  Spatial evolution is investigated in a simulated system of nine competing and
mutating bacterium strains, which mimics the biochemical war among bacteria
capable of producing two different bacteriocins (toxins) at most. Random
sequential dynamics on a square lattice is governed by very symmetrical
transition rules for neighborhood invasion of sensitive strains by killers,
killers by resistants, and resistants by by sensitives. The community of the
nine possible toxicity/resistance types undergoes a critical phase transition
as the uniform transmutation rates between the types decreases below a critical
value $P_c$ above which all the nine types of strain coexist with equal
frequencies. Passing the critical mutation rate from above, the system
collapses into one of the three topologically identical states, each consisting
of three strain types. Of the three final states each accrues with equal
probability and all three maintain themselves in a self-organizing polydomain
structure via cyclic invasions. Our Monte Carlo simulations support that this
symmetry breaking transition belongs to the universality class of the
three-state Potts model.
