  A model of six-species food web is studied in the viewpoint of spatial
interaction structures. Each species has two predators and two preys, and it
was previously known that the defensive alliances of three cyclically predating
species self-organize in two-dimensions. The alliance-breaking transition
occurs as either the mutation rate is increased or interaction topology is
randomized in the scheme of the Watts-Strogatz model. In the former case of
temporal disorder, via the finite-size scaling analysis the transition is
clearly shown to belong to the two-dimensional Ising universality class. In
contrast, the geometric or spatial randomness for the latter case yields a
discontinuous phase transition. The mean-field limit of the model is
analytically solved and then compared with numerical results. The dynamic
universality and the temporally periodic behaviors are also discussed.
