Biology · Introductory biology · Concept
Mark–recapture population estimates
Mark–recapture estimates how many animals live in an area without counting them all. Catch and mark M animals, release them to mix back in, then catch a second sample of C animals and count the R that carry marks. If marked animals make up the same fraction of the second catch as of the whole population, R/C = M/N, which gives the Lincoln–Petersen estimate N ≈ MC/R.
The proportion behind the estimate
After mixing, the marked animals are M out of N. A random second sample should hold about the same fraction of marked animals, R out of C. Solving R/C = M/N for N gives the estimate, written N̂ because it is an estimate.
The assumptions
The population is closed between the two samples: no births, deaths, immigration or emigration. Marks are not lost or overlooked and do not change an animal’s survival or behavior. Every animal is equally likely to be caught, and marked animals have time to mix back in. The estimate is only as good as these conditions.
Chapman’s correction
With few recaptures the Lincoln–Petersen estimate tends to run high. Chapman’s version adds 1 to each count and subtracts 1 at the end. It is less biased for small samples and stays finite when R = 0, although a second sample with no recaptures carries almost no information.
How precise is the estimate?
Few recaptures make an uncertain estimate. The approximate 95% interval, the estimate ± 1.96 standard errors, is wide when R is small and narrows as more marked animals are recaptured. It measures sampling chance only: it cannot detect a broken assumption.
When the assumptions fail
Trap-happy animals, which return to baited traps, raise R and push the estimate too low; trap-shy animals lower R and push it too high. Lost marks and newcomers arriving between the samples also make the estimate too high. Deaths that strike marked and unmarked animals alike leave the marked fraction unchanged, so the estimate still describes the population at the time of marking.
Common mistakes
- Putting R in the numerator: the recaptured count goes in the denominator.
- Treating the estimate as exact: with few recaptures its interval is wide.
- Leaving too little time for marked animals to mix back in, so the second catch holds too many of them.
- Ignoring trap-happy or trap-shy behavior, which pushes the estimate down or up.
Key terms
- Mark–recapture
- Estimating a population’s size by marking some individuals, releasing them, and seeing what share of a later sample is marked. It assumes marks stay on, animals mix, and all are equally likely to be caught.
- Lincoln–Petersen estimator
- N ≈ MC/R, with M marked in the first sample, C caught in the second and R of those marked. If no marked animals are recaptured (R = 0), it gives no estimate.
- Chapman correction
- The corrected estimate N ≈ (M + 1)(C + 1)/(R + 1) − 1, which is less biased for small samples. It can’t fix a study that breaks the method’s assumptions.
- Population closure
- The assumption that no births, deaths or migration change the population between the marking and recapture samples. Equal chances of capture is a separate assumption.
- Population
- All the individuals of one species living in a given area at a given time. Population size counts them; density divides the count by the area or volume.
- Normal approximation
- Treating an estimate’s uncertainty as normal, so an approximate 95% interval is the estimate ± 1.96 standard errors. With small samples, few recaptures or a skewed estimate, the real coverage can differ from 95%.
Work through an example
Biologists mark 60 turtles in a pond and release them. Two weeks later they catch 75 turtles, 15 of them marked. Estimate the population with the Lincoln–Petersen and Chapman formulas, and say how precise the estimate is.
Estimate population size with mark–recapture →Sources and scope
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