If we're studying animals in the wild then it'd be useful to know how many there are. We'll look at some techniques ecologists use. One key thing to think about is tradeoffs, mainly between how accurately we need to know the population and the costs in time and money of working it out.

We want to estimate how many ducks are in the pond, take out a large handful and hide them away so the numbers are at random. Kids may try and count, it works fine for rubber ducks, but they'll have issues if they try with real ones! They move around, all look the same, are right in the middle of the pond, fly off or are hiding. In reality we'll have to make do with an estimate! There's two ways of doing this.

[you may get some people guessing based on the numbers on the bottom, this is also very interesting but not in the context of ducks (which rarely come uniquely numbered). Its called the German tank problem and you can explain if you know about it, even though its not related to ecology!]

Capture Recapture

One way we could do this is via sampling. Take a sample of ducks (around 12-16 works well if you've removed a dozen or so) and mark on the whiteboard which numbers you saw. Replace the ducks and mix well. This represents our first sample and we've now made sure our next sample is 'independent' by shuffling it. Take another sample of ducks and count how many are in both. We then need to do some maths, the sample size over total number of ducks will be put probability of picking a duck from sample, 1 in samples 2. So if we times this by the sample size it gives how many ducks we'd expect to see both times. Doing the product of sample sizes divided by the number in both gives us our estimate. You can now ask questions about the population. Drawing a venn diagram may be useful.

Can we say anything about the minimum size? Yes, it's at least the number of unique ducks we saw... What about the maximum? Nothing at all, however we can think about it, if there were lots of ducks we'd not get any repeats and if there were only a few more than the sample size we'd get mostly repeats. Other ways to improve include making the sample size bigger.

You can talk about the effects of sample size on the estimate, what do you think increasing it does? Increase variance or uncertainty. Why don't we take big samples, it's expensive

You can also talk about bias, if you don't mix, you'll probably get some bias.

This is where you might see marked, chipped or collared animals as part of these estimates.

Areas

We should also do this. Taking the pond from robots that doesn't work and sewing lines onto it to form quadrants.

Biased Sampling

This is a quick demo to talk about it and isn't majorly about animals. Take an opaque bag with 20 small balls and 5 large of different weights. Tell people they can pick a sample to guess the weight of the bag of balls. Tell them there's 25 balls in it, but don't mention the different types. People will gravitate to picking bigger balls so it'll bias their sample and throw their weights off.

Penguins by poo

Even capture recapture gets expensive if we want to estimate penguins. Why? They're far away, not good infrastructure, it's chilly, etc. So we want to find a better way. As penguins live on ice sheets which are white we can use photos to pick them out. Show some photos from a satellite (a few are actually drone photos but very similar). It's hard to count penguins in this as they move and are slightly camouflaged. Huddles are confusing as varying density. So we count the amount of poo! You can pick it out in the photos. So how might we estimate the number of penguins. Count the area of poo, use the grids over the picture to work out the poo area. We now need to work out poo area a penguin produces! Here are some penguins, lift them up to reveal their poo areas.

You'll need to take a sample and average. You'll also notice the babies are a source of bias... This is similar to before. If you do the maths you can estimate the population.

Where are the errors? Where did our sample come from, zoos is a nice controlled environment for it, but might not give the best accuracy for wild penguins, different food and environment. There's also the depth factor which we ignore. Our measurements weren't perfect for the area either, however satellites can do much better.