Dragging in mutualistic networks

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March 2015, 10(1): 37-52. doi: 10.3934/nhm.2015.10.37

Dragging in mutualistic networks

Juan Manuel Pastor ^1, , Javier García-Algarra ^1, , José M. Iriondo ^2, , José J. Ramasco ^3, and Javier Galeano ^1,

1.	Complex System Group, Technical University of Madrid, Av. Puerta Hierro 4, 28040-Madrid, Spain, Spain, Spain
2.	Área de Biodiversidad y Conservación, Dept. Biología y Geologa, Universidad Rey Juan Carlos, 28933 Móstoles, Spain
3.	Instituto de Física Interdisciplinar y Sistemas Complejos IFISC (CSIC-UIB), 07122 Palma de Mallorca, Spain

Received July 2014 Revised December 2014 Published February 2015

Abstract
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Mutualistic networks are considered an example of resilience against perturbations. Mutualistic interactions are beneficial for the two sets of species involved. Network robustness has been usually measured in terms of extinction sequences, i.e., nodes are removed from the empirical bipartite network one subset (primary extinctions) and the number of extinctions on the other subset (secondary extinction) is computed. This is a first approach to study ecosystems extinction. However, each interacting species, depicted as a node of the mutualistic network, is really composed by certain number of individuals (population) and its shortage can diminish dramatically the population of its interacting partners, i.e. the population dynamics plays an important role in the robustness of the ecological networks. Although different models of population dynamics for mutualistic interacting species have been addressed, like Type II models, only recently a new mutualistic model has been proposed exhibiting bounded solutions and good properties for simulation. In this paper we show that population dynamics is as important as network topology when we are interested in the resilience of the community.

Keywords: dragging, Population dynamics, nestedness, mutualistic network, K-shell decomposition., cascade, extinction.

Mathematics Subject Classification: Primary: 92D25, 92C42; Secondary: 92D4.

Citation: Juan Manuel Pastor, Javier García-Algarra, José M. Iriondo, José J. Ramasco, Javier Galeano. Dragging in mutualistic networks. Networks and Heterogeneous Media, 2015, 10 (1) : 37-52. doi: 10.3934/nhm.2015.10.37

References:

