Question

Mendel crossed peas having round seeds and yellow cotyledons with peas having wrinkled seeds and green cotyledons. All the \(\mathrm{F}_{1}\) plants had round seeds with yellow cotyledons. Diagram this cross through the \(\mathrm{F}_{2}\) generation, using both the Punnett square and forked-line methods.

Short answer

Answer: The phenotypic ratio in the F2 generation is 9 round & yellow : 3 round & green : 3 wrinkled & yellow : 1 wrinkled and green.

Step-by-step solution

Determine the Parental Genotypes

We begin by determining the genotypes of the parent plants. The first parent has round seeds and yellow cotyledons, so its genotype must be RRYY. The second parent has wrinkled seeds and green cotyledons, so its genotype must be rryy.

Determine the F1 Generation Genotype

Next, we look at the F1 generation. Since all the F1 plants have round seeds and yellow cotyledons, their genotype must be RrYy.

Create a Punnett Square for the F2 Generation

In order to determine the F2 generation genotypes, we must first create a Punnett square. To do this, we will first find the possible gametes that can be formed from the F1 generation: Gametes from parent 1 (RrYy): RY, Ry, rY, ry Gametes from parent 2 (RrYy): RY, Ry, rY, ry Now, we use these gametes to construct a 4x4 Punnett square table.

Fill in the Punnett Square

Now we fill in the Punnett square table with the corresponding genotypes: \begin{tabular}{c|c|c|c|c} & RY & Ry & rY & ry \\ \hline RY & RRYY & RRYy & RrYY & RrYy \\ Ry & RRYy & RRyy & RrYy & Rryy \\ rY & RrYY & RrYy & rrYY & rrYy \\ ry & RrYy & Rryy & rrYy & rryy \end{tabular}

Determine the F2 Generation Phenotypes

Now we need to determine the phenotypes in the F2 generation based on the genotypes: 1. RRYY, RRYy, RrYY, and RrYy all result in round seeds and yellow cotyledons. 2. RRyy and Rryy result in round seeds and green cotyledons. 3. rrYY and rrYy result in wrinkled seeds and yellow cotyledons. 4. rryy results in wrinkled seeds and green cotyledons. Thus, we have a phenotypic ratio of 9 round & yellow : 3 round & green : 3 wrinkled & yellow : 1 wrinkled and green in the F2 generation.

Forked-Line Method

Now, let's use the forked-line method to confirm the phenotypic ratio. We will first look at the seed shape and then the cotyledon color: Seed Shape: Rr x Rr 3 round (1 RR, 2 Rr) : 1 wrinkled (rr) Cotyledon Color: Yy x Yy 3 yellow (1 YY, 2 Yy) : 1 green (yy) Now, we combine the traits using the forked-line method: (3 round : 1 wrinkled) x (3 yellow : 1 green) 9 round & yellow : 3 round & green : 3 wrinkled & yellow : 1 wrinkled and green We can see that both the Punnett square method and the forked-line method give us the same phenotypic ratio for the F2 generation.

Key concepts

Punnett Square Analysis

The Punnett square is a foundational tool in Mendelian genetics, providing a visual representation of genetic crosses. It allows us to predict the genotypes and phenotypes of offspring from parents with known genetic makeup. Let's begin by identifying the potential gametes from a given parent. For a genotype RrYy, the possible gametes are RY, Ry, rY, and ry.

To construct the Punnett square for an F2 generation with parents both having the RrYy genotype, we create a 4x4 grid. Each cell within the grid is filled by combining one gamete from the father and one from the mother. This simple method demonstrates all possible genetic combinations for the offspring, with each cell representing an equally likely genotype.

While analyzing the Punnett square, the phenotypic outcome can be determined by reviewing the genotypes. For instance, the genotype RRYY or RrYy would result in round seeds and yellow cotyledons, as R (round) and Y (yellow) are dominant traits over their recessive counterparts r (wrinkled) and y (green), respectively. Thus, the Punnett square is an intuitive way to visualize and calculate the expected outcomes of genetic crosses.

Forked-Line Method

The forked-line method, also known as the branching diagram method, is another approach to visualize Mendelian crosses and to verify phenotypic ratios determined by a Punnett square. This method is particularly efficient when dealing with dihybrid crosses (crosses involving two traits).

To apply this method, each trait is considered separately and probabilities for each phenotype are determined. For example, when considering seed shape (Rr x Rr), we obtain a 3:1 ratio for round to wrinkled seeds. Similarly, for cotyledon color (Yy x Yy), a 3:1 ratio for yellow to green is found.

Next, the phenotypic ratios of each trait are multiplied together, akin to the branches of a fork. This is where the method gets its name. For the given exercise, this process results in a combined phenotypic ratio of 9 round & yellow: 3 round & green: 3 wrinkled & yellow: 1 wrinkled & green seeds. The simplicity of multiplying separate trait ratios makes the forked-line method a faster alternative to the Punnett square, particularly for complex crosses.

Phenotypic Ratios

Phenotypic ratios are key to understanding the quantitative aspect of Mendelian genetics. They express the proportion of various phenotypes (observable traits) appearing in the offspring. From our F2 generation, the Punnett square and forked-line method both confirm a phenotypic ratio of 9:3:3:1 for round yellow, round green, wrinkled yellow, and wrinkled green seeds, respectively.

Each number in this ratio corresponds to a specific combination of characteristics determined by the dominant and recessive alleles inherited from the parents. The dominant traits, in this case, are round seeds (R) and yellow cotyledons (Y), overshadow the recessive traits, which are wrinkled seeds (r) and green cotyledons (y).

Understanding phenotypic ratios is crucial for predicting the outcome of genetic crosses and for identifying the dominant and recessive nature of specific traits. It can also help in understanding the concept of probability within genetics and the likelihood of an offspring displaying a particular phenotype.