Catch, mark, let go, catch again: Mobile animals cannot be counted in quadrats. Catch some, mark them, let them go, then catch a second sample and see how many are marked.
Capture
Catch a sample with traps or nets.
Mark
Mark each one harmlessly and count them (M).
Release
Let them go and wait for them to mix.
Recapture
Catch a second sample (N) and count the marked ones (R).
The points to remember
- Capture a sample, using the same method both times: live traps, nets, pitfall traps, bait.
- Mark each animal so the mark is harmless and lasts: paint dot, leg ring, tag, or a photo of its pattern.
- Release them where they were caught, and leave time for them to mix back in.
- Recapture a second sample and count how many are marked.
- Use the Lincoln index to estimate the population size.
Remember it as: Catch, mark, let go, catch again, count the marked.
Real example: each great crested newt has its own pattern of belly spots, so UK surveyors photograph the pattern instead of adding a mark.
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The Lincoln index: Population size = (M × N) ÷ R
How to use it
- Write the formula first: population size = (M × N) ÷ R.
- M = number caught and marked in the first sample.
- N = total number caught in the second sample.
- R = number of marked animals recaptured in the second sample.
- Multiply M by N, divide by R, and round to a whole number of animals.
R goes on the bottom: Divide by R, the marked animals caught again, not by N. A small R gives a large population.
Remember it as: marked first, times caught second, over marked again.
Worked example: A class catches and marks 40 woodlice under logs (M = 40). Two days later they catch 30 (N = 30), of which 8 are marked (R = 8). Population = (40 × 30) ÷ 8 = 1200 ÷ 8 = 150 woodlice.
Why it works: the share of marked animals in the second sample (R out of N) should match the share of marked animals in the whole population (M out of the total).
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The Lincoln index gives a fair estimate only if these assumptions hold. A trap-happy or trap-shy animal breaks the last one.
The assumptions
- The population is closed: no births, deaths, arrivals or departures between the samples.
- Marks are not lost before the second sample.
- Marks do not harm the animal or make it easier for predators to find.
- Marked animals mix evenly back into the population.
- Every animal has the same chance of being caught: none become trap-happy or trap-shy.
- Both samples use the same method and effort.
| If this goes wrong | Marked recaptured (R) | The estimate is |
|---|---|---|
| Marks rub off | Too few | Too high |
| Marked animals are eaten more | Too few | Too high |
| Animals become trap-shy | Too few | Too high |
| Animals become trap-happy | Too many | Too low |
Remember it as: Closed, marks stay, no harm, mixed, same chance, same method.
Example: bait in the traps can make mice trap-happy: marked mice come back for food, R is too big, and the estimate is too low.
Planning a reliable study: Each step of the method can be done in a way that keeps the assumptions true.
The points to remember
- Mark enough animals in the first sample.
- Spread the traps evenly across the whole habitat.
- Allow enough time to mix, but not so long that births and deaths change the population.
- Use harmless, durable marks, and release animals where they were caught.
- Avoid making animals trap-happy (bait) or trap-shy (rough handling).
- Repeat the recapture several times and average the estimates.
- Use it only for mobile species that stay in the study area.
Other ways to estimate mobile animals: Count them in aerial or satellite images, or with camera traps, over a representative area, then scale up to the whole area.
Real example: in pond surveys, water snails are often marked with a dot of nail varnish on the shell, which does not harm them and lasts for weeks.
Remember it as: Enough, spread, time, harmless, no bait trap, repeat, stays put.
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Counting a food chain: A pyramid of numbers needs the number of organisms at each level, in the same area. Each level needs its own method.
The points to remember
- Producers (plants): random quadrats, then mean × total area.
- Small, slow animals (snails, insects): quadrats, sweep nets or pitfall traps, or mark-recapture.
- Mobile animals (birds, mice, fish): mark-recapture and the Lincoln index.
- Large or shy animals: aerial photos, bird song counts or camera traps, then scale up.
- Draw each level as a bar whose width is proportional to its number.
Remember it as: Plants: quadrats. Movers: mark-recapture. Big and shy: photos.
Example: for grass, then grasshoppers, then shrews in a meadow: quadrats for the grass, sweep nets and mark-recapture for the grasshoppers, live traps and mark-recapture for the shrews.
Every level is an estimate: Repeat each method and sample in the same season, so the pyramid compares like with like.
How this comes up: Calculate a Lincoln index estimate [1]; describe the method [2-3]; ways to make it reliable or factors that affect accuracy [2-4]; collect data for a pyramid of numbers [7]; how reliable sampling can be [9].
Grey squirrels live in a large city park. The park's managers want to know how many there are.
Describe practical procedures for estimating the population size of the grey squirrels.
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