I do like that word (allochthonous), but it is usually used in ecology in relation to sources of organic material. Better terms for introduced species are exotic, introduced, alien, non-indigenous (my favorite), non-native, etc. Methods of eradication are: 

1. Keep them out!

2. Suppression or slowing the spread.

3. Biological control e.g. mating disruption or insect release.

4. Physical removal and destruction.

5. Etc! lol

I hope this helps :)

Dear Colleague

Thank you very much

Philippe  JOSEPH 

Island Conservation realized a great experience in Isla Choros (Chile) eradicating rabbits. You can contact CONAF - CHILE.

Dear Colleague

Thank you very much

Philippe  JOSEPH 

Eradication is rare to non-existent,, even at local scale. Local control at low levels occur in a few cases.

Attached is an exemplary case of an ineffective, expensive  case of local eradication. This article and its follow-up  may provide ideas on how more effective control could work.

Article Efficacy of Chromolaena odorata control in a South African c...

Article Invasion of an alien shrub across four land management regim...

Depends on spatial and temporal scale:  invasive species impacts tend increase over time whereas invasive species eradication impacts are mostly temporally limited and predictable, and therefore imaginable. Recovery is possible as many native species are released from the invader's impacts. Non-target impact literature is extensive. I hope you are careful to distinguish "eradication" from "control" especially in the context of islands.....

There is a good literature from Galapagos, Hawaii and New Zealand about non-target impacts in animal eradication.

Article Lessons from successful plant eradications in Galapagos: com...

The above respondents appear to have covered much of the ground.  Allochthonous I have encountered in geology to describe exotic rocks; for biota. exotic and non-indigenous are the usual adjectives.

There is a mass of literature on eradication and/or control of exotic species (including humans). The history of the extent of extinctions and gene pool bottle-necking following invasions by Homo sapiens and accompanying exotic biota (flora ad fauna0 is well documented. In Australia we have huge problems with exotic species over a vast continent. Our extinction record is appalling and many species survive only through constant attention to predator control and use of predator exclusion zones, all of which is very expensive. Logistics and expense make large, K-selected feral exotic species; camels, horses, goats, deer, water buffalo,  virtually impossible to eradicate, Those species with high reproduction rates; rodents, rabbits, pigs, foxes, cats, cane toads, carp, bitou bush, are usually targeted with either toxic baits,  pathogens or a combination of pathogens, predator species (biological control) and physical methods.The latter speecies unfortunately quickly develop resistance to vectors of death and new pathogen varieties and other control methods are ever required.  

Virtually all exotic species detrimentally impact native species. Local extinctions are common, and exotic families that have never been encountered in an ecosystem cause immense damage and may threaten hundreds of species. (for example feral cats in Australia).      

Biological control and removal procedure should be followed