Résumé
How can so many species coexist in natural ecosystems remains a fundamental question in ecology. Classical models suggest that competition for space and resources should maintain the number of coexisting species far below the staggering diversity commonly found in nature. To overcome this paradox, theoretical studies have long highlighted a number of mechanisms that can favour species coexistence, from the distribution of interaction strengths between species to the shape of population growth functions. In particular, a family of mathematical models finds that, when sublinear population growth (SG) rates are coupled with competition between species, species diversity can stabilize community dynamics. This could suggest that SG may explain the stable coexistence of many species in natural ecosystems. Here we clarify why SG models do not solve the paradox of species coexistence. This is because, in the SG model, coexistence emerges from an unrealistic property, in which population per capita growth rates tend to infinity at low abundance, preventing species from ever going extinct due to competitive exclusion. Infinite growth at low abundance can be regularized by assuming a minimal abundance threshold, below which a species goes extinct or follows non‐infinite growth curves. When this is done, the SG model recovers the classical result: increasing the diversity of the species pool leads to competitive exclusion and species extinctions.