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Title: Rock-paper-scissors games and biodiversity in microbial communities with non-hierarchical interactions

Abstract:

  Understanding the mechanisms allowing the maintenance of biodiversity is a central issue in theoretical biology and ecology. Evolutionary game theory, where the success of one species depends on what the others are doing, provides a promising framework to theoretically investigate co-evolving populations. Recent experiments on microbial populations have shown that the existence of local and cyclic interactions promotes the long-term coexistence of all species and the formation of spatial patterns. In this context, rock-paper-scissors games - in which rock crushes scissors, scissors cut paper, and paper wraps rock - have emerged  as a fruitful metaphor for non-hierarchical co-evolutionary dynamics.

In this forum, I shall discuss stochastic evolutionary models where three species cyclically dominate each other according to "rock-paper-scissors" interactions. In the first part of the talk I will give an overview of the biological motivation for some microbial communities and of the classic mathematical modelling in the absence of spatial structure [Phys. Rev. E 74, 051907 (2006)]. The second part of the forum will address the influence of spatial degrees of freedom and internal noise on the population's coexistence using an interacting particle approach. In particular, I will report on our recent findings [Nature 448, 1046 (2007)] about the subtle interplay between the individuals' mobility and local interactions, which leads to the loss of biodiversity above a certain mobility threshold. Below that critical value, all species coexist and form fascinating moving patterns of entangled spirals. We have also investigated those kaleidoscopic spatio-temporal structures and have elucidated that they stem from an interplay between the deterministic dynamics and internal noise [arXiv:0710.0383.v1]. I will illustrate how the theory of front propagation and the properties of the complex Ginzburg-Landau equation allow to derive analytical expressions for the velocity and the wavelength of the rotating spiral waves. The theoretical methods described in this talk can be broadly applied, e.g. to behavioural sciences, epidemic outbreaks, or in chemical reactions, as it will be briefly sketched.