Biology for AP Courses · Population and Community Ecology
Population Demography
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In 30 seconds
A population is a group of individuals of the same species living in the same area at the same time. Demography is the statistical study of populations — their size, density, distribution, Age structure Proportion of a population in each age class Full entry →, and the rates of birth, death, and movement that change them. Where a single organism has a life story, a population has statistics: size (N), density, Dispersion How individuals are spaced: clumped, uniform, or random Full entry →, age structure, and growth rate.
Demographers use two complementary tools. Life tables and survivorship curves summarize how survival and reproduction change with age. Growth models — exponential and logistic — describe how population size changes through time and why populations cannot grow unchecked forever. The same mathematics describe bacteria, deer, and human populations. Population size changes through births, deaths, immigration, and emigration — the four flows demography tracks.
Why this matters
Conservation biologists use population size, density, and age structure to decide whether a species is endangered; wildlife managers use Mark–recapture Sample, mark, release, resample to estimate mobile populations Full entry → and survivorship data to set hunting quotas; epidemiologists track disease spread with the same mathematics. Censuses and age pyramids determine how many schools and hospitals a country must build. For the AP Biology exam, demography questions test both concepts and calculation — survivorship curves, dispersion patterns, and exponential versus logistic growth are perennial topics.
The college version
Core Concepts
Size, density, and dispersion
Population size (N) is the total number of individuals; density is N divided by the area they occupy. Density matters because crowding changes competition, disease, and reproduction. Dispersion describes how individuals are arranged in space: clumped (the most common — patchy resources or social grouping, as in fish schools), uniform (competition or territoriality, as in nesting penguins), and random (evenly available resources, no attraction or repulsion, as in some wind-dispersed plants).
Sampling: quadrats and mark–recapture
For sessile (non-moving) organisms such as plants, they use quadrats — randomly placed frames of known area — and multiply the average count per quadrat by the total area. For mobile animals, they use mark–recapture: capture, mark, release, let them mix back in, then recapture. The commonly taught Lincoln–Petersen estimate is N = (M × C) / R, where M is the number first marked, C the number captured the second time, and R the number recaptured. The method assumes marks are not lost, animals mix evenly, and capture does not change behavior — assumptions often violated in the field.
Life tables and survivorship curves
A life table tracks a cohort (a group born at the same time) and records how many survive to each age and how many offspring each age class produces. Plotting survivors against age gives a Survivorship curve Plot of surviving individuals versus age (Types I, II, III) Full entry →, with three idealized shapes. Type I: most individuals survive to old age — humans, elephants. Type II: a constant chance of death at every age — a straight diagonal line, many birds. Type III: extremely high mortality early in life, the few survivors living long — typical of trees and insects.
Age structure: a snapshot with a crystal ball
Age structure is the proportion of a population in each age class, displayed as an age pyramid. A wide base — many young individuals — signals a growing population; roughly equal bars signal a stable one; a narrow base signals a declining one. Because the future parents are already present in the pyramid, age structure predicts short-term growth.
Exponential growth: the J-curve
If resources are unlimited and conditions constant, a population grows by a fixed percentage per unit time — a J-shaped curve. The commonly taught equation is dN/dt = rN, where N is population size, t is time, and r is the intrinsic rate of increase — per-capita growth (births minus deaths). Bacteria in a fresh culture and invasive species in new habitat grow exponentially at first — but it cannot last.
Logistic growth and carrying capacity: the S-curve
Real populations hit limits — food, water, space, disease, and waste. The logistic growth model adds a brake: dN/dt = rN((K − N)/K), where K is the carrying capacity — the maximum population size the environment can sustain. When N is tiny, (K − N)/K is near 1 and growth is nearly exponential; as N approaches K, growth slows; at N = K, it stops. The result is an S-shaped curve. Populations tend to stabilize near K, oscillate around it, or overshoot and crash if they exceed it.
