A shark behaviour expert says Tony Abbott “doesn’t understand the science” after the former prime minister called for sharks to be culled in the wake of an attack at a Sydney beach.

A woman, aged in her 30s, was in a critical but stable condition on Monday after being bitten on the leg and arm by what was thought to be a great white shark on Saturday morning.

Abbott said in a social media video it was “so wrong that we don’t cull sharks after attacks” and said a fishery to catch sharks needed to be established.

Emeritus professor Rob Harcourt, who leads the Marine Predator Research Group at Macquarie University, said a cull of sharks would make no difference to the risk of shark attacks at beaches.

“Tony Abbott doesn’t understand risk, he does not understand climate change, and he doesn’t understand the science when he calls for a cull,” Harcourt told the Guardian.

“What’s the point in a cull? A cull won’t change the risk unless you completely remove white sharks from the ocean. It’s not feasible and it would be an ecological catastrophe.

“This was a rare incident and it’s tragic. But calls for a cull are not based on any evidence that would change the risk. It’s a kneejerk reaction.”

Prof Culum Brown, who researches fish behaviour at Macquarie University, said calls for a shark cull were “a very naive way of scoring political points”.

He said: “We should be looking at ways we can coexist with nature. We should not be having this 18th-century approach to annihilating nature because it threatens us in some way.”

The New South Wales premier, Chris Minns, pointed out the great white shark is a protected species and ruled out a cull.

“I’m not convinced it would work and we’ve certainly had no expert evidence suggesting to us that we could ward away great whites from our beaches as a result of a cull,” he said.

“Because the reality is for those sharks, they may have come from New Zealand, they may have crossed the Pacific Ocean. I’m not convinced it would work and certainly we haven’t received evidence or information that it would work.”

He said there needed to be a “rethink” on the state’s approach on shark protection, including shark netting and the use of new technology – including drones.

Harcourt said using drones to survey beaches was a more practical way to reduce the risk of bites.

He said: “If you put drones over a beach and then call people in [when sharks are spotted] then you are less likely to be bitten.”

The Civil Aviation Safety Authority on Monday temporarily lifted a ban on using drones to survey for sharks at Coogee. The eastern suburb beach is close to Sydney airport flight paths.

Dr Daryl McPhee from Bond University, who is researching shark bite trends, said: “Had drones been able to fly, this is one bite that could have been avoided.”

He said it was “extremely rare” for a person to be bitten on a patrolled beach because “there are a lot of eyes on the water”.

McPhee said between 1980 and 1999 there was an average of 0.6 shark bites causing injury per year recorded in New South Wales, but the current rate was 4.16.

He said most of that rise had been driven by bites in the north of the state.

He said population rise meant people in the water and this was likely contributing to the rise. Increasing whale populations also attracted more great white sharks to the coast.

Lawrence Chlebeck, a marine biologist at Humane World for Animals, said culls could not work because sharks were migratory and swam thousands of kilometres.

He said any cull would probably involve attracting sharks with bait, which he said would increase shark activity. “In my opinion that would increase the risk,” he said.

Since 2012, he said 174 great white sharks had been killed as a result of the state’s shark nets, as well as 40 bull sharks and 42 tiger sharks.