They first arrived as pets the 1960s before escaping into the wild and colonising the wildlife havens of southern Florida.
Since then, green iguanas have taken over, wreaking havoc in the form of stripped vegetation, power outages and contaminated swimming pools.
This summer is looking like the worst year anyone can remember, with packs of the distinctive green lizards taking over pavements and gardens.
Richard Engeman, a biologist for the National Wildlife Research Centre, told The Sun Sentinel newspaper: “There’s no real way to come up with a valid estimate of the number of green iguanas in Florida. But the number would be gigantic.
“You could put any number of zeros behind a number, and I would believe it.”
Male animals can grow up to five feet in length and weigh as much as 17lb.
At that sort of size they can be prodigious burrowers, building tunnels and underground sanctuaries for the females to hatch their eggs. Problems come when their excavations erode over time, causing pavements to collapse, damaging electricity supplies and phone lines.
Grace DeVita, of Hollywood, saw the damage first hand when an iguana chewed through power lines at her office.
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“There was an iguana with a piece of wire hanging out of his mouth,” she told the newspaper. "It took two days for power to be restored the first time, and then it happened again two days later.”
Damage to levees, seawalls and patios have all been blamed on the invasive species.
Cold weather once kept the population in check but numbers have rebounded in recent years without an extended wintry spell since 2009, according to experts. This year's explosion seems to be unaffected by a cold spell when frozen iguanas dropped from trees in January.
Thomas Portuallo, the owner of Fort Lauderdale-based company called Iguana Control, told The Sun-Sentinel that many hundreds of thousands of iguanas had taken over a string of counties.
“This year is the most iguanas I’ve seen and I’ve been in business for nine years,” he said.
While the population explosion is good business for exterminators, householders are legally able to take things into their own hands.
Florida state law allows anyone to kill iguanas so long as it is done humanely, with a single blow from a shovel, a shot from a pellet gun, decapitation or other instantaneous methods.