A walk in this Garden of Eden is revelatory, like going to the supermarket via the chemists' and the zoo. These berries make soap, those plants are good contraceptives, this leaf is good for kidney and heart diseases. There are troops of spider and woolly monkeys, frogs smaller than a fingernail, tapirs the size of horses, as well as ants that taste of lemon and berries so poisonous you could die in seconds if you ate one. Most amazing is the "walking tree", which follows the light, hitches up its roots and moves 7m or more.
Last month, some Yale University undergrads stumbled across a mushroom capable of eating polyurethane plastic. It could revolutionise landfills. "Frankly," says Swing, "no-one knows what is here."
It wasn't until he and a colleague from San Francisco University in Quito paddled their way here 20 years ago to set up the science research station that anyone really understood the true abundance of life in Yasuni.
And it wasn't until 2007, when 960 million barrels of oil were discovered in one part of the Yasuni park, that people realised that the most biodiverse place on earth could be totally destroyed. The oil under Yasuni, it was calculated, would earn Ecuador US$7 billion ($8.3 billion) but would last the world just 10 days.
Oil was touted as the start of a new era of development: Ecuador joined Opec and borrowed massively. In the first years, oil built hospitals, schools and roads. But 45 years later, Ecuador has just half of its reserves left - 4.5 billion barrels, of which 20 per cent lies below Yasuni.
Albert Acosta was the oil and mines minister when the Yasuni find was made. Today, he is a radical ecologist, and will stand as a presidential candidate for a group of left-wing parties in next month's election.
"The reality is that oil has not brought development," says the charismatic academic. "It has helped our infrastructure, but it has brought us immense contamination and environmental destruction. Oil has not solved the problems of Ecuador."
While most politicians would have immediately sent for drillers, Acosta hesitated. He knew that the find presented the country with perhaps its last chance to develop in the traditional way, but he also knew it would push the oil frontier deeper into the Amazon, release 400m tonnes of climate-changing gases and make the destruction of a vast and pristine area inevitable. To extract oil from Yasuni would need wells, ports, pipelines, roads and villages. "And because this is a particularly heavy crude oil vast amounts of water will have to be injected back into the earth, inevitably leading to pollution.
"I knew the oil industry. I used to work in it. I could see the monster from the inside. I began to think we were poor because of our resources. I called it the curse of abundance."
Working with NGOs and academics, Acosta prepared two options - "Plan A", as it became known, was a revolutionary scheme to leave the oil in the ground in perpetuity in return for half of its value (around US$3.6 billion). Plan B was to send in a Chinese company. For the first time in history, a nation seriously considered not exploiting oil.
"We should be an intelligent country," says Acosta. "Oil is unsustainable. We must see it in the long-term. Climate change is a limit and we can't continue to keep burning oil. Perhaps we must change our model of life.
"We cannot live without nature but nature can live without us."
Plan A has received overwhelming support, with polls showing 95 per cent of Ecuadoreans want Yasuni preserved as a jewel of nature. The UN has now set up the Yasuni fund and, led by a US$50 million donation from Germany, more than US$300 million has been offered or received from national, regional and local governments, individuals, companies and institutions in Europe, Japan and the US. This alternative "aid" money is not touched by Ecuador's government, but is administered by a trust to develop renewable energy projects and conservation.
And it seems to be working. "So far, so good," says Ivonne Baki, secretary of state for the Yasuni initiative and Ecuador's former ambassador to the US, when I ask her how the project is going. "The world is watching. If this succeeds it may open a new era of conservation. If it fails, it will discourage developing countries from adopting bold climate measures."
To see what could happen to Yasuni if the oil there is exploited, I travel to Lago Agrio, Texaco's base camp in the 1970s, now an oil-rush town. The great primary forests have long gone. Lago Agrio and the area around it is a social and ecological disaster zone, after the company allegedly spilled nearly 17 million gallons (64 million litres) of crude oil and dumped 20 billion gallons of drilling wastewater between 1964 and 1990. Guerilla groups, drug traffickers and criminal gangs pour over the Colombian border into what is now an industrialised landscape; pipelines snake within metres of houses; companies flare gas night and day from refineries; and the pollution, although better than it was in the 1970s, continues.
I meet Luis Yanza, a local community leader who was 16 when his family moved to Lago Agrio from the pristine south of Ecuador. "It was like going to hell," Yanza said. "We would see huge smoke clouds - they used to spill the oil into pits and when they were full set fire to them. The water smelled of oil. We had an oil pipeline right by our house, which was close to the main Texaco camp, and we all had spots on our faces."
Yanza is one of a number of residents who has spent 20 years suing Texaco (bought by Chevron in 2001) to clean up the forests, through the Ecuadorean and US courts. Last year, the communities won US$18 billion damages, but Chevron has refused to pay, claiming corruption in the Ecuadorean courts.
Back in the deep forest at the Tiputini research station the primatologists tell me they now hear oil company planes flying overhead and say that the animals show signs of fear. Opinions at Tiputini are divided over whether Yasuni will be sooner or later exploited. The station's resident director, biologist Diego Mosquera, fears it cannot hold out for long. "Who owns the oil has the power," Mosquera tells me.
"Oil is 100 times bigger than anything else in Ecuador. Honestly, I don't think the companies can be stopped."
But Kelly Swing is more optimistic. "Yes, we are very nervous that all this will be lost and that Yasuni will become like Lago Agrio," he says.
"But this time we have a unique chance to save a lot of nature for very little. If we can't justify saving a place that has more species per square inch than anywhere else on the planet, then what hope is there for anything? What then do we keep? What then can we save?"
- Observer