This was, in other words, the first ever authenticated sighting of a live giant squid.Dr Steve O'Shea of the National Institute of Water and Atmospheric Research in Wellington, New Zealand, had been searching for the creatures for years, helped by sponsorship from the Discovery Channel "Finding them after all these years was great," he says. "Nobody even knew what they looked like prior to undertaking this work." Unintimidated by the giant squid's fearsome reputation, Dr O'Shea attempted to nurture the specimens in the laboratory. They died after a few days, which, he says, "was one of the worst experiences of my life." But he is confident that his life's quest is close to completion. "I am absolutely certain that, one day, we will be able to keep and breed giant squid in captivity. And I certainly believe that we'll not have to wait long to see the adult alive."This in itself is a fairly astonishing development: a creature once dismissed as a fantasy on a par with the yeti or the Loch Ness monster has been both observed alive and, it seems, all but tamed.But that, it now emerges, is only the beginning of the story. Last week brought even more dramatic news: the respected journal Australasian Science was reported to have announced that giant squid are currently growing so fast – both in size and in number – that, in terms of total biomass, they now surpass the human race.On the face of it, this is absurd.

Here is a species whose existence mankind has scarcely even noticed until now; for living examples of which scientists have spent whole careers searching in vain. How can they suddenly be occupying more of our planet than us? And how can scientists be so certain – when they are simultaneously so ignorant?But the article, based on the work of Dr George Jackson of Tasmania's Institute of Antarctic and Southern Ocean Studies, seemed plain enough Squid, it insisted, are the new "big players of the ocean". Previous constraints on their population – such as predation by sperm whales and tuna and competition for food by smaller "ground fish" such as flounder, halibut, cod and hake – have in recent years been abruptly removed, in both cases by overfishing. At the same time, global warming has heated the ocean to a temperature better suited than ever before to rapid growth – both for giant squid and for cephalopods in general.Jackson describes recent growth rates – inferred both from finds on beaches and in fishing nets and from squid remains in the bellies of sperm whales – as "exponential".

Warm water, it seems, encourages increased mating activity and increased metabolic efficiency; and, in the absence of predators, the sky – or the surface – is the limit. "Just as fast-growing weeds can quickly colonise an area of ground that has been denuded of vegetation, so the rapid growth-rate of squids and their short life-cycles have enabled them to move into regions that have been heavily over-fished," says Dr Jackson. "You just heat them up a little bit and everything just ticks over that much faster."Jackson calculates the mass of the human race at 400 million tonnes (an average of 11 stone each). But 60 per cent of our planet's living space consists of unexplored ocean depths more than a mile below sea level. "If you assume that the depths of our vast oceans are occupied by giant squid and average them out to around half a ton each," he told the Daily Mail, "they are going to outweigh humans."It sounds like a fairly giant "if", but Jackson is not alone in his beliefs. Statistics from the UN's Food and Agriculture Organisation imply a 200 per cent increase in squid tonnage in the ocean between 1970 and 1994 alone; and, according to Dr Daniel Pauly, professor at the Fisheries Centre of the University of British Columbia, Canada, "Very few scientists dispute that the phenomenon is near universal."Does that mean that giant squid are among the cephalopods affected? Not necessarily. Even Dr Jackson admits, when pressed, that "We can't know that the giant squid population will necessarily increase, because we don't know how global warming affects the deep ocean."But the fact remains that, even if they're not taking over the world, giant squid are spectacularly well-placed to do so They are, for a start, bigger than us.

They grow faster, have more room to expand, and, unlike us, have never had it so good environmentally. And it has to be said that, as rival species go, they are worthy contenders for the title of heavyweight champions of the world. Based, for the most part, in the great, dark depths of the unexplored trenches of all the world's oceans, they grow fast and die young (typically before the age of five), which is an ideal recipe for rapid population expansion. Their love-making techniques don't sound much fun (think "3ft muscular appendage", "staple-gun effect" and possible "post-coital disintegration"), but in other respects they are models of sophistication. They have proportionally bigger brains than any other invertebrates. They may well communicate, like other squid, by some form of the mysterious visual process known as bioluminescence. They move by jet propulsion ("They invented the jet engine," says David Pemberton) and do not, as far as we know, have any current plans for civilisation-threatening wars – although sucker scars found on sperm whales testify to the fact that they are no slouch in a fight.