Random Mating - Biology

1. Fundamental Concepts

Definition: Random mating is a condition in the Hardy-Weinberg equilibrium where individuals mate without preference for certain traits.
Assumptions: No natural selection, no mutation, no migration, and large population size are also assumed.
Equilibrium Condition: The gene pool remains constant from generation to generation.

2. Key Concepts

Gene Frequency Calculation: $p + q = 1$

Hardy-Weinberg Equation: $p^2 + 2pq + q^2 = 1$

Application: Used to predict allele frequencies in populations under ideal conditions

3. Examples

Example 1 (Basic)

Problem: In a population, the frequency of the recessive allele (q) is 0.4. Calculate the frequency of the dominant allele (p).

Step-by-Step Solution:

Use the equation: $p + q = 1$
Substitute q = 0.4: $p + 0.4 = 1$
Solve for p: $p = 1 - 0.4 = 0.6$

Validation: Substitute p = 0.6 and q = 0.4 into $p + q = 1$: 0.6 + 0.4 = 1 ✓

Example 2 (Intermediate)

Problem: If the frequency of homozygous recessive individuals (q²) is 0.16 in a population, calculate the frequency of heterozygous individuals (2pq).

Step-by-Step Solution:

First, find q: $q^2 = 0.16 \Rightarrow q = \sqrt{0.16} = 0.4$
Calculate p using $p + q = 1$: $p = 1 - 0.4 = 0.6$
Calculate 2pq: $2pq = 2 \cdot 0.6 \cdot 0.4 = 0.48$

Validation: Substitute p = 0.6 and q = 0.4 into $2pq = 0.48$: 2 * 0.6 * 0.4 = 0.48 ✓

4. Problem-Solving Techniques

Visual Strategy: Use pie charts to represent allele frequencies visually.
Error-Proofing: Always check if the sum of all allele frequencies equals 1.
Concept Reinforcement: Practice with different scenarios to understand the impact of each assumption on the Hardy-Weinberg equilibrium.