Gene Pools & Allele Frequency

The Principle: The Hardy-Weinberg principle states that allele and genotype frequencies in a population will remain constant from generation to generation in the absence of evolutionary influences. This theoretical state of 'genetic equilibrium' provides a baseline against which real-world population changes can be measured.

Mathematical Foundation: The principle is expressed through two linked equations. The first, $p + q = 1$, accounts for all alleles in the pool, while the second, $p^2 + 2pq + q^2 = 1$, accounts for all possible genotypes in a diploid population.

Required Conditions: For equilibrium to hold, the population must be large, mating must be random, and there must be no mutation, migration (gene flow), or natural selection. If any of these conditions are violated, allele frequencies will likely shift, indicating that evolution is occurring.

Step 1: Identify the Recessive Phenotype: In most problems, you must start with the frequency of the homozygous recessive individuals ($q^2$). This is because the recessive phenotype is the only one where the genotype is known with certainty (e.g., individuals showing the trait must be $aa$).

Step 2: Calculate q: Once $q^2$ is known, take the square root to find the frequency of the recessive allele ($q$). This value represents the proportion of the recessive allele in the total gene pool.

Step 3: Calculate p: Use the relationship $p = 1 - q$ to find the frequency of the dominant allele ($p$). This allows you to then calculate the frequencies of the homozygous dominant ($p^2$) and heterozygous ($2pq$) genotypes.

The $q^2$ Rule: Always look for the frequency of the recessive phenotype first. Students often mistakenly use the dominant phenotype frequency as $p^2$, but the dominant phenotype includes both $p^2$ and $2pq$ individuals, making it an unreliable starting point.

Check the Units: Ensure you distinguish between 'number of individuals' and 'frequency'. If a question gives you the number of individuals, you must divide by the total population size to get the frequency before applying the Hardy-Weinberg equations.

Sanity Check: Remember that $p + q$ must always equal $1$. If your calculated allele frequencies do not sum to unity, there is a calculation error in your square root or subtraction steps.

The Heterozygote Coefficient: A frequent error is forgetting the '2' in the $2pq$ term for heterozygotes. Because there are two ways to form a heterozygote (dominant from mother/recessive from father, or vice versa), the frequency is doubled compared to a simple product of $p$ and $q$.

Dominance vs. Frequency: A common misconception is that dominant alleles will naturally increase in frequency over time. In reality, dominance only describes how an allele is expressed in a phenotype; it does not determine whether the allele will become more common in the gene pool.