This lesson is squarely in the population-biology domain, about one-third of the CLEP exam. The math stays conceptual — you will square and multiply small decimals in your head. The bigger payoff is understanding what Hardy-Weinberg is a baseline for: it defines "no evolution" so that any deviation flags a mechanism at work.
A population's gene pool is all the alleles of all genes in that population. We describe it with frequencies: - Allele frequencies: for a gene with two alleles, we call them p and q, and p + q = 1. - Genotype frequencies: the proportions of each genotype (homozygous dominant, heterozygous, homozygous recessive).
Hardy-Weinberg describes a non-evolving population — allele frequencies stay constant across generations. It holds only when all five conditions are met: 1. No mutation 2. No gene flow (no migration in or out) 3. Random mating 4. No natural selection 5. Very large population (no drift)
If these hold, genotype frequencies follow:
p² + 2pq + q² = 1
| Term | Genotype | Meaning |
|---|---|---|
| p² | Homozygous dominant | frequency of the dominant homozygote |
| 2pq | Heterozygous | frequency of carriers |
| q² | Homozygous recessive | frequency of the recessive homozygote |
The point of the equilibrium is conceptual: it is the null model. If real frequencies drift away from these values, something — selection, drift, migration, mutation, or nonrandom mating — is driving evolution.
Two moves cover most CLEP items: - Given q, find p with p = 1 − q (since p + q = 1). - Square or multiply to get genotype proportions: q² for homozygous recessive, 2pq for heterozygotes.
Example: if q = 0.2, then p = 0.8; homozygous recessives = q² = 0.04; heterozygotes = 2pq = 2(0.8)(0.2) = 0.32.
Anything that breaks a Hardy-Weinberg condition can change allele frequencies:
| Mechanism | What it does |
|---|---|
| Mutation | Introduces entirely new alleles (the ultimate source of variation) |
| Gene flow | Movement of alleles between populations; tends to make them more similar |
| Genetic drift | Random frequency change, strong in small populations |
| Nonrandom mating | Alters genotype proportions (e.g., mate choice) |
Two special cases of drift: - Bottleneck effect — a population is drastically reduced (often by a random catastrophe), and the survivors' allele frequencies differ from the original. - Founder effect — a few individuals start a new population, which reflects only those founders' alleles.
1. D — All the alleles of all genes present in the population. Fix: The gene pool is the complete set of alleles available in a population. - A: Population size counts individuals, not alleles. - B: The gene pool includes recessive and dominant alleles alike. - C: Expressed traits are phenotypes, not the allele pool. - E: One individual's chromosome count is not the whole population's genetic pool. - Fix rule: Gene pool = every allele of every gene in the whole population.
2. C — 0.7. Fix: Since p + q = 1, p = 1 − 0.3 = 0.7. - A: 0.09 is q², a genotype frequency, not p. - B: 0.49 is p², not the allele frequency itself. - D: 0.3 repeats q instead of subtracting it from 1. - E: 0.91 is (1 − q²) and has no direct meaning here. - Fix rule: p = 1 − q; don't confuse an allele frequency with a squared genotype term.
3. B — No mutation, no gene flow, random mating, no selection, and a large population. Fix: All five conditions must hold for allele frequencies to stay constant. - A: Strong selection changes frequencies, breaking equilibrium. - C: Small populations experience drift, breaking equilibrium. - D: Nonrandom mating shifts genotype proportions, breaking equilibrium. - E: Frequent gene flow alters allele frequencies, breaking equilibrium. - Fix rule: Equilibrium = the "no-evolution" checklist of five conditions, all met.
4. A — 0.04. Fix: Homozygous recessive frequency is q² = 0.2 × 0.2 = 0.04. - B: 0.20 is q itself, not q². - C: 0.32 is 2pq (the heterozygotes), not q². - D: 0.16 comes from mistakenly squaring 0.4; with q = 0.2 the recessive homozygote is 0.2², not this value. - E: 0.64 is p² (0.8²), the homozygous dominant frequency. - Fix rule: Homozygous recessive = q²; square the recessive allele frequency.
5. D — 0.48. Fix: Heterozygote frequency is 2pq = 2 × 0.6 × 0.4 = 0.48. - A: 0.16 is q² (the homozygous recessives). - B: 0.36 is p² (the homozygous dominants). - C: 0.24 is pq, forgetting the factor of 2. - E: 0.60 simply repeats p. - Fix rule: Heterozygotes = 2pq; never forget the 2.
