Understanding dihybrid crosses is crucial for mastering Mendelian genetics. This guide provides answers and detailed explanations for common dihybrid cross practice problems, helping you solidify your understanding of inheritance patterns involving two genes. We'll cover the Punnett square method and the forked-line method, offering a comprehensive approach to solving these problems.
What is a Dihybrid Cross?
A dihybrid cross involves tracking the inheritance of two different traits, each controlled by a separate gene with two alleles. Unlike monohybrid crosses (which focus on one trait), dihybrid crosses reveal the independent assortment of genes during meiosis, leading to a greater variety of offspring genotypes and phenotypes.
Practice Problems and Solutions
Let's tackle some common dihybrid cross problems. We'll assume simple dominance for all alleles.
Problem 1: In pea plants, tall (T) is dominant to short (t), and round seeds (R) are dominant to wrinkled seeds (r). A homozygous tall, round plant (TTRR) is crossed with a homozygous short, wrinkled plant (ttrr).
a) What are the genotypes and phenotypes of the F1 generation?
- Solution: All F1 offspring will be TtRr, exhibiting the tall and round phenotype. This is because T and R are dominant alleles.
b) What are the possible genotypes and phenotypes of the F2 generation (obtained by self-crossing the F1 generation)?
- Solution: This requires a 16-square Punnett square (see below). The phenotypic ratio will be 9 tall, round : 3 tall, wrinkled : 3 short, round : 1 short, wrinkled.
TR Tr tR tr
TR TTRR TTRr TtRR TtRr
Tr TTRr TTrr TtRr Ttrr
tR TtRR TtRr ttRR ttRr
tr TtRr Ttrr ttRr ttrr
Problem 2: In dogs, black fur (B) is dominant to brown fur (b), and long hair (L) is dominant to short hair (l). A heterozygous black, long-haired dog (BbLl) is crossed with a brown, short-haired dog (bbll).
a) What is the probability of producing a black, long-haired puppy?
- Solution: Use a Punnett Square (or the forked-line method which is described later) to determine the probabilities of each genotype. The probability of a black, long-haired puppy (BbLl or BbLL) is 2/8 or 1/4.
b) What is the probability of producing a brown, short-haired puppy?
- Solution: Using the Punnett Square, the probability of a brown, short-haired puppy (bbll) is 2/8 or 1/4.
BL Bl bL bl
bl BbLl Bbll bbLl bbll
bl BbLl Bbll bbLl bbll
Problem 3: Using the Forked-Line Method
Let's revisit Problem 1(b) but use the forked-line method, a more efficient approach for larger crosses.
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Parental Genotypes: TtRr x TtRr
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Gametes from TtRr: TR, Tr, tR, tr (each with a probability of 1/4)
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Probability of TTRR: (1/4) * (1/4) = 1/16
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Probability of TTRr: (1/4) * (1/2) + (1/2) * (1/4) = 2/16 = 1/8
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Probability of TTrr: (1/2) * (1/2) = 1/4
By continuing this process for all possible genotypes, you arrive at the same 9:3:3:1 phenotypic ratio as with the Punnett square. This method is especially helpful when dealing with more complex crosses involving three or more genes.
Conclusion
Dihybrid crosses are a fundamental concept in genetics, illustrating the independent assortment of alleles. Mastering both the Punnett square and forked-line methods allows you to confidently predict the genotypes and phenotypes of offspring in various genetic crosses. Remember to always carefully consider the dominance relationships of the alleles involved. Regular practice with these problems will significantly improve your understanding of Mendelian genetics and related concepts.
