Ecosystems and interdependence · Investigation
Sampling an ecosystem
Nobody has ever counted the daisies in a field. Every number you have ever read about how many of something there are was worked out from a sample — and a sample can be taken badly.
Start here
How many daisies are in the school field?
It is a fair question with a real answer, and counting them would take a class about four days. Every ecologist, every conservation charity and every government report faces the same problem, and none of them counts.
What is the best way to get a trustworthy number?
Count a small number of small squares, chosen at random, and scale up. That is a quadrat survey, and everything that can go wrong with it comes down to two things: how the squares were chosen, and how many of them there were.
At the bench · a field you can check your answer against
Survey it, then see the truth
field unsurveyed
The daisies are not spread evenly — they never are.
Where you put the quadrats
How many
one hundred square metres, contents hidden
Mean per quadrat
0
Estimated total
0
Real total
hidden
The method, and the two ways it fails
More quadrats fixes one problem and not the other.
The method
Mean, then scale up
Add the counts, divide by the number of quadrats to get a mean per quadrat, then multiply by how many quadrat-sized areas fit in the whole site.
Failure one
Bias
Sampling where you chose to rather than where chance sent you. Every extra quadrat repeats the same error, so the estimate is wrong and confident.
Failure two
Too few quadrats
Chance alone can land three quadrats on a bare patch. The estimate is not biased, just unreliable, and more samples genuinely fix it.
Also worth knowing
Quadrat size and edges
The quadrat must suit the organism, and everyone must agree the rule for plants on the line — usually count two sides and not the others.
Key fact
Estimate a population by counting in randomly placed quadrats and scaling up: mean per quadrat, multiplied by the number of quadrat-sized areas in the whole site. Random placement removes bias; more quadrats reduces the effect of chance. They are different problems and need different fixes.
Think again
“Throw the quadrat over your shoulder — that makes it random.”
It makes it unpredictable, which is not the same thing. You throw further on open grass than into brambles, you throw away from the hedge because you do not want to climb into it, and you throw downhill more easily than up. Every one of those is a preference, and a preference is exactly what random placement is supposed to eliminate. It is also unsafe with a metal frame. The real method is dull and works: lay two tape measures at right angles to make a grid of coordinates, generate pairs of random numbers, and put a quadrat wherever each pair lands, whether that spot is convenient or not. The word random in science means chosen by a process with no preferences, not chosen without thinking — and a human trying to be random is one of the more reliably biased instruments available.
“We took twenty quadrats, so the answer is accurate.”
Twenty biased quadrats give a confidently wrong answer, and taking a hundred would make it no better — it would only make the wrong number more stable. Sample size and bias are independent problems. Chance error, the kind that comes from happening to land on a patch, does shrink as you take more samples: the estimate wobbles less. Bias does not shrink, because every extra sample is drawn the same crooked way, and the error does not average out. You can see both on the bench above by taking three random quadrats and then twenty-five, and then doing the same on the flower-rich corner. There is one more trap worth naming: choosing where to sample after looking at the field is bias even if you use random numbers afterwards, because the area you chose was not random.
Mastery ladder
Not started yet.
Rungs 3 and 4 you mark yourself.
Rung 1 · Do the calculation
Ten quadrats of 1 m² give a mean of 6 daisies each. The field is 800 m². What is the estimated population?
Rung 2 · The one that catches people
A group samples 30 quadrats, all along the sunny edge of the field where the flowers look best. What is wrong with their estimate?
Rung 3 · Write the method
Write a method for estimating the number of dandelions on a school field, as instructions another class could follow. Include how you make the placement random and how you calculate the final number.
Rung 4 · Take it somewhere new
A class wants to test whether daisies grow better in the mown half of a field than the unmown half. Explain how the survey design differs from simply estimating a total, and how they would decide whether any difference they find is real.
Key note
Populations are estimated, not counted. Place quadrats at random using coordinates from a grid, count what is inside each one, find the mean, and multiply by the number of quadrat areas in the whole site. Random placement removes bias; taking more quadrats reduces the effect of chance. A biased sample stays wrong however large it is.
Going further
Quadrats only work on things that stay still. To estimate a population of animals, ecologists use capture–mark–recapture: catch some, mark them harmlessly, release them, and come back a few days later. If a tenth of the animals in the second catch are marked, then the number you marked must be about a tenth of the population. It is elegant, and it rests on assumptions worth interrogating — that the marked animals mixed back in properly, that the mark did not make them easier for a predator to spot or more wary of traps, that nothing was born, died or moved away in between. Trap-shy and trap-happy animals are both real problems: a mouse that has once found free food in a live trap will often go straight back in. Every one of those assumptions is a way the estimate can go wrong, and knowing what they are is the difference between using a method and trusting it.
Before this lesson
Connects to
At GCSE this becomes
- Required practical fieldwork: random and systematic sampling, transects along an environmental gradient, and capture–mark–recapture.
Where to next
Ask Mr Badmus AI
Want to plan a survey of your own school grounds?
The field is generated once when the page loads, with the daisies clustered towards one corner as they usually are in real ground. Random quadrats are drawn without replacement, so a sample never counts the same square twice. The real total is the sum of the whole grid, which is a luxury no fieldworker has.
Lesson content © MrBadmusAI.