AP Environmental Science Populations — Worked Answer Explanations

Unit 3 · 12 questions explained

Below is a complete answer key for our AP Environmental Science Populations practice questions. For each question you'll find the correct choice, a full written explanation of how to get there, and — for every wrong answer — a short note on exactly why it's tempting and where it goes wrong. Reading these straight through is one of the fastest ways to find the gaps in a unit before exam day.

Prefer to test yourself first? Take the timed Populations practice test and come back here to review, or head back to the Populations unit overview.

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Question 1 · Easy
A population that initially grows slowly, then rapidly, then slows again as it approaches the environment's carrying capacity (K), is exhibiting:
- A
  Exponential (J-curve) growth
  Why not A: Exponential growth accelerates continuously and does not level off at K.
- B
  Logistic (S-curve) growthCorrect
- C
  Boom-and-bust population cycling
  Why not C: Boom-and-bust involves overshoot and crash past K, not smooth leveling off.
- D
  Linear growth
  Why not D: Linear growth adds the same number of individuals each time period regardless of population size.
Explanation
Logistic growth follows the equation dN/dt = rN(K−N)/K. As the population (N) approaches carrying capacity (K), the growth rate slows and levels off, producing an S-shaped (sigmoid) curve. This models resource limitation and density-dependent factors that increase as population density grows.

Key takeaway
Logistic growth = S-curve; slows as population approaches K (carrying capacity).
Question 2 · Easy
Dandelions produce thousands of lightweight seeds and have short life spans, reaching maturity quickly. This reproductive strategy classifies them as:
- A
  K-selected species
  Why not A: K-selected species produce few offspring, mature slowly, and invest heavily in each offspring — the opposite of dandelions.
- B
  r-selected speciesCorrect
- C
  Keystone species
  Why not C: Keystone species have disproportionate ecosystem impacts; this is an ecological role, not a reproductive strategy.
- D
  Indicator species
  Why not D: Indicator species signal environmental quality; this is also an ecological role, not a reproductive strategy.
Explanation
r-selected species maximize intrinsic rate of increase (r): many offspring, rapid maturation, small body size, little parental care, short lifespan. They thrive in variable, disturbed environments where population growth speed matters more than competitive ability. Examples: dandelions, mice, insects, annual plants. K-selected species (elephants, humans, whales) do the opposite.

Key takeaway
r-selected: many offspring, fast maturity, little care. K-selected: few offspring, slow maturity, high investment.
Question 3 · Medium
A population of 1,000 rabbits grows at an annual rate of 3.5%. Using the Rule of 70, approximately how many years will it take for the population to double?
- A
  10 years
  Why not A: 10 years corresponds to a 7% growth rate (70/7 = 10), not 3.5%.
- B
  20 yearsCorrect
- C
  35 years
  Why not C: 35 is the rate itself; the Rule of 70 divides 70 by the rate, not the other way around.
- D
  200 years
  Why not D: 200 years would imply a 0.35% growth rate, not 3.5%.
Explanation
The Rule of 70 (also called the doubling time formula) states: doubling time (years) = 70 ÷ annual growth rate (%). Here: 70 ÷ 3.5 = 20 years. This rule approximates exponential growth and is widely used in ecology and human demography.

Key takeaway
Doubling time ≈ 70 ÷ annual growth rate (%). Rule of 70.
Question 4 · Medium
A wildlife biologist documents that in a white-tailed deer population, mortality is highest during the first year of life and then remains relatively low and constant throughout adulthood. This describes a:
- A
  Type I survivorship curve
  Why not A: Type I describes low early mortality and high late-life mortality — typical of humans and large mammals with parental care.
- B
  Type II survivorship curve
  Why not B: Type II shows constant mortality rate at all ages — a straight line on a log-scale survivorship graph.
- C
  Type III survivorship curveCorrect
- D
  Type IV survivorship curve
  Why not D: There is no standard Type IV survivorship curve in ecology.
Explanation
Type III survivorship curves show very high early mortality (most individuals die young) with survivors then experiencing lower mortality rates. This is common in species that produce many offspring with little parental care (fish, oysters, oaks releasing acorns). While deer do provide some parental care, fawns face very high first-year predation — making this scenario match Type III.

