  A hallmark of topological phases is the occurrence of topologically protected
modes at the system`s boundary. Here we find topological phases in the
antisymmetric Lotka-Volterra equation (ALVE). The ALVE is a nonlinear dynamical
system and describes, e.g., the evolutionary dynamics of a rock-paper-scissors
cycle. On a one-dimensional chain of rock-paper-scissor cycles, topological
phases become manifest as robust polarization states. At the transition point
between left and right polarization, solitonic waves are observed. This
topological phase transition lies in symmetry class $D$ within the "ten-fold
way" classification as also realized by 1D topological superconductors.
