Forty years after "Jaws" turned blood-thirsty sharks into the stuff of pop culture legend, Samuel "Doc" Gruber is all too happy to prove that it's safe to go back in the water.

From a motor boat in the warm turquoise waters of the Bahamas, Gruber -- one of the world's top authorities on sharks -- throws scraps of barracuda, ladyfish and other bait to a dozen circling reef sharks happy for a mid-morning snack.

Also in the water: a similar number of humans in snorkeling gear, hanging from an anchor line, their initial galeophobia -- fear of sharks -- giving way to fascination at the feeding frenzy unfolding before their eyes.

"Kick it! Kick it!" shouts Gruber cheerfully whenever a curious shark gets too close to the snorkelers, prompting them to rattle their fins to shoo it away -- a trick that never fails to work.

Feeding done, braver souls are welcome to join the 77-year-old Gruber for an hour-long free dive with the sharks, who seem quite content just to cruise around casually for the entertainment of their land-dwelling visitors.

"You should watch them because they're beautiful," says the indefatigable American marine biologist who, in 1990, founded the Bimini Shark Lab in the Bahamas, a mandatory waypoint for shark scientists from around the world.

"They're not the death fish from hell."

- Few fatalities, but bad PR -

Swimming with sharks is not without its risks -- as apex predators, they do occupy the top of the marine food chain -- but in the 20-plus years the Shark Lab has been hosting such outings, nothing has gone amiss.

"A lot of the sharks that we see here have been in this area for 10 or 15 years," said Tristan Guttridge, the Shark Lab's British-born director and senior scientist. "They know exactly what to expect and they're very easily trained."

More than 500 species of sharks populate all the world's oceans, from the huge Greenland shark that lurks in Arctic waters to the dwarf lantern sharks off Colombia and Venezuela that fit in the palm of a hand.

But with an estimated 100 million sharks killed every year -- many for China's controversial high-value shark's fin soup trade -- nearly 30 percent are at risk of extinction, and just over a quarter are close to becoming threatened in the near future, scientists say.

"Of all the marine vertebrate species, they have the highest level of threat," said Imogen Zethoven, director of global shark conservation for the Pew Charitable Trusts in Washington.

They also have a nagging PR problem, even if shark fatalities are extremely few -- about six a year worldwide, says the International Shark Attack File program at the University of Florida, with surfers the most vulnerable.

"The fatalities rate has declined markedly over the last 110 years," even with more and more people taking to the water recreationally, said the program's curator, George Burgess.

While Australia is best known for great-white shark fatalities, the Florida coast is the most likely place to be bitten, Burgess said. Even then, the chances of a shark attack at a US beach are one in 11.5 million.

- 'Shark tourism' a $314 mn business -

Some blame "Jaws" -- Steven Spielberg's classic 1975 summer blockbuster about a New England resort town terrorized by a man-eating great white -- for the enduring image of sharks as the most feared of all marine apex predators.

"If you don't know anything else about sharks and the only thing you saw was 'Jaws,' then yeah, you're in trouble," said underwater cinematographer Andy Casagrande, best known for his work filming great white sharks off Australia.

But environmental campaigns and television specials like Discovery Channel's Shark Week, returning for a 28th season on July 5 in the United States, are credited with giving sharks a public relations fillip.

In the Bahamas, which in 2011 declared its waters a shark sanctuary with no shark fishing allowed, commercial or otherwise, scuba operators on Bimini and other islands actively promote shark diving expeditions.

In Mexico, "save the sharks by swimming with them" is the theme of an annual Whale Shark Festival at Isla Mujeres, near Cancun, that will host its eighth edition on July 18-24.

A 2013 study from the University of British Columbia in Canada called "shark tourism" an emerging industry that attracts 600,000 shark watchers a year, directly supports 10,000 jobs and generates $314 million a year -- a figure that could more than double to $780 million in two decades.

"It is abundantly clear that leaving sharks in the ocean is worth much more than putting them on the menu," said Andres Cisneros-Montemayor, lead author of the study published in the Oryx conservation journal.

Meanwhile, on social media, a great white named Mary Lee has become a Twitter celebrity as she roams the US East Coast with a pinger attached to her dorsal fin by the non-profit OCEARCH organization.

Back at the Shark Lab, Gruber revels in taking guests out to another attraction -- a shallow-water "shark pen" within wading distance from the beach that holds young lemon sharks for research.

Deftly, and with a big smile, he picks up a shark, turns it over and, with a bit of acupressure in the right spot, makes it fall asleep for a time, before letting it slip back into its proper habitat.

Overall, Gruber is optimistic for the future of sharks.

"Oh my God! There's been a huge change in perception, but we've still got a long way to go," he says.