There may be 8 million stories in the Big Apple, but one of them — that New York City is home to 8 million rats, or one for every human resident — is probably a tall tale, according to research by a Columbia University statistician.

In truth, the city's rat population is probably closer to 2 million, said Jonathan Auerbach, a Columbia doctoral student who wrote an essay on the subject published in Significance magazine.

The urban lore that there are as many rats as citizens dates back at least a century, Auerbach says. It may have endured in part because reliably estimating the city's rat population is difficult even though the creatures are hardly invisible, as most New Yorkers who see them skittering about the subway tracks or hear them rustling through trash piles will attest.

Auerbach used complaints from the public about rat sightings, which the city tracks and publishes online. Combining the data with a number of assumptions, he was able to extrapolate the number of rat-occupied lots to about 40,500 across the city, or less than 5 percent of the total.

If each inhabited lot is home to a typical colony of 50 rats, that would mean there are about 2 million rats in the city.