Hardy-Weinberg Equilibrium — AP Biology
1. What Is Hardy-Weinberg Equilibrium? ★★☆☆☆ ⏱ 3 min
Hardy-Weinberg Equilibrium (HWE, also called the Hardy-Weinberg principle or law) is a null model in population genetics that describes a population that is not evolving. In a population at HWE, allele and genotype frequencies remain constant across generations, in the absence of any evolutionary forces.
According to the AP Biology CED, HWE is a key topic within Unit 7 (Natural Selection), making up approximately 10-15% of the unit's exam weight. It appears in both multiple choice (MCQ) and free response (FRQ) sections of the AP exam.
Exam tip: Expect 1-2 MCQ and at least a partial FRQ question testing HWE concepts on your AP exam.
2. Core Hardy-Weinberg Equations and Frequency Calculation ★★☆☆☆ ⏱ 4 min
HWE is built on two core equations for bi-allelic loci, which is the only case AP Biology regularly tests. The first comes from the fact that the sum of all allele frequencies at a locus must equal 1 (100% of all alleles):
p + q = 1
The second equation for genotype frequencies comes directly from the product rule of probability. For a diploid individual, to get a homozygous dominant genotype (AA), you must inherit one A allele from each parent. The probability of inheriting A from each parent is $p$, so the probability of AA is $p \times p = p^2$. For homozygous recessive (aa), the same logic gives $q^2$. For heterozygotes, there are two possible combinations: A from mother + a from father, or a from mother + A from father. This gives $pq + qp = 2pq$. Summing these gives the second core equation:
p^2 + 2pq + q^2 = 1
Exam tip: Always start with $q^2$ when you know the recessive phenotype frequency. Only recessive individuals have a known genotype from their phenotype—dominant phenotypes can be either homozygous or heterozygous, so you cannot use their frequency directly to find $p$.
3. Hardy-Weinberg Equilibrium Core Assumptions ★★★☆☆ ⏱ 3 min
HWE only holds if five core assumptions are met. If any assumption is violated, allele and genotype frequencies will change across generations, meaning the population is evolving and is not in HWE. The key purpose of these assumptions is to define the null case: any deviation from HWE predictions means at least one assumption is broken, and evolution is occurring.
- No mutation: No new alleles are created or modified at the locus.
- No genetic drift: The population is infinitely large, so random sampling of alleles does not cause frequency changes.
- No gene flow: No individuals enter or leave the population, so no alleles are gained or lost.
- Random mating: Individuals choose mates without reference to their genotype at the locus.
- No natural selection: All genotypes have equal survival and reproductive fitness (no genotype is more likely to reproduce than another).
Exam tip: When asked to identify a violated assumption, match the scenario directly: mating preference = non-random mating, migration = gene flow, new trait = mutation, small population = genetic drift, differential survival/reproduction = natural selection.
4. Chi-Square Testing for HWE Deviation ★★★★☆ ⏱ 4 min
To formally test whether observed genotype frequencies differ significantly from HWE predictions, we use a chi-square goodness-of-fit test. The null hypothesis ($H_0$) is that the population is in HWE (no significant deviation, no evolution). The alternative hypothesis ($H_A$) is that the population is not in HWE (significant deviation, evolution is occurring). For bi-allelic HWE tests, degrees of freedom are always 1 (3 genotypes minus 2 estimated parameters: p and q). If your calculated chi-square value is larger than the critical value (usually 3.84 for p=0.05, df=1), you reject the null hypothesis and conclude the population is not in HWE.
Exam tip: Always use df = number of genotypes - 2 for HWE chi-square tests, not the default df = number of categories - 1 used for other chi-square tests. This is one of the most commonly tested mistakes on the AP exam.
5. AP Style Concept Check ★★★☆☆ ⏱ 3 min
Common Pitfalls
Why: Students confuse the frequency of the recessive allele ($q$) with the frequency of the recessive genotype ($q^2$).
Why: Students forget there are two distinct ways to inherit a heterozygous genotype, one from each parent.
Why: Students associate evolution with natural selection, but any broken HWE assumption causes deviation.
Why: Most chi-square tests use $df = categories - 1$, but HWE requires an extra correction because we estimate two parameters (p and q) from the data.
Why: Students associate "dominant" inheritance with "dominant (common) frequency" from basic Mendelian genetics.
Why: Students skip the step of calculating p from total alleles and use observed p directly.