Use mark and recapture to estimate the population of Smarties in a candy bowl.
You will need
- a big bag of Smarties
- a small bag of M&Ms
- a bowl
- a large spoon.
What to do
To estimate the population of Smarties in a candy bowl using mark and recapture you will need to:
- Empty the Smarties into the bowl.
- Ask your friends to estimate how many Smarties there are in the bowl.
- Count the M&Ms in the small packet and write this number down.
- Count out the same number of Smarties from the bowl, and replace them with the M&Ms.
- Mix the Smarties and M&Ms thoroughly.
- Using a large spoon, take a scoop of the Smarties/M&Ms mix from the bowl; this is your sample.
- Count the number of Smarties and the number of M&Ms in the sample.
- Write down how many lollies were in the sample altogether, plus the number of M&Ms in the sample.
- Use the following formula to estimate the total number of smarties.
Number of Smarties = total number of m&m's x sample size / number of m&m's in the sample.
Do you think it is a good estimate?
This method of counting is called mark and recapture, or tag and release, and it's commonly used to count animals. In this activity, the Smarties represent a population of animals, and the M&Ms represent a small group of those animals that have been tagged, or marked.
Mark and recapture works like this: First, you catch some animals, count them, and tag them (your M&Ms, in this activity). You then release them into the wild (mix them with the Smarties). Because you counted them, you know how many you tagged.
Later, you catch some more animals in the same area (your sample). Hopefully some of them have tags on them from your last survey (you'll get a mix of Smarties and some M&Ms). From this catch, you can estimate the percentage of the population that have tags on.
Percent of animals tagged = number of tagged animals in sample x 100% / total number of animals in sample.
You can combine the percentage tagged and the number tagged to get a good estimate of the total population.
Total number of animals = number of animals tagged x 100% /percent of animals tagged
If you only do one sample, then the population estimate might not be very accurate. But repeated captures, taggings and counts can even out the ‘luck factor’ and provide a good estimate.
Mark and recapture is a very popular method of estimating animal populations. It is really useful, because you don’t need to catch every single animal in order to work out the population size. It does, however, have some problems. The maths makes many assumptions that might not be true.
For example, if the animals move around a lot then the tagged ones might move away from your survey area, so you can’t catch them again. Similarly, if the tagged animals are easier to catch, then this could make the estimated population smaller than it should be. And if tagging animals make them easier for predators to catch, then you could be affecting the ecosystem.
Mathematicians have developed advanced techniques for analysing data from mark and recapture schemes. This allows scientists to estimate many of these factors while conducting surveys. It also allows them to work out other interesting facts, including how far the animal moves, and how long they live.
You can help too! Some birds have bands around their legs. If you find a bird with a band and can get close enough to read the code on the band, you can register the information with the Australian Bird and Bat Binding Scheme (ABBBS), and help scientists to monitor bird populations in your area! Please don’t try to catch birds, unless you have been properly trained. It is very easy to hurt them.
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