There are about eight million people living in New York City, and urban legend has it that there are just as many rats. We’ve all seen them scampering on the subway tracks and scurrying through parks after sundown -- but one rat for every person? No way, according to new statistical analysis published in Significance last week. Not even close.
Getting an accurate count is difficult. “Animals are terrible survey respondents,” Jonathan Auerbach of Columbia University writes. At first, he tried using the two-sample version of the capture-recapture estimation method, which is used by ecologists to approximate abundance of wildlife. But that would have required catching, marking, and releasing a random sample of rats, and then catching and releasing a second random sample to see what proportion were already marked. “Unfortunately, NYC’s Department of Health and Mental Hygiene is unlikely to approve a large-scale rat-releasing experiment (I know, because I asked),” he writes.
Instead, Auerbach’s team classified the 842,000 or so city lots in New York based on rat complaints from publically available city call logs. (Data on these calls to 311 include the location of each sighting, though these don’t account for rats living below ground.) The team observed the number of lots that reported a rat sighting in the first half of 2010 (these are the “marked” lots), and then the number of lots with reported sightings during the first half of 2011. Lots that reported sightings during both sampled periods were the equivalent to rats that were “recaptured.” By assuming that these lots are as likely to be reported as any other rat-inhabited lot, “the proportion of ‘recaptured’ lots in the second sample period will then provide an estimate of the total number of rat-inhabited lots,” Auerbach explains. They took into consideration factors such as how residents of some neighborhoods were more likely to report rat sightings than others (in fact, 20 percent of the city’s 195 or so neighborhoods account for 50 percent of all the calls).
The team estimated 40,500 rat-inhabited lots, plus or minus 3,000 -- that’s 4.75 percent of the city’s lots. Between 40 to 50 rats belong to a typical colony, and because they’re territorial, it’s unlikely that two colonies will live in the same lot simultaneously. If one full colony occupies each of these rat-inhabited lots (and that’s being very liberal), that still leaves us with just two million rats, give or take 150,000.
Even a generous estimate would put the ratio at 4-to-1, humans-to-rats. Every lot would need to support its own colony of about 180 rats for the “one-rat-one-person” scenario to be plausible in New York.
“While the rat population remains a serious problem in New York City, there appears to be no evidence supporting the 8 million number,” Auerbach says in a news release. “In problems like this, the city’s open data is invaluable for challenging rumors, evaluating community need and establishing government efficacy.”