Populations

Name: AP Environmental Science Unit 3: Populations
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10–15% of the exam6 lessons · 85 min33 terms

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What this unit covers

The topics below follow the published Env. Science course framework for Unit 3. This unit is worth 10–15% of the exam, so budget your time against that rather than against how long the unit takes to teach.

Population dynamicsSurvivorshipCarrying capacityDemographics

Lessons in this unit

Formulas in Unit 3

Population growth rate

growth rate (%) = [(births + immigration) − (deaths + emigration)] / N × 100

N is the starting population. A positive result means growth; a negative result means decline. If migration is negligible, growth rate ≈ (CBR − CDR) / 10 as a percent.

Matching strategy to curve

r-selected → many offspring, little care → Type III · K-selected → few offspring, much care → Type I

r-strategists bet on quantity and rebound fast; K-strategists bet on quality and recover slowly. Type II (constant mortality) sits between the extremes.

Two kinds of limiting factors

density-dependent: competition, predation, disease · density-independent: weather, natural disasters

If the factor gets worse as the population gets more crowded, it is density-dependent. If it strikes regardless of crowding (usually abiotic events), it is density-independent.

Rule of 70 (doubling time)

doubling time (years) ≈ 70 / annual growth rate (%)

Enter the growth rate as a plain percent number (a 2% rate → 70/2 = 35 years). Only works for steady exponential growth, and the growth rate must be positive.

Growth rate and the rule of 70

growth rate = [(births + immigration) − (deaths + emigration)] / population doubling time ≈ 70 / (% growth per year)

Immigration and emigration are frequently omitted by students and are frequently in the data.

Replacement fertility

TFR ≈ 2.1 for replacement in a low-mortality country; higher where child mortality is high

Above 2.1 means eventual growth, below means eventual decline — but age structure delays both.

Every term in Unit 3

All 33 terms we publish for Populations, with definitions. Reading them through is the fastest way to find the ones you cannot define — then drill those in cram mode until you can produce them without the prompt.

Rule of 70: Doubling time (years) = 70 ÷ percent annual growth rate. Rate of natural increase = (crude birth rate − crude death rate)/10 expressed as a percent. A faster growth rate must always give a SHORTER doubling time.
Population momentum: A population with a very young age structure keeps growing for decades even after fertility falls to replacement, because a huge cohort has yet to enter its reproductive years. A wide-based population pyramid signals built-in future growth.
Generalist vs specialist species: Generalists tolerate a wide range of conditions and diets and adapt to change; specialists are efficient in a narrow niche and vulnerable to disruption.
r-selected species: Many small offspring, little parental care, early maturity, short life. Recover quickly from disturbance and often become invasive.
K-selected species: Few offspring with heavy parental investment, late maturity, long life. Slow to recover from population crashes, so more extinction-prone.
Survivorship curves: Type I high survival until old age, Type II constant mortality, Type III heavy early mortality with few reaching adulthood.
Carrying capacity: The population an environment can sustain indefinitely. Exceeding it causes an overshoot followed by a die-off as resources are depleted.
Population growth rate calculation: r = [(births + immigration) − (deaths + emigration)]/N. APES expects all four terms.
Age structure diagram: A broad base means rapid growth ahead, a column means stability, a narrow base means decline and an aging population.
Total fertility rate: Average children per woman. Replacement level is about 2.1 — above 2 because not every child survives to reproduce.
Demographic transition: Stage 1 high birth and death rates; stage 2 death rate falls and population booms; stage 3 birth rate falls; stage 4 both low and population stabilizes.
Factors that lower birth rates: Education of women, access to family planning, urbanization, lower infant mortality and greater cost of raising children.
Infant mortality rate: Deaths under age one per 1,000 live births. Used as a proxy for healthcare quality and correlates inversely with development.
Calculating percent growth rate: Growth rate (%) = [(births − deaths)/N] × 100, or (CBR − CDR)/10 when using crude rates per 1,000.
Crude birth and death rates: Births or deaths per 1,000 people per year. Subtracting them and dividing by 10 gives the percentage natural increase.
Replacement level fertility: About 2.1 in developed countries and higher where child mortality is greater, since more births are needed for two to survive to adulthood.
IPAT equation: Impact = Population × Affluence × Technology. Explains why a small wealthy population can outweigh a large poor one.
Exponential growth equation: dN/dt = rN, giving a J-shaped curve. Growth is unlimited only while resources are, so exponential growth describes a population in a new or freshly emptied habitat, not a persistent state.
Logistic growth equation: dN/dt = rN(K − N)/K. The bracket is the fraction of carrying capacity still unused, so growth slows as N approaches K and stops at N = K. Growth in absolute numbers is fastest at K/2, not at low N.
Why a logistic curve is S-shaped: At low N there are few reproducers, so absolute growth is small. Near K, competition suppresses per-capita growth. The steepest part is in between, at about half the carrying capacity, which is also the point of maximum sustainable yield.
Overshoot and dieback: A population that grows past carrying capacity degrades the resource base, so it does not settle at K — it crashes below it, sometimes to a lower K than before. Reindeer introduced to St. Matthew Island are the textbook case.
Density-dependent limiting factors: Their effect intensifies as the population gets denser: competition for food, predation, and above all disease transmission. They regulate populations toward carrying capacity.
Density-independent limiting factors: They hit the same proportion of the population regardless of density — floods, fires, hurricanes, hard freezes. They cause crashes but do not regulate a population around a carrying capacity.
Biotic potential: The maximum reproductive rate a species could achieve under ideal conditions. High biotic potential (many offspring, short generation, early maturity) is what makes r-selected species able to recolonize fast after a disturbance.
Net migration rate: Immigrants minus emigrants per 1,000 people. Total population change is (CBR − CDR + net migration)/10 as a percent, so a country can grow while its natural increase is negative — Germany and Japan differ on exactly this term.
What doubling time is really telling you: At 2% growth a population doubles in 35 years, so infrastructure built for today's numbers is half-sized within one working lifetime. The number is useful because it converts an abstract percentage into a planning horizon.
Population pyramid shapes: Wide base and narrow top means rapid growth and a young population; near-vertical sides means stability; a narrow base under a bulging top means decline and an aging population. The shape encodes both past fertility and future momentum.
Dependency ratio: Dependents (under 15 plus over 64) per 100 working-age people. The same ratio can mean a school-building problem or a pension problem, so always say whether the dependents are young or old.
Why replacement fertility is 2.1, not 2.0: Two children replace two parents only if both survive to reproduce and the sex ratio is even. The extra 0.1 covers childhood mortality and the slight male birth surplus; in countries with high infant mortality replacement is higher still.
Why Stage 2 grows fastest: Death rates fall first — sanitation, vaccination, food supply — while birth rates stay high because family-size norms take a generation to shift. The gap between the two curves is the natural increase, and it is widest in Stage 2.
Natural decrease in Stage 5: Deaths exceed births, so natural increase is negative and doubling time is undefined. A shrinking working-age population must fund pensions and health care for a growing elderly one, which is why such countries debate retirement age and immigration.
Female education and fertility: The single strongest predictor of falling total fertility rate. Educated women marry later, have greater access to and use of contraception, and have higher-value alternatives to early childbearing — an effect that shows up within one generation.
Demographic momentum: A country can reach replacement-level fertility and keep growing for decades, because a wide-based pyramid means an unusually large cohort is still entering its childbearing years. Fertility falls first; population stabilizes long afterward.

