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We investigate the impact of cyclic competition on pattern formation in the rock-paper-scissors game. By separately considering random and prepared initial conditions, we observe a critical influence of the competition rate on the stability of spiral waves and on the emergence of biodiversity. In particular, while increasing values of promote biodiversity, they may act detrimentally on spatial pattern formation. For random initial conditions, we observe a phase transition from biodiversity to an absorbing phase, whereby the critical value of mobility grows linearly with increasing values of on a log-log scale but then saturates as becomes large. For prepared initial conditions, we observe the formation of single-armed spirals, but only for values of that are below a critical value. Once above that value, the spirals break up and form disordered spatial structures, mainly because of the percolation of vacant sites. Thus there exists a …