But the big bull sharks, despite their reputation as aggressive man-eaters, were strangely shy. An enormous and visibly pregnant one the divers called Big Mama seemed almost finicky as she warily sniffed at the flesh being offered her before turning up her nose entirely. Some of the bulls lurked in the distance, no more than silhouettes in the blue. Others swam languidly toward us, as if playing a lazy game of chicken before nonchalantly turning away.

R. Dean Grubbs, a shark expert at Florida State University, says this is probably the safest way to encounter bull sharks, in deep, clear water, where they are far less likely to mistake you for their normal prey, as they do with swimmers and surfers in the shallows or at the surface. Some sharks, including bulls, also have space issues, so the fact that they’ve come to you, not the other way around, means they’re less likely to feel crowded and testy.

But George H. Burgess, director of the Florida Program for Shark Research, contends that once you start luring big sharks all bets are off, pointing to the death of a tourist on a shark dive in the Bahamas last year. Still, he acknowledges that statistics don’t show that chum dives are any more dangerous than normal dives. In fact, the bigger concern for researchers like him and Dr. Grubbs is the impact on the sharks themselves.

Even Papa wonders if his beloved sharks have grown a little complacent under his care, though they still adhere to many of their natural habits, like migrating or disappearing up the rivers for weeks on end when it’s time to breed. And because some shark-diving profits go to the villages themselves, no one fishes along the reef or drops anchor on it, granting it a welcome reprieve from overfishing.

Some of the local divers say the reef certainly looks a lot healthier than it did before the shark diving started here 10 years ago. Long before Christianity, Papa said, the people of his village considered sharks their spiritual guardians and looked to them for protection before going into the water. Now, Papa said, he is the protector, boasting that he and his crew are deputized to impound illegal fishing boats that wander in the area to pluck from the healthy fish stocks there. He even speaks of the sharks as his children.

“They know Papa’s coming,” he said, heading out to sea one morning, his nickname emblazoned across his T-shirt. “They’re waiting for me.”