Nobody counts every daisy in a field or every beetle in a wood. Instead you count a small part carefully and scale it up. This page covers the two big methods — quadrats for things that stay still, and mark-release-recapture for things that run away.
📘 What you need to know
Sampling means measuring small parts of a habitat and using them to represent the whole thing.
Random sampling uses random co-ordinates and avoids bias. Systematic sampling places samples at fixed intervals, often along a transect.
A quadrat is a square frame used to record presence, frequency, percentage cover or abundance of non-motile species.
Sampling always produces some sampling error — the gap between your estimate and the true number.
Standard deviation tells you how spread out your quadrat counts are around the mean.
For motile organisms use capture–mark–release–recapture and the Lincoln index.
Why bother sampling?
If the area is tiny, or the organism is enormous, you can just count everything. Twelve oak trees in a small wood? Count them. But a grassland full of clover, or a rocky shore full of limpets, is impossible to count individually. You would never finish, and the ones you counted first would have moved or died by the end.
So you count a few small squares, work out an average, and multiply up to the size of the whole habitat. The estimate is never perfect, but a good sampling design gets it close.
Random or systematic?
These two words describe where you put your samples, and they are chosen for different reasons.
Randomly placed does not mean carelessly placed. You still generate co-ordinates properly — throwing a quadrat over your shoulder is not random.
Method
How sites are chosen
Use it when
Random
Lay a grid over the area, generate random number co-ordinates, sample the squares they land on
The habitat is reasonably uniform and you want an unbiased estimate
Systematic
Sample at fixed intervals, usually along a line called a transect
You want to see how species change away from a feature such as a river or the sea
Bias is the reason random sampling exists. If you pick spots that “look interesting”, you drift towards the colourful, busy patches and your estimate comes out far too high. Random co-ordinates take that choice out of your hands.
Quadrats: what you actually record
A frame quadrat is a square frame you place on the ground. Small ones (1 m2) suit grasses and limpets; huge ones (400 m2, usually marked with string) suit trees. What you record inside it depends on the question you are asking.
Type of data
What you write down
Good for
Presence or absence
Is the species there, yes or no
Distribution maps and chi-squared tests
Species frequency
How many individuals are inside the frame
Countable organisms such as daisies or limpets
Percentage cover
What percentage of the frame the species covers
Grasses, mosses and seaweeds you cannot count
ACFOR abundance
Abundant, common, frequent, occasional, rare or none
Quick surveys where exact numbers are not needed
Percentage cover made easy. Divide the quadrat into 100 small squares with string. Count a square if the species covers more than half of it. If 37 squares count, the cover is 37 %. It is quick, it is repeatable, and two people usually get answers within a few per cent of each other.
Sampling error — and why it is unavoidable
When you scale a sample up, you are assuming the organisms are spread evenly across the whole site. They almost never are. Soil depth, shade, water and competition all push species into patches.
So one of two things happens. Your quadrats miss a crowded patch, and your estimate comes out too low. Or they miss an empty patch, and your estimate comes out too high. That gap between your estimate and the real number is sampling error.
You cannot delete it. You can shrink it, by taking more samples and by choosing the right sampling method for the habitat. That is also why scientists publish their exact methods — so other people can judge how much error is likely.
Mean and standard deviation
Take ten quadrat counts and you get ten numbers. The mean tells you the average. The standard deviation tells you how tightly the numbers cluster around that mean — and that is really a statement about how evenly the species is spread.
Two surveys can report exactly the same mean number per quadrat while describing completely different habitats.
WORKED EXAMPLE
Mean and spread from quadrat counts
A student records the number of daisy plants in five 1 m2 quadrats: 12, 15, 9, 14, 10. Calculate the mean, calculate the standard deviation, and comment on what the spread suggests about the distribution of the daisies.
Step 1: mean(12 + 15 + 9 + 14 + 10) ÷ 5 = 60 ÷ 5 = 12Step 2: how far is each value from 12?0, +3, −3, +2, −2Step 3: square them and add0 + 9 + 9 + 4 + 4 = 26Step 4: divide by (n − 1), then square root26 ÷ 4 = 6.5 √6.5 = 2.5mean = 12 plants m⁻², s = 2.52.5 is small next to a mean of 12, so the daisies are fairly evenly spread
Organisms that run away: mark–release–recapture
Quadrats are useless for beetles, fish or woodlice — they simply leave. Instead you use the marked ones as a clue.
The logic is beautifully simple. Mark 100 animals and let them mix back in. If the population is small, marked animals will be a big fraction of your next catch. If the population is huge, you will barely see any marked ones again.
The waiting time in step 2 matters. Recapture too soon and the marked animals are still bunched near where you released them.
The Lincoln index
estimated population size = (M × n) ÷ R
M = number marked in the first sample. n = total number caught in the second sample. R = number of marked individuals recaptured in the second sample. Some textbooks write the same equation as M × N ÷ R — the letters change, the maths does not.
WORKED EXAMPLE
Estimating a beetle population
Students caught 120 ground beetles, marked a small dot of non-toxic paint on each wing case and released them. Four days later they caught 150 beetles, of which 40 carried a paint mark. Estimate the size of the beetle population.
Step 1: label the three numbersM = 120 marked, n = 150 caught second time, R = 40 marked ones recapturedStep 2: put them in the Lincoln indexestimate = (120 × 150) ÷ 40= 18 000 ÷ 40about 450 beetlessense check: 40 out of 150 caught were marked, so roughly a quarter of the population carried a mark — and 120 is roughly a quarter of 450
🧩 The assumptions behind the Lincoln index
The marked animals mix back in fully with the rest of the population.
The mark does not change survival. A bright mark that attracts predators would ruin the estimate.
The mark stays on and stays visible for the whole study.
The population size does not change — no big pulse of births or deaths.
No migration in or out of the study area between the two samples.
Questions love asking “suggest why the estimate may be inaccurate”. Pick one assumption and break it, then say which way the estimate goes. If marks rub off, R falls, so the estimate comes out too high.
💡 Exam tip
Write the equation out before substituting numbers — that alone often scores a mark.
Round population estimates to whole organisms. There is no such thing as 811.84 leafhoppers.
If asked how to improve a survey, say take more quadrats, not “be more careful”.
“Suggest why random sampling was used” → the answer is nearly always to avoid bias.
For a transect question, the key phrase is how the community changes along an environmental gradient.
Standard deviation questions want a comparison, so use the words close to or spread out around the mean.
⚠ Common mix-up
Random is not the same as haphazard. Random means generated co-ordinates; haphazard means you chose by eye and introduced bias.
Quadrats do not work for motile organisms. Do not offer them for beetles or fish.
Mixing up n and R. R is only the marked ones in the second sample; n is everything caught in it.
Percentage cover can add up to more than 100 % when species overlap in layers. That is normal, not an error.
Sampling error is not a mistake you made. It comes from sampling itself, so “the student was careless” earns nothing.
Standard deviation is not the range. Range uses only two values; standard deviation uses all of them.
Up next: What Limits Population Size — you can measure a population, so now look at why it stops growing instead of doubling forever.
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