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, for example, 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, solitary waves are observed. This topological phase transition lies in symmetry class D within the "tenfold way" classification as also realized by 1D topological superconductors.
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