3 S ep 2 00 7 Mobility promotes and jeopardizes biodiversity in rock - paper - scissors games

1 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 1−4. 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 subpopula-tions 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. The remarkable biodiversity present in ecosystems confounds a na¨ıve interpretation of Darwinian evolution in which interacting species compete for limited resources until only the fitter species survives. As a striking example, consider that a 30-g sample of soil from a Norwegian forest is estimated to contain some 20,000 common bacterial species 5. Evolutionary game theory 6−8 , in which the success of one species relies on the behaviour of others, provides a useful framework to investigate co-evolving populations theoretically. In this context, the rock-paper-scissors game has emerged as a paradigm to describe species diversity 1−4,9−11. If three subpopulations interact in this non-hierarchical way, one expects intuitively that diversity may be preserved: Each species dominates another only to be out-performed by the remaining one in an endlessly spinning wheel of species-chasing-species. Communities of subpopulations exhibiting such dynamics have been identified in numerous ecosystems, ranging from coral reef invertebrates 12 to lizards in the inner Coast Range of California 13. In particular, recent experimental studies using microbial laboratory cultures have been devoted to the influence of spatial structure on species coevolution 2,14,15. Investigating three strains of colicinogenic E.coli in different environments, it has been shown that 2 cyclic dominance alone is not sufficient to preserve biodiversity. Only when the interactions between individuals are …