Capture-Recapture (Edexcel GCSE Maths)

Capture-Recapture

What is the capture-recapture method?

• The capture-recapture method is a way to estimate the size of a population

  • It is used when it is impossible, time-consuming or impractical to count the whole population

  • Common examples include

    • the population of fish in a river/lake/sea

    • the population of wild animals, in their natural habitat

• The capture-recapture method is based on proportion

  • A first sample of the population is captured and each member is given an identifiable marker/tag

  • All members of the sample are then replaced (released) into the population

  • At a later time, a second sample of the population is taken

  • The proportion of the second sample that is tagged is assumed to be the same as the proportion of the population that is tagged

How do I use the capture-recapture method?

• Let N be the size of the population

• Take the first sample of size M, say

  • i.e.  M members of the population have been captured

  • Mark/tag every member in the sample (M members of the population now have tags)

  • Release all of the sample back into the population

  • Wait some time for those captured to mix with the rest of the population

    • the amount of time required will depend on the type of population
      e.g. fish may only need a few hours to mix but wild animals in a large habitat area may need days

• Take the second sample of size n, say

  • Let m be the number in the second sample that have marks/tags

  • i.e.  m previously tagged members of the population have been recaptured

• Form an equation by using the assumption of proportion

  • i.e.  the proportion of the second sample tagged is equal to the proportion of the population tagged

  • 

  • In words this is 

• Rearrange this equation to find an estimate for the population size N

  • 

What assumptions are made in the capture-recapture method?

• Each member (element) of the population has an equal chance of being selected

  • this applies to both the first and second sample

• Between the first and second samples

  • the tagged members have had sufficient time and opportunity to mix with the rest of the population

  • the population remains the same size (broadly speaking)

    • no (significant number of) births/deaths

    • no (significant number of) members leave the population - e.g. migration

  • No marks/tags have been removed or destroyed

    • e.g.  taken off, worn off