Mobility promotes and jeopardizes biodiversity in rock-paper-scissors games

Biodiversity is essential to the viability of ecological systems.
Species diversity in ecosystems is promoted by cyclic,
non-hierarchical interactions among competing populations. Such
non-transitive relations lead to an evolution with central features
represented by the 'rock-paper-scissors' game, where rock crushes
scissors, scissors cut paper, and paper wraps rock. In combination
with spatial dispersal of static populations, this type of
competition results in the stable coexistence of all species and
the long-term maintenance of biodiversity. However, population
mobility is a central feature of real ecosystems: animals migrate,
bacteria run and tumble. Here, we observe a critical influence of
mobility on species diversity. When mobility exceeds a certain
value, biodiversity is jeopardized and lost. In contrast, below
this critical threshold all subpopulations coexist and an
entanglement of travelling spiral waves forms in the course of
temporal evolution. We establish that this phenomenon is robust, it
does not depend on the details of cyclic competition or spatial
environment. These findings have important implications for
maintenance and evolution of ecological systems and are relevant
for the formation and propagation of patterns in excitable media,
such as chemical kinetics or epidemic outbreaks.