There is a small crowd of people by the ponds in Sydney’s Centennial Parklands, tossing bread to the clamouring waterbirds, when the dark form appears. It glides upwards with a lazy, powerful motion to swallow one of the crumbs before disappearing back into the murk.

A young girl takes a step back. Her mother smiles. “It’s just an eel,” she says. “There are lots of them in here.”

The girl just stares at the surface of the pond. Her expression suggests she is not reassured, or not quite, as if the eel has made her suddenly aware of other presences moving beneath the surface of this most cultivated of landscapes.

Her wariness is not entirely unreasonable. Mature Australian long-finned eels (Anguilla reinhardtii) average a metre in length, and can weigh up to 22 kilograms. As their powerful-looking jaws suggest, they are also efficient hunters. They eat carrion and prey on molluscs and insects, crustaceans and fish, even taking ducklings and small birds if the opportunity arises. And while in many cultures eel flesh is a delicacy, prized for its sweetness (in some places eels have been fished to the point of collapse), it’s difficult not to feel there is something unsettling about the cool purpose of these undulating predators, the way they lurk on the margins of our awareness.

For while they might spend most of their lives in these ponds (as they do in rivers and waterways up and down the eastern coast of mainland Australia and Tasmania), the eels are not born here, nor even anywhere nearby. Their secretive habits disguise much that is remarkable.

In November of each year, eels that have reached maturity – in the case of female eels this occurs at about 14 or 15 years of age, the males slightly younger – begin to migrate downstream towards the ocean. Exactly what triggers this migration isn’t clear – it may be the new moon, atmospheric pressure, even high rainfall – but the eels answer the call in great numbers.

Where possible, their journey follows the waterways, the eels slipping and sliding through the drains and culverts. If their way is obstructed they emerge from the water and slither across the ground, a spectacle sometimes observed at Sydney’s Randwick Racecourse. Describing the Northern Irish version of this phenomenon, Seamus Heaney writes of the eels moving “through the grass like hatched fears … as the field flowed / Past, a jellied road”. There is a similar power in the stories from the D’harawal people of the Sydney area about Parra’dowee the Great Eel calling his children back to him.

Were this the whole of their journey it would be remarkable enough, but it is just the beginning. When the eels reach the salt water they gather again in the estuaries, waiting while their bodies undergo a series of changes. Some, like the enlargement of their pectoral fins, are designed to allow them to survive in a marine environment; others, like the degeneration of their gut, reflect the fact that the journey they are about to undertake is one way, and once they have mated they will die, meaning there is no longer any need for them to hunt or eat.

And then, once they are ready, they begin to swim. Exactly where they go remains a mystery, as does their route and the mechanisms that guide them. Evidence suggests they descend to 200 or 300 metres and follow the East Australian Current northwards to a point in the Coral Sea somewhere north of New Caledonia. Wherever it is, getting there requires the eels to swim up to 3500 kilometres through the open ocean, before congregating in one particular spot.

The eels then spawn. Each female releases several million eggs that quickly hatch into flat, transparent larval form. Although the bodies of these larvae, known as leptocephali (“slim heads”), are surprisingly fragile, they grow quickly, developing eyes and sharp teeth and reaching several centimetres in length. Despite their teeth (and the predatory prowess of adult eels), leptocephali do not feed on the tiny marine animals known as zooplankton in the way many fish larvae do. They subsist instead on what is known as marine snow, a misleadingly poetic term for the particulate matter and waste that drifts down through the ocean.

Borne southwards by the currents, the leptocephali make their way down the Australian coast, reaching New South Wales in early summer, and estuaries further south between January and May. It is not known whether they seek out the waterways that were inhabited by their parents, in the way salmon do, but either way the encounter with fresh water triggers another series of transformations. The leptocephali metamorphose first into the transitional form known as glass eels and then again into juvenile eels, or elvers, so that by the time autumn comes they are ready to head upstream.

In many ways, this migration inland is no less remarkable than their parents’ migration seawards, as they slither up creeks and rivers, clambering around obstacles and up waterfalls. Even artificial barriers are regularly surmounted: the author Tom Fort writes of eels forcing their way up a “forty-foot-high expanse of concrete … moistened by a trickle of water from above” on a Victorian river, “so that the whole face of the structure shimmered in the moonlight with the squirming hordes”, while in New South Wales juvenile eels regularly make their way around the Warragamba Dam, which is more than a hundred metres high.

Yet in a way what is most astonishing about this migration is not its complexity or even the distance the eels cover, but that it goes on without us noticing. It is difficult not to suspect that this says something about the degree to which we have inured ourselves to the natural cycles around us. This was not always the case, of course. In 1798 David Collins, the former judge-advocate of New South Wales, wrote that every April the Indigenous people of the Sydney region “resort … to the lagoons, where they subsist on eels which they procure by laying hollow pieces of timber into the water, into which the eels creep”. In western Victoria the Gunditjmara people built elaborate systems of canals and rock traps to take advantage of this annual bounty.

Archaeological evidence in Victoria suggests these harvests have been taking place for more than 8000 years; until the arrival of Europeans they had been a feature of life on the eastern half of the continent since the waters rose at the end of the last ice age. In fact, the eels have been enacting this extraordinary annual cycle for far, far longer: palaeontological evidence suggests that the family they belong to, the Anguillidae, evolved in the Pacific in the Cretaceous period, meaning that the eels or their ancestors have probably been performing some version of this process for millions, if not tens of millions, of years.

These creatures offer us a way of comprehending the degree to which the natural world persists, even in the most urbanised of spaces. Their journeys trace the almost invisible lines of a landscape we have yet to entirely obliterate, and serve as reminders not just of the larger cycles of that world but also of the depth of time that inheres in it.