American Institute of Mathematical Sciences

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September  2012, 7(3): 429-440. doi: 10.3934/nhm.2012.7.429

Effects of topology on robustness in ecological bipartite networks

Juan Manuel Pastor 1, , Silvia Santamaría 2, , Marcos Méndez 3, and  Javier Galeano 1,

1. 

Dept. Ciencia y Tecnología Aplicada a la I.T. Agrícola, and Grupo de Sistemas Complejos, Universidad Politécnica de Madrid, 28040-Madrid, Spain, Spain
2. 

Áera de Biodiversidad y Conservación, Universidad Rey Juan Carlos, Móstoles, Spain
3. 

Área de Biodiversidad y Conservación, Universidad Rey Juan Carlos, Móstoles, Spain

Received  December 2011 Revised  June 2012 Published  October 2012

High robustness of complex ecological systems in the face of species extinction has been hypothesized based on the redundancy in species. We explored how differences in network topology may affect robustness. Ecological bipartite networks used to be small, asymmetric and sparse matrices. We created synthetic networks to study the influence of the properties of network dimensions asymmetry, connectance and type of degree distribution on network robustness. We used two extinction strategies: node extinction and link extinction, and three extinction sequences differing in the order of species removal (least-to-most connected, random, most-to-least connected). We assessed robustness to extinction of simulated networks, which differed in one of the three topological features. Simulated networks indicated that robustness decreases when (a) extinction involved those nodes belonging to the most species-rich guild and (b) networks had lower connectance. We also compared simulated networks with different degree- distribution networks, and they showed important differences in robustness depending on the extinction scenario. In the link extinction strategy, the robustness of synthetic networks was clearly determined by the asymmetry in the network dimensions, while the variation in connectance produced negligible differences.
Keywords: asymmetry., extinctions, Ecology networks, robustness.
Mathematics Subject Classification: Primary: 58F15, 58F17; Secondary: 53C3.
Citation: Juan Manuel Pastor, Silvia Santamaría, Marcos Méndez, Javier Galeano. Effects of topology on robustness in ecological bipartite networks. Networks & Heterogeneous Media, 2012, 7 (3) : 429-440. doi: 10.3934/nhm.2012.7.429
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J. Memmott, N. M. Waser and M. V. Price, Tolerance of pollination networks to species extinctions,, P. Roy. Soc. Lond. B. Bio., 271 (2004), 2605.  doi: 10.1098/rspb.2004.2909.  Google Scholar

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J. M. Olesen, J. Bascompte, Y. L. Dupont and P. Jordano, The modularity of pollination networks,, P. Natl. Acad. Sci. USA, 104 (2007), 19891.  doi: 10.1073/pnas.0706375104.  Google Scholar

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S. R. Proulx and P. C. Phillips, The opportunity for canalization and the evolution of genetic networks,, Am. Nat., 165 (2005), 147.  doi: 10.1086/426873.  Google Scholar

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M. Rosas-Casals, S. Valverde and R. V. Solé, Topological vulnerability of the European power grid under errors and attacks,, Int. J. Bifurcat. Chaos, 17 (2007), 2465.  doi: 10.1142/S0218127407018531.  Google Scholar

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S. Santamaría, J. M. Pastor, J. Galeano and M. Méndez, Alpine pollination networks exhibit a broad range of robustness to species extinction,, To be published., ().   Google Scholar

[24]

R. V. Solé and J. M. Montoya, Complexity and fragility in ecological networks,, P. Roy. Soc. Lond. B. Biol., 268 (2001), 2039.  doi: 10.1098/rspb.2001.1767.  Google Scholar

[25]

U. T. Srinivasan, J. A. Dunne, J. Harte and N. D. Martinez, Response of complex food webs to realistic extinction sequences,, Ecology, 88 (2007), 671.  doi: 10.1890/06-0971.  Google Scholar

[26]

P. Yodzis, The connectance of real ecosystems,, Nature, 284 (1980), 544.  doi: 10.1038/284544a0.  Google Scholar

show all references

References:
[1]

R. Albert, H. Jeong and A. L. Barabási, Error and attack tolerance of complex networks,, Nature, 406 (2000), 378.  doi: 10.1038/35019019.  Google Scholar

[2]

J. Bascompte, P. Jordano and J. M. Olesen, Asymmetric coevolutionary networks facilitate biodiversity maintenance,, Science, 312 (2006), 431.   Google Scholar

[3]

J. Bascompte and P. Jordano, Plant-animal mutualistic networks: The architecture of biodiversity,, Annu. Rev. Ecol. Evol. S., 38 (2007), 567.   Google Scholar

[4]

