plants, animals and soil microbiota have evolved as communities, not as isolated species...
Species that are not native, and again this is basic ecology, lack the connections with the other species in the habitat that evolved as part of similar communities...
Ascension Island, then, was an exception, not a rule...
There is another important question about how we define a native species as species move as a result of climate disruption...
I want to take some time to respond to the concepts you've put forward here, as I believe they're central to developing a more holistic understanding of both invasive and native species. First, the idea that ecological communities are 'intact' entities that are destined to be together forever is one that has largely been disproven and abandoned within the framework of general ecology, though invasion ecology still clings to this antiquated idea. Consider the debate between Clements and Gleason I described in my book - Clements the 'father' of succession put forward the idea that ecosystems are tightly bound networks of interactions headed toward some predictable climax state, Gleason found that they are mixtures of species that forged relationships based on available resources and conditions, and that the end state of any ecosystem is unknown. CS Holling (perhaps one of the most visionary ecologists of recent times) brought this idea even further to explain how ecosystems behave in terms of systems theory as they progress through what he called the Adaptive Cycle - constantly changing in response to selection pressures, but in a pattern of increasingly complexity, networking, and information and resource exchange until all of the energy coming into the system is utilized by fewer, larger organisms. Eventually these late-successional systems are prone to disturbance, and the process begins again, though there's no telling who the characters will be that make use of post-disturbance conditions - most likely those best adapted to the current conditions. The pattern of the Adaptive Cycle can be seen throughout systems everywhere (and fyi, this is what is meant by 'goal-seeking' in systems theory in my book - different from Gaia Theory - systems tend toward higher degrees of complexity over time). If you believe the likes of Holling, Meadows, and Margulis (and I do), then there is no reason to believe that Ascension Island is an exception, but instead an opportunity to observe on a small scale how some of the finer features of natural selection in the context of the Adaptive Cycle work, even on a short time-frame.
There's no doubt that for a certain period following the last ice age, some species had time to develop associations with other species, and there are unique interactions based on isolation and time that are a result of the relatively stable climatic scenario of the last 10,000 years. However, climate change is happening, the process of which has both made possible and been exacerbated by the practice of agriculture, deforestation, and colonization, which have been underway for millennia. The ecological and cultural shifts associated with these practices are not without ramifications for plant and animal communities as we all know, and its impossible to separate out the intensification of activities related to human livelihood provision from shifts in surrounding ecologies. If we accept that ecosystems (like all systems) are constantly in flux and adapting to changes in local and global conditions, then we should be able to anticipate changes in their structure and composition. If we want to preserve and enhance the biodiversity that we've come to know and love, we have to develop management systems that facilitate the resilience of these systems. Holling also offers some great advice on how to manage complexity in constantly evolving systems. We have to move beyond the idea that ecosystems are static, and begin the long process of learning how and when to intervene to promote regenerative qualities and maximum diversity.