Are there really 8 million rats living among the 8 million humans of New York City?
If you find that particular urban myth hard to believe, it seems you may be right. A study published in Significance, a publication of the Royal Statistical Society, finds that the number of rats scurrying around the Big Apple's five boroughs is closer to 2 million, and probably way less than that.
"There is no way that the data, as it exists, is consistent with the 8 million number," said Jonathan Auerbach, a PHD student in statistics at Columbia University, and the author of the paper.
To get to a more realistic estimate of the number of rats living in New York City, Auerbach turned to the capture-recapture method, which is frequently used by ecologists to determine the abundance of wildlife in a given area.
In a perfect world he would have captured a random sample of rats from around the city, marked them, and then released them. Then, after a period of time, he would have captured another random sample of rats and seen how many rats among the new sample were already marked.
For example, imagine he caught and marked 10,000 rats. Now imagine six months later he caught another 10,000 rats, but that just 1% of them had already been marked. He would then assume that the first 10,000 rats made up just 1% of the total population since a marked rat is just as likely to be caught as an unmarked rat. And since 10,000 is 1% of 1 million, that would mean there were 1 million rats in the city.
All of this is sort of moot though, because the NYC's Department of Health and Mental Hygiene didn't want him doing a large scale rat-releasing experiment. (He asked). So instead, Auerbach turned to a data set that the city has already made available to the public: A list of all the rat sightings reported to the city by 311 callers.
First he looked at the number of city buildings, where people had reported a rat sighting during the first half of 2010. Consider this the "marked" group of lots. Then he looked at the number of lots that reported sightings during the first half of 2011. Some of these lots were "marked" because they were the same lots where rats had been sighted before.
Because there were different rates of rat sightings reported in different neighborhoods, he did this evaluation for all the neighborhoods in New York City (nearly 200 neighborhoods in all), and determined that there are about 40,500 buildings in the city with rats living in them. If each of these lots had a full blown colony of 50 rats in it, then you get 2.025 million rats in New York City.
The number is likely lower than that Auerbach said, because some rats might be just passing through a building, or a colony could be smaller than 50.
Auerbach, who used to work in New York City government knows his model isn't perfect -- it doesn't take into account the rats in the subways or sewers, or in the parks -- but he said it is a good place to start.
As he writes in the paper: "This study is best seen as part of an ongoing investigation that will change as new evidence is brought to light and our underlying assumptions are refined."
But 8 million rats in New York City? Probably not.