The Scenario

• Two alleles: A1 and A2

• Initial frequencies:

  • A1: 0.6

  • A2: 0.4

• Mutation rates:

  • A1 → A2: μ = 1×10−51×10−5

  • A2 → A1: v = 2×10−52×10−5

• Population: Infinitely large, no selection, drift, or migration

Step 1: The Formula for Equilibrium Frequency

The equilibrium frequency of allele A1 (p∗p∗) under bidirectional mutation is:

p∗=vμ+vp∗=μ+vv

• $v$ = mutation rate from A2 to A1

• $\mu$ = mutation rate from A1 to A2

Step 2: Substitute the Given Values

p∗=2×10−51×10−5+2×10−5p∗=1×10−5+2×10−52×10−5p∗=2×10−53×10−5=23≈0.67p∗=3×10−52×10−5=32≈0.67

Step 3: Match With the Provided Options

• (1) 1.0

• (2) 0.5

• (3) 0.67

• (4) 0.33

The correct answer is (3) 0.67.

Why This Matters

• Predicts genetic stability: Shows how mutation rates alone can determine stable allele frequencies in the absence of other forces.

• Useful in conservation and evolutionary biology: Helps understand how rare alleles can persist or disappear over time.

Conclusion

When two alleles mutate back and forth at different rates, the equilibrium frequency is determined by the ratio of the reverse mutation rate to the sum of both mutation rates. For the given rates, the equilibrium frequency of allele A1 is 0.67.