Key takeaway
Type I = low early death (humans). Type II = constant death (birds). Type III = high early death (oysters, trees, many fish).
Question 5 · Medium
Country X has high birth rates, high death rates, and a young population with rapid growth. Country Y has low birth rates, low death rates, and a stable or slightly declining population. According to the demographic transition model, Country X is in _______ and Country Y is in _______.
- A
  Stage 4; Stage 1
  Why not A: Stage 4 has low birth AND low death rates with stable population — the reverse of Country X.
- B
  Stage 1; Stage 4Correct
- C
  Stage 2; Stage 3
  Why not C: Stage 2 has falling death rates but high birth rates (rapid growth); Stage 3 has falling birth rates — neither exactly matches.
- D
  Stage 3; Stage 2
  Why not D: Stage 3 has low death rates and declining birth rates; Stage 2 has still-high birth rates and falling death rates — reversed from what's described.
Explanation
The demographic transition model has four stages. Stage 1: high CBR, high CDR, near-zero growth (pre-industrial). Stage 2: CDR falls (medicine, sanitation) but CBR stays high → rapid growth. Stage 3: CBR falls as urbanization and education rise → slower growth. Stage 4: both rates low, stable population. Country X fits Stage 1; Country Y fits Stage 4.

Key takeaway
Stage 1: high BR + high DR = slow growth. Stage 4: low BR + low DR = stable. Industrialization drives the transition.
Question 6 · Medium
An age structure diagram (population pyramid) showing a very wide base (large proportion of young people) and narrow top (few elderly) indicates that the population will:
- A
  Decline in the near future because birth rates must be falling.
  Why not A: A wide base means many young people who will enter reproductive age, signaling future growth, not decline.
- B
  Remain stable because births balance deaths.
  Why not B: A wide base indicates more people entering reproductive age than leaving it — growth, not stability.
- C
  Grow rapidly in the future as the large young cohort reaches reproductive age.Correct
- D
  Experience population aging and decline like many European nations.
  Why not D: Population aging is shown by a narrow base and wide top (inverted pyramid), not a wide base.
Explanation
A wide-based pyramid means a large proportion of the population is pre-reproductive. As this cohort ages into reproductive years, it will produce many births even if per-capita fertility rates decline — a phenomenon called population momentum. This explains why population growth continues even after replacement-level fertility is reached.

Key takeaway
Wide-based pyramid → population momentum → future growth even if birth rates fall to replacement level.
Question 7 · Medium
Which factor is a density-DEPENDENT limiting factor for a deer population?
- A
  A severe drought that kills vegetation across the entire habitat
  Why not A: Drought affects all individuals regardless of population density — this is a density-INDEPENDENT factor.
- B
  A volcanic eruption that destroys forest habitat
  Why not B: A catastrophic event kills regardless of density — density-independent.
- C
  Disease spread that intensifies as deer congregate at shrinking water sourcesCorrect
- D
  A severe winter freeze that kills all age classes equally
  Why not D: Temperature extremes affect populations regardless of density — density-independent.
Explanation
Density-dependent factors intensify as population density increases. Disease transmission rate rises when animals crowd together (e.g., at shrinking water holes), making disease spread density-dependent. Other density-dependent factors: food competition, predation (predators focus on abundant prey), and intraspecific competition for territory. Density-independent factors (weather, fire, pollution) kill proportionally regardless of population size.

Key takeaway
Density-dependent: competition, disease, predation — effects worsen at high density. Density-independent: weather, fire — effect is same regardless of density.
Question 8 · Medium
Which of the following human demographic trends is associated with Stage 3 of the demographic transition?
- A
  High crude birth rate and high crude death rate
  Why not A: High CBR and CDR characterize Stage 1 (pre-industrial).
- B
  Rapidly falling death rates while birth rates remain high
  Why not B: Falling CDR with still-high CBR describes Stage 2, which produces the highest population growth rates.
- C
  Declining birth rates with already-low death ratesCorrect
- D
  Very low birth rates and slightly negative population growth
  Why not D: Negative growth (CBR < CDR) occurs in some Stage 4 or Stage 5 countries, not Stage 3.
Explanation
Stage 3 of the demographic transition is characterized by declining fertility (CBR falls) as countries urbanize, improve women's education and access to family planning, and shift from agricultural to industrial economies. Death rates are already low from Stage 2 gains. Population continues to grow but more slowly as the gap between CBR and CDR narrows.

