Scaling in a Multispecies Network Model Ecosystem

A new model ecosystem consisting of many interacting species is introduced. The species are connected through a random matrix with a given connectivity ${\cal C} \pi$. It is shown that the system is organized close to a boundary of marginal stability in such a way that fluctuations follow power-law distributions both in species abundance and their lifetimes for some slow-driving (immigration) regime. The connectivity and the number of species are linked through a scaling relation which is the one observed in real ecosystems. These results suggest that the basic macroscopic features of real, species-rich ecologies might be linked with a critical state. A natural link between lognormal and power-law distributions of species abundances is suggested.