Population Sampling: Quadrat and Mark-Recapture Methods
Population sampling is the use of a small, representative part of an area to estimate the number or abundance of organisms; quadrats are used for plants and slow-moving animals, and the mark-recapture method (Lincoln-Petersen) for mobile animals. In brief: to use a quadrat, count the organisms in randomly placed square frames and multiply the mean by the number of quadrats that would fit in the whole area. In mark-recapture, the estimate is N = (M × C) ÷ R, where M is the number marked in the first sample, C the total number caught in the second sample, and R the number of marked animals recaptured.
It is rarely possible to count every individual in a population, so ecologists estimate. This guide explains random sampling and quadrats, transects, mark-recapture and its assumptions, how to calculate density and percentage cover, how to reduce error, works through two numerical examples and corrects common mistakes.
Why do ecologists sample?
A complete count (census) of a population is possible only for small areas or for large, conspicuous animals. For most studies, it would take too long, cost too much and could damage the habitat. Instead, ecologists take samples, small parts of the population or area, and use them to estimate the whole. For the estimate to be reliable, the sample must be random (so that every part has the same chance of being chosen, and the sampler does not choose good-looking spots) and large enough (more samples give a smaller error).
How do quadrat surveys work?
A quadrat is a square frame, often 0.5 m × 0.5 m (0.25 m²) or 1 m × 1 m (1 m²), that marks out a sample area. It is used for plants, fungi, and animals that are sessile or move slowly, such as snails, barnacles and worms.
- Mark out the study area and measure its total area.
- Choose positions for the quadrats at random: lay out a grid with two tape measures at right angles and use random numbers from a calculator or a table for coordinates.
- Place the quadrat at each position, and count the individuals of the species (or estimate percentage cover, the proportion of ground covered by the species, which is used for plants that grow in dense mats such as grass).
- Record the results. Use enough quadrats, usually at least 10, and preferably more than 20.
- Calculate the mean number per quadrat, and then scale up.
The population estimate is: population = mean number per quadrat × (total area ÷ area of one quadrat). Density is the mean number per quadrat divided by the area of one quadrat. Other measures are frequency (the percentage of quadrats in which the species occurs) and percentage cover.
What are transects?
When conditions change gradually over a distance, as from the sea to the land or up a mountain, ecologists lay a line (a transect) across the gradient. Samples are taken at regular intervals along the line. In a line transect, only the species touching the line are recorded. In a belt transect, quadrats are placed along the line, or a strip is recorded, which gives more information. Transects show the changes in species distribution in relation to factors such as soil moisture, light or salinity.
How does the mark-recapture method work?
This method is used for animals that move, such as fish, beetles, small mammals and birds.
- Capture a sample of animals using traps or nets in the study area. Count them. This number is M.
- Mark them in a harmless way that does not affect their survival (a dot of paint on the shell, a ring, a tag, a clipped fur patch). Release them where they were caught.
- Allow time for the marked animals to mix randomly with the rest of the population.
- Capture a second sample. Count the total caught (C) and the number of marked individuals among them (R).
- Estimate: N = (M × C) ÷ R.
The logic is one of proportion. If the marked animals have mixed evenly, then the fraction of marked animals in the second sample (R ÷ C) equals the fraction of marked animals in the whole population (M ÷ N). Rearranging: N = M × C ÷ R. The method assumes:
- The population is closed: no significant births, deaths, immigration or emigration between the two samples.
- Marked animals mix randomly with the unmarked ones.
- Marking does not harm the animals, make them easier to see or change their chance of being recaptured, and marks are not lost.
- Every individual has an equal chance of being captured.
If the animals are “trap-happy” (attracted by bait) the estimate will be too low, and if they are “trap-shy”, it will be too high.
Sampling methods compared
| Method | Used for | What is measured | Main limitation |
|---|---|---|---|
| Random quadrats | Plants, sessile animals | Density, frequency, percentage cover | Sample may not represent the whole area |
| Transect | Gradients in the environment | Change in species along a line | Only covers the line or belt |
| Mark-recapture | Mobile animals | Population size | Depends on assumptions |
| Pitfall traps, nets | Ground insects, flying animals | Relative abundance, diversity | Biased toward active species |
Worked examples: a quadrat survey and a mark-recapture estimate
Example 1: quadrats
A meadow has an area of 2 000 m². A student places ten random quadrats of 0.5 m × 0.5 m and counts the buttercup plants: 4, 7, 3, 5, 6, 2, 8, 5, 4 and 6.
- Total: 4 + 7 + 3 + 5 + 6 + 2 + 8 + 5 + 4 + 6 = 50.
- Mean per quadrat: 50 ÷ 10 = 5.
- Area of one quadrat: 0.5 × 0.5 = 0.25 m².
- Density: 5 ÷ 0.25 = 20 plants per m².
- Population in the meadow: 20 × 2 000 = 40 000 plants. (Check: number of quadrats that fit = 2 000 ÷ 0.25 = 8 000; 5 × 8 000 = 40 000.)
Example 2: mark-recapture
On a pond, 60 snails are caught, marked and released. A week later, 50 snails are caught, of which 12 are marked.
- M = 60, C = 50, R = 12.
- N = (60 × 50) ÷ 12 = 3 000 ÷ 12 = 250 snails.
The estimate is about 250 snails in the pond. If only 6 had been marked in the second sample, the estimate would be 3 000 ÷ 6 = 500, double. This shows that the estimate is sensitive to small numbers of recaptures, which is why larger samples are better. A rough check: 12 out of 50 recaptured is 24 percent marked, so the 60 marked snails represent about 24 percent of the population, and 60 ÷ 0.24 = 250. ✓.
How can sampling error be reduced?
- Take more samples, since the mean becomes more reliable as the sample size increases. A running mean that stops changing much shows that enough samples have been taken.
- Choose positions randomly, to avoid bias.
- Use the same size of quadrat and the same method each time. Choose a quadrat size that suits the organism.
- Take samples at the same time of day and season.
- Calculate the standard deviation or standard error to describe the variation between samples.
- Record carefully and identify species correctly, with a key.
Ecologists should also minimize damage to habitats, avoid trampling, return animals safely and obtain permits when required.
How did sampling methods develop?
The mark-recapture principle was used by Pierre-Simon Laplace in the 1780s to estimate the population of France from birth registrations. C. G. J. Petersen used tags on plaice in Denmark in 1896, and Frederick Lincoln developed the method for waterfowl in the United States in 1930, which is why the estimate is called the Lincoln-Petersen index. Frederic Clements introduced quadrats to plant ecology in the early twentieth century. Today, camera traps and environmental DNA (eDNA) are used as well.
Which mistakes are common?
Mistake 1: Placing quadrats where there seem to be many plants
This introduces bias. Use random coordinates.
Mistake 2: Forgetting to scale up
The mean per quadrat must be multiplied by the number of quadrats that would cover the whole area.
Mistake 3: Using M, C and R incorrectly
M is the number marked in the first sample, C is the total of the second sample (not only the marked), and R is the marked animals in the second sample.
Mistake 4: Ignoring the assumptions of mark-recapture
If animals die, move or lose their marks, the estimate will not be accurate.