A self-similar hierarchical solution that is both dynamically and evolutionarily stable is found for the multidimensional Lotka-Volterra equation with a single chain of prey-predator relations. This gives a simple and natural explanation to the key features of hierarchical ecosystems, such as its ubiquity, pyramidal population distribution, and higher aggressiveness among higher trophic levels.

• Received 31 January 2003

DOI:https://doi.org/10.1103/PhysRevLett.90.258105