A sampling estimate uses a small, representative count to estimate a whole population. Every estimate rests on assumptions, and the exam expects you to say what they are. This skill sits in ecology and energy flow and also supports practical questions on fieldwork design.
How does quadrat sampling work?
A quadrat is a square frame of known area. You place it at random positions, count the organisms inside each, then scale up.
- Find the mean count per quadrat: total count ÷ number of quadrats.
- Convert to a count per square metre: divide by the area of one quadrat in m².
- Multiply by the total habitat area in m².
How does mark-recapture work?
Used for moving animals. Catch a sample, mark them harmlessly and release them. Later catch a second sample and count how many are marked.
Estimated population = (number marked first) × (size of second sample) ÷ (number of marked animals in second sample)
Worked example
A rectangular field is 40 m long and 25 m wide. Ten 1 m² quadrats are placed at random and the numbers of clover plants counted (invented data for practice):
4, 7, 3, 5, 6, 2, 5, 4, 6, 8
Estimate the number of clover plants in the field.
Step 1, total count: 4 + 7 + 3 + 5 + 6 + 2 + 5 + 4 + 6 + 8 = 50.
Step 2, mean per quadrat: 50 ÷ 10 = 5 plants per quadrat. Each quadrat is 1 m², so this is 5 per m².
Step 3, area of field: 40 × 25 = 1 000 m².
Step 4, estimate: 5 × 1 000 = 5 000 clover plants.
Step 5, assumptions: the quadrats were placed at random, the sample represents the whole field, and the clover is spread in a way that makes ten quadrats enough.
Checking the addition in pairs: (4 + 7) + (3 + 5) + (6 + 2) + (5 + 4) + (6 + 8) = 11 + 8 + 8 + 9 + 14 = 50. Both ways give 50.
The mistake to watch for
The usual slip is to multiply the mean by the number of quadrats, or to ignore the quadrat size.
Mistaken answer: “Mean = 5, and I used 10 quadrats, so 5 × 10 = 50 plants in the field.”
The student scaled to the sample, not to the field. The field is 1 000 m², not 10 m².
The correction is to convert to a density (per m²) first, then multiply by the habitat area. If the quadrats were 0.25 m², divide the mean by 0.25 to get per m².
Check yourself
1. Five quadrats of 0.5 m × 0.5 m gave counts of 2, 0, 3, 1 and 4. The habitat is 200 m². Estimate the population.
Show answer
Total = 10, mean = 2 per quadrat. Quadrat area = 0.5 × 0.5 = 0.25 m², so density = 2 ÷ 0.25 = 8 per m². Estimate = 8 × 200 = 1 600. Check: sampled area = 5 × 0.25 = 1.25 m², and 10 ÷ 1.25 = 8 per m², which matches.
2. In a pond, 50 beetles were caught, marked and released. A later sample had 40 beetles, of which 5 were marked. Estimate the population.
Show answer
50 × 40 ÷ 5 = 2 000 ÷ 5 = 400 beetles. Check: 5 of 40 is one eighth marked, and 50 marked is one eighth of 400.
3. Give one assumption of mark-recapture and explain what happens to the estimate if it fails.
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For example, if the marked animals do not mix with the rest, the second sample may contain more or fewer marked animals than expected, so the estimate may be too low or too high. Other valid assumptions: marking does not harm them, no animals enter or leave.
Where this leads next
Once you can scale a sample, move on to comparing biomass and organism counts. Your data from these calculations is also useful evidence when you interpret a food web change. The practice set mixes both calculation types.
If you lose marks on the assumption and evaluation parts, online one-to-one Biology tuition gives time to rehearse those written answers.