Populations
Unit 3 of AP Environmental Science, worth 10–15% of the exam. 13 questions below, each with the working. Every answer was checked by a second pass before it was published.
Generalist and specialist species, K- and r-selected species, survivorship curves, carrying capacity, population growth, age structure, human population dynamics.
How this unit is tested
Start by sorting the unit into two halves: species-level concepts (generalist/specialist, r- and K-selected traits, survivorship curves) and population-level math (exponential and logistic growth, carrying capacity, age structure, human demographics). The species-level half is mostly about matching traits to categories, so build a two-column comparison table in your head — niche breadth, reproductive rate, offspring number, parental care, body size, lifespan — and practice sorting example organisms into it rather than memorizing lists.
For the math half, know the two growth equations cold and understand what each symbol does physically: r is the intrinsic growth rate, N is current population size, K is carrying capacity. Exponential growth assumes no limits and produces a J-curve; logistic growth includes the (K−N)/K term that throttles growth as the population approaches K, producing an S-curve. AP free-response questions frequently ask you to plug numbers into dN/dt = rN(K−N)/K, so practice the arithmetic, not just the concept.
For age structure and human population, learn to read a pyramid shape (wide base = growing, columnar = stable, narrow base = declining) and connect it to the demographic transition model's four stages, since exam questions often give you a diagram or a scenario and ask which stage or growth pattern it represents. Always tie your answer back to a mechanism — falling death rates, contraceptive access, industrialization — rather than just naming a stage.
When answering FRQs, use precise vocabulary (carrying capacity, density-dependent, replacement-level fertility) and always explain the 'why,' since AP graders reward mechanistic reasoning over a bare label.
What you have to know
Exponential growth model
$\dfrac{dN}{dt} = rN$, where population growth rate is proportional to current population size and intrinsic growth rate r; produces unlimited J-shaped growth.
Logistic growth model
$\dfrac{dN}{dt} = rN\left(\dfrac{K-N}{K}\right)$, where growth slows as population size N approaches carrying capacity K, producing an S-shaped curve.
Rule of 70
Doubling time (in years) ≈ 70 divided by the annual percentage growth rate.
Population growth rate formula
Growth rate = (births − deaths + immigration − emigration), usually expressed per 1000 individuals per year or converted to a percentage.
Carrying capacity (K)
The maximum population size of a species that an environment can sustain indefinitely given available resources such as food, water, space, and mates.
13 practice questions
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A species that can tolerate a wide range of environmental conditions and eat many different foods is best described as a:
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Answer. Generalist species
Generalist species have a broad niche and flexible resource use, which lets them survive habitat disturbance better than specialists. Raccoons and coyotes are classic examples. -
Explain why specialist species are more vulnerable to extinction than generalist species when their habitat is disturbed.
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Answer. Specialists depend on a narrow set of resources or conditions, so if that specific food source or habitat is altered or destroyed, they have no alternative to fall back on.
Generalists can shift to other food sources or habitats when conditions change, but specialists like the koala (which relies almost exclusively on eucalyptus) cannot adapt quickly, making them prone to population decline or extinction. -
A population of mice reproduces early, produces large litters, provides minimal parental care, and experiences high offspring mortality. Is this population r-selected or K-selected? Justify your answer.
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Answer. r-selected
The combination of early reproduction, large litter size, low parental investment, and high offspring mortality matches the r-selected strategy, which compensates for high individual death rates by producing many offspring quickly. -
Which survivorship curve type is typical of species like humans and elephants that have low infant mortality and most individuals surviving to old age?
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Answer. Type I
Type I curves are convex, showing high survival through early and middle life with mortality concentrated in old age. This pattern is associated with K-selected species that provide extensive parental care. -
Describe the shape of a Type III survivorship curve and give an example organism.
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Answer. A Type III curve drops steeply at the start, showing very high mortality among young offspring, then levels off for the few survivors that reach adulthood; fish and insects (e.g., oysters) are typical examples.
This pattern reflects r-selected life history: producing huge numbers of offspring with almost no parental care, so most die young but the rare survivors face relatively low mortality afterward. -
Define carrying capacity and describe what typically happens to a population when it exceeds K.
