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      Biodiversity in models of cyclic dominance is preserved by heterogeneity in site-specific invasion rates

      a , 1 , b , 2 , 3

      Scientific Reports

      Nature Publishing Group

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          Abstract

          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.

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          Most cited references 23

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          Coevolutionary games--a mini review.

          Prevalence of cooperation within groups of selfish individuals is puzzling in that it contradicts with the basic premise of natural selection. Favoring players with higher fitness, the latter is key for understanding the challenges faced by cooperators when competing with defectors. Evolutionary game theory provides a competent theoretical framework for addressing the subtleties of cooperation in such situations, which are known as social dilemmas. Recent advances point towards the fact that the evolution of strategies alone may be insufficient to fully exploit the benefits offered by cooperative behavior. Indeed, while spatial structure and heterogeneity, for example, have been recognized as potent promoters of cooperation, coevolutionary rules can extend the potentials of such entities further, and even more importantly, lead to the understanding of their emergence. The introduction of coevolutionary rules to evolutionary games implies, that besides the evolution of strategies, another property may simultaneously be subject to evolution as well. Coevolutionary rules may affect the interaction network, the reproduction capability of players, their reputation, mobility or age. Here we review recent works on evolutionary games incorporating coevolutionary rules, as well as give a didactic description of potential pitfalls and misconceptions associated with the subject. In addition, we briefly outline directions for future research that we feel are promising, thereby particularly focusing on dynamical effects of coevolutionary rules on the evolution of cooperation, which are still widely open to research and thus hold promise of exciting new discoveries. Copyright (c) 2009 Elsevier Ireland Ltd. All rights reserved.
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            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.
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              Allelopathy in Spatially Distributed Populations

              In a homogeneously mixing population of E. coli, colicin-producing and colicin-sensitive strategies both may be evolutionarily stable for certain parameter ranges, with the outcome of competition determined by initial conditions. In contrast, in a spatially-structured population, there is a unique ESS for any given set of parameters; the outcome is determined by how effective allelopathy is in relation to its costs. Furthermore, in a spatially-structured environment, a dynamic equilibrium may be sustained among a colicin-sensitive type, a high colicin-producing type, and a "cheater" that expends less on colicin production but is resistant. Copyright 1997 Academic Press Limited
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                Author and article information

                Journal
                Sci Rep
                Sci Rep
                Scientific Reports
                Nature Publishing Group
                2045-2322
                05 December 2016
                2016
                : 6
                Affiliations
                [1 ]Institute of Technical Physics and Materials Science, Centre for Energy Research, Hungarian Academy of Sciences , P.O. Box 49, H-1525 Budapest, Hungary
                [2 ]Faculty of Natural Sciences and Mathematics, University of Maribor , Koroška cesta 160, SI-2000 Maribor, Slovenia
                [3 ]CAMTP – Center for Applied Mathematics and Theoretical Physics, University of Maribor , Krekova 2, SI-2000 Maribor, Slovenia
                Author notes
                Article
                srep38608
                10.1038/srep38608
                5137108
                27917952
                Copyright © 2016, The Author(s)

                This work is licensed under a Creative Commons Attribution 4.0 International License. The images or other third party material in this article are included in the article’s Creative Commons license, unless indicated otherwise in the credit line; if the material is not included under the Creative Commons license, users will need to obtain permission from the license holder to reproduce the material. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/

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