It is the final night of the Pacific Islands Forum in Tuvalu and the Fijian prime minister is explaining how to drink kava.

“You clap first,” says Frank Bainimarama, as the smooth wooden bowl is passed around the circle. “Then you have to gulp in one go; then you clap again – one, two, three.”

As with so many things in the region, there is a metaphor involving the sea. “Tsunami is the full bowl,” he says, explaining the different levels to which the small bowl is filled from the large tanoa, or kava bowl, in the middle of the circle. “Then full tide, low tide.”

“It’s a social drink,” he says. “You can sit for hours and drink this stuff and tell stories about nothing.”

Among the stories the prime minister tells over the next three hours as each person gulps down a dozen bowls of kava – about his fear of flying, his views on Trump, why he seized power in the infamous coup that saw him become Fiji’s leader – there is one theme he returns to over and over: the climate crisis.

Though the Pacific is estimated to contribute just 0.03% of global emissions despite making up 0.12% of the world’s population, the climate crisis is already having a devastating impact on the region.

The ocean, which has been the source of much of the region’s food and resources, is now the site of impending catastrophe. Rising sea levels, coastal erosion, the destruction of crucial reefs and warming that leads to more frequent and more severe cyclones all threaten the region.

As the crisis has hit the Pacific, leaders have emerged. Despite the tiny populations of their countries, they have had an outsized influence on the global climate fight.

As the world’s leaders gather for the United Nations General Assembly and climate summit, we speak to three Pacific leaders who have been on the frontline of the climate crisis and are taking the fight to New York.

Frank Bainimarama, prime minister of Fiji

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The fight against the climate crisis has been the great second act of Frank Bainimarama’s prime ministership.

After his role in the 2006 coup, which saw the Fijian commodore seize power and then refuse to call elections for eight years (Fiji has since held two, both of which Bainimarama has won), Bainimarama was ostracised by the international community. But in recent years, he has emerged as a leader in the global climate fight, becoming the president of COP23 in 2017, the UN’s leading climate change body, and the only Pacific leader to have held the title.

“I and my officials come from a little tiny island and we had to go onstage and fight these big emitters,” he says. “It’s not easy to be standing up on stage telling the big emitters: ‘Come down off your high horse and do what needs to be done to fight this’.”

But Bainimarama says it was important to have a Pacific leader in the role.

“By then we knew what climate change was doing, especially to Pacific Island nations,” says Bainimarama. “When we took up the presidency, our fight was really the fight of the Pacific and the vulnerable islands, low-lying islands.”

While Fiji, which is one of the most populous and more economically-developed countries in the Pacific, is not considered among the most vulnerable to the impacts of the climate crisis – that dubious honour goes to Tuvalu, Kiribati and the Marshall Islands – it is still feeling the effects.

“Everywhere I go in Fiji there are only two things people want, especially on the coastline. One is a seawall, the other is a hurricane shelter,” says Bainimarama. In 2016, Fiji was devastated by Cyclone Winston which killed 44 people and inflicted damage equal to one third of the country’s GDP.

Under Bainimarama’s leadership, Fiji has offered refuge to the entire populations of Tuvalu and Kiribati in the event that the countries become uninhabitable due to the climate crisis.

He is also willing to take the fight to much bigger powers, frequently making headlines and causing diplomatic tensions for his blunt assessments of the behaviour of wealthy countries unwilling to curb emissions (including neighbouring Australia). At this year’s climate summit and General Assembly in New York he will be demanding countries take immediate action to limit global warming to 1.5°C above pre-industrial temperatures and calling upon developed countries to mobilise at least $100bn in climate finance per year by 2020 to address the needs of developing countries.

“Our fight will never stop,” he says.

Enele Sopoaga, former prime minister of Tuvalu

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Enele Sopoaga hails from the fourth-smallest country in the world by area and the second-smallest by population. But he wants the world to know its name and to see in its fate, the fate of the planet.

