The interplay of those factors can lead to local extinction. And then of course, environmental effects such as three severe droughts in a row can wipe out one or several populations over a large area and wipe them out almost immediately. And if there are no individuals nearby to come back and repopulate, then the species will go extinct locally. These and other factors are the basis of the Theory of Island Biogeography, which you probably know about, that was developed by MacArthur and Wilson in 1967. They studied species on islands and developed a mathematical relationship between the number of species and the area of the island.
Larger islands support more species.
They developed a concept of turnover rates such that as species go extinct on an island they have a chance to be replaced by other species that can disperse onto the island.