Key takeaway
Stage 3: CDR already low, CBR declining → slowing growth. Urbanization and women's education drive falling fertility.
Question 9 · Medium
Total fertility rate (TFR) in a country falls from 4.2 to 2.1 children per woman. If TFR remains at 2.1, what will eventually happen to the population size (assuming no migration)?
- A
  Immediate population decline begins as soon as TFR reaches 2.1.
  Why not A: Due to population momentum (the large young cohort), population continues to grow even after reaching replacement TFR.
- B
  Population stabilizes immediately at its current size.
  Why not B: Stabilization takes decades, not immediate; momentum from age structure drives continued growth.
- C
  Population continues to grow for decades due to momentum, then stabilizes.Correct
- D
  Population grows exponentially because 2.1 children replaces both parents.
  Why not D: TFR 2.1 is approximately replacement level; exponential growth requires TFR significantly above 2.1.
Explanation
A TFR of ~2.1 is replacement-level fertility (each generation exactly replaces itself, accounting for some childhood mortality). However, population momentum means a country with many young people will continue growing for 40–70 years even at TFR 2.1, because the large youth cohort hasn't yet reproduced. Only after those generations pass through will population stabilize.

Key takeaway
TFR = 2.1 = replacement level, but population momentum causes continued growth for decades due to large youth cohorts.
Question 10 · Hard
A population of 500 deer occupies a 50 km² forest. Biologists find 40 births and 20 deaths in one year, with 5 deer immigrating and 10 emigrating. What is the net change in the population over the year?
- A
  ΔN = +15Correct
- B
  ΔN = +20
  Why not B: 20 is births minus deaths only (40−20); it ignores immigration and emigration.
- C
  ΔN = +25
  Why not C: 25 adds births and immigration (40+5=45) but forgets to subtract deaths and emigration.
- D
  ΔN = −15
  Why not D: A negative sign would indicate population decline; the birth rate exceeds death rate enough to yield net growth.
Explanation
Population change: ΔN = (Births − Deaths) + (Immigration − Emigration). ΔN = (40 − 20) + (5 − 10) = 20 + (−5) = +15. The population grows from 500 to 515. This formula is fundamental: population size depends on all four demographic processes.

Key takeaway
ΔN = (B − D) + (I − E). All four processes — births, deaths, immigration, emigration — affect population size.
Question 11 · Hard
A population of 200 squirrels lives in a woodland. Ecologists estimate the carrying capacity of that woodland at 400 squirrels. Using logistic growth, at what population size would the growth rate be at its maximum?
- A
  At N = 400 (at carrying capacity)
  Why not A: At N = K, the (K−N)/K term equals zero, so growth rate = 0.
- B
  At N = 200 (at K/2)Correct
- C
  At N = 1 (at the very start of growth)
  Why not C: At very small N, per-capita rate is highest but the number of reproducing individuals is so low that total growth rate is minimal.
- D
  At N = 600 (above K)
  Why not D: Above K, population growth rate is negative (population declines); it cannot be at maximum above K.
Explanation
In logistic growth (dN/dt = rN(K−N)/K), the growth rate is maximized at N = K/2. At this point, the product N(K−N) is maximized mathematically. With K = 400, maximum growth occurs at N = 200. This insight is used in fisheries management — harvesting a population down to K/2 maximizes sustainable yield.

Key takeaway
Maximum population growth rate in logistic growth occurs at N = K/2 (half the carrying capacity).
Question 12 · Hard
Wolves were reintroduced to a habitat with an existing deer population of 800. The area's carrying capacity for deer is 600. Based on logistic growth principles, what should happen to the deer population over the next few years even WITHOUT wolves?
- A
  Deer population grows because there are many individuals to reproduce.
  Why not A: Above K, the (K−N)/K term is negative, making the growth rate negative — the population declines even without predators.
- B
  Deer population declines toward 600 due to density-dependent resource limitation.Correct
- C
  Deer population remains stable at 800 because it has already reached equilibrium.
  Why not C: 800 > K (600), so the population is above equilibrium and will decline, not stay stable.
- D
  Deer population crashes to zero because the habitat is degraded past recovery.
  Why not D: K = 600 means the habitat can support 600 deer; a crash to zero is not predicted by logistic growth.
Explanation
When N > K in the logistic growth model, dN/dt = rN(K−N)/K is negative (since K−N < 0). The population declines back toward K. With N = 800 and K = 600, density-dependent factors (food competition, disease) increase death rates and reduce birth rates until the population returns to ~600 even without wolf predation.

Key takeaway
In logistic growth, populations above K decline; populations below K grow. K is a stable equilibrium.