm{dwg}\)) to form an offspring with the genotype \(\mathrm{DdWwGg}\). All plants in the F1 generation will be heterozygous for all traits and exhibit the dominant phenotype (tall, yellow, and round). (a) The gametes of the parents are \(\mathrm{DWG}\) and \(\mathrm{dwg}\), and the F1 generation will have the genotype \(\mathrm{DdWwGg}\).

Perform the cross between two F1 plants using the forked line method

(b) To find the possible offspring of a cross between two F1 plants, we need to use the forked line method. First, we identify all possible gametes produced by the F1 genotype: 1. \(\mathrm{DWG}\) 2. \(\mathrm{DwG}\) 3. \(\mathrm{DwG}\) 4. \(\mathrm{DWg}\) 5. \(\mathrm{Dwg}\) 6. \(\mathrm{dwG}\) 7. \(\mathrm{dwg}\) 8. \(\mathrm{DWg}\) Now, cross these gametes to find the offspring's genotypes and phenotypes: 1. \(\mathrm{DdWwGg}\) - Tall, Yellow, Round (9/64) 2. \(\mathrm{DdWwgG}\) - Tall, Yellow, Wrinkled (3/64) 3. \(\mathrm{DdwwGg}\) - Tall, Green, Round (3/64) 4. \(\mathrm{Ddwwgg}\) - Tall, Green, Wrinkled (1/64) 5. \(\mathrm{ddWwGg}\) - Dwarf, Yellow, Round (3/64) 6. \(\mathrm{ddWwgG}\) - Dwarf, Yellow, Wrinkled (1/64) 7. \(\mathrm{ddwwGg}\) - Dwarf, Green, Round (1/64) 8. \(\mathrm{ddwwgg}\) - Dwarf, Green, Wrinkled (1/64)

Cross between an F1 plant and a dwarf, green, wrinkled parent using the forked line method

(c) For the cross between the F1 plant (\(\mathrm{DdWwGg}\)) and the recessive parent (\(\mathrm{ddwwgg}\)), we use the same forked line method as in Step 4. The possible gametes are the same as before for the F1 plant, but the recessive parent can only provide \(\mathrm{dwg}\). Therefore, we have the possible offspring genotypes: 1. \(\mathrm{DdWwGg}\) - Tall, Yellow, Round (1/8) 2. \(\mathrm{DdWwgG}\) - Tall, Yellow, Wrinkled (1/8) 3. \(\mathrm{DdwwGg}\) - Tall, Green, Round (1/8) 4. \(\mathrm{Ddwwgg}\) - Tall, Green, Wrinkled (1/8) 5. \(\mathrm{ddWwGg}\) - Dwarf, Yellow, Round (1/8) 6. \(\mathrm{ddWwgG}\) - Dwarf, Yellow, Wrinkled (1/8) 7. \(\mathrm{ddwwGg}\) - Dwarf, Green, Round (1/8) 8. \(\mathrm{ddwwgg}\) - Dwarf, Green, Wrinkled (1/8) This results in a phenotypic ratio of 1:1:1:1:1:1:1:1 and a genotypic frequency of 1/8 for each offspring genotype.

Key concepts

Mendelian inheritance

Mendelian inheritance forms the foundation of classic genetics, as proposed by Gregor Mendel. It explains how traits are passed from parents to offspring through distinct units called genes. Mendel's principles were developed based on his experiments with garden peas, demonstrating predictable ratios in trait inheritance.
A crucial aspect of Mendelian inheritance is the distinction between dominant and recessive alleles. Dominant alleles mask the presence of recessive ones in heterozygotes, leading to the dominant trait being expressed in the organism's phenotype.
Understanding these fundamental ideas helps in predicting the probabilities of certain traits appearing in successive generations, as seen in the exercise involving tall, yellow, and round dominant traits in peas.

Forked line method

The forked line method, also known as the branch diagram, is a visual tool for predicting genetic outcomes from a cross. It breaks down complex problems into manageable sections, allowing the determination of possible genotypes and phenotypes.
Let's say you are crossing two heterozygous pea plants (\(DdWwGg\)). Using the forked line method, each gene is considered separately, ensuring that all combinations are accounted for.

• First, list the possible alleles for the first trait.
• From each of these, draw branches for possible alleles of the second trait.
• Continue branching for additional traits.

This method is particularly useful for multigenic crosses, where tracking every possible combination manually might become overwhelming.

Phenotypic ratio

The phenotypic ratio refers to the proportional occurrence of different physical traits in the offspring. It is an expression of how often a particular trait appears, based on the combinations of inherited alleles.
In the pea plant example, when two heterozygous \(F_1\) plants are crossed, various phenotypic outcomes such as tall or dwarf, yellow or green, and round or wrinkled emerge. Using the forked line method, these traits are quantified, such as 9/64 being tall, yellow, and round.
Phenotypic ratios are crucial for forecasting and understanding expected outcomes in genetic crosses, helping scientists and students grasp how genetic variation manifests in physical traits.

Genotypic frequency

Genotypic frequency measures the proportion of different genotypes within a given population or offspring group. It's a crucial concept for understanding the genetic composition and diversity in populations.
For instance, in the pea plant exercise, crossing an \(F_1\) plant with a fully recessive plant results in eight distinct genotypic outcomes, each with a frequency of 1/8. This frequency indicates how equally these outcomes occur, assuming each allele combination is equally likely.
Calculating genotypic frequencies allows geneticists to predict population genetics dynamics over generations, offering insights into how different traits might spread or diminish in occurrence over time. This helps in breeding experiments and understanding evolutionary processes.