Three fatal shark attacks off south-western Australia in the past two months have raised the spectre of a rogue shark preying on swimmers and divers, although marine scientists say the cluster of attacks is probably coincidental.

In the latest incident, a 32-year-old Texan, George Wainwright, was killed on Saturday while scuba diving off Rottnest Island, a popular day-tripper destination a short ferry ride from Perth. His two companions, who described seeing a flurry of bubbles just before his badly mutilated body surfaced next to their dive boat, identified the shark as a 3-metre great white.

A great white of the same size is believed to have taken a 64-year-old swimmer from off Perth's popular Cottesloe beach, which is 18km east of Rottnest, a fortnight ago. The man's remains have not been found, but his shredded swimming trunks indicated the size and type of shark involved.

The shark that killed a bodyboarder at a beach south of Perth in early September was said to be about 4.5 metres long. Witnesses were not sure what type it was. Although shark attacks occur periodically off Australia, the flurry of incidents has rattled authorities, who fear the impact on tourism. The south-west coast is known for its white, sandy beaches, whale and dolphin-watching cruises and surf breaks.

"This is a unique set of circumstances, and I'm desperately praying that this is not the beginning of a new trend," the Western Australian Fisheries Minister, Norman Moore, said yesterday.

The state government set tuna-baited hooks off Rottnest at the weekend, and the premier, Colin Barnett, said he would consider a shark cull. However, Barry Bruce, a federal government marine biologist and expert on great whites, said it was unlikely a single predator had killed the three men.

"What we've seen, tragically, is three cases of people being in the wrong place at the wrong time. This is the time of year when sharks move along the coast, and there are multiple sharks out there following this exact pattern."

Great white sharks are classed as endangered, and can only be killed to protect the public. Barbara Weuringer, a marine zoologist and shark researcher at the University of Western Australia, said it was impossible to know which sharks were responsible for the attacks unless their stomach contents were examined. She said the proposed cull "sounds a little bit like taking revenge".