Henri Rousseau's Surprised!, 1891. Human culture would lose immeasurably from the disappearance of the tiger from the natural world. Photograph: Carl De Souza/AFP/Getty Images
In a cave in south-west France an extinct animal materialises out of the dark. Drawn in vigorous black lines by an artist in the ice age, a woolly mammoth shakes hairs that hide its face and vaunts slender tusks that reach almost to the ground.
We didn't mean to help make the mammoth extinct. The wonderful portrait of a mammoth in Pech Merle cave reveals that early homo sapiens was fascinated by these marvellous creatures. This masterpiece of cave art is as acute as any modern work of naturalist observation. The hunters who painted in caves showed the same passion for the natural world as their descendants do. Their culture must have been bereft when the mammoth vanished – even as they helped it on its way.
In the 21st century the same paradox endures. Human activity endangers entire species, yet human culture is profoundly rooted in nature. The loss of a species is also a loss of the images, stories, symbols and wonders that we live by – to call it a cultural loss may sound too cerebral: what we lose when we lose animals is the very meaning of life. Those first artists in ancient caves portrayed animals far more than they portrayed people. It was in the wild herds around them that the power of the cosmos and the mystery of existence seemed to be located.
No species in modern times embodies that fascination more fully than the tiger, one of today's most endangered predators. Since the Romantic age tigers have been endowed in art and literature with the marvellous essence of life itself, a primeval power like the enigmatic strangeness the stone age artist saw in a mammoth. "What immortal hand or eye,/ Could frame thy fearful symmetry?" wonders William Blake in his 1794 poem The Tyger. That same childlike awe – Blake's poem appears in his child's eye Songs of Innocence and Experience – is shared by Henri Rousseau's 1891 painting Surprised! of an archetypal tiger in a fantastic jungle.
These artistic hymns to the tiger are just the noblest expressions of an imagery that pervades modern culture from tigers who come to tea to tigers with neat feet. It just seems unimaginable that a creature so familiar in our shared dreams should vanish from the natural world. Human culture would lose immeasurably from such a disappearance. And what about sharks? More ancient than dinosaurs, under threat for the first time in their mind-bogglingly long history, these creatures feed modern culture some of its darkest folklore. Shark films and scare stories are the modern equivalent of stone age hunters telling tales about bears and wolves around the fire. We fear them, but our culture needs them.
Cute creatures as well as scary ones inspire the stories and myths that humans cannot live without. Amphibians, most threatened animal group of all, are among the most universal stars of culture. While Blake was marvelling at tigers, the Grimms recorded the folk tale of the frog-prince. Long before that Plato said the ancient Greeks were like frogs around a pond. Aristophanes wrote a comedy called The Frogs. American frogswere depicted by the Aztecs as well as providing Amazonian peoples with arrow poison. The very naming of poison dart frogs reveals how deeply they are associated with cultures that are themselves on the brink of extinction.
In Britain too, the amphibious denizens of threatened waterlands have always inspired imaginations. Could our culture survive without Toad of Toad Hall?
Not so long ago British beaches were seasonally covered with "mermaid's purses", the eggs of sharks and rays. The name reveals how deeply nature feeds folk culture, in Britain as in the Amazon. Is it possible still to find masses of mermaid's purses on the Welsh rocks where I used to wonder what they were? I have to look for them with my daughter soon, before it is too late. The range of animals and plants threatened by the sixth extinction – as covered by the Guardian over this fortnight – is such that it menaces the foundations of culture as well as the diversity of nature. We are part of nature and it has always fed our imaginations. We face the bare walls of an empty museum, a gallery of the dead.