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Mark and Recapture

High schoolBiologyLincoln-Petersen estimate N = n₁n₂/m from random catches in a closed population

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About this experiment

How many fish live in a pond? You cannot count them all, but you can estimate the number by sampling twice. Catch some fish, mark them and put them back. After they have mixed in, catch a second sample and count how many are marked. If one fish in six of the second catch is marked, then the marked fish are probably about one sixth of the whole population. Run surveys on this pond, repeat them many times to see how reliable the method is, and find out what happens when its assumptions are broken.

Learning goals

  • Describe the mark and recapture method for estimating population size
  • Calculate an estimate with the Lincoln-Petersen formula
  • Explain why larger samples give more reliable estimates
  • List the assumptions of the method and explain how breaking them biases the estimate
  • Interpret the spread of results from repeated surveys

How to use it

  1. 1Run one survey with the default settings. Calculate the estimate yourself and check it.
  2. 2Press New survey a few times. Does the estimate come out the same each time?
  3. 3Press Repeat 200 surveys. Is the mean estimate close to the true number? How wide is the spread?
  4. 4Reduce both catches to 10 fish and repeat 200 surveys. What happens to the spread?
  5. 5Switch on Marked fish avoid the net and repeat 200 surveys. Is the estimate now too high or too low? Why?
  6. 6Hide the true number, let a partner set it, and estimate it with one survey.

The model

The share of marked fish in the second catch matches the share in the whole pond
Lincoln-Petersen estimate: n₁ marked, n₂ in the second catch, m of them marked
Chapman estimate: less biased for small samples and still defined when m = 0

Assumptions

  • The population is closed: no fish are born, die, arrive or leave between the two catches.
  • Marks do not fall off and do not harm the fish, and marked fish mix completely with the others.
  • Every fish has the same chance of being caught, unless Marked fish avoid the net is switched on.
  • Catches are random samples from a seeded generator, so the same survey number always gives the same catches.

Try this in class

  1. Q140 fish are marked. A second catch of 50 fish contains 8 marked fish. Estimate the population.
  2. Q2Why must the marked fish be given time to mix before the second catch?
  3. Q3If marks wash off some fish before the second catch, will the estimate be too high or too low?
  4. Q4Why would this method give a poor estimate for a population of snails that hardly move?
  5. Q5Repeated surveys give estimates that spread around the true value. How could an ecologist make the spread smaller?

Frequently asked questions

Why is the estimate sometimes far from the true number?

Chance decides which fish are caught. With small catches, one or two marked fish more or less changes the estimate a lot. Repeating the survey or using larger catches makes the estimate more reliable.

What if no marked fish are caught the second time?

Then the Lincoln-Petersen formula divides by zero. This usually means the samples were too small for the population. The Chapman version still gives a number, but it is very uncertain.

Is this method used in real ecology?

Yes, for fish, birds, butterflies, small mammals and many other animals. Real studies use marks that last, check the assumptions carefully and often take several samples over time.