How can we tell whether a population is evolving at a gene?
Topic 7.5 Hardy-Weinberg Equilibrium: use the Hardy-Weinberg equations to calculate allele and genotype frequencies and test whether a population is evolving.
A focused answer to AP Biology Topic 7.5, covering the Hardy-Weinberg conditions, the equations p + q = 1 and p squared plus 2pq plus q squared = 1, and how to calculate and interpret allele and genotype frequencies, with worked calculations.
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What this topic is asking
The College Board (Topic 7.5) wants you to use the Hardy-Weinberg equations to calculate allele and genotype frequencies, state the conditions for equilibrium, and use the model to test whether a population is evolving at a gene.
The equations and conditions
How to use it
The recessive phenotype (aa) is the only one you can count directly from phenotypes, so it gives ; take the square root to get , then find , then and . You cannot find directly from the dominant phenotype, because the dominant phenotype includes both homozygous dominant () and heterozygous () individuals, which look the same. This is why every Hardy-Weinberg problem starts from the recessive phenotype.
The five conditions map neatly onto the five mechanisms of evolution from the population-genetics topic. "No mutation" rules out new alleles, "no gene flow" rules out migration, "no selection" rules out differential reproduction, "random mating" rules out non-random mating, and "very large population" rules out genetic drift. Because each condition blocks one mechanism, a deviation from the predicted frequencies points to which mechanism is acting, which is what makes the model such a useful null hypothesis for detecting evolution.
The model is also useful for estimating the frequency of carriers of a recessive condition in a population, which is why it is applied in genetic counselling and conservation. Even though the conditions are rarely fully met, the predictions are often close enough to be informative, and large differences are the signal worth investigating.
Try this
Q1. State the two Hardy-Weinberg equations. [1 point]
- Cue. and .
Q2. Explain how the Hardy-Weinberg model can show that a population is evolving. [2 points]
- Cue. It predicts the genotype frequencies expected if the population is not evolving; if the observed frequencies differ significantly, one of the five conditions is violated, so the population is evolving at that gene.
Exam-style practice questions
Practice questions written in the style of College Board exam questions on this dot point, with worked answer explainers. The year tag is the paper they imitate, not the source.
AP 2020 (style)4 marksSection II (long FRQ excerpt, statistics). In a population in Hardy-Weinberg equilibrium, 9% of individuals are homozygous recessive (aa) for a trait. (a) Calculate the frequencies of the recessive and dominant alleles. (b) Calculate the percentage of the population that are heterozygous carriers (Aa).Show worked answer →
A 4-point Hardy-Weinberg calculation FRQ.
(a) Calculate (2 points): (1 point) , so ; (1 point) .
(b) Calculate (2 points): (1 point) heterozygotes are ; (1 point) , so 42% are carriers.
Markers reward taking the square root of to get , finding , and using for the heterozygotes.
AP 2017 (style)1 marksSection I (multiple choice). Which of the following is a condition required for a population to remain in Hardy-Weinberg equilibrium? (A) Natural selection is occurring. (B) The population is very small. (C) There is no gene flow (no migration). (D) Mating is non-random.Show worked answer →
The correct answer is (C).
Hardy-Weinberg equilibrium requires no gene flow, no mutation, no natural selection, random mating, and a very large population. Options (A), (B) and (D) each violate a condition, so they would cause allele frequencies to change.
Related dot points
- Topic 7.4 Population Genetics: explain how natural selection, mutation, gene flow, genetic drift and non-random mating change allele frequencies.
A focused answer to AP Biology Topic 7.4, covering the gene pool, allele frequencies, and the five mechanisms of microevolution (selection, mutation, gene flow, genetic drift, non-random mating), including bottleneck and founder effects, with a worked allele-frequency calculation.
- Topic 7.1 Introduction to Natural Selection: explain the conditions required for natural selection and how it leads to changes in a population.
A focused answer to AP Biology Topic 7.1, covering Darwin's reasoning, the conditions for natural selection (variation, heritability, overproduction, differential reproduction), fitness, and how selection changes allele frequencies, with a worked example.
- Topic 5.3 Mendelian Genetics: apply the laws of segregation and independent assortment to predict genotype and phenotype ratios.
A focused answer to AP Biology Topic 5.3, covering the laws of segregation and independent assortment, Punnett squares, monohybrid and dihybrid crosses, and the chi-square test for goodness of fit, with worked calculations.
- Topic 7.12 Variations in Populations: explain why genetic variation within a population is important for survival and the response to environmental change.
A focused answer to AP Biology Topic 7.12, covering the sources and importance of genetic diversity, how variation buffers populations against change, the risks of low diversity, and the role of variation in evolution, with a worked example.
- Topic 7.10 Speciation: explain how reproductive isolation leads to speciation, including allopatric and sympatric speciation.
A focused answer to AP Biology Topic 7.10, covering the biological species concept, reproductive isolation (prezygotic and postzygotic barriers), allopatric and sympatric speciation, and rates of speciation, with a worked example.
Sources & how we know this
- AP Biology Course and Exam Description — College Board (2020)