Hardy-Weinberg Equilibrium

The model uses two primary equations to describe the relationship between alleles and genotypes in a population with two alleles ($A$ and $a$).

Allele Frequency Equation

• Formula: $p + q = 1$
• Variables: $p$ represents the frequency of the dominant allele, and $q$ represents the frequency of the recessive allele. This equation accounts for the total gene pool.

Genotype Frequency Equation

• Formula: $p^2 + 2pq + q^2 = 1$
• Variables: $p^2$ is the frequency of homozygous dominant individuals ($AA$), $2pq$ is the frequency of heterozygous individuals ($Aa$), and $q^2$ is the frequency of homozygous recessive individuals ($aa$).

• Step 1: Identify the Recessive Phenotype: Always start with the individuals showing the recessive trait. Because the recessive phenotype only results from the homozygous recessive genotype ($aa$), its frequency in the population is equal to $q^2$.

• Step 2: Calculate q: Take the square root of the recessive phenotype frequency to find the frequency of the recessive allele ($q = \sqrt{q^2}$).

• Step 3: Calculate p: Use the allele frequency equation to find the dominant allele frequency ($p = 1 - q$).

• Step 4: Determine other Genotypes: Square $p$ to find the frequency of homozygous dominant individuals ($p^2$) and multiply $2 \times p \times q$ to find the frequency of heterozygotes ($2pq$).

• Step 5: Verify: Ensure that $p^2 + 2pq + q^2$ sums to approximately $1.0$ to check for calculation errors.

It is critical to distinguish between allele frequencies and genotype frequencies to avoid calculation errors.

• The 'q-first' Rule: In almost every exam problem, you must solve for $q$ first. You cannot solve for $p$ directly from the dominant phenotype because that phenotype includes both $p^2$ and $2pq$ individuals.

• Check the Question: Pay close attention to whether the question asks for the frequency of the allele (just $p$ or $q$) or the genotype/population percentage ($p^2$, $2pq$, or $q^2$).

• Sanity Check: Allele frequencies ($p$ and $q$) must always be between $0$ and $1$. If you calculate a value greater than $1$, you have likely confused a population count with a frequency.

• Percentage vs. Frequency: If a problem gives a percentage (e.g., $16\%$), convert it to a decimal frequency ($0.16$) before performing any square root or multiplication operations.