Nobody counts every daisy in a field or every beetle in a wood. Instead you count a small part properly and scale it up. Get the sampling right and your estimate is trustworthy; get it wrong and no amount of maths will save it. This page covers both halves — the method and the calculations.
📚 What you need to know
A population is everything you are interested in; a sample is the part you actually measure.
In random sampling every point has an equal chance of being chosen, which removes researcher bias.
In systematic sampling points follow a regular pattern — used when conditions change across the area.
Transects (line and belt) show how species change along an environmental gradient.
Quadrats are used for non-motile organisms, recording counts, percentage cover or percentage frequency.
Population size is estimated as (total area ÷ area sampled) × number counted.
For motile animals, use capture–mark–release–recapture and the Lincoln index.
Population, sample, census
If a teacher wants to know how long students revise, the population is every student in the year group. Measuring all of them is a census: completely accurate, but slow, expensive and heavy on data. Measuring thirty of them is a sample: quick and cheap, but only as good as the way those thirty were chosen.
Approach
Advantages
Disadvantages
Census (whole population)
Accurate; every individual is included, so nothing is missed
Slow, expensive, and produces a huge amount of data to handle
Sample (a subset)
Quicker, cheaper, far less data to analyse
May be biased or unrepresentative, especially if the sample is small
Two samples from the same population can give different answers. That is normal, not a mistake. It is also why larger samples and repeat sampling matter — they reduce the effect of chance.
Random or systematic?
Random placement protects you from your own preferences. Left to ourselves, we put quadrats where the ground is flat, dry and easy to count — which is exactly how bias creeps in.
Random sampling uses a random number generator to produce coordinates, so no part of the area is favoured. Use it when the area is fairly uniform or has no obvious pattern.
Systematic sampling places points in a regular pattern, usually along a line. Use it when something changes across the area — altitude, soil pH, shade, distance from a river.
The risk with systematic sampling is that the person choosing may favour or avoid certain areas, and a regular pattern can miss a repeating feature.
Transects: sampling along a gradient
A transect is simply a measuring tape laid across the area. It lets you show how a community changes with distance, which a scatter of random quadrats cannot do.
Type
What you do
Line transect
Lay the tape in a straight line and record every organism that touches the line at set distances, for example every 2 m.
Belt transect
Place quadrats at regular intervals along the tape and record abundance or percentage cover inside each one.
A belt transect running from the water’s edge up a shore, or from an open field into woodland, will show species appearing and disappearing in a clear order — and that order matches the abiotic gradient you measured alongside it.
Quadrats and what you record
A quadrat is a square frame, often 0.5 m × 0.5 m or 1 m × 1 m. Drop it, then record what is inside. There are three ways to record.
🧩 Estimating population size with quadrats
Mark out the survey area with two tape measures, for example 20 m × 20 m.
Use a random number generator to pick coordinates for each quadrat.
Place the quadrat and count the individuals of your chosen species.
Repeat for at least ten quadrats, recording each result in a table.
Scale up using the equation below.
Estimating population size
estimate = total area ÷ area sampled × total number counted
Percentage cover is the share of the quadrat area covered by a species. Percentage frequency is the share of the small squares in which the species appears. Frequency is easier and more reliable when individual plants are impossible to count, such as grass or moss.
Percentage frequency
% frequency = (squares containing the species ÷ total squares) × 100
If a square is more than half filled by a species, count it as present. Agree that rule with your group before you start, or your results will not be comparable.
Counting animals that move
Quadrats work for plants and other organisms that stay put. For beetles, fish or leafhoppers you need capture–mark–release–recapture.
🧩 The capture–mark–release–recapture method
Catch a large first sample, count it and mark each individual harmlessly — a dot of non-toxic paint in a hidden place.
Release them and allow enough time for them to mix back into the population.
Catch a second large sample using the same method.
Count how many of the second sample are marked.
