The problem asks to create a completed dihybrid cross for two heterozygous parents. We need to highlight four genotypically different squares of their offspring and identify their corresponding phenotypes. Finally, we need to predict the genotype outcomes for this cross. Let's assume the two traits are represented by genes A and B, where A is dominant over a, and B is dominant over b. The heterozygous parents have the genotype AaBb.

Discrete MathematicsGeneticsPunnett SquareProbabilityDihybrid CrossRatiosMendelian Genetics
2025/3/31

1. Problem Description

The problem asks to create a completed dihybrid cross for two heterozygous parents. We need to highlight four genotypically different squares of their offspring and identify their corresponding phenotypes. Finally, we need to predict the genotype outcomes for this cross.
Let's assume the two traits are represented by genes A and B, where A is dominant over a, and B is dominant over b. The heterozygous parents have the genotype AaBb.

2. Solution Steps

Step 1: Set up the Punnett square.
Since both parents are AaBb, we need to determine the possible gametes each parent can produce. These are AB, Ab, aB, and ab. We'll create a 4x4 Punnett square with these gametes.
Step 2: Fill in the Punnett square.
| | AB | Ab | aB | ab |
| :---- | :--- | :--- | :--- | :--- |
| AB | AABB | AABb | AaBB | AaBb |
| Ab | AABb | AAbb | AaBb | Aabb |
| aB | AaBB | AaBb | aaBB | aaBb |
| ab | AaBb | Aabb | aaBb | aabb |
Step 3: Identify four genotypically different squares and their phenotypes.
We need to choose four squares with different genotypes. Here are four examples:
* AABB: Dominant phenotype for both traits (e.g., Tall and Purple)
* AAbb: Dominant phenotype for trait A, recessive phenotype for trait B (e.g., Tall and White)
* aaBB: Recessive phenotype for trait A, dominant phenotype for trait B (e.g., Short and Purple)
* aabb: Recessive phenotype for both traits (e.g., Short and White)
Step 4: Predict the genotype outcomes.
From the Punnett square, we can count the frequency of each genotype. The genotypes and their counts are as follows:
* AABB: 1
* AABb: 2
* AaBB: 2
* AaBb: 4
* AAbb: 1
* Aabb: 2
* aaBB: 1
* aaBb: 2
* aabb: 1
There are 16 possible combinations in total. So the genotype outcomes are:
AABB (1/16), AABb (2/16), AaBB (2/16), AaBb (4/16), AAbb (1/16), Aabb (2/16), aaBB (1/16), aaBb (2/16), aabb (1/16)
Alternatively, the genotypic ratio is 1:2:2:4:1:2:1:2:
1.
Step 5: Predict the phenotype outcomes.
* Dominant A, Dominant B: AABB, AABb, AaBB, AaBb (9/16)
* Dominant A, recessive b: AAbb, Aabb (3/16)
* recessive a, Dominant B: aaBB, aaBb (3/16)
* recessive a, recessive b: aabb (1/16)
Therefore the phenotypic ratio is 9:3:3:
1.

3. Final Answer

Completed Dihybrid Cross:
| | AB | Ab | aB | ab |
| :---- | :--- | :--- | :--- | :--- |
| AB | AABB | AABb | AaBB | AaBb |
| Ab | AABb | AAbb | AaBb | Aabb |
| aB | AaBB | AaBb | aaBB | aaBb |
| ab | AaBb | Aabb | aaBb | aabb |
Highlighted Genotypes and Phenotypes:
* AABB: Dominant for both traits
* AAbb: Dominant for trait A, recessive for trait B
* aaBB: Recessive for trait A, dominant for trait B
* aabb: Recessive for both traits
Genotype Outcomes: AABB (1/16), AABb (2/16), AaBB (2/16), AaBb (4/16), AAbb (1/16), Aabb (2/16), aaBB (1/16), aaBb (2/16), aabb (1/16). Genotypic ratio is 1:2:2:4:1:2:1:2:
1.

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