Which principle says that allele frequencies in a population are stable and is constant generation to generation. `p^(2)+2pq+q^(2) = 1`

Answer

**Step-by-Step Solution:**

1. **Understanding the Question**: The question asks about a principle that states that allele frequencies in a population remain stable and constant from generation to generation, represented by the equation \( p^2 + 2pq + q^2 = 1 \).

2. **Identifying the Principle**: The principle that describes the stability of allele frequencies in a population is known as the Hardy-Weinberg principle.

3. **Explaining Hardy-Weinberg Equilibrium**: According to the Hardy-Weinberg principle, if allele frequencies are the same across generations, the population is said to be in Hardy-Weinberg equilibrium. This means that the genetic variation in a population will remain constant from one generation to the next in the absence of disturbing factors.

4. **Conditions for Hardy-Weinberg Equilibrium**: For a population to be in Hardy-Weinberg equilibrium, certain conditions must be met:
- No mutations
- Random mating
- No natural selection
- Extremely large population size (no genetic drift)
- No gene flow (immigration or emigration)

5. **Understanding the Equation**: The equation \( p^2 + 2pq + q^2 = 1 \) represents the frequencies of the genotypes in a population:
- \( p^2 \) is the frequency of homozygous dominant individuals (AA).
- \( 2pq \) is the frequency of heterozygous individuals (Aa).
- \( q^2 \) is the frequency of homozygous recessive individuals (aa).
- Here, \( p \) is the frequency of the dominant allele (A), and \( q \) is the frequency of the recessive allele (a).

6. **Conclusion**: Therefore, the principle that states that allele frequencies in a population are stable and constant from generation to generation is the Hardy-Weinberg principle.

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