MathBench>Environmental Science

Killer Housecats

Moving along... another issue that's been in the news lately is the possibility that housecats have been decimating songbirds. One post I read suggested that a pet cat who is let outside can kill 20 to 50 birds per year.

Of course, cats might only be getting those birds that would have been caught by hawks or foxes, or that would have succumbed to cold or heat or hunger. And not every cat is a lean mean killing machine.

So, how could you design a study to test whether housecats are really having an impact? You could approach it like the fish ponds, and look for towns with cats and towns without cats. There's a problem, though: at 90 million strong, cats are the favorite American pet. You probably won't find many towns without them.

Instead, you could sample the populations in a number of towns, and record both how many cats and how many birds there are, like this:

town cats songbirds
1 2000 1600
2 3000 600
3 4000 200
4 2800 1200
5 600 2000
6 3500 400
7 1800 1800
8 500 4800
9 2500 1600
10 700 2200

Note on the data: I made up these numbers, but I based them on real information: an estimate of US bird population of about 6 billion birds (in the summer), and the year-round pet cat population of about 80 million. I assumed cats were concentrated in residential areas, where there would be 1 cat for every 3 people. I assumed that birds would be evenly spread throughout the country. Finally, each sample area was 1 square mile, with a density of about 6000 people (typical of suburban areas).

Now we just need to figure out how to analyze this data. Here's a way that does NOT help:

• average # of cats: (2000+3000+4000...)/10 = 2140 cats
• average # of birds: (1600+600+200...)/10 = 1640 birds

Why not? We're trying to show that the number of birds DEPENDS on the number of cats. Just taking the average for each is not going to show that. Its an example of MATH RUN AMOK -- you CAN do this, but it doesn't do any good.