IB Biology HLPopulations & CommunitiesPaper 1 & 2~14 min read
Estimating Population Size
Nobody counts every dandelion in a meadow. Instead you count a small part of it properly and scale up — and the whole skill lies in choosing that small part fairly. This page covers quadrats for things that stay still, and mark–release–recapture for things that run away.
📘 What you need to know
Counting every organism only works for very small areas or very large species. Otherwise, sample.
Sampling measures small samples that represent the whole population.
Random sampling: positions chosen at random, which avoids bias.
Systematic sampling: positions at fixed intervals, e.g. along a transect, to study the effect of an environmental feature.
Sampling error is the difference between the estimated population size and the true population size. Sampling always risks it.
Frame quadrats sample sessile organisms. Record presence/absence, frequency, abundance (ACFOR) or percentage cover.
Standard deviation measures the spread of data around the mean. Small = little variation; large = a lot.
For motile organisms use capture–mark–release–recapture and the Lincoln index.
Random and systematic sampling
There are two ways to decide where your samples go, and the choice is not a matter of taste. Each one answers a different question.
Random sampling
Systematic sampling
Where samples go
Positions selected at random
Positions at fixed intervals, e.g. along a line
Main advantage
Avoids bias from the person sampling
Avoids missing sections of habitat by chance
Use it when
The area is reasonably uniform
You want the effect of an environmental feature
Typical example
Random co–ordinates across a grassland
A transect running away from a river
Bias is the reason random sampling exists. A student who picks spots that “look interesting” will choose the flowery corner over the bare patch, and the results will suggest the habitat holds more species than it really does.
🧩 Choosing random sample sites
Lay out a grid over the area to be studied.
Generate random number co–ordinates.
Place a sample site in each grid square that matches a pair of co–ordinates.
Systematic sampling is what you want when something changes across the habitat — distance from a river, height up a rocky shore — because the pattern of samples matches the pattern you are testing.
Nature of science: sampling always brings error
Any estimate built from samples assumes that individuals are distributed evenly across the sample site. In real habitats they never are.
If random sampling happens to miss an area with no individuals, the estimate comes out too high.
If it happens to miss an area packed with individuals, the estimate comes out too low.
So many factors influence how a population is spread out that an even distribution is very unlikely, and the chance of sampling error is high. A sampling error is the difference between an estimated population size and the true population size, and it happens whenever a sample is not truly representative of the whole population.
How you reduce it. Good investigation design: the right type of sampling for the habitat, and a large enough sample size. And when scientists publish, they must include full details of their methods, so readers can judge for themselves what error might be sitting in the results.
Frame quadrats
A frame quadrat is a square frame placed within the area being studied to provide a sample. Quadrats work for sessile organisms — plants, limpets, barnacles — anything that will still be there when you come back to count it.
A 1 m² quadrat suits small organisms: herbaceous plants in grassland, limpets on a rocky shore.
A 400 m² quadrat suits large organisms such as trees, and is usually marked out with string rather than an actual frame.
Quadrats can be placed randomly (random co–ordinates) or systematically (along a transect).
What you record
What it means
Presence or absence
Simply whether the species is in the quadrat
Species frequency
How many individuals are in the quadrat
Species abundance
The ACFOR scale: abundant, common, frequent, occasional, rare, none
Percentage cover
The percentage of the quadrat covered by the species
Percentage cover sounds fiddly but there is a trick to it. Divide the quadrat into smaller squares with string, then count a square for a species if that species covers more than half of it. With 100 small squares, the count is the percentage. It is fast, and it is consistent between different people.
Mean and standard deviation
Once you have counts from many quadrats, you summarise them with a mean and a standard deviation.
The mean is the average value of the data set.
The standard deviation measures the spread of the data around the mean.
A small standard deviation means results lie close to the mean, so there is little variation.
A large standard deviation means results are more spread out, so there is a lot of variation.
