1. Fundamental Definitions
Before analyzing the cross, we must establish the allele definitions and dominance relationships defined on the board.
| Symbol |
Meaning |
Type |
| A |
Good Allele |
Dominant |
| a |
Harmful Allele |
Recessive |
Key Relationship: A is dominant over a.
Key Formula: Hz = 1 - Ht (Homozygosity = 1 - Heterozygosity)
🧠Quick Check:
If 'a' is a harmful allele, why does it not show its effect in an 'Aa' individual?
Because 'A' is dominant. The 'Aa' individual is Heterozygous and carries the harmful allele, but the phenotype is determined by the dominant 'Good' allele.
2. Parental Cross & F1 Generation
Parents: Aa × Aa
This is a monohybrid cross between two heterozygotes.
Genotype Ratios:
- AA (Homozygous Dominant): 25%
- Aa (Heterozygous): 50%
- aa (Homozygous Recessive): 25%
Grouped Stats:
- Total Homozygous (AA + aa): 50%
- Total Heterozygous (Aa): 50%
- Recessive Individuals (aa): 25%
🧠Analytical Question:
In this F1 generation, what percentage of the population carries the 'Good Allele' (A)?
75%. The AA individuals (25%) and the Aa individuals (50%) both possess the 'A' allele. Only the 'aa' group lacks it.
3. Advanced Concept: Selfing of F1
The whiteboard diagrams "Selfing of 1st one," showing what happens if the F1 generation reproduces within itself (or self-pollinates). This effectively creates 3 sub-populations based on the F1 parents.
Group 1: AA × AA
Derived from the 25% AA of F1.
Result: All AA
Contribution to pool:
4 × AA
Group 2: Aa × Aa
Derived from the 50% Aa of F1. (Note: Since this group is twice as large, its contribution is doubled).
Result: 1AA : 2Aa : 1aa
Contribution to pool (x2):
2 AA : 4 Aa : 2 aa
Group 3: aa × aa
Derived from the 25% aa of F1.
Result: All aa
Contribution to pool:
4 × aa
🧠Critical Thinking:
Why does the middle group (Aa x Aa) contribute double the offspring to the calculation pool?
In the F1 generation, Heterozygotes (Aa) made up 50% of the population, while AA and aa were only 25% each. Therefore, when calculating the total F2 pool, the output of the Aa parents is weighted double compared to the others.
4. The Final Calculation (Whiteboard Right Side)
Combining the results from the selfing event above, we calculate the total population statistics out of a theoretical pool of 16.
| Genotype |
Source (AA Parents) |
Source (Aa Parents) |
Source (aa Parents) |
Total |
| AA |
4 |
2 |
0 |
6 |
| Aa |
0 |
4 |
0 |
4 |
| aa |
0 |
2 |
4 |
6 |
| Total Population |
16 |
Final Percentages
Homozygous (AA + aa)
Total: 6 (AA) + 6 (aa) = 12
Calculation: 12 / 16 × 100
75%
Heterozygous (Aa)
Total: 4
Calculation: 4 / 16 × 100
25%
Recessive / Harmful (aa)
Total: 6
Calculation: 6 / 16 × 100
37.5%
Observation: Inbreeding (selfing) increased Homozygosity from 50% (in F1) to 75% (in F2), and increased the expression of the harmful recessive trait from 25% to 37.5%.