  Quantum frameworks for modeling competitive ecological systems and
self-organizing structures have been investigated under multiple perspectives
yielded by quantum mechanics. These comprise the description of the phase-space
prey-predator competition dynamics in the framework of the Weyl-Wigner quantum
mechanics. In this case, from the classical dynamics described by the
Lotka-Volterra (LV) Hamiltonian, quantum states convoluted by statistical
gaussian ensembles can be analytically evaluated. Quantum modifications on the
patterns of equilibrium and stability of the prey-predator dynamics can then be
identified. These include quantum distortions over the equilibrium point
drivers of the LV dynamics which are quantified through the Wigner current
fluxes obtained from an onset Hamiltonian background. In addition, for gaussian
ensembles highly localized around the equilibrium point, stability properties
are shown to be affected by emergent topological quantum domains which, in some
cases, could lead either to extinction and revival scenarios or to the
perpetual coexistence of both prey and predator agents identified as quantum
observables in microscopic systems. Conclusively, quantum and gaussian
statistical driving parameters are shown to affect the stability criteria and
the time evolution pattern for such microbiological-like communities.
