Rewilding is here to stay. The term broadly refers to restoring areas of wilderness to their former glory, but it is the reintroduction of large mammals, from wolves to beavers, that has captured the popular imagination, and come to define this ambitious conservation strategy.

Such projects are not without controversy. Some ecologists worry that reintroducing extinct animals to our radically changed modern ecosystems might have unforeseen impacts.

Farmers and landowners, meanwhile, express concern about the effect interlopers like wolves or lynxes might have on their livelihoods.

Just imagine how they might react to the ideas proposed by a small but dedicated subset of extreme rewilders. In their vision, the plains of North America and Europe would become home to an even wilder array of species, including lions, elephants and cheetahs.

"In the beginning when we told people about this project they just laughed at us," says Ole Sommer Bach, curator of Randers Rainforest zoo, referring to his institution's plan to introduce a population of Asian elephants in northern Denmark. "I think most people thought it was some kind of provocation, or a practical joke; but it really wasn't."

This is Pleistocene rewilding. Advocates want to set the clock back not hundreds, but thousands of years. Around 13,000 years in fact, to when the Pleistocene era was drawing to a close: an almost incomprehensible length of time for us mortals, but the mere blink of an eye for Earth's ecosystems.

One correspondent labelled Greene a "goofball, dipwad, doofus with a scrambled brain"

Today, the planet's remaining 'megafauna' are largely restricted to Africa and Asia. But during the Pleistocene every continent was populated with enormous mammals, from the giant wombats of Australia to the various species of elephant that roamed North America and Europe.

The animals themselves are now gone. But the ecosystems that evolved with them remain, and their function is severely reduced in the absence of such keystone species.

But help could be at hand. Pleistocene rewilders suggest that some animals still found in Africa and Asia, many of which are on the verge of extinction themselves, are similar enough to their extinct counterparts to serve as effective proxies.

These ideas were first proposed by geoscientist Paul Martin as part of his Pleistocene overkill hypothesis, which holds that humanity was the key instigator of global megafauna extinctions. However, they were crystallised in their current form a decade ago by a team led by two researchers from Cornell University in Ithaca, New York: Josh Donlan and Harry Greene.

A team of what Greene calls "experts and visionaries" gathered together on a dusty New Mexico ranch. Together, they established a framework by which Pleistocene-type animals could be re-introduced to the US.

The underlying rationale was that current conservation efforts to return the US to a pre-Columbian benchmark (i.e. prior to 1492) are totally arbitrary. By this point, humans had already contributed to the extinction of dozens of species.

The result of this meeting was a landmark paper published in Nature simply entitled "Re-wilding North America". In it, the team envisages the release of, among others, Bactrian camels to replace the late Pleistocene Camelops, African lions to stand in for American lions, and elephants to take the place of the mammoths, mastodons and gomphotheres.

In the beginning when we told people about this project they just laughed at us

Their core aims were twofold. First, they wanted to restore North American ecosystems and re-establish long-gone ecological processes. Second, they offered "a compelling vision for 21st Century conservation biology: conserving animals away from Africa".

The response to the paper was extensive and frenzied. Fellow scientists, the media and members of the public all weighed in, with one correspondent labelling Greene a "goofball, dipwad, doofus with a scrambled brain".

More eloquent criticism came from the likes of evolutionary ecologist Dustin Rubenstein, who described Pleistocene rewilding as "only a slightly less sensational proposal" than Jurassic Park. Crucially, he and his fellow researchers opined that the resources invested in this kind of rewilding would be better spent protecting African animals in Africa.

But perhaps Pleistocene rewilding is not as outrageous as it first appears. Donlan, Greene and their colleagues were not, after all, suggesting a free-for-all on wild animal releases across North America. Instead, they suggested controlled, experimental releases to test their ideas.

That was in 2006. Ten years later, there are still no African lions prowling the Wild West, and barring the bolson tortoises reintroduced to their prehistoric range in New Mexico, rewilding efforts in the US have been few and far between.

What we want is to create room for natural processes

"In terms of realising Pleistocene rewilding projects, it's still pretty limited," says Jens-Christian Svenning, a researcher Aarhus University, Denmark, and advisor for the Randers elephant project. "The scientific literature on the subject is filled with debate, but the empirical work is really missing."

Across the Atlantic, however, governments and the public have been more amenable to rewilding in general. There have been many successful projects across Europe, and one or two have even had the 'Pleistocene' label applied to them.

Oostvaardersplassen in the Netherlands is an area of reclaimed wetland that is home to introduced Heck cattle, Konik ponies and red deer, mimicking the herbivore assemblages of ancient grasslands.

"What we want is to create room for natural processes," says Perry Cornelissen, an ecologist at the park. Instead of opting for artificial management systems to create the perfect habitat for wetland birds – the park's primary remit – its creators opted for a wilder approach. "The results of our monitoring show that the herbivores indeed create large-scale grasslands for geese and meadow birds such as lapwings and golden plovers," he enthuses.

More explicitly, there is Russia's Pleistocene Park, an attempt to "restore the mammoth steppe ecosystem" of the late Pleistocene. Much like Oostvaardersplassen, though, the park has so far drawn the line at introducing anything as exotic as lions or elephants.

When we mentioned them as a possibility for rewilding almost 15 years ago, people were also laughing at us

"The animals being released in these parks are still mainly from the Holocene era [11,700 years ago to present day]," says Svenning. "This is less provocative, and only a small step beyond traditional nature management where you use domestic horses or cattle to graze."

