Estimating Population Size by Mark, Release and Recapture
Estimate a mobile animal population from the marked proportion in a second catch. Calculate the estimate, check its sampling assumptions, and explain how lost or harmful marks can bias the result.
What a learner can do afterwards
- Calculate a population estimate from the number marked in the first catch, the total in the second catch and the number marked in the second catch
- State the assumptions about population closure, mixing, capture chances, survival and retained marks
- Explain how a mark that makes an animal easier for a predator to see biases the estimate, and in which direction
1 · Read
Quadrats sample organisms that stay still or move slowly. Transects help investigate change along a habitat gradient. For suitable mobile animals, mark and recapture offers another way to estimate a population. Researchers capture a sample, mark and release it, allow mixing, then capture another sample and count its marked animals. Handling and marking need appropriate permission and animal care.
Researchers mark and release 16 fish. A later catch contains 24 fish, including 4 marked fish. The marked share is 4/24, or 1/6. If this represents the population, the 16 marked fish are about one sixth of the total: 6 × 16 = 96 fish. Use first marked count × second catch size ÷ marked count in the second catch. A zero marked count cannot be used as the divisor.
The two-catch method assumes no births, deaths, arrivals or departures between catches. Marks must remain readable and must not change survival or capture chances. Marked and unmarked animals need comparable chances of capture. Mixing should let the second catch represent the population's marked share; small groups do not all need to have the same fraction. Allow time for mixing without a long gap that permits major population change.
With catch sizes fixed, fewer recognised marks in the second catch make the estimate larger; more make it smaller. Lost marks or extra predation on marked animals can therefore cause upward bias. A catch from a marked-heavy release area before mixing can cause downward bias. These are expected directions under the stated conditions, not a guarantee for every sample.
Report an estimate rather than an exact census total. Chance affects which animals enter the samples even when the assumptions hold. Explain the method, uncertainty and suspected bias. Repeated, well-designed sampling helps assess uncertainty, but repeating a biased method does not remove its bias.
Estimate the total from a second catch's marked share. Check mixing, capture chances, population change and marks, and report uncertainty.
Lesson, questions, worked solutions and flashcards written for this dataset. Population-demography sources informed the facts and teaching design.
Readings and flashcards written for this dataset. Linked video: Khan Academy, "Estimating a population count from a random sample".
More to read
Reading a marked fraction
Imagine a researcher marks 21 animals and releases them. After mixing, another catch contains 35 animals. Seven carry a recognised mark. The observed marked fraction is 7/35, or one fifth.
To estimate the population, treat the 21 originally marked animals as one fifth of the total. Five shares of 21 give an estimate of 105 animals. The formula gives the same result: 21 × 35 ÷ 7 = 105.
This reasoning depends on the sample representing the population. The population should remain closed between catches, marks should remain readable, and marking should not change survival or capture chances. Animals also need suitable mixing and comparable chances of capture.
A second catch with no recognised marks cannot be used as a divisor in this formula. Even a usable result is an estimate rather than a census. The report should describe both the calculation and the conditions that may limit it.
How sampling can distort the result
A second capture is useful only if marked animals remain representative of the population. A lost mark makes a marked animal appear unmarked. A mark that attracts predators can reduce marked animals' survival. Either problem can reduce the recognised marked share and push the estimate upward.
Behaviour can change capture chances too. Previously caught animals may avoid traps. Others may return more readily if capture provides food. With catch sizes fixed, fewer recognised marks increase the calculated estimate, while more recognised marks decrease it. These describe expected bias mechanisms, not a guaranteed outcome for every individual sample.
The time between catches presents a trade-off. Too little time may leave marked animals clustered near the release site. Too much time may allow births, deaths or movement across the study boundary. Researchers need a gap suited to the organism and study.
More observations help assess sampling uncertainty. They do not repair a repeated marking or capture bias by themselves.
Different questions need different samples
A quadrat defines an area in which to record organisms. It does not fence them in. It is often suitable for plants and slow-moving organisms that can be counted within its boundary.
For a whole-field plant estimate, randomly selected quadrats can reduce location-selection bias. Calculate a mean count per unit area, then scale it to the field area. Keep the species and counting rules consistent.
A transect answers a different kind of question: how do observations change with position? Sampling at regular distances from a field edge can help reveal a gradient. A transect does not need random positions along its length to serve that purpose, although the placement plan still affects what can be concluded.
For suitable mobile animals, mark and recapture estimates a population from the marked share of a later catch. Method choice depends on the organism and question. No method guarantees that a meadow, lawn or other habitat will have a particular biodiversity ranking.
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