P. Crucitti, V. Latora, M. Marchiori and A. Rapisarda, Error and attack tolerance of complex networks,, Physica A, 340 (2004), 388.  doi: 10.1016/j.physa.2004.04.031.  Google Scholar

[5]

C. F. Dormann, J. Fründ, N. Blüthgen and B. Gruber, Indices, graphs and null models: analyzing bipartite ecological networks,, The Open Ecology Journal, 2 (2009), 7.   Google Scholar

[6]

J. A. Dunne, R. J. Williams and N. D. Martinez, Network structure and biodiversity loss in food webs: Robustness increases with connectance,, Ecol. Lett., 5 (2002), 558.   Google Scholar

[7]

J. A. Dunne and R. J. Williams, Cascading extinctions and community collapse in model food webs,, Philos. T. R. Soc. B., 364 (2009), 1711.   Google Scholar

[8]

H. Elberling and J. M. Olesen, The structure of a high latitude plant-flower visitor system: tthe dominance of flies,, Ecography, 22 (1999), 314.   Google Scholar

[9]

M. R. Gardner and W. R. Ashby, Connectance of large dynamic (cybernetic) systems: Critical values for stability,, Nature, 228 (1970), 784.  doi: 10.1038/228784a0.  Google Scholar

[10]

J. Gómez-Gardeñez, V. Latora, Y. Moreno and E. Profumo, Spreading of sexually transmitted diseasesin heterosexual populations,, P. Natl. Acad. Sci. USA, 105 (2008), 1399.  doi: 10.1073/pnas.0707332105.  Google Scholar

[11]

P. Jordano, J. Bascompte and J. M. Olesen, Invariant properties in coevolutionary networks of plant-animal interactions,, Ecol. Lett., 6 (2003), 69.   Google Scholar

[12]

C. N. Kaiser-Bunbury, S. Muff, J. Memmott and C. B. Muller, The robustness of pollination networks to the loss of species and interactions: a quantitative approach incorporating pollinator behaviour,, Ecol. Lett., 13 (2010), 442.   Google Scholar

[13]

Y. Lai, A. Motter and T. Nishikawa, Attacks and cascades in complex networks,, Lec. Notes Phys., 310 (2004), 299.  doi: 10.1007/978-3-540-44485-5_14.  Google Scholar

[14]

R. May, Will a large complex system be stable?,, Nature, 238 (1972), 413.   Google Scholar

[15]

R. May, "Stability and Complexity in Model Ecosystems,", Princeton Univ. Press, (2001).   Google Scholar

[16]

J. Memmott, N. M. Waser and M. V. Price, Tolerance of pollination networks to species extinctions,, P. Roy. Soc. Lond. B. Bio., 271 (2004), 2605.  doi: 10.1098/rspb.2004.2909.  Google Scholar

[17]

A. Motter and Y. Lai, Cascade-based attacks on complex networks,, Phys. Rev. E, 66 (2002), 065102.  doi: 10.1103/PhysRevE.66.065102.  Google Scholar

[18]

, NCEAS interaction webs database,, , ().   Google Scholar

[19]

J. M. Olesen and P. Jordano, Geographic patterns in plant-pollinator mutualistic networks,, Ecology, 83 (2002), 2416.   Google Scholar

[20]

J. M. Olesen, J. Bascompte, Y. L. Dupont and P. Jordano, The modularity of pollination networks,, P. Natl. Acad. Sci. USA, 104 (2007), 19891.  doi: 10.1073/pnas.0706375104.  Google Scholar

[21]

S. R. Proulx and P. C. Phillips, The opportunity for canalization and the evolution of genetic networks,, Am. Nat., 165 (2005), 147.  doi: 10.1086/426873.  Google Scholar

[22]

M. Rosas-Casals, S. Valverde and R. V. Solé, Topological vulnerability of the European power grid under errors and attacks,, Int. J. Bifurcat. Chaos, 17 (2007), 2465.  doi: 10.1142/S0218127407018531.  Google Scholar

[23]

S. Santamaría, J. M. Pastor, J. Galeano and M. Méndez, Alpine pollination networks exhibit a broad range of robustness to species extinction,, To be published., ().   Google Scholar

[24]

R. V. Solé and J. M. Montoya, Complexity and fragility in ecological networks,, P. Roy. Soc. Lond. B. Biol., 268 (2001), 2039.  doi: 10.1098/rspb.2001.1767.  Google Scholar

[25]

U. T. Srinivasan, J. A. Dunne, J. Harte and N. D. Martinez, Response of complex food webs to realistic extinction sequences,, Ecology, 88 (2007), 671.  doi: 10.1890/06-0971.  Google Scholar

[26]

P. Yodzis, The connectance of real ecosystems,, Nature, 284 (1980), 544.  doi: 10.1038/284544a0.  Google Scholar

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