A trihybrid cross results in a phenotypic ratio of 27:9:9:9:3:3:3:1. Using a branch diagram show the proportion of each of the following traits: black/white, tall/short, rough/smooth. Black, tall, rough are dominant.
The Correct Answer and Explanation is :
To solve the trihybrid cross involving the traits black/white, tall/short, and rough/smooth, where black, tall, and rough are dominant, we’ll first assume that the alleles for each trait are represented as follows:
- Black (B) vs. white (b)
- Tall (T) vs. short (t)
- Rough (R) vs. smooth (r)
The given phenotypic ratio of 27:9:9:9:3:3:3:1 suggests the cross between two heterozygous individuals for all traits (BbTtRr x BbTtRr).
Step-by-Step Branch Diagram
To generate the branch diagram, we start by assigning probabilities to each possible outcome of a single trait, considering simple Mendelian inheritance:
- Black vs. White (Bb x Bb):
- BB (Black): ( \frac{1}{4} )
- Bb (Black): ( \frac{1}{2} )
- bb (White): ( \frac{1}{4} )
- Tall vs. Short (Tt x Tt):
- TT (Tall): ( \frac{1}{4} )
- Tt (Tall): ( \frac{1}{2} )
- tt (Short): ( \frac{1}{4} )
- Rough vs. Smooth (Rr x Rr):
- RR (Rough): ( \frac{1}{4} )
- Rr (Rough): ( \frac{1}{2} )
- rr (Smooth): ( \frac{1}{4} )
Using these, we’ll create a branch diagram that multiplies the probabilities across traits:
- Black, Tall, Rough (27): ( \left(\frac{3}{4} \times \frac{3}{4} \times \frac{3}{4}\right) = \frac{27}{64} )
- Black, Tall, Smooth (9): ( \left(\frac{3}{4} \times \frac{3}{4} \times \frac{1}{4}\right) = \frac{9}{64} )
- Black, Short, Rough (9): ( \left(\frac{3}{4} \times \frac{1}{4} \times \frac{3}{4}\right) = \frac{9}{64} )
- White, Tall, Rough (9): ( \left(\frac{1}{4} \times \frac{3}{4} \times \frac{3}{4}\right) = \frac{9}{64} )
- Black, Short, Smooth (3): ( \left(\frac{3}{4} \times \frac{1}{4} \times \frac{1}{4}\right) = \frac{3}{64} )
- White, Tall, Smooth (3): ( \left(\frac{1}{4} \times \frac{3}{4} \times \frac{1}{4}\right) = \frac{3}{64} )
- White, Short, Rough (3): ( \left(\frac{1}{4} \times \frac{1}{4} \times \frac{3}{4}\right) = \frac{3}{64} )
- White, Short, Smooth (1): ( \left(\frac{1}{4} \times \frac{1}{4} \times \frac{1}{4}\right) = \frac{1}{64} )
Explanation
This branch diagram approach allows us to visualize the distribution of phenotypic traits in offspring when considering multiple genes, each exhibiting simple dominance. The diagram helps us multiply the probabilities of each gene’s outcome, ensuring we account for all possible combinations in the cross. The resulting proportions correspond to the phenotypic ratio given (27:9:9:9:3:3:3:1), which sums up to 64 possible outcomes reflecting the ( 2^6 ) combinations possible with three genes each segregating two ways.
This method highlights how dominant and recessive traits interact in a hybrid cross, with dominant traits appearing more frequently due to their presence in both homozygous dominant and heterozygous genotypes.
I will now generate an image that visualizes this branch diagram.
Here is the branch diagram visualizing the trihybrid cross for the traits black/white, tall/short, and rough/smooth, with black, tall, and rough being the dominant traits. This diagram illustrates the pathways for each combination with the corresponding probabilities and phenotypic ratios.
You can view and use this diagram to better understand how the different traits are inherited and how the phenotypic ratios are derived from the genetic combinations.
