# Population Dynamics and Sampling

> Measuring populations with quadrats, transects and capture-recapture, population growth, carrying capacity and predator-prey cycles.

From HSC Biology on WhizzNotes, free study notes for NSW students: https://whizznotes.com/biology/populations-and-sampling/. Updated 3 November 2026.
Year 11 and Year 12 boxes go deeper than the Year 10 text around them.

### Story time: Counting koalas from the sky
How do you count koalas in a forest of thousands of tall gum trees? Walking around and looking up misses most of them. They sit still, high up, and look like part of the tree.

Scientists now fly drones with heat cameras over forests at night. A warm koala glows white against the cool leaves. In some surveys the drones found more koalas than people on foot, in a fraction of the time. Counting a population accurately is the first step to protecting it.

**In short:** Ecologists estimate population size by sampling, because counting every organism is rarely possible. Quadrats and transects sample plants and slow animals, and capture-mark-recapture estimates moving animals with $N = \dfrac{M \times C}{R}$. Populations grow until they reach the carrying capacity.

## Starting point: what you already know

- A population is all the members of one species in an area (see the previous chapter).
- Calculating a mean and a percentage.
- Working scientifically: a larger sample gives a more reliable result.

## Why sample?

Counting every organism is usually impossible. Instead, ecologists count a **sample** and use it to **estimate** the whole population. Samples must be **random** (to avoid bias) and **large enough** to be reliable.

**Population density** = number of individuals ÷ area.

## Quadrats: for plants and slow animals

A **quadrat** is a square frame, often $1 \text{ m} \times 1 \text{ m}$. Place it randomly many times and count the organisms inside.

### Worked example: Estimating daisies on an oval
Ten random $1 \text{ m}^2$ quadrats contain 3, 5, 2, 4, 6, 3, 4, 5, 2, 6 daisies. The oval is $5000 \text{ m}^2$.

$$\text{mean per quadrat} = \frac{40}{10} = 4 \text{ daisies per m}^2$$
$$\text{estimate} = 4 \times 5000 = 20\,000 \text{ daisies}$$

When counting is hard (grasses), use **percentage cover**: estimate how much of the quadrat each species covers.

## Transects: for changes across an area

A **transect** is a line across a habitat, such as from the water's edge up a beach or across a rock platform. Organisms are recorded at regular intervals along it. A **belt transect** places quadrats along the line. Transects show how species change with an abiotic factor like height above the tide.

## Capture-mark-recapture: for moving animals

1. Catch a sample of animals, mark them harmlessly and release them.
2. Later, catch a second sample and count how many are marked.

$$N = \frac{M \times C}{R}$$

where $N$ = population estimate, $M$ = number marked first, $C$ = total caught second time, $R$ = number recaptured with marks. This is the **Lincoln index**.

### Worked example: Skinks in a garden
30 skinks are marked and released. A week later 40 are caught, and 8 are marked.
$$N = \frac{30 \times 40}{8} = 150 \text{ skinks}$$

The method assumes marked animals mix back in evenly, marks do not fall off or make animals easier to catch, and no animals are born, die or move in between samples.

## How populations change

A population grows by **births** and **immigration** (moving in). It shrinks by **deaths** and **emigration** (moving out).

When a few animals enter a new place with plenty of food, numbers grow slowly, then very fast (**exponential growth**). As food and space run short, growth slows and numbers level off at the **carrying capacity**: the largest population the environment can support. This makes an S-shaped curve.

**Limiting factors** stop growth: food, water, shelter, disease, predators.

## Predator and prey

*Diagram: Graph of prey and predator numbers rising and falling in cycles, with the predator peaks slightly after the prey peaks*
*Predator numbers rise after prey numbers rise, then fall after prey numbers fall.*

1. Lots of prey: predators have plenty to eat and their numbers rise.
2. More predators eat more prey, so prey numbers fall.
3. With less food, predator numbers fall.
4. With fewer predators, prey recover, and the cycle repeats.

**Mind map**

```text
Populations
  Sampling
    Random and large
    Density = number ÷ area
  Methods
    Quadrats: plants
    Transects: change across area
    Capture-recapture: N = MC ÷ R
  Change
    Births and immigration add
    Deaths and emigration remove
    S curve to carrying capacity
  Limiting factors
    Food, water, shelter
    Disease and predators
  Predator and prey
    Cycles, predator lags
```

### Year 11: Using sampling in a depth study
A Year 11 fieldwork depth study might compare two sites, like burnt and unburnt bush, or a rock platform at different tide heights. Good practice:

- Use **random** numbers to place quadrats, or regular intervals along a transect.
- Measure **abiotic** factors at each point (light with a light meter, soil moisture, temperature, salinity) so you can link them to species.
- Use enough samples. Plot a running mean: when adding more quadrats no longer changes the mean much, you have enough.
- Remember ethics: return rocks you lift, handle animals as little as possible, and do not remove organisms.

Newer methods include **environmental DNA** (eDNA): testing water or soil for tiny traces of DNA to show which species live there without catching any.

### Year 12: Population thinking in Modules 5 to 7
**Allele frequencies** (Module 5 and 6) are measured in populations, not individuals. **Epidemics** (Module 7) follow growth curves too: an infectious disease spreads exponentially until immunity, isolation or vaccination slows it. The basic reproduction number $R_0$ is the average number of people one case infects.

## Quick summary

- Samples must be random and large enough. Density = number ÷ area.
- Quadrats estimate plants and slow animals. Transects show change across a habitat.
- Capture-mark-recapture: $N = \dfrac{M \times C}{R}$.
- Populations grow toward the carrying capacity, limited by food, space, disease and predators.
- Predator numbers rise and fall after prey numbers.

## Quiz

Try these questions from the chapter quiz.

1. Which method is best for estimating the number of lizards in a garden?
   - A. Quadrats
   - B. Capture-mark-recapture
   - C. A single transect
   - D. Counting leaves
   - Answer: B. Capture-mark-recapture. Lizards move around, so mark and recapture them.

2. A quadrat is best for sampling
   - A. plants on a lawn
   - B. birds flying overhead
   - C. fish in the ocean
   - D. bats in a cave
   - Answer: A. plants on a lawn. Quadrats suit organisms that do not move much.

3. Why should quadrats be placed randomly?
   - A. To make it faster
   - B. To avoid bias in the sample
   - C. To find the most plants
   - D. To keep the results the same
   - Answer: B. To avoid bias in the sample. Choosing spots yourself can bias the estimate.

The whole chapter quiz is on the page, for signed-in students: https://whizznotes.com/biology/populations-and-sampling/#quiz