Scaling in a network model of a multispecies ecosystem

A new model ecosystem of many interacting species is introduced in which the species are connected through a random matrix with a given connectivity. The model is studied both analytically and by numerical simulations. A probability distribution derived from the model is in good agreement with simulations and field data. It is also shown that the connectivity, C, and the number of species, S, are linked through the scaling relation 〈S〉=k(C)−1+ε, which is observed in real ecosystems. Our approach suggests a natural link between log-normal and power-law distributions of species abundances.