Question

Mendel crossed peas having green seeds with peas having yellow seeds. The \(F_{1}\) generation produced only yellow seeds. In the \(F_{2}\) the progeny consisted of 6022 plants with yellow seeds and 2001 plants with green seeds. Of the \(\mathrm{F}_{2}\) yellow-seeded plants, 519 were self-fertilized with the following results: 166 bred true for yellow and 353 produced an \(\mathrm{F}_{3}\) ratio of \(3 / 4\) yellow: \(1 / 4\) green. Explain these results by diagramming the crosses.

Short answer

Question: Explain Mendel's results when he crossed peas with green seeds and yellow seeds, including the genotypes and phenotypes observed in the F1, F2, and F3 generations. Answer: Mendel crossed green-seeded (yy) and yellow-seeded (YY) peas, producing an F1 generation of all yellow-seeded heterozygous (Yy) plants. Crossing the F1 generation resulted in an F2 generation with a 3:1 ratio of yellow:green plants, comprised of 1/4 homozygous dominant (YY), 1/2 heterozygous (Yy), and 1/4 homozygous recessive (yy) individuals. Self-fertilizing the F2 yellow-seeded plants led to the F3 generation, where homozygous dominant plants (YY) bred true for yellow seeds, while heterozygous plants (Yy) produced a 3:1 ratio of yellow:green seeds.

Step-by-step solution

Identify the dominant and recessive traits

In Mendel's experiment, the \(F_{1}\) generation produced only yellow seeds. This suggests that the yellow seed color is the dominant trait, while green seed color is the recessive trait. Let's represent the dominant trait (yellow) with "Y" and the recessive trait (green) with "y".

Determine the genotypes of the parents

Since Mendel crossed peas with green seeds and yellow seeds, we can assume that the green-seeded parent was homozygous recessive (yy) and the yellow-seeded parent was homozygous dominant (YY).

Determine the genotypes and phenotypes of the F1 generation

We can find the genotypes of the \(F_{1}\) generation by creating a Punnett square using the genotypes of the parent generation: YY x yy - which results in all the \(F_{1}\) offspring having the Yy genotype. Since yellow seeds are the dominant trait, all offspring in the \(F_{1}\) generation will have a yellow phenotype.

Determine the genotypes and phenotypes of the F2 generation

To find the genotypes and phenotypes of the \(F_{2}\) generation, we can cross two \(F_{1}\) individuals with the Yy genotype. By creating a Punnett square (Yy x Yy), we can see that the resulting offspring will have the following genotypes and phenotypes: - \(\frac{1}{4}\) YY: Yellow seeds (homozygous dominant) - \(\frac{1}{2}\) Yy: Yellow seeds (heterozygous) - \(\frac{1}{4}\) yy: Green seeds (homozygous recessive) These ratios are consistent with the results observed in Mendel's experiment, where there were 6022 yellow-seeded plants and 2001 green-seeded plants in the \(F_{2}\) generation.

Analyze the F3 generation results

Of the \(F_{2}\) yellow-seeded plants, 519 were self-fertilized and produced the following results: - 166 bred true for yellow - 353 produced an \(F_{3}\) ratio of \(3 / 4\) yellow: \(1 / 4\) green These results make sense due to the genotypic ratios analyzed earlier. Only the homozygous dominant (YY) plants would breed true for yellow in the \(F_{3}\) generation, while the heterozygous (Yy x Yy) plants would result in the same \(3 / 4\) yellow: \(1 / 4\) green ratio observed in the \(F_{2}\) generation.

Diagram the crosses

Now, we can illustrate Mendel's experiment with a diagram of the crosses. The parent generation (green-seeded yy x yellow-seeded YY) produced an \(F_{1}\) generation of all yellow-seeded Yy plants. Then, the \(F_{1}\) generation was crossed to produce the \(F_{2}\) generation, resulting in a ratio of \(\frac{1}{4}\) YY (yellow), \(\frac{1}{2}\) Yy (yellow), and \(\frac{1}{4}\) yy (green) plants. Lastly, the \(F_{2}\) yellow-seeded plants (YY and Yy) were self-fertilized, resulting in a true-breeding \(F_{3}\) generation for yellow seeds (YY) and a \(3 / 4\) yellow: \(1 / 4\) green ratio in the heterozygous Yy self-fertilized plants.

Key concepts

Dominant and Recessive Traits

Understanding the concept of dominant and recessive traits is foundational to Mendelian genetics. In Mendel's pea plant experiments, he discovered that some traits, such as the yellow seed color, will always show up when present, making them dominant. On the other hand, traits like the green seed color recede or do not express themselves when a dominant trait is present, hence they are called recessive.

Each trait is represented by letters: typically, uppercase for dominant (Y for yellow) and lowercase for recessive (y for green). Whenever offspring inherit a dominant allele, it overshadows the presence of a recessive allele, resulting in the dominant trait being expressed. Only when two recessive alleles are present, as in homozygous recessive individuals (yy), will the recessive trait be visible.

Punnett Square

A Punnett Square is a simple graphical way to predict the outcome of a genetic cross. For Mendel's Pea Plant experiments, a Punnett Square helps visualize how alleles from each parent combine and what possible genotypes their offspring can have.

If we look at the crossing of two heterozygous plants (Yy), the Punnett Square would consist of four boxes, each representing a possible genetic combination for the offspring: one YY, two Yy, and one yy. This illustrates how the phenotypic and genotypic ratios are determined.

Genotypic and Phenotypic Ratios

When studying Mendelian Inheritance, it's essential to differentiate between genotypic and phenotypic ratios. The genotypic ratio involves the proportions of different genetic makeups (genotypes) within a generation, while the phenotypic ratio refers to the observable characteristics (phenotypes).

For example, in the F₂ generation of Mendel's experiment, the genotypic ratio was 1 YY : 2 Yy : 1 yy, leading to a phenotypic ratio of 3 yellow seeds to 1 green seed. Understanding these ratios clarifies how certain traits are passed down through generations.

Homozygous and Heterozygous

The terms homozygous and heterozygous pertain to whether a pair of alleles for a particular gene is the same or different. Homozygous organisms have two copies of the same allele, either dominant (YY) or recessive (yy), while heterozygous organisms have one dominant and one recessive allele (Yy).

This distinction is crucial for predicting trait inheritance. Homozygous dominant or recessive individuals will always produce offspring with their respective traits, whereas heterozygous individuals can produce offspring with either dominant or recessive traits, depending on the alleles they contribute.

Mendelian Inheritance

Mendelian Inheritance is the pattern of inheriting traits as discovered by Gregor Mendel. His pea plant experiments showed that traits are inherited as discrete units (genes), which segregate independently during gamete formation. Each parent contributes one allele for each trait, resulting in offspring with a genotype composed of the alleles received.

Mendel's Laws of Inheritance, including the Law of Segregation and the Law of Independent Assortment, explain the distribution of traits across generations and lay the groundwork for classical genetics. These laws predict how traits can appear, disappear, and reappear through generations, as observable in the genotypic and phenotypic patterns of Mendel's plants.