7 Mins Read | By Simon Tang

Key Points Summary

• Mark Release Recapture (or Capture Mark Recapture) is a way to sample the population of mobile organisms (organisms that move around)
• You first capture a set number of organisms and tag them with something inconspicuous.
• You then release them back into the wild. After a period of time, you recapture a set number of organisms.
• The percentage of tagged organisms out of your recaptured sample represents their presence in the total population. Thus, you would multiply the number of initially tagged organisms with the reciprocal of their percentage in the recaptured population for the total population.

Content

Introduction

After successfully using the quadrat method to count fields of daffodils, your ever-impatient manager drives you to a mystery location for some more work. You wonder how many daffodils you will need to count this time, and also wonder why you’re going in the middle of the night. Maybe there are some rare glow-in-the-dark daffodils?

However, when you arrive, you are shocked to see that there is not a single flower in sight.

It’s an entire cave of bats! Before you could even utter a word to your manager, they leave with the same instructions as last time – count them all by the end of the week, or you are fired.

You already know how to sample organisms using the quadrat method, but this wouldn’t help you here – imagine tossing a plastic square at a colony of bats, they would just fly away! The quadrat method only works for organisms that do not move. For organisms that move around a lot, you need to use a different method, called the capture-mark-recapture method.

Capture-Mark-Recapture

Imagine you’re trying to count the number of balls in a bag. You are not allowed to tip it over nor take out all the balls. The bag is always jostled around, so all the balls get mixed up every so often.

You may be able to count thirteen balls right now but imagine that you can’t. In the actual cave of bats, you do not know the true number of bats there, but you are trying to figure it out. 

The idea is that you take out a small number of balls from the bag, such as five balls, and then you mark them.

You then return them back into the bag and then shake the bag. Now, the number of marked, or green, balls out of the total number of balls in the bag represents a fraction, or a percentage. We already know it is 5/13, since we were told the original number, but if this were the cave of bats, we would NOT know.

The way that this is done is by taking a sample of the population AFTER the marked individuals have been returned, and then assuming the sample fraction of green balls vs total sampled balls and the total number of green balls vs TOTAL population is the same. Let’s write this assumption down, and then see how this plays out in our example here.

After the bag is mixed, we take out five balls:

Here, in our recaptured sample of balls, 2/5ths are green, or 40%. This means that we are ASSUMING that in the bag, 40% of the balls are green. Because we already know how many balls are green (five) we just need to find the total population that gives us the same ratio.

Cross-multiplying them gives: 

13! Which is exactly the number of balls in our bag! Keep in mind that while we predicted it accurately here, it is not always that accurate, so you might want to take multiple samples and then average the results.

With this in mind, you’re ready to use capture mark recapture to estimate the number of bats in this cave. One night, you trap 50 bats, and you put a small, blue tag on their ankles, small enough so that they are not affected by it. This means that the fraction of marked bats out of the total bats in the cave can be written as: 

Once again, ‘?’ represents the unknown total population.

You let the bats fly around randomly for a few days, and then recapture 50 bats. Here, you find that only 10 of them have been tagged from before. This means that in the sample population, 10/50 or 20% of the bats are tagged.

Equating this to the number of tagged bats over the total population, we get the following:

Conclusion

As the sun sets on the last day of the week, you send your calculations over to your manager. They review your work and give you the thumbs up. Hurrah (again)!

Equipped with your bat traps, you’re ready to take on any cave in the world. You glance at your calculations and marvel at how maths can take you so far.