[1]	M. Almeida-Neto, P. Guimarães, P. R. Guimarães Jr., R. D. Loyola and W. Ulrich, A consistent metric for nestedness analysis in ecological systems: Reconciling concept and quantification, Oikos, 117 (2008), 1227-1239.
[2]	A. I. L. Araujo, M. A. de Almeida, Z. M. Cardoso and G. Corso, Abundance and nestedness in interaction networks, Ecological complexity, 7 (2010), 494-499. doi: 10.1016/j.ecocom.2010.02.004.
[3]	D. Balcan, V. Colizza, B. Gonçalves, H. Hu, J. Ramasco and J. Vespignani, Multiscale mobility networks and the spatial spreading of infectious diseases, Proc. Natl. Acad. Scie., 106 (2009), 21484-21489. doi: 10.1073/pnas.0906910106.
[4]	J. Bascompte and P. Jordano, Plant-Animal mutualistic networks: The architecture of biodiversity, Annu. Rev. Ecol. Evol. Syst., 38 (2007), 567-593. doi: 10.1146/annurev.ecolsys.38.091206.095818.
[5]	E. Burgos, H. Ceva, R. P. J. Perazzo, M. Devoto, D. Medan, M. Zimmermannd and A. M. Delbuee, Why nestedness in mutualistic networks?, Journal of Theorethical Biology, 249 (2007), 307-313. doi: 10.1016/j.jtbi.2007.07.030.
[6]	C. Campbell, S. Yang, K. Shea and R. Albert, Topology of plant-pollinator network that are vulnerable to collapse from species extinction, Physical Review E, 86 (2012), 021924. doi: 10.1103/PhysRevE.86.021924.
[7]	S. Carmi, S. Havlin, S. Kirkpatrick, Y. Shavitt and E. Shir, A model of Internet topology using k-shell decomposition, Proc. Natl. Acad. Scie., 104 (2007), 11150-11154. doi: 10.1073/pnas.0701175104.
[8]	S. N. Dorogovtsev, A. V. Goltsev and J. F. F. Mendes, k-core architecture and k-core percolation in complex networks, Physica D, 224 (2006), 7-19. doi: 10.1016/j.physd.2006.09.027.
[9]	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.
[10]	J. A. Dunne, R. J. Williams and N. D. Martinez, Network structure and biodiversity loss in food webs: robustness increases with connectance, Ecology Letters, 5 (2002), 558-567. doi: 10.1046/j.1461-0248.2002.00354.x.
[11]	M. A. Fortuna, D. B. Stouffer, J. M. Olesen, P. Jordano, D. Mouillot, B. R. Krasnov, R. Poulin and J. Bascompte, Nestedness versus modularity in ecological networks: two sides of the same coin?, J. Anim. Ecol., 79 (2010), 811-817. doi: 10.1111/j.1365-2656.2010.01688.x.
[12]	J. García-Algarra, J. Galeano, J. M. Pastor, J. M. Iriondo and J. J. Ramasco, Rethinking the logistic approach for population dynamics of mutualistic interactions, Journal of Theoretical Biology, 363 (2014), 332-343. doi: 10.1016/j.jtbi.2014.08.039.
[13]	Z. Jing, T. Lin, Y. Hong, L. Jian-Hua, C. Zhi-Wei and L. Yi-Xue, The effects of degree correlations on network topologies and robustness, Chinese Physics, 16 (2007), 3571-3580.
[14]	C. N. Kaiser-Bunbury, S. Muff, J. Memmott, C. B. Müller and A. Caflisch, The robustness of pollination networks to the loss of species and interactions: A quantitative approach incorporating pollinator behaviour, Ecology Letters, 13 (2010), 442-452.
[15]	J. J. Lever, E. H. van Nes, M. Scheffer and J. Bascompte, The sudden collapse of pollinator communities, Ecology Letters 17 (2014), 350-359. doi: 10.1111/ele.12236.
[16]	I. M. D. Maclean and R. J. Wilson, Recent ecological responses to climate change support predictions of high extinction risk, Proceedings of the Natinal Academy of Sciences of the United States of America, 108 (2011), 12337-12342.
[17]	J. Memmott, M. N. Waser and M. P. Price, Tolerance of pollination networks to species extinctions, Proceedings of the Royal Society B, 271 (2004), 2605-2611. doi: 10.1098/rspb.2004.2909.
[18]	J. Memmott, P. G. Craze, N. M. Waser and M. P. Price, Global warming and the disruption of plant-pollinator interactions, Ecology Letters, 10 (2007), 710-717. doi: 10.1111/j.1461-0248.2007.01061.x.
[19]	J. Memmott, C. Carvell, R. F. Pywell and P. G. Craze, The potential impact of global warming on the efficacy of field margins sown for the conservation of bumble-bees, Philosophical Transactions of the Royal Society. B, 365 (2010), 2071-2079. doi: 10.1098/rstb.2010.0015.
[20]	, NCEAS interaction webs database, Available from: http://www.nceas.ucsb.edu.
[21]	J. M. Pastor, S. Santamaría, M. Méndez and J. Galeano, Effects of topology on robustness in ecological bipartite networks, Networks and Heterogeneous Media, 7 (2012), 429-440. doi: 10.3934/nhm.2012.7.429.
[22]	S. Santamaría, J. M. Pastor, J. Galeano and M. Méndez, Robustness of alpine pollination networks: Effects of network structure and consequences for endemic plants, Arctic, Antarctic, and Alpine Research, 46 (2014), 568-580. doi: 10.1657/1938-4246-46.3.568.
[23]	T. Säterberg, S. Sellman and Bo. Ebenman, High frequency of functional extinctions in ecological networks, Nature, 7459, 468-470.
[24]	E. Thébault and C. Fontaine, Stability of ecological communities and the architecture of mutualistic and trophic networks, Science, 329 (2010), 853-856. doi: 10.1126/science.1188321.
[25]	W. Ulrich, M. Almeida-Neto and N. J. Gotelli, A consumer's guide to nestedness analysis, Oikos, 118 (2009), 3-17. doi: 10.1111/j.1600-0706.2008.17053.x.
[26]	H. B. Wilson, B. E. Kendall and H. P. Possingham, Variability in population abundance and the classification of extinction risk, Conservatin Biology, 25 (2011), 747-757.
[27]	D. H. Wright, A simple, stable model of mutualism incorporating handling time, The American Naturalist, 134 (1989), 664-667.

show all references

References:

