Question

In a population, there are two morphs, A and B, which reproduce at equal rates. A mutates to B with probability \(p_1\), and B mutates to A with probability \(p_2\) such that \(p_1 \gg p_2\) (that is, \(p_1\) is much greater than \(p_2\)). Over time, which one of the following statements would be true about this population?

• A. Both morphs A and B will become equally abundant.
• B. Morph A will dominate the population.
• C. Morph B will dominate the population.
• D. Both morphs A and B will go extinct.

Hint:

For mutation and population dynamics:
1. Compare transition probabilities between morphs to predict long-term outcomes.
2. The morph with the higher net conversion rate will dominate over time.
3. Consider reproductive rates and mutation rates together to assess population trends.

Answer 1

The Correct Option is C

Step 1: Understand mutation dynamics. In this scenario: Morph A mutates to Morph B with a high probability \(p_1\).
- Morph B mutates to Morph A with a much lower probability \(p_2\).
Over time, the population will tend to shift toward the morph with the higher net conversion rate. Step 2: Long-term population outcome. Since \(p_1 \gg p_2\), Morph A is much more likely to mutate into Morph B than vice versa. As a result: The proportion of Morph B will continuously increase in the population.
Morph B will dominate over time because the transition from A to B is much more frequent than the reverse.
Step 3: Evaluate the options. Option (A): Incorrect. Equal abundance would require \(p_1 = p_2\), which is not the case here.
Option (B): Incorrect. Morph A will not dominate because it transitions to Morph B at a much higher rate.
Option (C): Correct. Morph B will dominate the population due to the high probability \(p_1 \gg p_2\).
Option (D): Incorrect. Extinction of both morphs is not implied, as the morphs are reproducing at equal rates.