Chapter 10 Dihybrid Cross Worksheet Answers

Chapter 10: Dihybrid Cross Worksheet Answers: A Comprehensive Guide

Understanding dihybrid crosses is crucial for grasping fundamental genetics principles. This chapter often presents challenges for students, but mastering the concepts will significantly improve your understanding of inheritance patterns. This comprehensive guide will walk you through the complexities of dihybrid crosses, providing detailed explanations and answers to common worksheet questions. We'll cover the Punnett square method, probability calculations, and the significance of independent assortment. By the end, you'll be confidently tackling any dihybrid cross problem.

Understanding Dihybrid Crosses: Beyond Mendel's Monohybrid Crosses

Before diving into dihybrid crosses, let's briefly review monohybrid crosses. Mendel's monohybrid crosses focused on one trait, like flower color (purple or white). Dihybrid crosses, however, examine the inheritance of two traits simultaneously. For example, we might consider both flower color and plant height (tall or short) in pea plants.

Key Concepts:

• Alleles: Different versions of a gene (e.g., purple allele and white allele for flower color).
• Homozygous: Having two identical alleles for a trait (e.g., PP or pp).
• Heterozygous: Having two different alleles for a trait (e.g., Pp).
• Genotype: The genetic makeup of an organism (e.g., PP, Pp, pp).
• Phenotype: The observable characteristics of an organism (e.g., purple flowers, white flowers).
• Independent Assortment: Mendel's Law of Independent Assortment states that during gamete formation, the alleles for different traits separate independently of one another. This means the inheritance of one trait doesn't influence the inheritance of another.

The Punnett Square Method for Dihybrid Crosses

The Punnett square remains a valuable tool, even for dihybrid crosses, though it becomes significantly larger. For a dihybrid cross, involving two heterozygous parents (e.g., PpTt x PpTt), you'll need a 16-square Punnett square.

Constructing the Punnett Square:

1. Determine the possible gametes: For a parent with genotype PpTt, the possible gametes are PT, Pt, pT, and pt. This is because each allele pair segregates independently during meiosis.

2. Create the square: Draw a 4x4 grid. Label the top row and left column with the possible gametes from each parent.

3. Fill in the genotypes: Combine the alleles from the corresponding rows and columns to determine the genotypes of the offspring.

4. Determine the phenotypes: Based on the genotypes, determine the phenotypes of the offspring. Remember to consider the dominance relationships between alleles.

Example:

Let's consider a dihybrid cross between two pea plants heterozygous for both flower color (P = purple, p = white) and plant height (T = tall, t = short). The parental cross is PpTt x PpTt.

Analyzing the Results:

From this Punnett square, we can determine the phenotypic ratios:

• 9/16: Purple, Tall
• 3/16: Purple, Short
• 3/16: White, Tall
• 1/16: White, Short

This classic 9:3:3:1 phenotypic ratio is characteristic of a dihybrid cross between two heterozygotes with complete dominance.

Beyond the Punnett Square: Using Probability

While the Punnett square is helpful for visualizing dihybrid crosses, using probability can be more efficient, especially for more complex crosses. The principle of independent assortment allows us to calculate the probability of each phenotype separately and then combine those probabilities.

Example using Probability:

Let's revisit the PpTt x PpTt cross. To determine the probability of a purple, tall offspring:

1. Probability of Purple: The probability of getting a purple flower (P_) is 3/4 (PP, Pp, Pp).

2. Probability of Tall: The probability of getting a tall plant (T_) is 3/4 (TT, Tt, Tt).

3. Combined Probability: Since the traits assort independently, we multiply the probabilities: (3/4) * (3/4) = 9/16. This matches the result from the Punnett square.

Working Through Worksheet Problems: Step-by-Step Examples

Let's tackle some typical worksheet problems step by step.

Problem 1: In guinea pigs, black fur (B) is dominant to white fur (b), and rough fur (R) is dominant to smooth fur (r). A heterozygous black, rough guinea pig is crossed with a white, smooth guinea pig. What are the expected phenotypic ratios of the offspring?

Solution:

1. Parental Genotypes: The heterozygous black, rough guinea pig is BbRr. The white, smooth guinea pig is bbrr.

2. Gametes: BbRr can produce BR, Br, bR, br gametes. bbrr can only produce br gametes.

3. Punnett Square (simplified): Since one parent only produces one type of gamete, a smaller Punnett square is sufficient.

4. Phenotypic Ratios: Analyzing the Punnett square, the expected phenotypic ratio is 1:1:1:1 (Black, Rough: Black, Smooth: White, Rough: White, Smooth).

Problem 2: A plant with red flowers (R) and tall stems (T) is crossed with a plant with white flowers (r) and short stems (t). All the offspring have red flowers and tall stems. Determine the genotypes of the parents.

Solution: Since all offspring are red and tall, the red and tall parent must be homozygous dominant (RR TT). The white, short parent must be homozygous recessive (rr tt).

Problem 3: In fruit flies, gray body (G) is dominant to black body (g), and long wings (L) are dominant to short wings (l). A gray-bodied, long-winged fly is crossed with a black-bodied, short-winged fly, and the following offspring are produced: 50 gray, long; 50 black, short. Determine the genotypes of the parents.

Solution: This 1:1 phenotypic ratio suggests a test cross. The gray, long-winged parent must be heterozygous for both traits (GgLl), while the black, short-winged parent is homozygous recessive (ggll).

Advanced Dihybrid Crosses: Considering Incomplete Dominance and Codominance

The principles of dihybrid crosses extend to situations with incomplete dominance or codominance.

Incomplete Dominance: Neither allele is completely dominant, resulting in a blended phenotype in heterozygotes. For example, a red flower (R) crossed with a white flower (W) might produce pink flowers (RW).

Codominance: Both alleles are fully expressed in heterozygotes. For example, a red flower (R) crossed with a white flower (W) might produce flowers with both red and white patches (RW).

Solving these crosses involves applying the same Punnett square or probability methods but carefully considering the resulting phenotypes based on the type of dominance.

Troubleshooting Common Mistakes

• Confusing Genotypes and Phenotypes: Remember to clearly distinguish between genotypes (genetic makeup) and phenotypes (observable traits).

• Incorrect Gamete Formation: Carefully consider all possible gamete combinations during meiosis. Remember independent assortment!

• Mathematical Errors: Double-check your calculations, particularly when using probability methods.

• Ignoring Dominance Relationships: Always consider which alleles are dominant and recessive when determining phenotypes.

Conclusion: Mastering Dihybrid Crosses for Genetic Success

Dihybrid crosses can seem challenging initially, but by understanding the fundamental principles, applying the Punnett square method or probability, and working through practice problems, you'll confidently solve any dihybrid cross question. Remember to break down complex problems into smaller, manageable steps, carefully consider gamete combinations, and always double-check your work. With practice, you'll master this critical concept in genetics and build a strong foundation for more advanced genetic studies.