[1]	M. Almeida-Neto, P. Guimarães, P. R. Guimarães Jr., R. D. Loyola and W. Ulrich, A consistent metric for nestedness analysis in ecological systems: Reconciling concept and quantification, Oikos, 117 (2008), 1227-1239.
[2]	A. I. L. Araujo, M. A. de Almeida, Z. M. Cardoso and G. Corso, Abundance and nestedness in interaction networks, Ecological complexity, 7 (2010), 494-499. doi: 10.1016/j.ecocom.2010.02.004.
[3]	D. Balcan, V. Colizza, B. Gonçalves, H. Hu, J. Ramasco and J. Vespignani, Multiscale mobility networks and the spatial spreading of infectious diseases, Proc. Natl. Acad. Scie., 106 (2009), 21484-21489. doi: 10.1073/pnas.0906910106.
[4]	J. Bascompte and P. Jordano, Plant-Animal mutualistic networks: The architecture of biodiversity, Annu. Rev. Ecol. Evol. Syst., 38 (2007), 567-593. doi: 10.1146/annurev.ecolsys.38.091206.095818.
[5]	E. Burgos, H. Ceva, R. P. J. Perazzo, M. Devoto, D. Medan, M. Zimmermannd and A. M. Delbuee, Why nestedness in mutualistic networks?, Journal of Theorethical Biology, 249 (2007), 307-313. doi: 10.1016/j.jtbi.2007.07.030.
[6]	C. Campbell, S. Yang, K. Shea and R. Albert, Topology of plant-pollinator network that are vulnerable to collapse from species extinction, Physical Review E, 86 (2012), 021924. doi: 10.1103/PhysRevE.86.021924.
[7]	S. Carmi, S. Havlin, S. Kirkpatrick, Y. Shavitt and E. Shir, A model of Internet topology using k-shell decomposition, Proc. Natl. Acad. Scie., 104 (2007), 11150-11154. doi: 10.1073/pnas.0701175104.
[8]	S. N. Dorogovtsev, A. V. Goltsev and J. F. F. Mendes, k-core architecture and k-core percolation in complex networks, Physica D, 224 (2006), 7-19. doi: 10.1016/j.physd.2006.09.027.
[9]	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.
[10]	J. A. Dunne, R. J. Williams and N. D. Martinez, Network structure and biodiversity loss in food webs: robustness increases with connectance, Ecology Letters, 5 (2002), 558-567. doi: 10.1046/j.1461-0248.2002.00354.x.
[11]	M. A. Fortuna, D. B. Stouffer, J. M. Olesen, P. Jordano, D. Mouillot, B. R. Krasnov, R. Poulin and J. Bascompte, Nestedness versus modularity in ecological networks: two sides of the same coin?, J. Anim. Ecol., 79 (2010), 811-817. doi: 10.1111/j.1365-2656.2010.01688.x.
[12]	J. García-Algarra, J. Galeano, J. M. Pastor, J. M. Iriondo and J. J. Ramasco, Rethinking the logistic approach for population dynamics of mutualistic interactions, Journal of Theoretical Biology, 363 (2014), 332-343. doi: 10.1016/j.jtbi.2014.08.039.
[13]	Z. Jing, T. Lin, Y. Hong, L. Jian-Hua, C. Zhi-Wei and L. Yi-Xue, The effects of degree correlations on network topologies and robustness, Chinese Physics, 16 (2007), 3571-3580.
[14]	C. N. Kaiser-Bunbury, S. Muff, J. Memmott, C. B. Müller and A. Caflisch, The robustness of pollination networks to the loss of species and interactions: A quantitative approach incorporating pollinator behaviour, Ecology Letters, 13 (2010), 442-452.
[15]	J. J. Lever, E. H. van Nes, M. Scheffer and J. Bascompte, The sudden collapse of pollinator communities, Ecology Letters 17 (2014), 350-359. doi: 10.1111/ele.12236.
[16]	I. M. D. Maclean and R. J. Wilson, Recent ecological responses to climate change support predictions of high extinction risk, Proceedings of the Natinal Academy of Sciences of the United States of America, 108 (2011), 12337-12342.
[17]	J. Memmott, M. N. Waser and M. P. Price, Tolerance of pollination networks to species extinctions, Proceedings of the Royal Society B, 271 (2004), 2605-2611. doi: 10.1098/rspb.2004.2909.
[18]	J. Memmott, P. G. Craze, N. M. Waser and M. P. Price, Global warming and the disruption of plant-pollinator interactions, Ecology Letters, 10 (2007), 710-717. doi: 10.1111/j.1461-0248.2007.01061.x.
[19]	J. Memmott, C. Carvell, R. F. Pywell and P. G. Craze, The potential impact of global warming on the efficacy of field margins sown for the conservation of bumble-bees, Philosophical Transactions of the Royal Society. B, 365 (2010), 2071-2079. doi: 10.1098/rstb.2010.0015.
[20]	, NCEAS interaction webs database, Available from: http://www.nceas.ucsb.edu.
[21]	J. M. Pastor, S. Santamaría, M. Méndez and J. Galeano, Effects of topology on robustness in ecological bipartite networks, Networks and Heterogeneous Media, 7 (2012), 429-440. doi: 10.3934/nhm.2012.7.429.
[22]	S. Santamaría, J. M. Pastor, J. Galeano and M. Méndez, Robustness of alpine pollination networks: Effects of network structure and consequences for endemic plants, Arctic, Antarctic, and Alpine Research, 46 (2014), 568-580. doi: 10.1657/1938-4246-46.3.568.
[23]	T. Säterberg, S. Sellman and Bo. Ebenman, High frequency of functional extinctions in ecological networks, Nature, 7459, 468-470.
[24]	E. Thébault and C. Fontaine, Stability of ecological communities and the architecture of mutualistic and trophic networks, Science, 329 (2010), 853-856. doi: 10.1126/science.1188321.
[25]	W. Ulrich, M. Almeida-Neto and N. J. Gotelli, A consumer's guide to nestedness analysis, Oikos, 118 (2009), 3-17. doi: 10.1111/j.1600-0706.2008.17053.x.
[26]	H. B. Wilson, B. E. Kendall and H. P. Possingham, Variability in population abundance and the classification of extinction risk, Conservatin Biology, 25 (2011), 747-757.
[27]	D. H. Wright, A simple, stable model of mutualism incorporating handling time, The American Naturalist, 134 (1989), 664-667.

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