Problem 12 - Biology Concepts and Applications

Question

12\. Red-flowering snapdragons are homozygous for allele \(R^{1}\). White-flowering snapdragons are homozygous for a different allele \(\left(R^{2}\right)\). Heterozygous plants \(\left(R^{1} R^{2}\right)\) bear pink flowers. What phenotypes should appear among first-generation offspring of the crosses listed? What are the expected proportions for each phenotype? a. \(R^{1} R^{1} \times R^{1} R^{2}\) b. \(R^{1} R^{1} \times R^{2} R^{2}\) c. \(R^{1} R^{2} \times R^{1} R^{2}\) d. \(R^{1} R^{2} \times R^{2} R^{2}\) (In cases of incomplete dominance, alleles are usually designated by superscript numerals, as shown here, not by the uppercase letters for dominance and lowercase letters for recessiveness.

Step-by-Step Solution

Answer

Cross a: 50% Red, 50% Pink. Cross b: 100% Pink. Cross c: 25% Red, 50% Pink, 25% White. Cross d: 50% Pink, 50% White.

Step 1: Determine Genotype Combinations

For each cross provided, determine possible genotype combinations of offspring. This involves using Punnett squares for each parental cross.

Step 2: Analyze Cross a - R^1R^1 x R^1R^2

Parent 1 is homozygous R^1 (R^1R^1), and Parent 2 is heterozygous (R^1R^2). Their offspring can be R^1R^1 or R^1R^2. - Offspring: 50% R^1R^1 (Red), 50% R^1R^2 (Pink).

Step 3: Analyze Cross b - R^1R^1 x R^2R^2

Parent 1 is homozygous R^1 (R^1R^1), and Parent 2 is homozygous R^2 (R^2R^2). The offspring will all be heterozygous R^1R^2. - Offspring: 100% R^1R^2 (Pink).

Step 4: Analyze Cross c - R^1R^2 x R^1R^2

Both parents are heterozygous R^1R^2. Their offspring can be R^1R^1, R^1R^2, or R^2R^2. - Offspring: 25% R^1R^1 (Red), 50% R^1R^2 (Pink), 25% R^2R^2 (White).

Step 5: Analyze Cross d - R^1R^2 x R^2R^2

Parent 1 is heterozygous (R^1R^2), and Parent 2 is homozygous R^2 (R^2R^2). The offspring can be R^1R^2 or R^2R^2. - Offspring: 50% R^1R^2 (Pink), 50% R^2R^2 (White).

Step 6: Summarize Phenotype Proportions

- Cross a: 50% Red, 50% Pink - Cross b: 100% Pink - Cross c: 25% Red, 50% Pink, 25% White - Cross d: 50% Pink, 50% White

Key Concepts

Punnett squares

Punnett squares are a simple diagrammatic tool used in genetics to predict the possible genetic outcomes in offspring from two parental genotypes. This method involves placing the alleles of one parent on the top row and the alleles of the other parent on the side column. Each box within the square is then filled in by combining the respective alleles from the row and column. This tool provides a clear visualization of how alleles combine and what the potential genetic makeup of the offspring will be.
For example, in a cross between a red-flowering snapdragon (homozygous \( R^1R^1 \)) and a pink-flowering snapdragon (heterozygous \( R^1R^2 \)), the Punnett square helps to show that the offspring have a 50% chance of being homozygous \( R^1R^1 \) and a 50% chance of being heterozygous \( R^1R^2 \). This means 50% red and 50% pink flowering offspring.

Incomplete dominance

Incomplete dominance occurs in genetics when the phenotype of the heterozygous genotype is distinct from and often intermediate to the phenotypes of the homozygous genotypes. In simpler terms, neither allele is fully dominant over the other, resulting in a third phenotype that is a blend of the traits.
For example, in snapdragons, the red allele \( R^1 \) does not completely dominate over the white allele \( R^2 \). Instead, a heterozygous plant \( R^1R^2 \) expresses a pink color, which is an intermediate phenotype. This phenomenon is crucial in understanding variations within species and predicting genetic combinations in breeding.

Homozygous and heterozygous alleles

In genetics, the terms homozygous and heterozygous refer to the genetic makeup regarding a specific gene. When an organism has two identical alleles for a trait, it's said to be homozygous. Conversely, if there are two different alleles, the organism is heterozygous.
For snapdragon flowers, a homozygous genotype for the red color is \( R^1R^1 \) and for the white color is \( R^2R^2 \). A heterozygous genotype would be \( R^1R^2 \), exhibiting pink flowers due to incomplete dominance. Understanding these terms allows you to categorize genetic differences and predict outcomes when these are combined in various breeding scenarios.

Phenotypic ratios

Phenotypic ratios describe the relative number of offspring manifesting a particular trait or combination of traits. This is derived from the combinations formed in a Punnett square analysis.
With the snapdragon breeding examples:

• In cross \( a \) \( R^1R^1 \) x \( R^1R^2 \), the phenotypic ratio of offspring is 50% red, 50% pink.
• In cross \( b \) \( R^1R^1 \) x \( R^2R^2 \), all offspring exhibit the pink phenotype (100% pink).
• In cross \( c \) \( R^1R^2 \) x \( R^1R^2 \), the ratio is 25% red, 50% pink, and 25% white.
• In cross \( d \) \( R^1R^2 \) x \( R^2R^2 \), the phenotypic result is 50% pink and 50% white.

These ratios help predict the appearance of traits in future generations, aiding in breeding and genetic study.