Inbreeding Depression & Genetics

From Theory to Calculation (Based on NCERT & Class Whiteboard)

1. Inbreeding Depression in Plants

Definition: Inbreeding depression refers to the reduced biological fitness in a population due to increased homozygosity, which results in the expression of deleterious recessive alleles.

[Image of self-pollination in plants]
Cause

Continued Self-Pollination

Mechanism

Increased Homozygosity
(Recessive traits appear)

Effect

Reduced Vigor, Lower Yield, Sterility

2. Mathematical Proof of Homozygosity

When a heterozygous plant (Aa) undergoes self-pollination, Heterozygosity ($H_n$) decreases by half every generation.

Hn = H0 × (1/2)n

Where n = Number of generations

Step 2: Heterozygosity Decay Table

Generation (n) Heterozygosity (Aa) Total Homozygosity (AA + aa)
0100% (1.00)0%
150% (0.50)50%
225% (0.25)75%
312.5% (0.125)87.5%
46.25% (0.0625)93.75%
53.1% (0.03125)96.88%

Step 3: The Danger Zone (Recessive Accumulation)

The "Bad" alleles (aa) accumulate alongside the "Good" alleles (AA). By the 5th generation, nearly half the crop is genetically compromised.

Generation (n) Total Homozygosity Harmful Recessive (aa) Only
00%0%
150%25%
275%37.5%
387.5%43.75%
493.75%46.87%
596.88%48.44%
❓ Checkpoint: Why is 48.44% recessive a problem?
In a crop field, this means nearly half of your plants are showing the "harmful" trait (weak roots, low yield, etc.), leading to massive economic loss.

3. Whiteboard Case Study: Generation 2 Calculation

Let's verify the "Generation 2" data (from the table above) using the specific calculation from the whiteboard image.

The Setup

  • A = Good Allele (Dominant)
  • a = Harmful Allele (Recessive)
  • Initial Cross (F1): Aa × Aa
A
a
A
AA
Aa
a
Aa
aa

The "Selfing" Event (Gen 2)

The whiteboard tracks offspring from the F1 parents (1 AA : 2 Aa : 1 aa) assuming a total pool of 16.

Parent Type Offspring (AA) Offspring (Aa) Offspring (aa)
AA Parents (x4) 400
Aa Parents (x4) 1 *2 = 2 2 *2 = 4 1 *2 = 2
aa Parents (x4) 004
TOTAL (16) 6 4 6

Final Whiteboard Results

Comparing the calculated numbers to the percentage table:

Heterozygous (Aa)
25%
(4 out of 16)
Matches Gen 2 Table!
Harmful Recessive (aa)
37.5%
(6 out of 16)
Matches Gen 2 Table!
❓ Conclusion: How does this prove Inbreeding Depression?
We started with 100% Heterozygosity (Aa). By Generation 2 (Selfing), the healthy Heterozygotes dropped to 25%, and the harmful Recessive phenotype jumped to 37.5%. This rapid appearance of bad traits is Inbreeding Depression.