Dihybrid Crosses Practice Problems Answer Key

Unlocking the complexities of genetics requires a solid understanding of dihybrid crosses. A dihybrid cross, a fundamental concept in Mendelian genetics, explores the inheritance patterns of two different traits simultaneously. Mastering this concept is crucial for anyone delving into the fascinating world of heredity and genetic variation.

Understanding Dihybrid Crosses: The Foundation

Before diving into practice problems, let's establish a firm understanding of what a dihybrid cross entails. A dihybrid cross examines the inheritance of two distinct traits controlled by two different genes. Each gene has two alleles, one dominant and one recessive. The classic example involves pea plants, where traits like seed color (yellow or green) and seed shape (round or wrinkled) are studied together.

• Alleles: Alternative forms of a gene (e.g., Y for yellow seeds, y for green seeds).
• Genotype: The genetic makeup of an organism (e.g., YY, Yy, yy).
• Phenotype: The observable characteristics of an organism (e.g., yellow seeds, green seeds).
• Dominant Allele: The allele that masks the expression of the recessive allele when present in a heterozygous state (e.g., Y is dominant over y).
• Recessive Allele: The allele that is only expressed when present in a homozygous state (e.g., y is only expressed when the genotype is yy).

In a dihybrid cross, we're essentially tracking how these alleles assort independently during gamete formation and subsequently combine during fertilization. The cornerstone of dihybrid crosses lies in Mendel's Law of Independent Assortment, which states that the alleles of two (or more) different genes get sorted into gametes independently of one another. In other words, the allele a gamete receives for one gene does not influence the allele it receives for another gene. This law holds true when genes are located on different chromosomes or are far apart on the same chromosome.

Setting Up a Dihybrid Cross: The Punnett Square

The Punnett square is an invaluable tool for visualizing and predicting the possible genotypes and phenotypes of offspring from a dihybrid cross. Here's a step-by-step guide to setting up and using a Punnett square for a dihybrid cross:

1. Determine the Genotypes of the Parents: Identify the genotypes of the two parents involved in the cross. For example, let's consider a cross between two pea plants that are heterozygous for both seed color and seed shape (YyRr).

2. Determine the Gametes Each Parent Can Produce: This is where the Law of Independent Assortment comes into play. Each parent can produce four different types of gametes, each containing one allele for each trait. For the YyRr parent, the possible gametes are YR, Yr, yR, and yr.

3. Construct the Punnett Square: Draw a 4x4 grid. Write the possible gametes from one parent along the top of the grid and the possible gametes from the other parent along the side.

4. Fill in the Punnett Square: Combine the alleles from the corresponding row and column to determine the genotype of each offspring. For example, the cell where the YR gamete from one parent and the yr gamete from the other parent meet would contain the genotype YyRr.

5. Determine the Phenotypic Ratio: Once the Punnett square is filled, count the number of offspring with each possible phenotype. In a dihybrid cross involving two heterozygous parents (YyRr x YyRr), the expected phenotypic ratio is typically 9:3:3:1. This represents:

   • 9 offspring with both dominant traits (e.g., yellow and round seeds).
   • 3 offspring with the first dominant trait and the second recessive trait (e.g., yellow and wrinkled seeds).
   • 3 offspring with the first recessive trait and the second dominant trait (e.g., green and round seeds).
   • 1 offspring with both recessive traits (e.g., green and wrinkled seeds).

Dihybrid Cross Practice Problems: Putting Knowledge to the Test

Now, let's solidify your understanding with some practice problems. We'll work through each problem step-by-step, providing the answer key and a detailed explanation.

Problem 1:

In guinea pigs, black fur (B) is dominant to brown fur (b), and rough coat (R) is dominant to smooth coat (r). A male guinea pig heterozygous for both traits is crossed with a female guinea pig with brown fur and a smooth coat. What are the possible genotypes and phenotypes of the offspring, and in what proportion would they be expected?

Solution:

• Parental Genotypes: Male: BbRr, Female: bbrr
• Male Gametes: BR, Br, bR, br
• Female Gametes: br (all gametes are the same since the female is homozygous recessive for both traits)

Punnett Square:

Genotypic Ratio:

• BbRr: 1/4
• Bbrr: 1/4
• bbRr: 1/4
• bbrr: 1/4

Phenotypic Ratio:

• Black fur, rough coat (BbRr): 1/4
• Black fur, smooth coat (Bbrr): 1/4
• Brown fur, rough coat (bbRr): 1/4
• Brown fur, smooth coat (bbrr): 1/4

Answer: The offspring will have the following phenotypes in equal proportions: black fur and rough coat, black fur and smooth coat, brown fur and rough coat, and brown fur and smooth coat.

Explanation: Since the female guinea pig is homozygous recessive for both traits, she can only produce one type of gamete (br). The male guinea pig, being heterozygous for both traits, produces four different types of gametes (BR, Br, bR, br). The Punnett square shows all possible combinations of these gametes, resulting in the equal distribution of the four phenotypes.

Problem 2:

In tomatoes, red fruit (R) is dominant to yellow fruit (r), and tall plants (T) are dominant to dwarf plants (t). A tomato plant heterozygous for both traits is crossed with a tomato plant that is homozygous recessive for both traits. What proportion of the offspring will have red fruit and be tall?

Solution:

• Parental Genotypes: Plant 1: RrTt, Plant 2: rrtt
• Plant 1 Gametes: RT, Rt, rT, rt
• Plant 2 Gametes: rt (all gametes are the same)

Punnett Square:

Genotypic Ratio:

• RrTt: 1/4
• Rrtt: 1/4
• rrTt: 1/4
• rrtt: 1/4

Phenotypic Ratio:

• Red fruit, tall plants (RrTt): 1/4
• Red fruit, dwarf plants (Rrtt): 1/4
• Yellow fruit, tall plants (rrTt): 1/4
• Yellow fruit, dwarf plants (rrtt): 1/4

Answer: 1/4 (25%) of the offspring will have red fruit and be tall.

