Random replicators with high-order interactions
We use tools of the equilibrium statistical mechanics of disordered systems to study analytically the statistical properties of an ecosystem composed of N species interacting via random mutual interactions, as well as via deterministic self-interactions of order p>/=2. We show that the main effect of increasing the order of the interactions among the species is to make the system less competitive, in the sense that the fraction of extinct species is greatly reduced. In addition, we find that for p>2 there is a threshold value which gives a lower bound to the concentration of the surviving species, preventing then the existence of rare species and, consequently, increasing the robustness of the ecosystem to external perturbations.
de Oliveira VM
Instituto de Fisica de Sao Carlos, Universidade de Sao Paulo, Caixa Postal 369, 13560-970 Sao Carlos SP, Brazil.
Fontanari
JF