In a quadrat study, that spread tells you something biological: it indicates how evenly distributed the population is across the habitat. Same mean, bigger standard deviation, patchier population.
Motile organisms: capture–mark–release–recapture
Quadrats are useless for beetles, fish and mice, because they will not stay put. For motile organisms you use the mark–release–recapture method instead.
Marking must not harm the animal or make it stand out to predators. A dab of non–toxic paint on the underside of a beetle’s wing cases is the classic method.
The Lincoln index
estimated population size = ( M × N ) ÷ R
M = number of individuals marked in the first sample
N = total number of individuals in the second sample, marked and unmarked
R = number of marked individuals recaptured in the second sample
The index only works if a list of assumptions holds. Examiners love asking about these, because they are where the method is weakest.
Assumption
What breaks it
Marked individuals disperse and mix fully back into the population
Not leaving enough time before the second sample
Marking does not affect survival
A bright mark that makes an animal easier to spot and eat
The mark stays visible throughout
Paint that rubs off, or an animal that moults
The population stays the same size
Births, deaths, or migration into or out of the area
Worked examples
WE 1
Using the Lincoln index
Ecologists caught, marked and released 164 ground beetles in a woodland. A week later they caught 198 beetles, of which 37 carried marks. Estimate the population size. (3 marks)
Step 1: identify the letters
M = 164 marked in the first sample, N = 198 caught in the second, R = 37 marked ones recaptured.
Step 2: substitute into the formula
estimated population = (164 × 198) ÷ 37 = 32 472 ÷ 37
Step 3: calculate and round sensibly
= 877.6, so about 878 beetlesRoughly 878 beetles in the woodlandround to a whole organism — you cannot have 0.6 of a beetle
WE 2
Scaling up from quadrats
Five randomly placed 1 m² quadrats in a 450 m² meadow contained 12, 9, 15, 11 and 13 daisy plants. Estimate the total number of daisies. (2 marks)
Step 1: mean per quadrat
(12 + 9 + 15 + 11 + 13) ÷ 5 = 60 ÷ 5 = 12 daisies per m²Step 2: scale to the whole area
12 × 450 = 5400 daisiesAbout 5400 daisies in the meadowsay “about” — it is an estimate carrying sampling error, not a count
WE 3
Evaluating a method
A student marked woodlice with a bright white correction fluid and recaptured them two hours later. Suggest two reasons why the estimate may be inaccurate. (2 marks)
Reason 1: not enough mixing
Two hours is too short for the marked woodlice to disperse and mix fully back into the population, so too many marked ones are recaptured and the estimate is too low.
Reason 2: marking affects survival
A bright white mark makes the woodlice more visible to predators, so marked individuals may be eaten more often, reducing R and pushing the estimate too high.
Poor mixing and a mark that changes survivalsay which way the estimate is pushed — “it would be wrong” is not an answer
💡 Exam tips
Match the method to the organism: quadrats for sessile, mark–release–recapture for motile.
Random sampling avoids bias; systematic sampling reveals the effect of a feature.
Define sampling error precisely: estimated minus true population size.
Learn the four Lincoln index assumptions — they are easy marks in evaluation questions.
Quote estimates to a sensible precision and label them as estimates.
For “how would you improve it”, reach for larger sample size and appropriate sampling type.
⚠ Common mistakes
Mixing up N and R in the Lincoln index. N is everything in the second sample; R is only the marked ones.
Calling random sampling “throwing the quadrat over your shoulder”. That is not random — use a grid and random co–ordinates.
Saying sampling error means the scientist made a mistake. It is a built–in consequence of sampling.
Using quadrats for animals that move. They will simply walk out of your frame.
Describing standard deviation as “the average”. That is the mean; standard deviation is the spread around it.
Forgetting to multiply by the total area when scaling quadrat counts up.
Up next: What Limits Population Size. You can now estimate how many there are — the next question is why that number stops climbing.
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