Direct ecological management is unfortunately a bit of a game of using a bucket to fix a leaky ship. The equilibrium that established the ecosystem dynamics in the first place is disrupted. A new equilibrium might form over time, but we enforce the old one because that is what we documented when we first came to a place, even though it is no longer thermodynamically favorable.
Ironically, the ecology of an island itself came from events like a random animal swimming to it over the historical record and finding sufficient spare resources or an ecological niche they could satisfy sufficiently to reproduce. Distance from mainland and species diversity is very strongly correlated reflecting increasingly scarce odds of these "heroic journeys" at greater distances. Species themselves are capable of exhausting an islands resources and putting themselves into local extinction even with no human intervention (such as the case of the last of the mammoths on wrangel island).
Ironically, the ecology of an island itself came from events like a random animal swimming to it over the historical record and finding sufficient spare resources or an ecological niche they could satisfy sufficiently to reproduce. Distance from mainland and species diversity is very strongly correlated reflecting increasingly scarce odds of these "heroic journeys" at greater distances. Species themselves are capable of exhausting an islands resources and putting themselves into local extinction even with no human intervention (such as the case of the last of the mammoths on wrangel island).