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.
Deep Dive into 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 phe
Biodiversity is essential to the viability of ecological systems. Species diversity in ecosystems is promoted by cyclic, non-hierarchical interactions among competing populations. Central features of such non-transitive relations are 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 1-5 . 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 time. 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 temporal development of ecological systems and are relevant for the formation and propagation of patterns in microbial populations or excitable media.
The remarkable biodiversity present in ecosystems confounds a naïve 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 6 . Evolutionary game theory 7-9 , in which the success of one species relies on the behaviour of others, provides a useful framework to investigate co-development of populations theoretically. In this context, the rock-paper-scissors game has emerged as a paradigm to describe species diversity 1-5,10-12 . If three subpopulations interact in this non-hierarchical way, one expects intuitively that diversity may be preserved: Each species dominates another only to be outperformed by the remaining one in an endlessly spinning wheel of species-chasingspecies.
Communities of subpopulations exhibiting such dynamics have been identified in numerous ecosystems, ranging from coral reef invertebrates 13 to lizards in the inner Coast Range of California 14 . In particular, recent experimental studies using microbial laboratory cultures have been devoted to the influence of spatial structure on time development and coexistence of species 3,15 . Investigating three strains of colicinogenic E.coli in different environments, it has been shown that cyclic dominance alone is not sufficient to preserve biodiversity. Only when the interactions between individuals are local (e.g. bacteria arranged on a Petri dish), spatially separated domains dominated by one subpopulation can form and lead to stable coexistence 1,3 .
In this Letter, we show that biodiversity is affected drastically by spatial migration of individuals, a ubiquitous feature of real ecosystems. Migration competes with local interactions such as reproduction and selection, thereby mediating species preservation and biodiversity.
For low values of mobility, the temporal development is dominated by interactions among neighbouring individuals, resulting in the long-term maintenance of species diversity. In contrast, when species mobility is high, spatial homogeneity results and biodiversity is lost.
Interestingly, a critical value of mobility sharply delineates these two scenarios. We obtain concise predictions for the fate of the ecological system as a function of species mobility, thereby gaining a comprehensive understanding of its biodiversity.
The influence of mobility on species coexistence was previously studied within the framework of coupled habitat patches (“island models”) 16-19 . In particular, Levin considered an idealized two-patch system and observed a critical mobility for stable coexistence 16 .
Other models comprising many spatially arranged patches were shown to facilitate pattern formation 17,18 . As often in nature spatial degrees of freedom vary continuously (e.g. bacteria can visit the entire area of a Petri dish), we relax the simplifying assumption of habitat patches and consider continuous spatial distribution of individuals. Moreover, as an inherent feature of real ecosystems and in contrast to previous deterministic investigations 16-19 , we explicitly take the stochastic character of the interactions among the populations into account. Such interacting particle systems, where individuals are discrete and space is treated explicitly, were already considered in ecological contexts 1,2,4,5,20 . The behaviour of these models often differs from what is inferred from deterministic reaction-diffusion equations, or from interconnected patches 20 . In the case of cyclic competition, such stochastic spatial systems have been shown to allo
…(Full text truncated)…
This content is AI-processed based on ArXiv data.
