Hardy-Weinberg Equilibrium

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AP Biology › Hardy-Weinberg Equilibrium

Questions 1 - 10
1

A bird population has a beak-shape locus with alleles A and a. In a given year, allele frequencies are $p(A)=0.30$ and $q(a)=0.70$. The population is large, and mating is random with respect to beak shape. A severe drought occurs, and individuals with genotype aa have substantially lower survival to reproduction than individuals with AA or Aa. No migration is detected during the drought year. Assume allele frequencies are measured among the breeders that produce the next generation.

Which change in allele frequency is most likely after one generation?

The frequency of allele A will decrease because selection acts only on homozygous dominant genotypes.

Allele frequencies will oscillate each generation because $p+q$ is less than 1 in drought conditions.

The frequency of allele a will increase because allele a is initially more common than allele A.

Allele frequencies will remain constant because random mating prevents selection from changing $p$ and $q$.

The frequency of allele a will decrease because aa individuals contribute fewer alleles to the next generation.

Explanation

This question assesses the skill of analyzing Hardy-Weinberg equilibrium in populations. The frequency of allele a will decrease because aa individuals have lower survival, contributing fewer a alleles to the next generation and shifting q from 0.70 toward a lower value while p increases from 0.30. This selection against the recessive homozygote alters allele frequencies under non-equilibrium conditions, despite random mating and large population size. No migration reinforces that selection is the driving force for the change in breeders' allele frequencies. A tempting distractor is choice B, which predicts allele a will increase because it is initially more common, stemming from the misconception that majority alleles always rise without considering selection's directional effect. To predict allele frequency changes, calculate relative fitness contributions of genotypes and track allele inputs to the next generation.

2

In a large population, allele $M$ has frequency 0.3 and allele $m$ has frequency 0.7. The population is in Hardy-Weinberg equilibrium. Which expected proportion of individuals carry at least one $M$ allele?

0.09

0.42

0.49

0.51

0.91

Explanation

This question tests Hardy-Weinberg equilibrium analysis by calculating the frequency of individuals carrying at least one dominant allele. With p(M) = 0.3 and q(m) = 0.7, we need MM + Mm frequencies. Under Hardy-Weinberg: MM = p² = 0.09 and Mm = 2pq = 0.42, so MM + Mm = 0.09 + 0.42 = 0.51. Alternatively, we can calculate as 1 - q² = 1 - 0.49 = 0.51, since q² represents individuals with no M alleles. Choice C (0.49) represents mm homozygotes who lack the M allele entirely. To find carriers of at least one dominant allele, calculate 1 - q² or sum the frequencies of both genotypes containing that allele.

3

In a small island population of 50 rabbits, allele F has frequency $p=0.50$ and allele f has frequency $q=0.50$. There is no selection, migration, or mutation, and mating is random. After several generations, allele frequencies differ among replicate island populations founded the same way. Which evolutionary force best explains the differences?

Gene flow equalizing allele frequencies among populations.

Heterozygote advantage maintaining both alleles.

Genetic drift due to small population size.

Nonrandom mating changing allele frequencies directly each generation.

Mutation rapidly converting F alleles into f alleles.

Explanation

This question identifies genetic drift as the evolutionary force causing allele frequency differences in small populations. With only 50 rabbits per island and no selection, migration, or mutation, random sampling effects (genetic drift) cause allele frequencies to fluctuate randomly each generation. Different islands experience different random changes, leading to divergent allele frequencies over time despite identical starting conditions. Option E incorrectly claims nonrandom mating changes allele frequencies directly, but nonrandom mating only affects genotype frequencies within a generation, not allele frequencies across generations. Remember: in small populations, genetic drift causes random allele frequency changes that accumulate over generations, while large populations buffer against these random effects.

4

A mammal population has allele D frequency $p=0.90$ and allele d frequency $q=0.10$. The population is in Hardy-Weinberg equilibrium. Which statement best describes the expected frequency of dd individuals?

It equals $2pq=0.18$.

It equals $pq=0.09$.

It equals $p^2=0.81$.

It equals $q^2=0.01$.

It equals $1-q^2=0.99$.

Explanation

This question tests calculating homozygous recessive frequency under Hardy-Weinberg equilibrium. With allele d frequency q = 0.10, the frequency of dd individuals equals q² = (0.10)² = 0.01, making option B correct. This represents 1% of the population being homozygous recessive. Option A (0.18) represents 2pq, the heterozygote frequency, not the dd frequency—a common error where students confuse different genotype categories. Always match the genotype to its Hardy-Weinberg formula: DD = p², Dd = 2pq, dd = q².