What examiners penalize here

On the AP exam, "growth rate" almost always wants a percentage: compute the net change, divide by the starting population N, and multiply by 100. Show every step — even a wrong final number earns partial credit if the setup is right. Watch your units and don’t drop the ×100.
Link the concepts in one chain for the exam: r-selected → many offspring, little care → Type III → fast recovery / often invasive. K-selected → few offspring, much care → Type I → slow recovery / often threatened. Being able to run this chain both directions answers most population-strategy questions.
On graphs, carrying capacity K appears as a horizontal line the population fluctuates around. If the curve shoots above the line then plunges, label it overshoot and dieback. If it rises and flattens smoothly onto the line, that is logistic growth reaching K.
Read population pyramids by their base: wide base → growing (young population), straight sides → stable, pinched base → shrinking (aging population). Pair this with the demographic transition — Stage 2 shows the widest base and the fastest growth.
On the demographic transition, state that population grew because **death rates fell**, not because birth rates rose. Most wrong answers assume the opposite, and getting the mechanism right signals you understand the model rather than having memorized a curve.

Practice Env. Science

Our practice bank is drawn from across the whole course rather than filtered to one unit, which is closer to how the exam asks anyway — it will not tell you which unit a question is testing.

168 practice questionsEvery one with a written explanation FRQ trainerWritten answers scored against the rubric Env. Science study guideAll units, weights and score data in one place All 9 Env. Science unitsThe full course

Questions about this unit

How much of the AP Environmental Science exam is Unit 3?

Unit 3, Populations, is worth 10–15% of the Env. Science multiple-choice section according to the published course framework. Across all 9 units that makes it a substantial share — heavier than an even split would give it.

What topics are covered in Env. Science Unit 3?

Populations covers Population dynamics, Survivorship, Carrying capacity and Demographics. We publish 33 terms with definitions for this unit, all of them on this page.

How should I study Env. Science Unit 3?

Read the 6 lessons below first — about 85 minutes — then drill the 33 terms in cram mode until you can produce each definition from memory rather than just recognize it. Recognition is what makes a unit feel finished when it is not. Finish with practice questions and read the explanation for every one you get right by elimination as well as the ones you miss.

All 9 units of AP Environmental Science

Unit names, topics and exam weights follow the published College Board course framework for AP Environmental Science. AP® is a trademark registered by the College Board, which does not endorse this site.