So far we have discussed how scientists determine the sizes of penguin colonies, but we haven't yet discussed their findings. I would like to focus on a particular site, called Petermann Island, because it has a long history of penguin surveys.

In January of 1909, Jean-Baptiste Charcot and his men arrived at Petermann Island on a ship called Porquoi Pas? (Why Not?) during Charcot's second Antarctic expedition. The group would spend a year on the Antarctic peninsula, surveying 1250 miles of coastline, taking 3,000 photos, and keeping 28 volumes of scientific data. It was a very fruitful expedition for many reasons, but one important thing they did was study the penguins there. In fact, Charcot enjoyed the penguins so much, that Oceanites reports, "There are pictures of Charcot lying prone in the snow at Booth, attempting conversations with nearby penguins, or marching among groups of them, seeking their acquaintance." They enjoyed the penguins so much, they even took a gramophone ashore to play music for the penguins on Christmas!

During their time on Petermann Island, they counted 925 breeding pairs of Adélie penguins and only about 50 breeding pairs of Gentoo penguins. This was one of the first expeditions to study penguins in Antarctica, and because of it, Petermann Island is one of the rare places with data that spans over a century. And comparing this old data with newer data, it's interesting to see that the two species have effectively switched positions: while the Adélies previously outnumbered the Gentoos by an order of magnitude, now the Gentoos outnumber the Adélies by an order of magnitude. The most recent data I have seen indicates 3,516 nesting pairs of Gentoo penguins and 238 nesting pairs of Adélie penguins in 2017.

There are many reasons for these changes. One suggestion is that Gentoos have a more varied diet, so they can survive more easily when food resources shift. Another suggestion is that climage change has forced Adélies to head further south, as they struggle to thrive in warmer climates. And lastly, Gentoos are much larger than Adélies, and frankly, capable of bullying them and stealing their nests.

Below, you will use data provided by Oceanites to look at how the Gentoo and Adélie populations on Petermann Island have changed over the years.

Sample Problems

1. Use the data from the table below and Google Sheets to make a scatter plot representing the Gentoo penguin populations for each season (measured in nesting pairs).

2. Do the same for the Adélie penguin populations for each season.

3. Use Google Sheets to determine a linear trendline (line of best fit) for each set of data. (Google Sheets will do this for you: select "Trendline" and "Use Equation" for the label under the "Series" settings for the scatter plot.)

4. What are the R² values for each trendline? (Google Sheets will calculate this for you: select "Show R²" under the "Series" settings for the scatter plot.)

5. Using the R² values and a visual inspection of the trendline on the scatter plot, determine whether or not the trendline is a good representation of the data.

6. Use the trendlines to predict the Gentoo and Adélie penguin populations in 1909, when Charcot overwintered and counted the penguins on Petermann Island. Note that the actual counts included 50 nesting pairs of Gentoo penguins and 925 nesting pairs of Adélie penguins. What are the residuals (in other words, what was the difference between the actual values and the predictions from the trendline)?

7. What conclusions should be drawn about using trendlines for extrapolating data outside of the starting range?

8. What could go wrong with using trendlines to predict future penguin populations on Petermann Island?