  The rock-paper-scissors game is a paradigmatic model for biodiversity, with
applications ranging from microbial populations to human societies. Research
has shown, however, that mobility jeopardizes biodiversity by promoting the
formation of spiral waves, especially if there is no conservation law in place
for the total number of competing players. Firstly, we show that even if such a
conservation law applies, mobility still jeopardizes biodiversity in the
spatial rock-paper-scissors game if only a small fraction of links of the
square lattice is randomly rewired. Secondly, we show that zealots are very
effective in taming the amplitude of oscillations that emerge due to mobility
and/or interaction randomness, and this regardless of whether the later is
quenched or annealed. While even a tiny fraction of zealots brings significant
benefits, at 5\% occupancy zealots practically destroy all oscillations
regardless of the intensity of mobility, and regardless of the type and
strength of randomness in the interaction structure. Interestingly, by annealed
randomness the impact of zealots is qualitatively the same as by mobility,
which highlights that fast diffusion does not necessarily destroy the
coexistence of species, and that zealotry thus helps to recover the stable
mean-field solution. Our results strengthen the important role of zealots in
models of cyclic dominance, and they reveal fascinating evolutionary outcomes
in structured populations that are a unique consequence of such uncompromising
behavior.