5

In a population of 800 snails, genotype counts are 320 GG, 160 Gg, and 320 gg. The population is large, and there is no mutation, migration, or selection at this locus. Which conclusion is best supported about Hardy-Weinberg equilibrium in this generation?

The population is not in equilibrium because observed heterozygotes are fewer than $2pq$.

The population is in equilibrium because $p=q=0.50$.

The population is not in equilibrium because allele frequencies cannot be computed from counts.

The population is in equilibrium because heterozygotes are exactly half the population.

The population is in equilibrium because homozygotes are equally frequent.

Explanation

This question tests detecting Hardy-Weinberg equilibrium violations by comparing observed and expected heterozygote frequencies. From counts (320 GG, 160 Gg, 320 gg), allele frequencies are p(G) = (640 + 160)/1600 = 0.50 and q(g) = 0.50. Under Hardy-Weinberg, expected Gg frequency = 2pq = 2(0.50)(0.50) = 0.50, meaning 400 heterozygotes expected. With only 160 observed (0.20 frequency vs 0.50 expected), there's a significant heterozygote deficit, indicating the population is not in equilibrium (option C). Option E incorrectly focuses on heterozygotes being "half the population" without checking if this matches 2pq expectations. Remember: even with equal allele frequencies, Hardy-Weinberg predicts specific genotype ratios—always calculate and compare to observations.

6

A population has alleles M and m. Observed genotype frequencies are MM: 0.64, Mm: 0.32, mm: 0.04. Assume Hardy-Weinberg conditions are met. Which allele frequency is most consistent with these data?

$p(M)=0.40$

$p(M)=0.64$

$p(M)=0.32$

$q(m)=0.04$

$q(m)=0.20$

Explanation

This question tests calculating allele frequencies from genotype frequencies under Hardy-Weinberg equilibrium. Given genotype frequencies MM: 0.64, Mm: 0.32, mm: 0.04, we can verify these follow Hardy-Weinberg proportions. Since mm = q² = 0.04, we get q(m) = √0.04 = 0.20 (option B). We can verify: p(M) = 1 - 0.20 = 0.80, so MM = p² = 0.64 ✓ and Mm = 2pq = 2(0.80)(0.20) = 0.32 ✓. Option C (0.40) might result from incorrectly taking the square root of MM frequency (√0.64 = 0.80) and subtracting from 1. Always use the homozygous recessive frequency (q²) to find q directly by taking its square root.

7

A bird population has allele B at frequency $p=0.20$ and allele b at frequency $q=0.80$. The population meets Hardy-Weinberg conditions. Which value is expected for the frequency of heterozygotes (Bb)?

$0.64$

$0.80$

$0.16$

$0.32$

$0.04$

Explanation

This question applies Hardy-Weinberg equilibrium to calculate heterozygote frequency from allele frequencies. Given p(B) = 0.20 and q(b) = 0.80, the frequency of heterozygotes (Bb) under Hardy-Weinberg equilibrium is 2pq = 2(0.20)(0.80) = 0.32. This makes option D correct. Option B (0.04) represents p² (frequency of BB homozygotes), not heterozygotes—a common error where students forget the factor of 2 in the heterozygote formula. Remember the complete Hardy-Weinberg equation: p² + 2pq + q² = 1, where 2pq specifically represents heterozygote frequency.

8

In a population of island lizards, a single locus with alleles T and t affects scale pattern. Before a hurricane, allele frequencies are $p(T)=0.50$ and $q(t)=0.50$. Immediately after the hurricane, only 40 adults remain, and allele frequencies among the survivors are $p(T)=0.65$ and $q(t)=0.35$. The hurricane did not differentially damage habitats based on scale pattern, and no consistent differences in survival among genotypes were observed; the change is attributed to which individuals happened to survive. In the next generation, mating among survivors is random.

Which evolutionary force best explains the allele-frequency change?

Natural selection, because the hurricane favored the T allele over the t allele.

Mutation, because the t allele was converted into the T allele during the hurricane.

Genetic drift, because a chance reduction in population size altered allele frequencies.

Gene flow, because new alleles entered the population after the hurricane.

Nonrandom mating, because survivors must preferentially mate with similar scale patterns.

