Evolutionary and ecosystem dynamics are often treated as different processes -operating at separate timescales- even if evidence reveals that rapid evolutionary changes can feed back into ecological interactions. A recent long-term field experiment has explicitly shown that communities of competing plant species can experience very fast phenotypic diversification, and that this gives rise to enhanced complementarity in resource exploitation and to enlarged ecosystem-level productivity. Here, we build on progress made in recent years in the integration of eco-evolutionary dynamics, and present a computational approach aimed at describing these empirical findings in detail. In particular we model a community of organisms of different but similar species evolving in time through mechanisms of birth, competition, sexual reproduction, descent with modification, and death. Based on simple rules, this model provides a rationalization for the emergence of rapid phenotypic diversification in species-rich communities. Furthermore, it also leads to non-trivial predictions about long-term phenotypic change and ecological interactions. Our results illustrate that the presence of highly specialized, non-competing species leads to very stable communities and reveals that phenotypically equivalent species occupying the same niche may emerge and coexist for very long times. Thus, the framework presented here provides a simple approach -complementing existing theories, but specifically devised to account for the specificities of the recent empirical findings for plant communities- to explain the collective emergence of diversification at a community level, and paves the way to further scrutinize the intimate entanglement of ecological and evolutionary processes, especially in species-rich communities.