Effects of topology on robustness in ecological bipartite networks

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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

Abstract
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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 and Heterogeneous Media, 2012, 7 (3) : 429-440. doi: 10.3934/nhm.2012.7.429

References:

[1]	R. Albert, H. Jeong and A. L. Barabási, Error and attack tolerance of complex networks, Nature, 406 (2000), 378-382. doi: 10.1038/35019019.
[2]	J. Bascompte, P. Jordano and J. M. Olesen, Asymmetric coevolutionary networks facilitate biodiversity maintenance, Science, 312 (2006), 431-433.
[3]	J. Bascompte and P. Jordano, Plant-animal mutualistic networks: The architecture of biodiversity, Annu. Rev. Ecol. Evol. S., 38 (2007), 567-593.
[4]	P. Crucitti, V. Latora, M. Marchiori and A. Rapisarda, Error and attack tolerance of complex networks, Physica A, 340 (2004), 388-394. doi: 10.1016/j.physa.2004.04.031.
[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), 7-24.
[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), 558-567.
[7]	J. A. Dunne and R. J. Williams, Cascading extinctions and community collapse in model food webs, Philos. T. R. Soc. B., 364 (2009), 1711-1723.
[8]	H. Elberling and J. M. Olesen, The structure of a high latitude plant-flower visitor system: tthe dominance of flies, Ecography, 22 (1999), 314-323.
[9]	M. R. Gardner and W. R. Ashby, Connectance of large dynamic (cybernetic) systems: Critical values for stability, Nature, 228 (1970), 784-784. doi: 10.1038/228784a0.
[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), 1399-1404. doi: 10.1073/pnas.0707332105.
[11]	P. Jordano, J. Bascompte and J. M. Olesen, Invariant properties in coevolutionary networks of plant-animal interactions, Ecol. Lett., 6 (2003), 69-81.
[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), 442-452.
[13]	Y. Lai, A. Motter and T. Nishikawa, Attacks and cascades in complex networks, Lec. Notes Phys., 310 (2004), 299-310. doi: 10.1007/978-3-540-44485-5_14.
[14]	R. May, Will a large complex system be stable?, Nature, 238 (1972), 413-414.
[15]	R. May, "Stability and Complexity in Model Ecosystems," Princeton Univ. Press, 2001.
[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), 2605-2611. doi: 10.1098/rspb.2004.2909.
[17]	A. Motter and Y. Lai, Cascade-based attacks on complex networks, Phys. Rev. E, 66 (2002), 065102-4. doi: 10.1103/PhysRevE.66.065102.
[18]	, NCEAS interaction webs database, http://www.nceas.ucsb.edu/.
[19]	J. M. Olesen and P. Jordano, Geographic patterns in plant-pollinator mutualistic networks, Ecology, 83 (2002), 2416-2424.
[20]	J. M. Olesen, J. Bascompte, Y. L. Dupont and P. Jordano, The modularity of pollination networks, P. Natl. Acad. Sci. USA, 104 (2007), 19891-19896. doi: 10.1073/pnas.0706375104.
[21]	S. R. Proulx and P. C. Phillips, The opportunity for canalization and the evolution of genetic networks, Am. Nat., 165 (2005), 147-162. doi: 10.1086/426873.
[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), 2465-2475. doi: 10.1142/S0218127407018531.
[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.
[24]	R. V. Solé and J. M. Montoya, Complexity and fragility in ecological networks, P. Roy. Soc. Lond. B. Biol., 268 (2001), 2039-2045. doi: 10.1098/rspb.2001.1767.
[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), 671-682. doi: 10.1890/06-0971.
[26]	P. Yodzis, The connectance of real ecosystems, Nature, 284 (1980), 544-545. doi: 10.1038/284544a0.

show all references

References:

[1]	R. Albert, H. Jeong and A. L. Barabási, Error and attack tolerance of complex networks, Nature, 406 (2000), 378-382. doi: 10.1038/35019019.
[2]	J. Bascompte, P. Jordano and J. M. Olesen, Asymmetric coevolutionary networks facilitate biodiversity maintenance, Science, 312 (2006), 431-433.
[3]	J. Bascompte and P. Jordano, Plant-animal mutualistic networks: The architecture of biodiversity, Annu. Rev. Ecol. Evol. S., 38 (2007), 567-593.
[4]	P. Crucitti, V. Latora, M. Marchiori and A. Rapisarda, Error and attack tolerance of complex networks, Physica A, 340 (2004), 388-394. doi: 10.1016/j.physa.2004.04.031.
[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), 7-24.
[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), 558-567.
[7]	J. A. Dunne and R. J. Williams, Cascading extinctions and community collapse in model food webs, Philos. T. R. Soc. B., 364 (2009), 1711-1723.
[8]	H. Elberling and J. M. Olesen, The structure of a high latitude plant-flower visitor system: tthe dominance of flies, Ecography, 22 (1999), 314-323.
[9]	M. R. Gardner and W. R. Ashby, Connectance of large dynamic (cybernetic) systems: Critical values for stability, Nature, 228 (1970), 784-784. doi: 10.1038/228784a0.
[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), 1399-1404. doi: 10.1073/pnas.0707332105.
[11]	P. Jordano, J. Bascompte and J. M. Olesen, Invariant properties in coevolutionary networks of plant-animal interactions, Ecol. Lett., 6 (2003), 69-81.
[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), 442-452.
[13]	Y. Lai, A. Motter and T. Nishikawa, Attacks and cascades in complex networks, Lec. Notes Phys., 310 (2004), 299-310. doi: 10.1007/978-3-540-44485-5_14.
[14]	R. May, Will a large complex system be stable?, Nature, 238 (1972), 413-414.
[15]	R. May, "Stability and Complexity in Model Ecosystems," Princeton Univ. Press, 2001.
[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), 2605-2611. doi: 10.1098/rspb.2004.2909.
[17]	A. Motter and Y. Lai, Cascade-based attacks on complex networks, Phys. Rev. E, 66 (2002), 065102-4. doi: 10.1103/PhysRevE.66.065102.
[18]	, NCEAS interaction webs database, http://www.nceas.ucsb.edu/.
[19]	J. M. Olesen and P. Jordano, Geographic patterns in plant-pollinator mutualistic networks, Ecology, 83 (2002), 2416-2424.
[20]	J. M. Olesen, J. Bascompte, Y. L. Dupont and P. Jordano, The modularity of pollination networks, P. Natl. Acad. Sci. USA, 104 (2007), 19891-19896. doi: 10.1073/pnas.0706375104.
[21]	S. R. Proulx and P. C. Phillips, The opportunity for canalization and the evolution of genetic networks, Am. Nat., 165 (2005), 147-162. doi: 10.1086/426873.
[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), 2465-2475. doi: 10.1142/S0218127407018531.
[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.
[24]	R. V. Solé and J. M. Montoya, Complexity and fragility in ecological networks, P. Roy. Soc. Lond. B. Biol., 268 (2001), 2039-2045. doi: 10.1098/rspb.2001.1767.
[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), 671-682. doi: 10.1890/06-0971.
[26]	P. Yodzis, The connectance of real ecosystems, Nature, 284 (1980), 544-545. doi: 10.1038/284544a0.

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