The study sought to nail down how many shelters exist in the United States, estimates of which vary widely. Based on a telephone survey of 413 shelters, it used capture-recapture methodology — which is used to estimate human and wildlife populations — to determine that there are nearly 7,100 shelters nationwide.

Using data collected from the surveyed shelters, the researchers then concluded that more than 5.5 million dogs enter shelters each year and that fewer than 780,000 are euthanized. The remainder are returned to their owners, transferred to other rescues or shelters or adopted, the researchers found.

Mark Cushing of the Animal Policy Group, the lobbying firm that crunched the numbers on demand for dogs, says the data show that U.S. shelters can’t meet Americans’ demand for 8 million dogs a year.

“It’s a total myth for anybody to say or think that every American who wants a dog can go to a shelter and find one,” Cushing said. “Increasingly the ones we are euthanizing are very sick or dangerous.”