No, Donald Trump does not have a yellow Labrador retriever named Spinee that is recovering from surgery. Neither does Hillary Clinton. Those rumors, curiously enough, are propagated by an internet hoax site that seems to delight in pranking celebrities.

But Clinton does have two dogs, Tally and Maisie, which, if she were elected president, would be the latest in an illustrious and colorful line of first pets.

Trump, if elected, would be the first president since Harry Truman without a pet. (Truman’s family was given a couple of dogs that did not take up permanent residence at the White House.)

It is one of the many things that set the two major party nominees apart, though how much this matters to the public is unclear. But owning a cute dog or mischievous cat can be a political asset: When Gov. Scott Walker of Wisconsin was running for the Republican nomination, his allergy to pet dander was seen as a potential liability.

Entire books have been written about presidential pets, and presidents are frequently given animals once they reach office (though often those animals are re-gifted). So presumably, if Trump reached office, he would receive some animals as a reward. (Feel free to speculate about the type and breed.)

While dogs have been the most popular option for leaders of the free world, there have been many exotic animals in the White House: John Quincy Adams kept an alligator in a bathtub near the yet-to-be-finished East Room; William Howard Taft brought his cow, Mooly Wooly, with him to Washington; and Theodore Roosevelt and his large family owned, at various times, a pig named Maude, a snake named Emily Spinach and a badger named Josiah.

Dave Baker, co-owner of the Presidential Pet Museum, is partial to the story of Andrew Jackson’s pet parrot, Poll.

“It was taught to curse like a sailor, and caused such a ruckus at Jackson’s funeral that the bird was promptly escorted out,” said Baker, of Queens, a 41-year-old copy editor who also runs a website called Petful. The story of Poll, he said, “keeps going viral on Reddit.”

The Presidential Pet Museum — such as it is — exists as a website full of information and pictures, plus a motley collection of memorabilia currently in storage.

The items were lovingly collected and curated by Claire D. McLean, a retired dog groomer who took care of President Ronald Reagan’s bouvier des Flandres, Lucky. McLean spirited out some of Lucky’s fur trimmings in a bag, and her mother made a portrait of the dog that incorporated them, inspiring her daughter to start the museum.

McLean, who is no longer able to operate the museum, and Baker, who has other things to attend to, are trying to sell the website and artifacts in an online auction, so far without luck.

So how do the current candidates fit into this mostly four-legged history?

Clinton is a well-known dog lover who has spoken out against puppy mills. Her dog Maisie is a curly-haired mutt, and Tally is a toy poodle mix.

When Bill Clinton was in the White House, the couple acquired a chocolate brown Labrador retriever named Buddy, who was a comfort to the president during the difficult days of his impeachment over the Monica Lewinsky scandal. Buddy later died after being hit by a car in Chappaqua, N.Y., where the couple reside. The Clintons adopted a great-nephew of Buddy’s, Seamus, in 2002; he died recently, apparently of old age.

Socks, the Clintons’ White House cat, was a favorite of the first daughter, Chelsea, but not of her parents, both of whom are allergic to cats, or of Buddy. So great was the acrimony that when the family decamped for Chappaqua after Bill Clinton’s second term, Socks did not make the trip; he was sent into “exile,” as news reports described it, with Bill Clinton’s secretary, Betty Currie, in suburban Virginia.

Chelsea Clinton is now a dog person. Her Yorkshire terrier, Soren, is named after the Danish existential philosopher Soren Kierkegaard.

When it comes to animals, the Trump family is better known for hunting them. Trump’s two eldest sons have been criticized for a safari they took in Zimbabwe in 2011, when they posed for pictures next to a large water buffalo and other creatures they had shot for sport.

Hillary Clinton used this episode as a political weapon in August, telling animal rights protesters that the Trumps had “killed a lot of animals.”

Trump has no pets, according to his campaign. However, a curious hoax website called MediaMass has for years been pumping out the fiction that “Donald Trump’s adored Labrador retriever ‘Spinee’ has undergone a risky surgery on Wednesday and is luckily beginning the slow process of recovery.”

People have been sending Trump heartfelt tweets wishing Spinee a speedy recovery since at least 2013.

But wait, there’s more: MediaMass — a site that says its goal is “media criticism through satire” — has been spreading the exact same Spinee rumor about thousands of celebrities and public figures, including Clinton. The identical article has been written about Stephen King, Miley Cyrus, Denzel Washington and Steve Martin, to name a few.

An email to MediaMass, which seems to be based in China, went unanswered.

© 2016 The New York Times Company