Until this week, Sopoaga was prime minister of Tuvalu, which scientists predict could become uninhabitable in the next 50 to 100 years due to the climate crisis. An election in early September saw him retain his seat in parliament, but lose the leadership of the country, so he will not be attending the climate summit and UN General Assembly in New York, though he has spoken at many of them, as well as COP summits, since becoming prime minister in 2013.

“As soon as I took on the leadership of my country I went to the first conference of parties in 2014 … I said, ‘Unless we save Tuvalu, we cannot save the world. Save Tuvalu to save the world’.”

Sopoaga has been outspoken on behalf of his country. As the main spokesman for the Pacific Small Island Developing States at the 2009 UN climate conference in Copenhagen he proposed amending the draft climate treaty to require countries to limit warming to 1.5C, a proposal that was rejected. At the recent Pacific Islands Forum, hosted by Tuvalu, he was one of the main leaders urging Australia to stop opening new coal mines, saying he told prime minister Scott Morrison: “You are trying to save your economy, I am trying to save my people.”

Tuvalu is home to just 11,000 people. Its total land area accounts for less than 26 sq km and according to its government, two of Tuvalu’s nine islands are on the verge of going under due to sea-rise and coastal erosion.

When UN secretary general Antonio Guterres visited the country in May, he said Tuvalu was “on the extreme frontlines of the global climate emergency” and that climate change was “striking in Tuvalu is a more dramatic way than anywhere else in the world.”

“We are predicted by IPCC scientists to be the first victims of submersion into the sea,” says Sopoaga. “Now, if that happens it doesn’t mean climate change is going to stop, it is going to continue ... We may be the first one, but others will follow. So my call to save Tuvalu, save the world, is not irrational, it is very pragmatic.”

Sopoaga says that anyone who doubts the effects of climate change should visit Tuvalu – partly to see the impacts of the crisis on his tiny nation and partly to experience the nation’s rich culture, which would be lost if the country is lost to the waves.

“Come to Tuvalu, I will show you how these islands have been badly affected and eaten by erosion, but also come so I can show you how the salinity has eaten into the freshwater table, how it has eaten into the basis of the food supply here.

“You come here I’ll show you how the beautiful coral reefs … are now white-ish because they are attacked by acidification and plastic and carbon,” he says. “But the thing is, do you need to see this in order to be convinced that climate change is happening? I don’t think so.”

Hilda Heine, president of the Marshall Islands

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Hilda Heine is a leader of firsts: when she was elected president in 2016 she became the first female leader of her country (she is currently the only female Pacific leader except for Jacinda Ardern in a region with the lowest rate of female political representation in the world). She is the first person in the Marshall Islands to ever get a doctorate, her country was first to submit its targets to meet the Paris agreement and it could be one of the first to see large-scale migration as a result of rising sea levels.

In April, one of the local governments in Marshall Islands, purchased 283 acres of land in Hawaii as a climate change bolthole for citizens, if dire predictions for the country’s future come to pass.

“I think all of us as leaders realise that we’re coming to the end of this,” she tells the Guardian. “If we don’t take action now, when are we going to take action? There is no time left for us to be indecisive … otherwise the future of our Pacific Island countries will be lost.”

But Heine is not ready to accept that outcome yet. She, like many leaders of the Pacific, will be speaking at the climate summit in New York on Monday, where she will demand countries provide “commitments to enhance ambition in line with the IPCC special report on 1.5C”.

“We’ve made the conscious choice to lead from the front, because otherwise, who would take the moral responsibility and the leadership on this? Even though we don’t cause this, it impacts our livelihoods more than it impacts others, so for us to just wait to take action would not make sense to our people,” she says.

Heine is adamant that the most vulnerable members of society should be prominent in discussions around the climate emergency. She is the chair of the Climate Vulnerable Forum, a group of around 50 countries that have contributed negligible amounts of greenhouse gases but are particularly endangered by climate change, and a key advocate for more women being brought into the climate debate.

“Like any other vulnerable members of our society, [women] are more impacted by climate change,” she says. “That’s why I think it’s important for women to understand the issues and also to be brought to the table too, to help make policies that are relevant to them as a marginalised group.”