But now, Bach and his colleagues want to stake their claim for the wildest rewilding experiment yet. Under their watch, they hope to see elephants roam the Danish landscape for the first time in millennia.

The zoo has form when it comes to rewilding. Having successfully overseen the reintroduction of European bison in Randers, Bach and his colleagues see elephants as the natural progression.

"European bison have been extinct in Denmark for maybe 8,000 years, and when we mentioned them as a possibility for rewilding almost 15 years ago, people were also laughing at us," he recalls. "Now that is a reality."

Absolutely crucial to the project will be detailed preparation and monitoring. "We don't intend to just set them free and wait for them to end up in Spain or somewhere," explains Bach. "We will set up a fenced area, release the elephants and then carefully follow what happens."

If you built a machine that could do the same things as an elephant, you would probably become very rich

The team intends to follow everything from their interaction with native trees to the impact their dung has on insect communities.

This is exactly the kind of relatively small-scale experiment Greene and Donlan had in mind. Only with the hard data that result from hypothesis testing and science-based monitoring will it be possible to ascertain how effective such seemingly radical strategies are at creating positive ecosystem change of the type seen in Oostvaardersplassen.

Then there are the economic benefits that arise from preserving ecosystems in this way. "If you built a machine that could do the same things as an elephant, you would probably become very rich," says Bach. "They can do everything from coppicing to spreading seeds, and they already exist! We just need to use them."

And what about that other Pleistocene rewilding goal: realistically, how feasible is the idea of using rewilding as a conservation strategy for endangered, exotic mammals? The answer to this may come from the most unlikely of places: Australia.

Nowhere is the issue of species introduction more contentious than in Australia. Decades of accidental and intentional species introductions have left the continent with highly fragile ecosystems.

The mission is to airlift a population of white and black rhinos 11,000km from South Africa to Australia

Even relatively modest science-based efforts by Rewilding Australia to introduce native marsupials like quolls and Tasmanian devils to former parts of their ranges on the mainland have had setbacks to deal with.

In this climate, it seems foolhardy to suggest further large-scale introductions of alien species, but this is exactly what David Bowman, professor of environmental change biology at the University of Tasmania, did back in 2012.

Bowman argued that the way to deal with the influx of the giant African gamba grass, which has been implicated in the increase in bushfires in Australia, would be to introduce rhinos and elephants – the only herbivores large enough to eat it. These animals, while far removed evolutionarily speaking from Australia's gigantic Pleistocene marsupials, might still serve as viable stand-ins.

Remarkably, a project of this nature actually is underway, albeit for rather different reasons.

The Australian Rhino Project is a drastic response to the disastrous situation currently unfolding on the African continent. If poaching continues at its current rate, rhinos will be extinct in the wild by 2024.

It could actually have a beneficial effect in Australia as a whole, as well as safeguarding the rhinos

This issue is what led project founder Ray Dearlove and his collaborators to arrive at the same conclusion as the Pleistocene rewilders: these animals must be conserved away from Africa.

The mission is to airlift a population of white and black rhinos 11,000km from South Africa to Australia. If all goes to plan the first batch will be sent over this year.

Once there, the similar conditions in Australia – and, crucially, its relative lack of poachers – should provide the rhinos with a safe haven.

For Svenning, this project marks an interesting opportunity: "If they add an ecological component, then it could actually have a beneficial effect in Australia as a whole, as well as safeguarding the rhinos," he suggests.

The Australian banteng actually outnumber their endangered Asian counterparts

While careful monitoring of the rhinos and their interaction with the Australian environment will be key to the success of the project, Dearlove does not see such habitat management as the key element. Instead, he sees this project as an exciting new approach to ex-situ conservation.

"It has been suggested that this could become a model for other endangered species, whereby you take them to a safer place until things are sorted out in their native country, then you can return them," he says.

"I think rhinos should be in Africa. I would prefer them to be surviving and breeding where they are, but the reality is that they're not. They've roamed the continent for millions of years, and now South Africa holds around 95% of the rhinos in the world. They've been wiped out."

Intriguingly, Australia already has form when it comes to providing a refuge for threatened mammals. A population of banteng – wild cattle from Southeast Asia – was established on the continent in 1849, and now, owing to habitat decline in their homeland, the Australian banteng actually outnumber their endangered Asian counterparts.

Researchers have highlighted the precedent set by this accidental success story, stressing the role these banteng may play in the survival of the species.

The success of all these projects – whether or not they operate under the banner of Pleistocene rewilding – will provide crucial insights into the efficacy of transferring exotic creatures in order to protect either them or their adopted ecosystems.

Within the next 50 years, Asian elephants might be gone from the world entirely

In fact, maybe Pleistocene rewilding itself is an unhelpful label, which detracts from the bigger picture of enabling natural processes and preserving species. "We are not aiming at restoration of Pleistocene or indeed Holocene ecosystems or landscapes. Those eras are over," says Cornelissen. "We now live in the Anthropocene."

The Anthropocene is by definition a period of highly altered ecosystems resulting from human activity. In this context, bringing elephants to Denmark, or rhinos to Australia, might be seen as just another extreme alteration to our planet's wildlife assemblages.

But extreme times call for extreme measures, and bold conservation strategies such as these could go a long way to revitalising some of our most treasured ecosystems and creatures in a manner that is not only effective but self-sustaining.

"Within the next 50 years, Asian elephants might be gone from the world entirely," says Bach. "Most people in Europe see elephants as exotic, and don't consider it our responsibility to conserve exotic animals, but I think it is a global responsibility."

We can never get back everything that has been lost, but we can still make good use of the resources that remain at our disposal. To do that, we will need to think big.

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