Explanation

This question assesses the skill of analyzing Hardy-Weinberg equilibrium in populations. Genetic drift best explains the allele-frequency change because the hurricane caused a random reduction in population size to 40 individuals, leading to a chance shift from p(T) = 0.50 to 0.65 and q(t) = 0.50 to 0.35 among survivors. This bottleneck effect alters allele frequencies due to sampling error in small populations, without directional forces like selection or gene flow. The lack of differential survival by genotype and random post-hurricane mating further supports drift as the primary force. A tempting distractor is choice B, which attributes the change to natural selection favoring the T allele, based on the misconception that any environmental event like a hurricane must impose selection, but the question states no genotype-based survival differences. When evaluating evolutionary forces, identify random changes in small populations as genetic drift and rule out selection without evidence of fitness differences.

9

In a population of flowering plants, petal pigment is influenced by alleles R and r at one locus. Researchers estimate allele frequencies as $p(R)=0.80$ and $q(r)=0.20$. The population is large, and no differences in survival or fecundity among genotypes are detected. However, pollen-transfer observations show that pollinators move primarily between nearby plants, and plants occur in clustered patches separated by open ground. Genotype frequencies in the combined population show a deficit of heterozygotes compared with $2pq$.

Which Hardy-Weinberg condition is most directly violated?

Large population size, because $p=0.80$ indicates a small population.

Random mating, because limited pollen movement can increase mating among nearby relatives.

No mutation, because patchy plant distributions increase mutation rates at the R locus.

No selection, because heterozygote deficits always indicate selection against heterozygotes.

No gene flow, because clustered patches guarantee alleles move between patches each generation.

Explanation

This question assesses the skill of analyzing Hardy-Weinberg equilibrium in populations. Random mating is most directly violated because limited pollen movement between clustered patches increases mating among nearby relatives, leading to a deficit of heterozygotes compared to the expected 2pq = 2(0.80)(0.20) = 0.32. This nonrandom mating disrupts genotype frequency expectations without necessarily changing allele frequencies p = 0.80 and q = 0.20. The patchy distribution promotes inbreeding, violating the random mating assumption despite large population size and no selection. A tempting distractor is choice E, which claims no selection is violated because heterozygote deficits indicate selection against them, based on the misconception that deviations always imply selection, but inbreeding can cause similar patterns without fitness differences. When heterozygote deficits occur, evaluate mating patterns or population structure before assuming selection as a transferable strategy.

10

A population of freshwater snails has a shell-band gene with alleles S and s. In a sample of 500 snails, the genotype counts are 245 SS, 210 Ss, and 45 ss. From these counts, allele frequencies are $p(S)=0.70$ and $q(s)=0.30$. If the population were in Hardy-Weinberg equilibrium, expected genotype frequencies would be $p^2=0.49$, $2pq=0.42$, and $q^2=0.09$. The observed genotype frequencies are 0.49 SS, 0.42 Ss, and 0.09 ss. No migration into or out of the pond is detected during the sampling interval.

Which conclusion is best supported by the data?

The population is not in equilibrium because the SS genotype must be less common than the Ss genotype.

The population is in Hardy-Weinberg equilibrium because observed and expected genotype frequencies match closely.

The population is not in equilibrium because the allele frequencies are not $p=0.50$ and $q=0.50$.

The population is not in equilibrium because the heterozygote frequency equals $2pq$ only by coincidence.

The population is in equilibrium only if mutation is increasing the s allele frequency each generation.

Explanation

This question assesses the skill of analyzing Hardy-Weinberg equilibrium in populations. The population is in Hardy-Weinberg equilibrium because the observed genotype frequencies of 0.49 SS, 0.42 Ss, and 0.09 ss closely match the expected frequencies of p² = (0.70)² = 0.49, 2pq = 2(0.70)(0.30) = 0.42, and q² = (0.30)² = 0.09. These allele frequencies p = 0.70 and q = 0.30 remain consistent with no deviations, and the absence of migration supports equilibrium conditions. The matching frequencies indicate no violations of assumptions like random mating or no selection. A tempting distractor is choice A, which states the population is not in equilibrium because allele frequencies are not p = q = 0.50, arising from the misconception that equilibrium requires equal allele frequencies, but Hardy-Weinberg holds for any p and q as long as conditions are met. To assess equilibrium, compute expected genotype frequencies from observed allele frequencies and compare them to observed counts for discrepancies.

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