Online social networks have significantly changed global communication dynamics. Despite the complexity of such dynamics, emergent patterns from empirical microblogging data on hashtag usage, such as meme popularity power-law distributions, have been observed. However, going beyond empirical or simulation-based studies, highlighting and distinguishing fundamental mechanisms at the origin of such patterns are still open problems. Herein, inspired by the neutral theory of ecology, we provide an analytical formalism capable of capturing the competition for attention in online social systems and explaining several emergent patterns observed in the context of information ecosystems. Specifically, besides meme popularity distributions, we study the persistence distributions of memes within the network and the capacity of the system to sustain several coexisting diverse memes. Such properties have a clear analogy to extinction time and biodiversity in natural ecosystems. In the social network context, diversity of ideas is indeed an identifying characteristic of the “health” of the communication process. We show how our theoretical framework is successful in explaining real data collected from the Twitter online social network. The proposed framework introduced here provides both insight into the roles played by competition and network structure on meme diversity and persistence, and an applicable null model to be tested against real data.