They are red-necked immigrants from Down Under who now face the loss of their adopted Scottish island home for the last 60 years because they have become too greedy.
Around 60 wild wallabies have set tourist tongues wagging on the Loch Lomond island of Inchconnachan, near Luss - nicknamed Wallaby Island by locals in homage to its furry population.
The Australian imports and their descendants who have survived years of Scotland's chilly climate face the threat of losing their home after feasting their way through oak, holly and birch saplings and gorging on plants.
Island managers fear the wallabies' unusual eating habits have caused the growth of unpalatable bracken and rhododendrons, which were introduced to Scotland from Africa in the 18th century, but are also lethal.
They believe that the overgrazing by the wallabies threatens native plant and animal species such as capercaillie and otters that live on the island.
A deer count on Inchconnachan last year also found that grazing on the island was high and that diverse vegetation was required to survive.
A decision on what will happen to the marsupials will be taken by Luss Estates, which manages Inchconnachan, one of Loch Lomond's 23 islands.
It will liaise with other authorities including Loch Lomond and The Trossachs National Park, Scottish Natural Heritage and the Deer Commission.
Iain Sheves, the factor, said no final decisions had been taken about the wallabies, which he described as "something of a freak show".
He said: "We would rather, if you think about it, tourists were coming to Scotland to see native species, native habitats, some of the iconic Scottish species such as red squirrels and capercaillie and otters.
"It is an oddity of history, a bit gimmicky that the wallabies are there. If I wanted to go and see wallabies, I would much rather go on a plane to Australia.
"I am sure there is interest to see them and what-not but I think every land manager has a duty to promote conservation, and that's about preserving native species and native habitats.
"As we develop a management plan we will have to formulate a policy towards the wallabies. Now it might be we leave them alone, we might reduce their numbers a bit or we might get rid of them. But we are not at a stage to make a decision yet.
"They are not a native species, they are not protected but we do not have enough information at our fingertips to make a decision at this stage."
But Advocates for Animals opposed any proposals to cull. A spokesman said: "They may be a non-indigenous species but they did not choose to come over here. It is crass to kill in the name of conservation when they are living there quite successfully. It is morally all over the place.
"Our organisation is principally against culls, but the reality is that if you are going to take an extreme measure, it should be a last resort."
The wallabies were first introduced to the island in the first half of the last century by Fiona Bryde Colquhoun, or Lady Arran, sister of Sir Ivan Colquhoun, once the fastest woman on water, having broken her last power boat record at the age of 62. A wooden bungalow was used by her as a holiday home and the wallabies were part of a private collection.
It was believed by some that a wildlife park would be established there, but when the idea was abandoned so, it appears, were the wallabies.
But the wallaby clan has grown and now there are double the numbers there were eight years ago.
They have survived by eating shrubs and plants and have become accustomed to the climate, and some have been known to have made their escape by swimming to the mainland.
A spokesman for The Loch Lomond & The Trossachs National Park Authority said: "Whilst the National Park Authority recognises that wallabies can be of novel interest to visitors, as a national park our role is to promote, conserve and enhance Scotland's native species for the future.
"Wallabies are a non-native species that don't belong on this internationally important nature conservation site."
It said the grazing wallabies eat young tree saplings "and this influences the regeneration of the woodlands on the islands".
Martin Varley, director of Friends of Loch Lomond, said: "Our native species have to be protected and if an introduced species is having a detrimental effect on them, then that's something that has to be managed."
The red-necked wallaby is one of the largest of the wallaby family and has been mistaken for a kangaroo, weighing in at more than 20kg and reaching head to body length of 90cm.
They are distinguished by their black nose and paws, white stripe on the upper lip, and grizzled medium grey coat with a reddish wash across the shoulders. Scotland's non-native species New Zealand flatworms, unintentionally introduced, prey upon earthworms and can cause their local extinction. Grey squirrels deliberately released from 1890-1920, to "enrich" the native fauna threaten our native red squirrel with extinction. American mink first escaped from Scottish fur farms in 1938. They are carnivores with a wide range of prey, including seabird chicks, which has led to the extinction of several seabird colonies on Scottish islands. Night herons - a free flying population lives in the vicinity of Edinburgh Zoo. Signal crayfish, native to North America, have been found in at least six locations around Scotland since the first self-sustaining population was discovered in the Kirkcudbrightshire Dee catchment in 1995. Ruddy ducks, a native of North and Central America, which have settled in Fife, Tayside and the Lothians. They wipe out native ducks through inter-breeding and competition for food.
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