6. E — The population is not evolving at that locus. Fix: Constant allele frequencies over generations is the definition of no evolution at that gene. - A: Rapid evolution would change the frequencies, not hold them constant. - B: Strong selection would shift frequencies, not maintain them. - C: Small size promotes drift and change, not stability. - D: Many mutations would introduce change over time. - Fix rule: Frequencies unchanged across generations = no evolution there.
7. D — Genetic drift. Fix: Random, directionless change in allele frequencies, pronounced in small populations, is genetic drift. - A: Selection is non-random and favors particular traits. - B: Gene flow requires movement between populations, not internal chance. - C: Mutation adds new alleles; it is not the random resampling described. - E: "Directional adaptation" implies a consistent selective direction, unlike random drift. - Fix rule: Random frequency change, no direction, small population = drift.
8. E — The bottleneck effect. Fix: A random catastrophe slashes the population, and the survivors' frequencies differ from the original — a bottleneck. - A: The founder effect starts a new population from a few colonists, not a catastrophe on the original. - B: There is no "gene flow effect"; no migration is described. - C: The deaths are random, not selection favoring a trait. - D: Mutation does not describe a sudden loss of most individuals. - Fix rule: Catastrophe crushes a population → survivors' skewed frequencies = bottleneck.
9. A — The founder effect. Fix: A few individuals starting a new population carry only a sample of the original alleles — the founder effect. - B: The bottleneck effect involves a crash of an existing population, not colonization. - C: Gene flow is ongoing exchange, not a one-time founding event. - D: Stabilizing selection is about favoring intermediates, not colonization sampling. - E: Frequencies here shift by chance; equilibrium is not maintained. - Fix rule: A few colonists found a new population → founder effect.
10. E — Make the allele frequencies of the two populations more similar. Fix: Migration plus interbreeding mixes alleles, pulling the two populations' frequencies together. - A: Gene flow reduces, not increases, differences between populations. - B: Gene flow tends to prevent speciation by keeping gene pools connected. - C: It blends variation between groups; it does not erase all variation. - D: Introducing alleles from another population does change frequencies. - Fix rule: Gene flow = a homogenizer; it makes populations more alike.
11. C — Mutation. Fix: Mutation is the only listed process that creates brand-new alleles. - A: Drift only reshuffles the frequencies of existing alleles. - B: Nonrandom mating changes genotype proportions, not the allele menu. - D: The bottleneck effect removes alleles by chance; it does not create new ones. - E: The founder effect samples existing alleles; it adds nothing new. - Fix rule: New alleles come only from mutation; the rest just rearrange what's there.
12. B — Meiosis and fertilization, through recombination and independent assortment. Fix: Sexual reproduction shuffles existing alleles via crossing over, independent assortment, and the random union of gametes, creating new combinations each generation. - A: Binary fission is asexual and produces clones, not new combinations. - C: Replication errors are mutations (new alleles), not recombination of existing ones. - D: Drift changes frequencies randomly; it does not generate new allele combinations within offspring. - E: Mitosis copies cells faithfully, producing no new combinations. - Fix rule: New combinations of existing alleles = meiosis + fertilization (recombination and assortment).
1. D — All the alleles of all genes present in the population. Fix: The gene pool is the complete set of alleles available in a population. - A: Population size counts individuals, not alleles. - B: The gene pool includes recessive and dominant alleles alike. - C: Expressed traits are phenotypes, not the allele pool. - E: One individual's chromosome count is not the whole population's genetic pool. - Fix rule: Gene pool = every allele of every gene in the whole population.
2. C — 0.7. Fix: Since p + q = 1, p = 1 − 0.3 = 0.7. - A: 0.09 is q², a genotype frequency, not p. - B: 0.49 is p², not the allele frequency itself. - D: 0.3 repeats q instead of subtracting it from 1. - E: 0.91 is (1 − q²) and has no direct meaning here. - Fix rule: p = 1 − q; don't confuse an allele frequency with a squared genotype term.
