Cyclical interactions with alliance-specific heterogeneous invasion rates.

We study a six-species Lotka-Volterra-type system on different two-dimensional lattices when each species has two superior and two inferior partners. The invasion rates from predator sites to a randomly chosen neighboring prey site depend on the predator-prey pair, whereby cyclic symmetries within the two three-species defensive alliances are conserved. Monte Carlo simulations reveal an unexpected nonmonotonous dependence of alliance survival on the difference of alliance-specific invasion rates. This behavior is qualitatively reproduced by a four-point mean-field approximation. The study addresses fundamental problems of stability for the competition of two defensive alliances and thus has important implications in natural and social sciences.