Lincoln Index for Estimating Population Sizes

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One common method for estimating population sizes in a given ecosystem is called the capture-mark-recapture method. To begin, a large group of animals must be captured or caught in some way. Those individuals are then marked in some way (often with a
harmless tag) that can be recognized later. The animals are then released back to their environment. After a period of time, the same capture method is used. This time, the total number of individuals caught is recorded, as well the number of those which have marks from the initial capture.

With those values, a statistical method referred to as the Lincoln Index can then be used to estimate a population size for that particular environment. The estimate can be made with just two samples, but the more sampling that is done, the more accurate the estimate becomes.

Below is an app that will generate random data. Use the data to estimate the population size of the sample species. Check your answers when finished.

Lincoln Index for Estimating Population Sizes

Lincoln Index Practice (Capture–Mark–Recapture)
Use N = (n1 × n2) ÷ m2 to estimate population size.
Problem
n1
# captured & marked (sample 1)
n2
# captured (sample 2)
m2
# marked recaptured (sample 2)
Score
0
Correct
0
Incorrect
0
Streak
Tip: Reasonable answers depend on sampling—expect an estimate, not a perfect count.
Formula
N = (n1 × n2) ÷ m2
N = estimated population size
n1 = marked in first sample
n2 = captured in second sample
m2 = marked recaptured in second sample

Limitations of the Lincoln Index

The Lincoln index relies on several assumptions that may not always hold true in real-world scenarios. These limitations include:

  1. Closed population: The method assumes that the population size remains constant between the two sampling periods. Immigration and emigration can affect the accuracy of the estimate.
  2. Equal catchability: The method assumes that all individuals in the population have an equal chance of being captured in both samples. This may not be the case if certain individuals are more or less trap-happy than others.
  3. Random sampling: The method assumes that the samples are representative of the entire population. Biased sampling can lead to inaccurate estimates.
  4. Mark retention: The method assumes that the marks applied to the individuals in the first sample remain visible and do not affect their survival or catchability. Marks that are lost or that affect behavior can bias the results.
  5. Sufficient sample size: The method requires a sufficiently large sample size to ensure that the estimate is reliable. Small sample sizes can lead to large errors.
Lincoln Index

AICE Marine Practice Test

When you feel that you’re ready and you’d like to test your level of knowledge, take our online AICE Marine Practice Test to see where you’re at and the areas that still need some focus. Good luck!

If you need more help, here is the textbook from Cambridge Press:

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