Explanation: Similar to the previous problem, one parent is homozygous recessive for both traits, simplifying the Punnett square. Only one out of the four possible offspring genotypes results in the red fruit and tall plant phenotype (RrTt).

Problem 3:

In cats, black fur (B) is dominant to brown fur (b), and short hair (S) is dominant to long hair (s). A cat with the genotype BbSs is crossed with a cat with the genotype bbSs. What is the probability of producing an offspring with brown fur and long hair?

Solution:

• Parental Genotypes: Cat 1: BbSs, Cat 2: bbSs
• Cat 1 Gametes: BS, Bs, bS, bs
• Cat 2 Gametes: bS, bs

Punnett Square:

Genotypes with brown fur and long hair (bbss):

• Only one genotype in the Punnett square corresponds to brown fur and long hair: bbss.

Calculating Probability:

• There are 8 total boxes in the Punnett square.
• One of those boxes is bbss.
• Therefore, the probability of producing an offspring with brown fur and long hair is 1/8.

Answer: The probability of producing an offspring with brown fur and long hair is 1/8.

Explanation: This problem requires careful attention to the desired phenotype. We need to identify the genotype that produces brown fur (bb) and long hair (ss). By examining the Punnett square, we find only one instance of this genotype (bbss) out of the eight possible combinations.

Problem 4:

In corn, purple kernels (P) are dominant to yellow kernels (p), and smooth kernels (S) are dominant to wrinkled kernels (s). A farmer crosses two corn plants with the genotypes PpSs. What proportion of the offspring will have purple, wrinkled kernels?

Solution:

• Parental Genotypes: Plant 1: PpSs, Plant 2: PpSs
• Plant 1 Gametes: PS, Ps, pS, ps
• Plant 2 Gametes: PS, Ps, pS, ps

Punnett Square:

Genotypes with purple, wrinkled kernels (Pp ss or PP ss):

• Pp ss: 2
• PP ss: 1

Calculating Proportion:

• Total number of boxes in the Punnett Square: 16
• Number of boxes with the desired genotypes (Pp ss or PP ss): 3
• Proportion of offspring with purple, wrinkled kernels: 3/16

Answer: 3/16 of the offspring will have purple, wrinkled kernels.

Explanation: This problem involves a standard dihybrid cross with two heterozygous parents. To obtain the purple, wrinkled phenotype, the offspring must have at least one dominant P allele and be homozygous recessive for the s allele (ss). By examining the Punnett square, we find that 3 out of the 16 possible combinations result in this phenotype.

Problem 5:

In rabbits, black coat color (B) is dominant over white (b), and long ears (L) are dominant over short ears (l). A breeder crosses a rabbit that is heterozygous for both traits with a rabbit that is homozygous recessive for coat color but heterozygous for ear length. What is the probability that the offspring will have a white coat and long ears?

Solution:

• Parental Genotypes: Rabbit 1: BbLl, Rabbit 2: bbLl
• Rabbit 1 Gametes: BL, Bl, bL, bl
• Rabbit 2 Gametes: bL, bl

Punnett Square:

Genotypes with a white coat and long ears (bbLL or bbLl):

• bbLL: 1
• bbLl: 2

Calculating Probability:

• Total number of boxes in the Punnett Square: 8
• Number of boxes with the desired genotypes (bbLL or bbLl): 3
• Probability of offspring with a white coat and long ears: 3/8

Answer: The probability that the offspring will have a white coat and long ears is 3/8.

Explanation: This problem requires careful attention to the genotypes of the parents. One parent is heterozygous for both traits, while the other is homozygous recessive for coat color but heterozygous for ear length. We need to identify the genotypes that produce a white coat (bb) and long ears (at least one dominant L allele). By examining the Punnett square, we find that 3 out of the 8 possible combinations result in this phenotype.

Beyond the Basics: Expanding Your Dihybrid Cross Knowledge

While the problems above cover the core principles of dihybrid crosses, there are nuances and complexities to consider. Here are a few additional points to expand your understanding:

• Testcrosses: A testcross involves crossing an individual with an unknown genotype to a homozygous recessive individual. This helps determine the genotype of the unknown individual based on the phenotypic ratios of the offspring.

• Linked Genes: Genes that are located close together on the same chromosome are called linked genes. They tend to be inherited together, deviating from the Law of Independent Assortment. Recombination (crossing over) can separate linked genes, but the frequency of recombination is related to the distance between the genes.

• Chi-Square Analysis: Chi-square analysis is a statistical test used to determine if the observed results of a genetic cross differ significantly from the expected results. This helps determine if deviations from expected ratios are due to chance or other factors, such as linked genes.

• Real-World Applications: Dihybrid crosses have numerous real-world applications in agriculture, medicine, and evolutionary biology. They are used to develop new crop varieties with desirable traits, understand the inheritance of genetic diseases, and study the mechanisms of evolution.

Conclusion: Mastering the Dihybrid Cross

Dihybrid crosses are a cornerstone of genetics, providing a framework for understanding how two traits are inherited simultaneously. By mastering the concepts of alleles, genotypes, phenotypes, Punnett squares, and the Law of Independent Assortment, you can confidently tackle dihybrid cross problems and apply this knowledge to a wide range of biological applications. The practice problems presented here offer a solid foundation, and further exploration of related topics will deepen your understanding of this fundamental genetic principle. Keep practicing, and you'll unlock the secrets of heredity one cross at a time.