Occasionally you read in the news that parasite x, plant y or animal z has been found in country abc which shouldn’t be the case and causes problems.
This is often a result of the ongoing climate change, increasing travel and global trade that allows many species to enter into new regions.
Because of the lack of natural predators or competitors, these new species can become locally dominant and replace established species.
My questions: what is the end game?
Will global biodiversity decline significantly to a few “core” species that are flexible in multiple climate zones or environment?
Or will the native species adapt or evolve further?


Your question appears to ask about invasive species more than biodiversity on the whole.
On the former, an invasive species can completely destroy local populations of indigenous species and become established. Sometimes just partially, sometimes completely.
The endgame of biodiversity? Evolution has no endgame, it just is. A constant adaptation where some species die out and new speciation fills any spaces created by their absence. Nature abhors a vaccum.
i’d say that nature abhors the vacuum as much as you abhor cake. namely, you eliminate it by feeding on it; likewise nature just sees it as a growth opportunity.