The question of how species diversity is maintained in coexisting populations arises in a variety of contexts, from ecology to immunology, but its mechanisms are not fully understood. Two competing species, or strains of the same species, might coexist for a long time in an ecosystem, especially if they occupy different ecological niches. However, if they compete for a limited shared resource (the niche) it is likely that one or
the other of them will rapidly go extinct. Even in a stable system, extinction can occur due to stochastic fluctuations.
I have calculated the mean time to extinction in the coupled logistic model, which captures the basic dynamics of two species that completely, or even partly, share an ecological niche. This is done by solving the backward master equation. Fitting an ansatz to the results indicates that there is a stark contrast between species competing for the exact same resources rather than when there is only partial niche overlap. In the former case a species quickly goes to extinction; in the latter, their coexistence is exponentially long in the system size.