3. B — No mutation, no gene flow, random mating, no selection, and a large population. Fix: All five conditions must hold for allele frequencies to stay constant. - A: Strong selection changes frequencies, breaking equilibrium. - C: Small populations experience drift, breaking equilibrium. - D: Nonrandom mating shifts genotype proportions, breaking equilibrium. - E: Frequent gene flow alters allele frequencies, breaking equilibrium. - Fix rule: Equilibrium = the "no-evolution" checklist of five conditions, all met.
4. A — 0.04. Fix: Homozygous recessive frequency is q² = 0.2 × 0.2 = 0.04. - B: 0.20 is q itself, not q². - C: 0.32 is 2pq (the heterozygotes), not q². - D: 0.16 comes from mistakenly squaring 0.4; with q = 0.2 the recessive homozygote is 0.2², not this value. - E: 0.64 is p² (0.8²), the homozygous dominant frequency. - Fix rule: Homozygous recessive = q²; square the recessive allele frequency.
5. D — 0.48. Fix: Heterozygote frequency is 2pq = 2 × 0.6 × 0.4 = 0.48. - A: 0.16 is q² (the homozygous recessives). - B: 0.36 is p² (the homozygous dominants). - C: 0.24 is pq, forgetting the factor of 2. - E: 0.60 simply repeats p. - Fix rule: Heterozygotes = 2pq; never forget the 2.
6. E — The population is not evolving at that locus. Fix: Constant allele frequencies over generations is the definition of no evolution at that gene. - A: Rapid evolution would change the frequencies, not hold them constant. - B: Strong selection would shift frequencies, not maintain them. - C: Small size promotes drift and change, not stability. - D: Many mutations would introduce change over time. - Fix rule: Frequencies unchanged across generations = no evolution there.
7. D — Genetic drift. Fix: Random, directionless change in allele frequencies, pronounced in small populations, is genetic drift. - A: Selection is non-random and favors particular traits. - B: Gene flow requires movement between populations, not internal chance. - C: Mutation adds new alleles; it is not the random resampling described. - E: "Directional adaptation" implies a consistent selective direction, unlike random drift. - Fix rule: Random frequency change, no direction, small population = drift.
8. E — The bottleneck effect. Fix: A random catastrophe slashes the population, and the survivors' frequencies differ from the original — a bottleneck. - A: The founder effect starts a new population from a few colonists, not a catastrophe on the original. - B: There is no "gene flow effect"; no migration is described. - C: The deaths are random, not selection favoring a trait. - D: Mutation does not describe a sudden loss of most individuals. - Fix rule: Catastrophe crushes a population → survivors' skewed frequencies = bottleneck.
9. A — The founder effect. Fix: A few individuals starting a new population carry only a sample of the original alleles — the founder effect. - B: The bottleneck effect involves a crash of an existing population, not colonization. - C: Gene flow is ongoing exchange, not a one-time founding event. - D: Stabilizing selection is about favoring intermediates, not colonization sampling. - E: Frequencies here shift by chance; equilibrium is not maintained. - Fix rule: A few colonists found a new population → founder effect.
10. E — Make the allele frequencies of the two populations more similar. Fix: Migration plus interbreeding mixes alleles, pulling the two populations' frequencies together. - A: Gene flow reduces, not increases, differences between populations. - B: Gene flow tends to prevent speciation by keeping gene pools connected. - C: It blends variation between groups; it does not erase all variation. - D: Introducing alleles from another population does change frequencies. - Fix rule: Gene flow = a homogenizer; it makes populations more alike.
11. C — Mutation. Fix: Mutation is the only listed process that creates brand-new alleles. - A: Drift only reshuffles the frequencies of existing alleles. - B: Nonrandom mating changes genotype proportions, not the allele menu. - D: The bottleneck effect removes alleles by chance; it does not create new ones. - E: The founder effect samples existing alleles; it adds nothing new. - Fix rule: New alleles come only from mutation; the rest just rearrange what's there.
12. B — Meiosis and fertilization, through recombination and independent assortment. Fix: Sexual reproduction shuffles existing alleles via crossing over, independent assortment, and the random union of gametes, creating new combinations each generation. - A: Binary fission is asexual and produces clones, not new combinations. - C: Replication errors are mutations (new alleles), not recombination of existing ones. - D: Drift changes frequencies randomly; it does not generate new allele combinations within offspring. - E: Mitosis copies cells faithfully, producing no new combinations. - Fix rule: New combinations of existing alleles = meiosis + fertilization (recombination and assortment).