No Selection - Biology

1. Fundamental Concepts

Definition: The Hardy-Weinberg equilibrium is a principle that states allele and genotype frequencies in a population will remain constant from generation to generation in the absence of other evolutionary influences.
Assumptions: No selection, no mutation, no migration, random mating, and large population size.
Equation: $$p^2 + 2pq + q^2 = 1$$ where $$p$$ and $$q$$ are the frequencies of the two alleles in the population.

2. Key Concepts

No Selection: $${\text{No differential survival or reproduction among genotypes}}$$

Genetic Stability: $${\text{Allele frequencies remain constant over generations if no evolutionary forces act upon them}}$$

Application: $${\text{Used to test for genetic drift and natural selection in populations}}$$

3. Examples

Example 1 (Basic)

Problem: In a population, the frequency of the recessive allele ($$q$$) is 0.4. Calculate the expected frequency of the homozygous recessive genotype.

Step-by-Step Solution:

Identify the given value: $$q = 0.4$$
Calculate the frequency of the homozygous recessive genotype: $$q^2 = 0.4^2$$
Compute the result: $$0.4 \cdot 0.4 = 0.16$$

Validation: Given $$q = 0.4$$, then $$q^2 = 0.16$$ which matches the calculated result.

Example 2 (Intermediate)

Problem: If the frequency of the heterozygous genotype ($$2pq$$) is 0.48 in a population, and the frequency of the dominant allele ($$p$$) is 0.7, calculate the frequency of the recessive allele ($$q$$).

Step-by-Step Solution:

Given values: $$2pq = 0.48$$, $$p = 0.7$$
Solve for $$q$$ using the equation $$2pq = 0.48$$: $$2 \cdot 0.7 \cdot q = 0.48$$
Isolate $$q$$: $$q = \frac{0.48}{2 \cdot 0.7} = \frac{0.48}{1.4} = 0.34$$

Validation: Given $$p = 0.7$$ and $$2pq = 0.48$$, solving for $$q$$ yields $$q = 0.34$$, which satisfies the equation.

4. Problem-Solving Techniques

Check Assumptions: Always verify that the conditions for Hardy-Weinberg equilibrium are met before applying the formula.
Use Algebraic Manipulation: Rearrange the Hardy-Weinberg equation to solve for unknown variables.
Substitute Known Values: Plug in known allele frequencies to find missing values.