A report to a UN ocean conference in New York points out that more than 60% of the ocean has no rules because it’s outside national jurisdiction.
It says the open ocean is at risk from climate change, over-fishing, deep sea mining, farm pollution and plastics.
The authors say one area – the Bay of Bengal - is at a tipping point which could impact on global fish stocks.
The report was commissioned to inform delegates preparing a UN resolution on governance of the open ocean.
Representatives in New York are preparing a text that could cover everything from establishing marine protected areas to distributing the benefits of valuable biotech products generated from the seas.
One of the report’s authors, Prof Alex Rogers from Oxford University, told BBC News: “This is very, very important. A lot of states are looking towards developing industrial activities in the ocean – fishing, deep-sea mining, renewable energy… even aquaculture offshore.
“It’s really vital that we come to some international agreement on how to protect or manage biodiversity on high seas in the face of all these pressures.”
The UN is focusing discussion on three areas:
Together they are categorised under a new UN acronym – BBNJ. That’s Biodiversity Beyond National Jurisdiction.
Prof Rogers’ report is a review of new science over the past five years. He says he realises how little is known about some essential ocean processes, and mentions the Bay of Bengal issue as a source of great concern.
The issue there is nitrogen, which performs an positive role in fertilising algae at the bottom of the food chain, but can also have negative effects if there’s too much of it in the water.
At the moment, nitrogen fertilisers in the Bay of Bengal are running off farmland and over-fertilising algae. This in turn encourages bacteria, which capture oxygen. Slowly marine life in the area disappears.
But the Bay of Bengal is now on the verge of going one destructive stage more.
The report says if oxygen levels decrease further as a result of run-off or increasing water temperatures, then the entire ocean basin may flip to a no-oxygen status.
In one of Nature’s paradoxes, this would then lead to different bacteria actually removing nitrogen from the water.
Prof Rogers said the de-nitrified water would then be carried away by ocean currents, and greatly reduce ocean productivity elsewhere.
Dr Greg Cowie from Edinburgh University told BBC News that the growing dead zone in the Bay of Bengal would have enormous local consequences.
“You have to remember there are 400 million people living round the rim of the bay. There are half a million fishers. If the situation gets much worse we are going to get a huge human problem,” he said.
Christiana Figueres, a former chief climate negotiator, is joining a push at the UN for a formal treaty process to safeguard the high seas.
She says a healthy ocean can buffer the planet against changing climate by continuing to soak up CO2 emissions from the air.
She told BBC News: “As with the atmosphere, the high seas belong to everyone. But they have also been damaged by all.  What could be seen by some as the tragedy of the commons can also be recognized now as an opportunity for a radical recovery of the commons.”
The deep sea is the biggest store of CO2 emissions from humanity, as ocean circulation pulls in carbon from the atmosphere and tiny marine plants called phytoplankton soak it up.
These are then eaten by creatures called zooplankton and their bodies sink to the ocean floor.
The Oxford scientists say as the seas warm, the abundance of phytoplankton may fall. This will impact the whole food web, including fish stocks and the rate at which CO2 is locked up on the sea bed.
They also say raised sea temperatures have resulted in the rise of Vibriobacteria, which live in warm seas and have been associated with a global increase in illnesses like cholera, gastroenteritis, wound infections and septicaemia.
They echo the many recent warnings about increasing quantities of plastics large and small, although they say the effects are as yet poorly understood.
Their report says the effects of ocean mining must be carefully monitored, too.
Meanwhile, a third UK pub group has announced it will stop using plastic straws is a small contribution to reducing ocean plastic waste. The Liberation Group, based in the West Country and the Channel Islands, is supporting Jersey’s Straws Suck campaign.
It follows a BBC News story highlighting a plea for plastic straws to be taxed because  so many of them get blown into water courses.
Follow Roger on Twitter @rharrabin
New rules are urgently needed to protect the open seas, scientists have warned.