The Sundarbans nature reserve in Bangladesh's south-west is one of the last untouched places on Earth - and home to the largest population of tigers left in the wild. But the trees in the Sundarbans have suddenly started dying. And not just that: they have started dying in a way nobody has seen before, from the top down.

Nobody is sure what the cause is, but the country's leading scientists think the trees are dying because, in recent years, the water has turned from fresh to salty. The Sundarbans is a massive mangrove swamp, and the sea has begun encroaching. What we are seeing may be one of the first casualties of rising sea levels caused by global warming. "Nobody can say for sure whether it is climate change because there haven't been proper in-depth studies," says Professor Ainun Nishat, one of the country's leading environmentalists, and one of those involved in the UN's recent climate change report. "But this is the sort of effect rising sea levels will have on Bangladesh. We are fighting climate change on the front line. But the battle has to be integrated across all countries."

Then there were the deaths of thousands of fishermen off Bangladesh last summer. The Bay of Bengal was unusually rough. Usually, the authorities only issue a storm warning to fishermen to stay at home once or twice a year. Last year, four warnings were issued in the space of two months. Every warning meant the fishermen lost valuable days at sea. When the last warning came, they could not afford to stay ashore and went to sea anyway. Officially 1,700 drowned, but many Bangladeshis believe the real number may be closer to 10,000.

"Was it climate change? We don't know," says Dr Nishat. "Was it unusual? Yes."

The weather in Bangladesh is going crazy. Last week, a freak tornado struck. Tornadoes occur regularly in Bangladesh - but usually only in the tornado season, in April. A tornado in February is almost unheard of.

Also, there were the strange events of 2004, when the tides in the estuaries of the Ganges, Brahmaputra and Meghna rivers stopped ebbing and flowing. The water level just stayed at high tide. The same year, the capital, Dhaka, was hit by floods so severe the ground floors of most buildings were under water, and a catfish was caught in one of the government buildings.

And in 2005, the country had no winter at all. Westerners tend to assume the whole of the subcontinent is hot all year round; in fact, Bangladesh, like much of northern India, gets quite cold in winter. Except that it didn't last year. Winter never came - with serious effects on the year's potato crop. This year, too, it has not been as cold as usual.

"We have a saying, in February, even the tigers feel the cold," says Arun Karmaker, the environment correspondent for Prothom Alo newspaper. "But these days, a visitor to Bangladesh would find it hard to believe."

Bangladesh is particularly vulnerable to climate change. The entire country is basically one vast river delta, and that has always left it at the mercy of weather extremes. The villages of the south-east may often lack electricity or clean water, but a cyclone shelter is never far away. In Dhaka, the rent for a typical first-floor apartment is £52 a month. On the ground floor of the same building, it is just £37 - because the ground floor gets flooded almost every year.

But the country's climate experts say the weather is growing more extreme - and becoming unpredictable. And this is in the most densely populated country in the world, if you don't count city-states or small islands, home to 147 million people. That leaves a worrying question: what happens to those 147 million people if parts of this already overcrowded country become uninhabitable due to rising sea levels.

The problem is, nobody really knows just how much effect climate change will have on Bangladesh. "We still don't have a proper study of the impact of global warming here," says Mr Karmaker. "Up till now, no one has done one." The classic scenario of climate change disaster in Bangladesh is of rising sea levels flooding most of the country, forcing as many as 40 million people to flee. Scientists have measured small rises in the sea level at various points around the coast, and almost all of Bangladesh lies less than 10m (30ft) above sea level.

But what is less well known is that Bangladesh has a defence against that scenario: a huge series of dykes made of boulders that stretch along the entire coast - a literal fortification in the battle to survive climate change. The dykes were put up to protect against the storm surges Bangladesh periodically suffers from, but should be high enough to withstand the predicted rise in sea levels.

But that doesn't mean Bangladesh is safe from climate change, says Dr Nishat. "The dykes create their own problems," he says. "By trapping rainfall on the inside, they could end up causing flooding. And they do nothing to stop salinity spreading through our water."

It is not just the Sundarbans that is already suffering the effects of rising salinity. Farmers in coastal areas who used to grow rice have switched to farming prawns, after the water in their paddy fields got too salty. The country has just developed a new strain of rice that will grow in salty water. For a country where agriculture makes up 21 per cent of GDP - and with 147 million people to feed - rising levels of salinity are a serious threat. Already, Bangladeshi farmers can only produce 8 tons of rice per hectare, compared to 17 tons in China.

But it could be more serious than that, Dr Nishat warns. "The direction of the monsoon has changed in the last few years," he says. "The depression that brings the rain used to advance north across Bangladesh. Now it is heading west." That could have devastating implications in the event of a tropical cyclone, he says.

Bangladesh has suffered cyclones many times. But Dr Nishat says the change in direction of the monsoon may mean any cyclone spends more time gathering pace over the Bay of Bengal.

"When Hurricane Katrina devastated New Orleans in 2005, it was only a category three hurricane while it was over Florida," he says. "It was when it headed across the Gulf of Mexico that it turned into a category five. It gathered heat from the sea. And the Bay of Bengal is hot."

Flooding could also be a problem - not from rising sea levels, but from the increasingly erratic rainfall. "We are used to flooding here, we need it for our agriculture and people are used to being knee-deep in water," says Dr Nishat. "But now we are seeing extremely high rainfalls - more than people can easily cope with, and it damages the crops. In 2004, we saw 352mm [14in] of rainfall in a day."

But if the classic scenario is of Bangladesh flooding, there is a risk that climate change may bring drought instead. Already, the north-west of the country faced an unprecedented drought last year, when the monsoon rains failed, and had to resort to pumping ground water for irrigation. The irony was that the north-west was experiencing a drought even as the north-east was suffering its heaviest rainfall ever.

"What I'm worried about is the melting of the glaciers in the Himalayas," says Dr Nishat. Bangladesh relies on the annual melting of snow in the mountains to feed its rivers. "At the moment, we're probably seeing a slight increase in the river flow because of it. But what happens in two to five years when the glaciers are gone?"

The Bangladeshi government is taking the problem seriously, according to Dr Nishat. "Things are much better than they used to be," he says. "We used to go to the Environment Ministry and they'd say: "Climate change? That's the West's problem, they're making all the carbon emissions. What does it have to do with us? Now they understand that it affects Bangladesh."

But, he says, problems are still caused by turf battles between ministries, and the country's lack of joined-up government.

With its own annual carbon dioxide emissions only 172kg (380lb) per capita, compared to 21 tons in the US, Bangladesh has some reason to feel aggrieved to be suffering the effects of climate change before others do.

What is happening in Bangladesh may be a warning of what is to come, but the country is not the only one facing the dangers of climate change.

"People always come to Bangladesh to talk about rising sea levels," says Dr Nishat. "Have you considered that London is the same height above sea level as most of Bangladesh? You have the Thames barrier, and we have our dykes. By the time Bangladesh is flooded, you will have lost London."