Step-by-Step Reasoning: Is This Population Evolving?

Scenario: A population of 500 birds has 120 white birds (recessive) and 380 coloured birds. Five years later: 100 white, 400 coloured. Is this population evolving?

Step 1: Calculate initial allele frequencies (Year 0)

$q^{2}$ = 120/500 = 0.24 → q = √0.24 ≈ 0.49
p = 1 - 0.49 = 0.51

Step 2: Calculate expected H-W genotype frequencies at Year 0

Expected AA = $p^{2}$ × 500 = (0.51)^{2} × 500 = 0.26 × 500 = 130
Expected Aa = 2pq × 500 = 2 × 0.51 × 0.49 × 500 = 0.50 × 500 = 250
Expected aa = $q^{2}$ × 500 = 0.24 × 500 = 120
Total = 130 + 250 + 120 = 500 ✓

Step 3: Calculate Year 5 allele frequencies

$q^{2}$ = 100/500 = 0.20 → q = √0.20 ≈ 0.447
p = 1 - 0.447 = 0.553

Step 4: Compare allele frequencies across years

Year 0: q = 0.49
Year 5: q = 0.447
Change: q decreased by ~0.04

Step 5: Conclusion

Allele frequency has changed → the population IS evolving.
Likely cause: selection against white birds (directional selection) OR
genetic drift (if the population size is insufficient for H-W stability).

Step 6: Identify the H-W condition violated

If predators selectively eat white birds → "No natural selection" condition violated
If population size is small → "Large population" condition violated
Both could operate simultaneously

General Reasoning Framework

1. Calculate $q^{2}$ from recessive phenotype frequency → get q
2. Calculate p → calculate expected frequencies
3. Compare observed vs expected (chi-square if needed)
4. Deviation → identify which H-W condition is violated
5. Name the evolutionary force driving change