Mendelian Laws & Gene Interactions using Seeds/Beads
Aim
To demonstrate Mendel’s laws (monohybrid & dihybrid) and common gene interactions using seeds/beads and verify observed ratios with the Chi-square test.
Materials
1. Two contrasting seed types (e.g., yellow/green peas) or two sets of beads differing by colour/shape
2. Small opaque cups or bags (2 for parents’ gametes)
3. Labels, record sheet, marker, calculator
4. Tally sheet or spreadsheet (recommended)
Experimental Design
Choose one or more of the following experiments:
A. Monohybrid simulation (expected F₂ phenotypic ratio = 3:1)
1. Assign allele tokens:
A (dominant) = yellow bead/seed,
a (recessive) = green.
2. Prepare two gamete cups representing gamete pools of Aa × Aa parents. In each cup place equal numbers of A and a tokens (e.g., 50 A, 50 a).
3. For each simulated offspring: draw one token from cup 1 and one from cup 2 (sampling with replacement). Combine to record genotype (AA, Aa, aa).
4. Score phenotype: AA and Aa = dominant; aa = recessive.
5. Repeat till N ≥ 100; record counts.
B. Dihybrid simulation (expected F₂ phenotypic ratio = 9:3:3:1)
1. Assign two trait token-sets:
A/a (colour), and B/b (shape).
Create four token types: AB, Ab, aB, ab.
2. Prepare two gamete cups with equal numbers of each gamete type to simulate AaBb × AaBb.
3. Draw one gamete from each cup, combine to form offspring genotype. Score phenotype into four classes: AABB, AaBb, aaBB, aabb.
4. Repeat until N ≥ 320 for stable proportions (or at least 160 for demonstration).
C. Gene interactions (epistasis: 9:7, 9:3:4, 12:3:1 etc.)
1. Use token rules that map genotype combinations to phenotypes for the interaction you want to demonstrate (e.g., complementary genes 9:7 → phenotype present only when at least one dominant allele at both loci).
2. Simulate as dihybrid (AaBb × AaBb) but score phenotypes according to the interaction rule.
3. Aim for N ≥ 200.
Observation Tables
Monohybrid (3:1)
Phenotype | Observed (O) | Expected ratio | Expected (E) |
Dominant |
| 3/4 |
|
Recessive |
| 1/4 |
|
Total (N) |
|
| N |
Dihybrid (9:3:3:1)
Phenotype class | Observed (O) | Ratio | Expected (E) |
A_B_ |
| 9/16 |
|
A_bb |
| 3/16 |
|
aaB_ |
| 3/16 |
|
aabb |
| 1/16 |
|
Total (N) |
|
| N |
Chi-square (χ²) Analysis
1. Compute expected counts: E = ratio × N.
2. For each class compute (O − E)² / E.
3. Sum to get χ².
4. Degrees of freedom = (number of phenotypic classes − 1).
5. Compare χ² to critical value at α = 0.05. If χ² ≤ critical → fits expected ratio and if > → reject.
6. If any E < 5, combine classes or increase N.
Worked Example (Monohybrid)
Mendel’s observed ratios often closely matched expected ratios (e.g., 3:1). To test reliability, modern genetics uses the Chi-square test (χ²).
Formula:
χ² = Σ (O - E)² / E
Where:
O = Observed value
E = Expected value
Interpretation:
If χ² < critical value → no significant difference (data supports hypothesis).
If χ² > critical value → deviation significant (may indicate other genetic factors).
Example: Monohybrid Cross (Rr × Rr)
Expected ratio = 3 Round : 1 Wrinkled
Suppose we perform the cross and observe:
Observed (O): Round = 290, Wrinkled = 110
Total = 400 seeds
Step 1: Calculate Expected Numbers
Expected ratio = 3:1
Round = (3/4 × 400) = 300
Wrinkled = (1/4 × 400) = 100
So:
Expected (E): Round = 300, Wrinkled = 100
Step 2: Apply χ² Formula
χ² = Σ (O - E)² / E
For Round:
((290 - 300)² / 300) = 100 / 300 = 0.33
For Wrinkled:
((110 - 100)² / 100) = 100 / 100 = 1.0
Total χ² = 0.33 + 1.0 = 1.33
Step 3: Degrees of Freedom (df)
df = n - 1
Here, n = number of categories = 2 (Round, Wrinkled)
So, df = 2 - 1 = 1
Step 4: Compare with Critical Value
At df = 1 and p = 0.05, the critical value = 3.84
If χ² < 3.84 → No significant difference (Mendel’s ratio holds true)
If χ² > 3.84 → Significant difference (other factors may influence)
Here: χ² = 1.33 < 3.84 → No significant difference.
Data supports Mendelian 3:1 ratio.
Conclusion
The Chi-square test confirms that the observed data does not significantly differ from the expected Mendelian ratio.
Applications of Mendel’s Data
1. Predicting offspring traits in agriculture and animal breeding.
2. Medical genetics (inheritance of genetic disorders).
3. Evolutionary studies.
4. Forensic science and paternity testing.
5. Conservation biology (maintaining genetic diversity).
Precautions & Tips
a. Always sample with replacement to model independent gamete formation.
b. Keep N large enough (mono ≥100, dihybrid ≥320 recommended).
c. Use clear scoring rules.
d. Use a spreadsheet to auto-calculate expected counts and χ².
Viva Questions
1. Define segregation and independent assortment.
2. Why use χ² test in genetics?
3. What to do if expected counts are < 5?
4. Give examples of epistasis and their phenotypic ratios.
FAQs
Q: Can beads produce the same learning outcome as live crosses?
A: Yes — excellent for teaching segregation and assortment.
Q: Minimum sample size?
A: Mono ≥100, dihybrid ≥160–320 for reasonable approximation.
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