Donald Gibson found the first vertebra Oct. 23, just as he had begun to dig out the space for the sunroom he had promised to build in the back yard of his parents’ home in Calvert County.

Over the following week, his brother Shawn found another vertebra, and then another, and then a few more — each one about 18 inches deep into the ground. Soon, Shawn Gibson’s 7-year-old, Caleb, joined in on the digging. He’s at an age of being “thrilled to go out and not just play in the dirt, but actually find pieces,” Gibson said of his son.

After all, it’s not that unusual to dig up fossils in the Calvert Cliffs neighborhood. But then they found something more: a straight column of vertebrae, two feet long. And at the end, a tooth.

The digging stopped.

What the Gibsons unearthed were the remains of a 15-million-year-old snaggletooth shark, which paleontologists say is more complete than any other fossil of its kind in the world.

Stephen Godfrey, curator of paleontology for the Calvert Marine Museum, said that the Gibsons’ discovery is so unusual because of the number of bones they found — more than 80 vertebrae and hundreds of teeth, all from the same shark — as well as the position they were in and their unusually good preservation.

In fact, the discovery is so rare that when Shawn Gibson called museum officials and asked them to come out immediately — on Halloween night — Godfrey said he had his doubts.

The description Gibson provided — of a complete snaggletooth shark skeleton, including the spine and the skull cavity — seemed so outlandish to Godfrey that he could scarcely believe it.

But he and John Nance, an assistant curator, were intrigued enough to hop in the car right away.

“While we’re driving up there, I’m thinking to myself, ‘This can’t be an actual fossil of a shark,’ ” Godfrey said. “But it couldn’t be a horse or a cow. It had to be a shark.”

Once he laid eyes on it, he had no doubt.

“It was immediately obvious,” he said. “It was a genuine article.”

The Gibsons showed him about 50 vertebrae they had unearthed, and Godfrey was grateful that they had stopped digging once they reached the teeth. Godfrey and Nance wrapped the entire skull cavity in a stiff plaster cast, like one used to set a broken bone.

Sharks’ skulls are made mostly of cartilage, not bone, so they almost never withstand the ravages of time, Godfrey said. Yet somehow, the shark that came to rest in the Gibsons’ back yard sank belly-up when it died during the Miocene Epoch. It became buried in sand, then by sediment eroding from the Appalachian Mountains. And its skull cavity — containing hundreds of the distinctively shaped teeth, up to an inch-and-a-half long, that give the snaggletooth its name — kept its shape.

Using a microscope, the scientists digging in the Gibsons’ yard were able to see the distinctive hexagonal shape of shark cartilage, fossilized and preserved.

Donald Gibson said he had pulled vertebrae out of the ground, one by one in a straight line, just as they were positioned in the back of the shark, which Godfrey said was 8 to 10 feet long during its life.

Having preserved the teeth and surrounding remnants of cartilage in exactly the positions they were found in, the paleontologists will be able to take CT scans of the cast and analyze the specific three-dimensional layout of the prehistoric shark’s mouth, something scientists have never done.

“For the first time, we’re going to be able to know what the dentition — what the teeth — looked like in this kind of shark,” Godfrey said.

Then they will remove the cast, gently clean each piece and put the discovery on exhibit.

Shawn Gibson said that his parents had lent the fossil to the museum but might bring it home eventually.

“Obviously, we wanted to make sure it was able to be studied,” he said. “We wanted to make sure that the historical significance was documented and the specimen’s there to be studied. But it came from the yard, and it was a family affair. ”

There’s also the issue of the value of the fossil. Shawn Gibson said he doesn’t know what the shark might be worth.

“There’s obviously not a Blue Book for shark fossils and certainly not a one-of-a-kind find,” he said.

Godfrey said he is receiving e-mails from paleontologists up and down the East Coast who are excited about the discovery.

The skeleton will allow scientists to compare the prehistoric snaggletooth, an extinct species, and modern snaggletooths, a descendant species that lives in the Pacific.

Comparing the teeth of snaggletooths then and now will help scientists understand the workings of shark evolution, the likely diet of prehistoric species and the climate during the Miocene Epoch.

And the fact that the spine and the skull cavity of the shark found by the Gibsons are definitively associated with each other, the most complete snaggletooth skeleton ever found will allow scientists to identify whether smaller pieces of future fossils come from snaggletooths or other species.

“When in the future we find just a single vertebra, we’ll be able to say, ‘This comes from that kind of shark.’ And only because we have this association being made,” Godfrey said. “It’s just in­cred­ibly unlikely that we would make this kind of discovery.”

As for the Gibsons, the family now has a new hobby. While the sunroom goes up in the back yard, they have continued to dig. Caleb has found less-valuable bits of four more shark species.

“He had the day off of school for Election Day. I told him we could go fishing,” Shawn Gibson said. “He said, ‘I’d like to go look for shark’s teeth.’ ”