Cyclic dominant systems, like rock-paper-scissors game, are frequently used
to explain biodiversity in nature, where mobility, reproduction and
intransitive competition are on stage to provide the coexistence of
competitors. A significantly new situation emerges if we introduce an apex
predator who can superior all members of the mentioned three-species system. In
the latter case the evolution may terminate into three qualitatively different
destinations depending on the apex predator decaying ratio q. In particular,
the whole population goes extinct or all four species survive or only the
original three-species system remains alive as we vary the control parameter.
These solutions are separated by a discontinuous and a continuous phase
transitions at critical q values. Our results highlight that cyclic dominant
competition can offer a stable way to survive even in a predator-prey-like
system that can be maintained for large interval of critical parameter values.Comment: version to appear in EPL. 7 pages, 7 figure
