Heavy-tailed abundance distributions from stochastic Lotka-Volterra models

Microbial communities found in nature are composed of many rare species and few abundant ones, as reflected by their heavy-tailed abundance distributions. How a large number of species can coexist in those complex communities and why they are dominated by rare species is still not fully understood. We show how heavy-tailed distributions arise as an emergent property from large communities with many interacting species in population-level models. To do so we rely on stochastic logistic and generalized Lotka-Volterra models for which we introduce a global maximal capacity. This maximal capacity accounts for the fact that communities are limited by available resources and space. In a parallel ad-hoc approach, we obtain heavy-tailed abundance distributions from non-interacting models through specific distributions of the parameters. We expect both mechanisms, interactions between many species and specific parameter distributions, to be relevant to explain the observed heavy tails.