"The Galapagos is still the best preserved archipelago in the world. But what's at stake if current trends continue is that the Galapagos will be lost. Yes the Galapagos will still be there but the richness will be lost."
The rising numbers have led to a boom in the construction of hotels and a surge in imports from mainland Ecuador.
And the result is a sharp spike in the number of alien species arriving in this fragile ecosystem: 112 were recorded in 1900 but by 2007 the total had leaped to 1,321.
At the harbour in the main town of Puerto Ayora, I watched dock workers transfer crates and sacks of rice and maize from cargo ships on to barges for the journey ashore.
The airport on Baltra island, which serves the archipelago, sometimes handles half a dozen flights every day - the number has doubled in the last eight years. The aircraft cabins are sprayed before landing but evidently some insects are getting through.
One of the most aggressive is the fire ant - tiny but with a powerful sting - an example in its own right of the evolutionary principle of survival of the vicious.
In a field outside the village of Bellavista, insect specialist Henri Herrera scraped away leaf litter to reveal a seething mass of the tiny red creatures.
"They're getting everywhere - it's a disaster. It could even mean that for some species the ants stop evolution."
A balance must be found between economic needs and those of wildlife
Fire ants are known to attack baby birds and young tortoises and their march from one island to another seems inexorable.
Other threats include a parasitic fly which attacks young finches and mosquitoes - which could serve as a vector for diseases which are known to exist on the mainland but have not yet arrived here.
The government of Ecuador has drawn up an action plan to curb this menace. Criticised by the UN agency UNESCO - which in 2007 listed the Galapagos as a world heritage site in danger - the authorities are now introducing tougher measures.
The director of the Galapagos National Park, Edgar Munoz, accepts that invasive species pose the most serious risk to the islands but says the government's actions will tackle the threat.
Some birds are threatened by invasive creatures
"What we're hoping to accomplish is fifty more years in which any problems will be diminished."
Earlier conservation efforts - to cull several islands of feral goats which eat the plants giant tortoises depend on - have proved successful but some experts warn that eliminating particular insects will be far harder.
For Ecuador, a developing country, the Galapagos provides a major source of revenue. But a balance will need to found if the islands are to preserve what makes them so special.
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