I get that there's in-species competition, and that the successful competitors will come to dominate, perhaps completely. But what I'm thinking is that when a

I get that there's in-species competition, and that the successful competitors will come to dominate, perhaps completely. But what I'm thinking is that when a species is established in a niche, the direction of that competition is arbitrary rather than being limited to competing for resources. Once the level of resources needed to procreate are generally available, the individuals can compete over anything at hand. As you say, "fitness" is a key concept, but fitness for what? If you don't need more resources, then on what basis are you competing to be more fit? If you happen to be a social tool using species, then it could be based on those things: more complex and subtle social structures (and the language to support that), more complex and subtle tool use (and the abstract thinking to support that).