The Hardy-Weinberg principle cannot operate if

Options

A. a population does not migrate for a longtime to a new habitat
B. frequent mutations occur in the population
C. the population has no change of interaction with other populations
D. free interbreeding occurs among all membres of the population.

Explanation

### Step-by-Step Solution

1. **Understanding the Hardy-Weinberg Principle**: The Hardy-Weinberg principle states that allele frequencies in a population will remain constant from generation to generation in the absence of evolutionary influences. This principle is based on several assumptions, including random mating, no mutations, no migration, large population size, and no selection.

2. **Identifying Factors that Disturb Equilibrium**: The equilibrium can be disturbed by several factors:
- Non-random mating
- Mutations
- Migration (gene flow)
- Genetic drift (in small populations)
- Natural selection

3. **Analyzing the Given Options**:
- **Option 1**: A population does not migrate for a long time to a new habitat. This would support the Hardy-Weinberg equilibrium as it maintains allele frequencies.
- **Option 2**: Frequent mutations occur in a population. This would disturb the equilibrium because mutations introduce new alleles, changing allele frequencies.
- **Option 3**: A population has no chance of interaction with other populations. This would also support stability, similar to option 1.
- **Option 4**: Free interbreeding occurs among all members. This promotes random mating, which supports Hardy-Weinberg equilibrium.

4. **Conclusion**: The only situation among the options that would prevent the Hardy-Weinberg principle from operating is when frequent mutations occur in a population. This is because mutations alter the genetic makeup and allele frequencies, leading to instability.

### Final Answer
The Hardy-Weinberg principle cannot operate if **frequent mutations occur in a population**.

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