Islands, such as the British Isles, can be adversely affected by the introduction of non-native species. Many species have been introduced to Britain during historical times. Some species have been introduced with no adverse consequences. However, others have had a severe impact both economically and ecologically.

One good example of an invasive species is the gray squirrel which, at the turn of the 20th century, was introduced into South Africa, Ireland, and England from North America. On mainland Britain, it has almost entirely displaced the populations of native red squirrels. Schemes have been introduced to control the population in Ireland to encourage the native red squirrels. In the wild, gray squirrels can be found living in large areas of mature, dense woodland. These forests usually contain large amounts of dense understory vegetation that provides them sufficient amount of food sources and favorable shelters. On very rare occasions, when their usual food sources are scarce, gray squirrels will eat insects and small birds. However, in general gray squirrels exist mainly on nuts and seeds. They even have a high enough tolerance for humans to inhabit residential neighborhoods and are known to raid bird feeders.
Among those species which have been introduced with little harm to the local ecosystem is the rainbow trout which is native only to the rivers and lakes of North America but its value as a hard-fighting game fish and tasty meal has led to its introduction throughout the world. Rainbow trout are gorgeous fish, with coloring and patterns that vary widely depending on habitat, age, and spawning condition. They are members of the salmon family and, like their salmon cousins, can grow quite large. They prefer cool, clear rivers and lakes and survive on insects and small fish.
Adapted from the following sources:  http://en.wikipedia.org/wiki/Eastern_gray_squirrel, http://en.wikipedia.org/wiki/Introduced_species_of_the_British_Isles