Random replicators with high-order interactions

Details Random replicators with high-order interactions Random replicators with high-order interactions

2000-05-04

arxiv.org/abs/cond-mat/0005099v1

Physics

Condensed Matter

Statistical Mechanics

7 pages, 4 Postscript figures

Scientific paper

10.1103/PhysRevLett.85.4984

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, Gaussian interactions of order p >= 2, and deterministic self-interactions u <= 0. We show that for nonzero u the effect of increasing the order of the interactions is to make the system more cooperative, in the sense that the fraction of extinct species is greatly reduced. Furthermore, 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.

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