Put the three numbers into the Lincoln index.
The Lincoln index
population estimate = (M × C) ÷ R
M = number caught, marked and released in the first sample
C = total number caught in the second sample, marked and unmarked
R = number of marked individuals in the second sample
The logic is a proportion. If marked animals make up one tenth of your second catch, then the animals you marked are probably about one tenth of the whole population.
Assumptions the method depends on
Marked individuals mix fully back into the population before you sample again.
The marking does not affect survival — it must not make an animal easier for a predator to spot.
The mark does not rub off or fade during the study.
The population does not change size in between: no significant births, deaths or migration.
Every one of those assumptions is a ready-made answer to “suggest why the estimate may be inaccurate”. Pick one, say what would happen to the numbers, and you have the mark. If marks rub off, R falls, and a smaller R makes the estimate too large.
Worked examples
WORKED EXAMPLE
A field measures 20 m × 20 m. Ten 1 m² quadrats are placed at random and 30 daisies are counted in total. Estimate the daisy population.
Step 1: work out the two areastotal area = 20 × 20 = 400 m²area sampled = 10 × 1 = 10 m²Step 2: substitute into the equationestimate = (400 ÷ 10) × 30estimate = 40 × 30about 1 200 daisiesSay “about” or “estimated”. It is a sample, so it is never an exact count.
WORKED EXAMPLE
Ecologists catch and mark 120 beetles. Two days later they catch 150 beetles, of which 25 are marked. Estimate the population.
Step 1: label the numbers
M = 120 marked and released, C = 150 caught second time, R = 25 marked recaptured
Step 2: substitute into the Lincoln indexestimate = (120 × 150) ÷ 25estimate = 18 000 ÷ 25about 720 beetlesStep 3: sense-check it
Marked beetles were 25 out of 150, roughly one sixth of the catch, and 120 × 6 = 720. The answer is sensible.
Label M, C and R before calculating. Most lost marks here come from swapping C and R.
WORKED EXAMPLE
A student wants to investigate how plant species change from the edge of a pond to the top of a bank. Suggest a sampling method and justify it.
Step 1: spot the gradient
Conditions change steadily with distance from the water: soil moisture, and probably light and soil type too.
Step 2: choose the method
A belt transect — a tape from the pond edge up the bank, with a quadrat placed every 2 m.
Step 3: justify it
Random quadrats would show which species are present but not how they change with distance. A transect records that pattern directly, and abiotic factors can be measured at each quadrat for comparison.
Belt transect, quadrats at fixed intervalsWhenever a question mentions a gradient, distance or “from A to B”, the answer is a transect.
💡 Exam tip
Write the equation, then substitute, then answer. Three lines, three chances at method marks even if the arithmetic slips.
Keep your units consistent. Mixing m² and cm² is the most common wrecking mistake in this topic.
Say random number generator, not “chosen at random”. The examiner wants to see how randomness was achieved.
Round animal and plant counts to whole numbers — there is no such thing as 719.6 beetles.
If asked to improve a method, say take more quadrats or repeat the sampling, and explain that this reduces the effect of chance.
Percentage cover and frequency show abundance, not population size. Do not offer them when the question asks for numbers of individuals.
⚠ Common mix-up
Population and sample. The population is everything you are interested in; the sample is the part you measure.
Swapping C and R in the Lincoln index. C is everything caught the second time; R is only the marked ones among them.
Using quadrats for animals that move. They will simply walk out of the frame; use capture–mark–release–recapture.
Thinking systematic sampling is more scientific because it looks neat. It is only better when there is a gradient to follow.
Forgetting to multiply by the number of quadrats. Scaling up needs the total area sampled, not the area of one quadrat.
Treating an estimate as exact. Always describe the answer as an estimate and be ready to name a source of error.
Up next: How Ecosystems Keep Functioning — steady state, nutrient flows, tipping points, keystone species and what conservation is actually protecting.
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