Many island environments have been physically and biotically devastated by goats. Predators like cats and dogs also a problem. Rapid use of plants at levels far higher than they have evolved to withstand. Nearly total absence of successful seedling regeneration. Replacement of favored plant species with non-favored species.
Erosion begins and accelerates, severely altering the physical environment.
Eventually we have ecosystem collapse and wholesale extinction. This is similar to the demonstrated affects of overgrazing on western rangeland during the past century. In some cases, control may be achieved via biocontrol , that is, using a natural enemy, parasite, disease, or herbivore to control an exotic. In biocontrol it is imperative that the control agent be proved to specialize on the target species without ever expanding to alternative host species. Because of this requirement, biocontrol agents are always insects, bacteria, or viruses.