Competing associations in six-species predator-prey models

We study a set of six-species ecological models where each species has two predators and two prey. On a square lattice the time evolution is governed by iterated invasions between the neighbouring predator-prey pairs chosen at random and by a site exchange with a probability X, between the neutral pairs. These models involve the possibility of spontaneous formation of different defensive alliances whose members protect each other from the external invaders. The Monte Carlo simulations show a surprisingly rich variety of the stable spatial distributions of species and subsequent phase transitions when tuning the control parameter X-s. These very simple models are able to demonstrate that the competition between these associations influences their composition. Sometimes the dominant association is developed via a domain growth. In other cases larger and larger invasion processes precede the prevalence of one of the stable associations. Under some conditions the survival of all the species can be maintained by the cyclic dominance occurring between these associations.