Advanced Search
Article Contents
Article Contents

Biodiversity and vulnerability in a 3D mutualistic system

Abstract Related Papers Cited by
  • In this paper we study a three dimensional mutualistic model of two plants in competition and a pollinator with cooperative relation with plants. We compare the dynamical properties of this system with the associated one under absence of the pollinator. We observe how cooperation is a common fact to increase biodiversity, which it is known that, generically, holds for general mutualistic dynamical systems in Ecology as introduced in [4]. We also give mathematical evidence on how a cooperative species induces an increased biodiversity, even if the species is push to extinction. For this fact, we propose a necessary change in the model formulation which could explain this kind of phenomenon.
    Mathematics Subject Classification: Primary: 92B05, 34A34, 34D05, 34D23.


    \begin{equation} \\ \end{equation}
  • [1]

    J. Bascompte, P. Jordano, C. J. Melián and J. M. Olesen, The nested assembly of plant-animal mutualistic networks, Proc. Natl Acad. Sci. USA, 100 (2003), 9383-9387.doi: 10.1073/pnas.1633576100.


    J. Bascompte, P. Jordano and J. M. Olesen, Asymmetric coevolutionary networks facilitate biodiversity maintenance, Science, 312 (2006), 431-433.doi: 10.1126/science.1123412.


    J. Bascompte and P. Jordano, The structure of plant-animal mutualistic networks: The architecture of biodiversity, Annu. Rev. Ecol. Evol. Syst., 38 (2007), 567-593.


    U. Bastolla, M. A. Fortuna, A. Pascual-García, A. Ferrera, B. Luque and J. Bascompte, The architecture of mutualistic networks minimizes competition and increases biodiversity, Nature, 458 (2009), 1018-1020.doi: 10.1038/nature07950.


    R. S. Cantrell and C. Cosner, Spatial Ecology Via Reaction-Diffusion Equations, Wiley Series in Mathematical and Computational Biology, John Wiley & Sons, Ltd., Chichester, 2003.doi: 10.1002/0470871296.


    C. E. Clark and T. G. Hallam, The community matrix in three species community models, J. Math. Biology, 16 (1982), 25-31.doi: 10.1007/BF00275158.


    B. S. Goh, Stability in models of mutualism, The American Naturalist, 111 (1977), 135-143.doi: 10.1086/283384.


    B. S. Goh, Stability in models of mutualism, The American Naturalist, 113 (1979), 261-275.doi: 10.1086/283384.


    V. Hutson, A theorem on average Lyapunov functions, Monatsch. Math., 98 (1984), 267-275.doi: 10.1007/BF01540776.


    J. D. Murray, Mathematical Biology, Springer, New York, 1993doi: 10.1007/b98869.


    S. Saavedra, D. B. Stouffer, B. Uzzi and J. Bascompte, Strong contributors to network persistence are the most vulnerable to extinction, Nature, 478 (2011), 233-235.doi: 10.1038/nature10433.


    H. L. Smith, Competing subcommunities of mutualists and a generalized Kamke theorem, SIAM J. Appl. Math., 46 (1986), 856-874.doi: 10.1137/0146052.


    G. Sugihara and H. Ye, Cooperative network dynamics, Nature (News and View), 458 (2009), 979-980.doi: 10.1038/458979a.


    Y. Takeuchi, Global Dynamical Properties of Lotka-Volterra Systems, World Scientific Publishing Co., Inc., River Edge, NJ, 1996.doi: 10.1142/9789812830548.


    Y. Wang and H. Wu, Dynamics of a cooperation-competition model for the WWW market, Physica A, 339 (2004), 609-620.doi: 10.1016/j.physa.2004.03.067.

  • 加载中

Article Metrics

HTML views() PDF downloads(56) Cited by(0)

Access History



    DownLoad:  Full-Size Img  PowerPoint