Step 1: Understanding the Problem:
The ABO blood group system is governed by a single gene (I) with three alleles: \(I^A\), \(I^B\), and \(I^O\) (or \(i\)). Both \(I^A\) and \(I^B\) exhibit complete dominance over \(I^O\) but are co-dominant when present together.
Step 2: Approach and Formula:
Construct a genetic cross using a Punnett square to systematically determine all possible combinations of offspring genotypes, and then map them to their corresponding phenotypes.
Step 3: Detailed Explanation:
Husband's genotype: \(I^A I^B\) $\rightarrow$ produces two types of gametes: \(I^A\) and \(I^B\).
Wife's genotype: \(I^A I^O\) $\rightarrow$ produces two types of gametes: \(I^A\) and \(I^O\).
Crossing the gametes yields the following offspring combinations:
1. \(I^A\) (from husband) + \(I^A\) (from wife) = \(I^A I^A\)
2. \(I^A\) (from husband) + \(I^O\) (from wife) = \(I^A I^O\)
3. \(I^B\) (from husband) + \(I^A\) (from wife) = \(I^A I^B\)
4. \(I^B\) (from husband) + \(I^O\) (from wife) = \(I^B I^O\)
Counting the unique outcomes:
Genotypes formed:
There are 4 distinct genotypes: \(I^A I^A\), \(I^A I^O\), \(I^A I^B\), and \(I^B I^O\).
Phenotypes corresponding to these genotypes:
- \(I^A I^A\) expresses as Blood Group A.
- \(I^A I^O\) expresses as Blood Group A.
- \(I^A I^B\) expresses as Blood Group AB.
- \(I^B I^O\) expresses as Blood Group B.
Thus, there are 3 distinct phenotypes observed: A, AB, and B.
Step 4: Final Answer:
There are 4 genotypes and 3 phenotypes possible.