  Global, population-wide oscillations in models of cyclic dominance may result
in the collapse of biodiversity due to the accidental extinction of one species
in the loop. Previous research has shown that such oscillations can emerge if
the interaction network has small-world properties, and more generally, because
of long-range interactions among individuals or because of mobility. But
although these features are all common in nature, global oscillations are
rarely observed in actual biological systems. This begets the question what is
the missing ingredient that would prevent local oscillations to synchronize
across the population to form global oscillations. Here we show that, although
heterogeneous species-specific invasion rates fail to have a noticeable impact
on species coexistence, randomness in site-specific invasion rates successfully
hinders the emergence of global oscillations and thus preserves biodiversity.
Our model takes into account that the environment is often not uniform but
rather spatially heterogeneous, which may influence the success of microscopic
dynamics locally. This prevents the synchronization of locally emerging
oscillations, and ultimately results in a phenomenon where one type of
randomness is used to mitigate the adverse effects of other types of randomness
in the system.