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Answer. Carrying capacity is the maximum population size an environment can sustain indefinitely; when a population overshoots K, resources become depleted and the population usually experiences a die-off (crash) back toward or below K.
Overshoot occurs because population growth has momentum (reproducing individuals continue adding offspring even as resources run low), so the correction is often a sharp decline rather than a smooth leveling off. -
Using the logistic growth equation dN/dt = rN(K−N)/K, calculate the population growth rate for a population with N = 500, K = 1000, and r = 0.3 per year.
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Answer. 75 individuals per year
Plug in values: dN/dt = 0.3 × 500 × (1000−500)/1000 = 0.3 × 500 × 0.5 = 75. Growth rate is highest at intermediate population sizes and slows as N approaches K. -
Which type of population growth curve is J-shaped and occurs when resources are effectively unlimited?
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Answer. Exponential growth
Exponential growth follows dN/dt = rN with no limiting term, producing a J-shaped curve that accelerates indefinitely, unlike logistic growth which levels off near carrying capacity. -
An age structure diagram with a wide base and a narrow top most likely indicates:
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Answer. A rapidly growing population with high birth rates
A wide base means a large proportion of young individuals about to enter reproductive age, which predicts continued rapid population growth as they mature and reproduce. -
Explain what population momentum means and why a country's population can keep growing even after its fertility rate falls to replacement level.
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Answer. Population momentum is continued population growth caused by a large number of young people already in or approaching their reproductive years, even after fertility rates drop; because that large cohort will still have children, total births exceed deaths for years before growth stabilizes.
This explains why countries with a history of high birth rates see population size keep rising for a generation or more after fertility policy successfully reduces the TFR to replacement level. -
Define total fertility rate (TFR) and state the approximate replacement-level TFR for developed countries.
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Answer. TFR is the average number of children a woman is expected to have over her reproductive lifetime; the replacement level in developed countries is about 2.1 children per woman.
The extra 0.1 above 2.0 accounts for children who do not survive to reproductive age themselves, ensuring the population exactly replaces itself across generations. -
According to the demographic transition model, in which stage do death rates fall sharply while birth rates remain high, causing rapid population growth?
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Answer. Stage 2
In Stage 2, improvements in sanitation, medicine, and food supply reduce death rates quickly, but cultural norms keep birth rates high, creating a large gap between births and deaths and rapid population growth. -
List two density-dependent limiting factors and two density-independent limiting factors on population growth.
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Answer. Density-dependent: disease/predation and competition for food (their effect intensifies as population density increases). Density-independent: natural disasters (e.g., wildfire, flood) and extreme weather (their effect is unrelated to population size).
Density-dependent factors regulate populations more strongly as crowding increases, while density-independent factors can reduce a population regardless of how many individuals are present, illustrating two different mechanisms limiting growth.
What people get wrong
- Memorizing r-selected and K-selected trait lists without understanding why — instead, reason from the strategy: r-selected species gamble on quantity (many offspring, little care) because their environment is unstable, while K-selected species invest in quality (few offspring, high care) because their environment is stable near carrying capacity.
- Treating carrying capacity as a fixed number — instead, remember K can rise or fall with resource availability, climate, disease, or human impact, and populations can temporarily overshoot K before crashing.
- Mixing up Type I and Type III survivorship curves — instead, anchor each to a concrete example: Type I (humans, elephants) loses individuals mostly in old age; Type III (fish, insects) loses most offspring early, with few reaching adulthood.
- Assuming logistic growth stops abruptly at K — instead, recognize that dN/dt gradually approaches zero as N approaches K because of the (K−N)/K term, not because growth halts instantly.
- Reading an age structure diagram only by its width at the base — instead, compare the full shape (base, middle, top) to judge whether the population is growing, stable, or shrinking, since a wide base alone doesn't guarantee continued rapid growth if fertility is already falling.
- Assuming global population growth rate matches that of any single developing country — instead, remember that global growth rate has been declining even though total population continues rising due to population momentum from a large existing youth cohort.
Drill this unit until it sticks
These questions come back on a schedule built from what you get wrong, alongside the rest of AP Environmental Science. Free, and no account needed to start.