It depends on if they occupy the exact same niche and are consuming the same species as a food source. If they are they are competing species. If this is the case it depends which species is better suited. Many times an invasive species may have an edge on native species. More often than not, if both species are native, they are more likely to diverge, and evolve to occupy a slightly different niches to the benefit of both organisms.

Also another thing to consider is that if the two populations are abundant or not. If one or more of these co-evolving species are existing at low population numbers, they will be more likely to be overrun by the larger population, because there will be food shortages due to the larger population's needs.