Populations

• Allele Frequency Equation: For a gene with two alleles (dominant $p$ and recessive $q$), the sum of their frequencies must equal 1. This is expressed as:

$p + q = 1$

• Genotype Frequency Equation: This equation describes the distribution of genotypes in a population. It is derived from the expansion of $(p+q)^2$ and is expressed as:

$p^2 + 2pq + q^2 = 1$

• Variable Definitions: In these equations, $p^2$ represents the frequency of the homozygous dominant genotype, $2pq$ represents the frequency of the heterozygous genotype, and $q^2$ represents the frequency of the homozygous recessive genotype.

• The $q^2$ Starting Point: In practical applications, you almost always start calculations with $q^2$ because individuals showing the recessive phenotype are the only ones whose genotype is known with certainty (they must be homozygous recessive).

• Identify the Given Value: Always check if the question provides the frequency of an allele ($p$ or $q$) or a genotype/phenotype ($p^2$, $2pq$, or $q^2$). Misidentifying these is the most common source of error.

• The Square Root Step: If you are given the percentage of the population with a recessive trait, convert it to a decimal ($q^2$) and take the square root to find $q$ before attempting to find $p$.

• Sanity Checks: Ensure that $p + q$ always equals 1 and that $p^2 + 2pq + q^2$ also equals 1. If your calculated frequencies do not sum to unity, there is an error in your arithmetic.

• Confusing $q$ and $q^2$: Students often use the frequency of the recessive phenotype as $q$ instead of $q^2$. Remember that the phenotype is the result of the genotype ($q^2$), not the single allele ($q$).

• Assuming HW Equilibrium: The Hardy-Weinberg principle only applies if specific conditions are met (e.g., no selection, large population). In reality, these conditions are rarely all satisfied, but the model serves as a vital null hypothesis for detecting evolution.

• Small Populations: In small populations, chance events (genetic drift) can cause large fluctuations in allele frequencies, violating the Hardy-Weinberg assumption of a 'large population' and leading to inaccurate predictions.