Estimating population size & sampling

The big idea: Counting every single organism in a habitat is almost always impossible — there are too many, they hide, and many of them move.

So ecologists estimate the population size by counting a small sample and scaling up to the whole habitat.

The method you choose depends on whether the organism moves: quadrats for still organisms like plants, and capture–mark–release–recapture for animals that move.

Population

All the organisms of the same species living in the same area at the same time.

Population size

The total number of individuals of that species in the area — the value we are trying to estimate.

Sample

A small part of the population that is actually counted, used to estimate the whole.

Random sampling

Choosing sample positions by chance (for example using random numbers as coordinates) so the sample is not biased.

Quadrat

A square frame of known area placed on the ground; the organisms inside it are counted.

Why sampling must be RANDOM: If you place your quadrats where the plants 'look nice' or are easy to reach, your sample is biased and the estimate is wrong.

Choosing positions at random (for example by generating random coordinates) makes the sample representative of the whole habitat.

Moves or not? That decides the method: Plants and other non-moving organisms stay put, so you can count them in fixed areas → use quadrats.

Animals move, so they will not sit still inside a quadrat → use capture–mark–release–recapture instead.

There are two methods on the syllabus. Quadrats handle organisms that stay put; capture–mark–release–recapture handles organisms that move.

Both work the same way underneath — count a sample, then scale up to estimate the whole population.

Method 1 — quadrat sampling (for plants): Place several quadrats at random positions in the habitat and count the organisms inside each one.

Find the mean number per quadrat, then scale up: multiply by how many quadrat-sized areas would fit in the whole habitat.

Example: if a 1 m² quadrat holds a mean of 8 daisies and the field is 500 m², the estimate is 8 × 500 = 4000 daisies.

Method 2 — capture–mark–release–recapture (for animals): You cannot count moving animals in a fixed area, so instead you compare two samples:

Capture a first sample and count it (this is M). Mark each one harmlessly and release them.

Later, recapture a second sample (size n) and count how many are already marked (this is m).

The proportion that is marked tells you how big the whole population must be — worked out with the Lincoln index.

The Lincoln index: The estimate comes from one short calculation, the Lincoln index:

N = (M × n) ÷ m

where M = number marked in the first sample, n = total caught in the second sample, and m = number in the second sample that were already marked.

The logic: the marked fraction of the second sample (m ÷ n) should match the marked fraction of the whole population (M ÷ N) — rearranging gives N = (M × n) ÷ m.

A memory hook: Sit still → quadrat. Runs away → recapture.

For the Lincoln index, remember the two marked numbers go together: M (marked at the start) on top, m (marked when you come back) on the bottom.

How this is tested: On Paper 1B / Paper 2 an Explain or Describe question commonly asks how capture–mark–release–recapture could estimate a moving animal's population (for example a tick or insect population) — give the steps in order and name the Lincoln index.

A data-style follow-up gives you values for M, n and m and asks you to Calculate the estimated population — show N = (M × n) ÷ m and the working.

A higher-mark version asks you to state the assumptions that must hold for the estimate to be valid (even mixing, no births/deaths, marks not lost).

✓ Why this scores full marks: The three marks are three distinct stages — mark a first sample, recapture a second, and use the proportion marked to scale up.

Naming the Lincoln index and saying the result is an estimate of the total locks in the final mark.