Time to absorption for a heterogeneous neutral competition model

Neutral models aspire to explain biodiversity patterns in ecosystems where species difference can be neglected, as it might occur at a specific trophic level, and perfect symmetry is assumed between species. Voter-like models capture the essential ingredients of the neutral hypothesis and represent a paradigm for other disciplines like social studies and chemical reactions. In a system where each individual can interact with all the other members of the community, the typical time to reach an absorbing state with a single species scales linearly with the community size. Here we show, by using a rigorous approach within a large deviation principle and confirming previous approximate and numerical results, that in a heterogeneous voter model the typical time to reach an absorbing state scales exponentially with the system size, suggestive of an asymptotic active phase.