Common Confusions
| Do not confuse | With | Difference |
|---|---|---|
| Population size (N) | Population density | N is the total count; density is N per unit area |
| Exponential growth | Logistic growth | Exponential is unchecked (J-curve); logistic slows and stops at carrying capacity (S-curve) |
| r (intrinsic rate of increase) | K (carrying capacity) | r is per-capita growth rate; K is the maximum sustainable population size |
| Type I survivorship | Type III survivorship | Type I: most die old (humans); Type III: most die young (trees, insects) |
| Mark–recapture formula | M × R / C | The estimate is N = (M × C) / R — more recaptures (R) means a smaller estimated population |
| Wide-base age pyramid | Narrow-base pyramid | Wide base = many young = growing; narrow base = few young = declining |
| Immigration | Emigration | Immigration is individuals entering; emigration is individuals leaving |
Eli explains
The same idea, in plain words
Explain it like I’m 10
Demography is like taking attendance for a whole school: how many students, how crowded the classrooms, how the kids are spread out, and how many are in each grade. If the kindergarten classes are huge, you know the school will grow for years. Counting a few classrooms and multiplying tells you about the whole school — that's how scientists count fish in a lake or deer in a forest without counting every one.
Worked example
A wildlife biologist wants to estimate the deer population of a 50 km² reserve. She traps and marks 40 deer (M = 40), releases them, and two weeks later captures 50 deer (C = 50), of which 10 are marked (R = 10). Using the Lincoln–Petersen estimate, N = (M × C) / R = (40 × 50) / 10 = 200 deer — a density of 4 deer per km². For logistic thinking: the reserve supports a carrying capacity of about K = 400 deer, with intrinsic rate of increase r = 0.4 per year. At N = 200, dN/dt = 0.4 × 200 × ((400 − 200)/400) = 80 × 0.5 = 40 deer added per year; at N = 380, dN/dt = 0.4 × 380 × (20/400) ≈ 7.6 per year — growth nearly stops as N approaches K. That slowdown is the S-curve in action: the herd hovers near carrying capacity rather than doubling.
Key takeaways
- Population = same species, same area, same time.
- Dispersion: clumped (patchy resources/social), uniform (territoriality), random (even resources, no interaction).
- Quadrats for sessile organisms; mark–recapture (N = M×C/R) for mobile ones.
- Survivorship curves: Type I (late death, humans), Type II (constant mortality, birds), Type III (early death, trees/insects).
- Age pyramids: wide base = growing; equal bars = stable; narrow base = declining.
- Exponential growth: dN/dt = rN (J-curve); logistic growth: dN/dt = rN((K−N)/K) (S-curve, slows at carrying capacity K).
- Four engines of change: births, deaths, immigration, emigration.
Check yourself
6 review questions from the chapter. Try each one, then open the answer.
A population of 500 fish lives in a 100-hectare lake. What is its density, and why does density matter ecologically?
Show answer
Density = 500/100 = 5 fish per hectare. Crowding affects competition, disease transmission, and reproductive success.
In a mark–recapture study, 30 animals are marked and released; a second capture of 60 animals includes 12 marked ones. Estimate N.
Show answer
N = (M × C) / R = (30 × 60) / 12 = 150 individuals.
Which survivorship curve describes most trees, and what life-history traits produce it?
Show answer
Type III — huge numbers of offspring, very high early mortality, and the few survivors living long.
Write the exponential and logistic growth equations and identify what each symbol means.
Show answer
Exponential: dN/dt = rN (N = population size, t = time, r = intrinsic per-capita growth rate). Logistic: dN/dt = rN((K − N)/K), adding K = carrying capacity.
If a population is at 900 individuals and K = 1,000 with r = 0.2, what is dN/dt, and what does the answer tell you?
Show answer
dN/dt = 0.2 × 900 × ((1,000 − 900)/1,000) = 180 × 0.1 = 18 individuals per time unit — growth is slowing as the population nears carrying capacity.
How can an age pyramid predict a country's future need for schools?
Show answer
A wide base (many young) means many future parents and continued growth, so more schools will be needed; a narrow base predicts fewer school-age children.
Study tools & related lessonsKey vocabulary · Related
Key vocabulary
- Population density
- Number of individuals per unit area or volume
- Dispersion
- How individuals are spaced: clumped, uniform, or random
- Mark–recapture
- Sample, mark, release, resample to estimate mobile populations
- Survivorship curve
- Plot of surviving individuals versus age (Types I, II, III)
- Age structure
- Proportion of a population in each age class
- Intrinsic rate of increase (r)
- Per-capita growth rate: births minus deaths per individual
- Carrying capacity (K)
- Maximum population size an environment can sustain
Sources & references
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