Measuring populations
Ecologists study population dynamics: how populations change in size, density and age structure over time.
Ways to estimate population size:
| Method | How it works | Best for |
|---|---|---|
| Quadrat sampling | Count individuals in sample squares and scale up | Plants, slow-moving animals |
| Mark–recapture | Capture, mark, release, then recapture | Mobile animals |
| Transect | Count along a line | Changes across a gradient |
| Aerial or camera surveys | Count from above or with trail cameras | Large animals |
Mark–recapture formula (Lincoln–Petersen index):
N = (M × C) ÷ R
where M = number marked first, C = total caught second time, R = marked animals recaptured.
Example: 40 fish are marked. Later, 50 are caught and 8 are marked. N = (40 × 50) ÷ 8 = 250 fish.
Growth models
Exponential growth
When resources are unlimited, populations grow at a constant per-capita rate:
dN/dt = rN
where r is the intrinsic growth rate and N is population size. This gives a J-shaped curve. Exponential growth occurs briefly, for example when a species colonizes a new habitat or after a disturbance.
Logistic growth
In reality, resources run short. Logistic growth slows as N approaches the carrying capacity (K):
dN/dt = rN × (K − N) ÷ K
- When N is small, growth is nearly exponential.
- When N = K/2, growth is fastest.
- When N = K, growth stops.
This gives an S-shaped (sigmoid) curve.
Limiting factors
| Type | Examples | How effect changes with density |
|---|---|---|
| Density-dependent factor | Competition, predation, disease, parasites, waste build-up | Stronger in dense populations |
| Density-independent factor | Weather, natural disasters, fires, human habitat destruction | Unrelated to density |
Density-dependent factors create negative feedback that tends to keep populations near K.
Life-history strategies
| Trait | r-selected species | K-selected species |
|---|---|---|
| Offspring number | Many | Few |
| Offspring size | Small | Large |
| Parental care | Little or none | Extensive |
| Maturity | Early | Late |
| Lifespan | Short | Long |
| Population size | Fluctuates widely | Stable, near K |
| Examples | Insects, mice, dandelions | Elephants, whales, humans, oaks |
Most species fall somewhere between these extremes.
Survivorship curves
| Type | Pattern | Example |
|---|---|---|
| Type I | Most survive to old age | Humans, elephants |
| Type II | Constant death rate at all ages | Many birds, lizards |
| Type III | Most die young; few survive | Fish, frogs, oak trees |
Predator–prey dynamics
The Lotka–Volterra model predicts linked oscillations in predator and prey populations, with predator peaks lagging behind prey peaks. Real data, like the Canada lynx and snowshoe hare cycles recorded in fur trade records, show similar 8–11 year cycles, though food supply for hares also plays a role.
Human population growth
- The world population reached 1 billion around 1804 and passed 8 billion in November 2022.
- Growth was nearly exponential through the 20th century thanks to improved agriculture, medicine and sanitation.
- Growth rates are now slowing as birth rates fall in most countries. The United Nations projects a peak of roughly 10.3 billion in the 2080s.
- Age-structure diagrams show proportions of people in each age group. A wide base means rapid growth; a narrow base means slow growth or decline.
- The demographic transition model describes how countries shift from high birth and death rates to low ones as they industrialize.
Earth’s carrying capacity for humans is debated, because it depends on technology, consumption and how resources are shared.
Common mistakes
- Thinking K never changes. Carrying capacity changes with the environment.
- Mixing up r (growth rate) and K (carrying capacity).
- Assuming exponential growth can continue indefinitely.
Try it yourself
- Researchers mark 60 rabbits. Later they catch 45, of which 9 are marked. Estimate the population.
- A population has r = 0.5 per year and K = 1000. Calculate the growth rate when N = 100 and when N = 900. Explain the difference.
- Classify a sea turtle and a gorilla as more r- or K-selected, giving two reasons each.
(Answers: 300 rabbits; 45 per year and 45 per year, because growth is slowed by crowding near K but limited by small size when N is low)
Quick recap
- Population size can be estimated by sampling and mark–recapture.
- Exponential growth makes a J-curve; logistic growth makes an S-curve levelling at K.
- Density-dependent factors regulate populations near carrying capacity.
- r-selected species have many offspring; K-selected species invest heavily in few.
- Human population growth is slowing but still rising.