In a reasonably stable ecosystem predators do not wipe out their prey species.  If they did, they would have lost a source of food.  The predators and the prey will have evolved together.  For example if a species of snake eats a species of newt as one of its main foods, the newt might have evolved poison to deter the snake, and the snake might then evolve some resistance to the poison, keeping the two in some sort of balance.

Another thing that usually does not happen is for the prey species to reach plague proportions.  That is, in a well balance ecosystem predators will usually be able to control excessive numbers of their prey, and prey species are more often controlled by predators rather than by starvation.  This also means that plants can be in some sort of balance with the herbivores.

Foxes and Rabbits

European Foxes and European Rabbits have evolved together in a number of places.  In popular stories the Fox is the deadly enemy of the Rabbit.  In fact, this is true on an individual basis.  That is Foxes certainly kill a lot of Rabbits.

But the presence of Foxes is not necessarily bad for Rabbits.  For example, in many places there are animals like the weasel which are voracious Rabbit killers, but are kept in check to some extent by Foxes.

Introducing Animals

If you introduce an animal into a totally different ecosystem you cannot assume that the same nice balance between predator and prey will happen.

Australia

Australia was a totally different ecosystem from anywhere else in the world.  The animals and plants were largely endemic to Australasia.

Then Humans started to introduce animals from other parts of the world.  Excluding the Cat which did not survive until 1788, the first one was probably the Dingo.  This was brought in as a domestic Dog a long time ago.  We do not really know how long ago it was brought here, or all the disruptions that happened when it went wild.  The ecosystem had had long enough to settle down.  If any animals became extinct because of the Dingo they were already gone when the British came in 1788.

The animals still surviving were in some sort of balance with this predator.

January the 26^th 1788

This is when Europeans first came as permanent settlers rather than explorers.  It is celebrated as Australia Day officially.  Unofficially it is sometimes referred to by the Aboriginal inhabitants of Australia as Invasion Day.

If they could talk, the animals of Australia that are not already extinct might have a very bad name for this day.

Europeans have been disastrous for the ecology of mainland Australia.

Rabbits

Rabbits were brought out with the First Fleet in 1788.  Although they were released they failed to survive in any numbers.

Unfortunately I have never seen a study of why they failed to get established.  It is generally assumed that the Rabbits brought were too domesticated to survive in the wild.  However, I think that this is a gross oversimplification of the situation.  If tame Rabbits are released in England, they would probably fall prey to things like Foxes, Weasels, Cats and Dogs.  None of these were present in reasonable numbers in Sydney Cove where the Rabbits were released.  The obvious suggestion is that most of them were killed by native predators.  That is, a Predator Prey Mismatch.  The introduced Rabbits could not survive with the Australian Native predators.

But in 1859, wild European Rabbits were released in Victoria and took over the continent.

The Ecosystem they were released into was already in disarray from the other things Humans had done.  Foxes were already in the area they were released into.  Foxes had been released in Victoria in 1845.  Foxes also spread quickly, although not as fast as the Rabbits.  Foxes kill a lot of potential Rabbit predators.

The native predators that might have kept the Rabbits in some sort of balance were already in very serous decline.  The Wedge-tailed Eagles that eat Rabbits in large numbers were already being killed by Humans with guns, and their nests were being deliberately destroyed.

There was a serious predator prey mismatch and the Rabbits invaded the mainland of Australia.  The Goannas which might have slowed them down were already in decline from the destruction of vegetation both by Humans directly, and particularly by their animals.  Grazing was already being carried out over much of the continent.

Kangaroo Island

Rabbits were introduced to Kangaroo Island.  But this island had not had its ecosystem as badly damaged as that of the mainland.  There was much less grazing because of trace element deficiencies that were not identified until the pioneering work of Edward D. Carter in the 1950’s.

 Foxes had not been introduced so the native predators were still present in sufficient numbers to wipe out the Rabbits.  Apart from Wedge-tailed Eagles attacking from above, the Rabbits had to contend with the Goannas that could simply walk into the Rabbit burrows and eat the baby Rabbits.

This was another Predator Prey Mismatch.