American Institute of Mathematical Sciences

Advanced
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

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 & Heterogeneous Media, 2015, 10 (1) : 37-52. doi: 10.3934/nhm.2015.10.37
References:
[1]

Oikos, 117 (2008), 1227-1239. Google Scholar

[2]

Ecological complexity, 7 (2010), 494-499. doi: 10.1016/j.ecocom.2010.02.004.  Google Scholar

[3]

Proc. Natl. Acad. Scie., 106 (2009), 21484-21489. doi: 10.1073/pnas.0906910106.  Google Scholar

[4]

Annu. Rev. Ecol. Evol. Syst., 38 (2007), 567-593. doi: 10.1146/annurev.ecolsys.38.091206.095818.  Google Scholar

[5]

Journal of Theorethical Biology, 249 (2007), 307-313. doi: 10.1016/j.jtbi.2007.07.030.  Google Scholar

[6]

Physical Review E, 86 (2012), 021924. doi: 10.1103/PhysRevE.86.021924.  Google Scholar

[7]

Proc. Natl. Acad. Scie., 104 (2007), 11150-11154. doi: 10.1073/pnas.0701175104.  Google Scholar

[8]

Physica D, 224 (2006), 7-19. doi: 10.1016/j.physd.2006.09.027.  Google Scholar

[9]

The Open Ecology Journal, 2 (2009), 7-24. Google Scholar

[10]

Ecology Letters, 5 (2002), 558-567. doi: 10.1046/j.1461-0248.2002.00354.x.  Google Scholar

[11]

J. Anim. Ecol., 79 (2010), 811-817. doi: 10.1111/j.1365-2656.2010.01688.x.  Google Scholar

[12]

Journal of Theoretical Biology, 363 (2014), 332-343. doi: 10.1016/j.jtbi.2014.08.039.  Google Scholar

[13]

Chinese Physics, 16 (2007), 3571-3580. Google Scholar

[14]

Ecology Letters, 13 (2010), 442-452. Google Scholar

[15]

Ecology Letters 17 (2014), 350-359. doi: 10.1111/ele.12236.  Google Scholar

[16]

Proceedings of the Natinal Academy of Sciences of the United States of America, 108 (2011), 12337-12342. Google Scholar

[17]

Proceedings of the Royal Society B, 271 (2004), 2605-2611. doi: 10.1098/rspb.2004.2909.  Google Scholar

[18]

Ecology Letters, 10 (2007), 710-717. doi: 10.1111/j.1461-0248.2007.01061.x.  Google Scholar

[19]

Philosophical Transactions of the Royal Society. B, 365 (2010), 2071-2079. doi: 10.1098/rstb.2010.0015.  Google Scholar

[20]

, NCEAS interaction webs database,, Available from: , ().   Google Scholar

[21]

Networks and Heterogeneous Media, 7 (2012), 429-440. doi: 10.3934/nhm.2012.7.429.  Google Scholar

[22]

Arctic, Antarctic, and Alpine Research, 46 (2014), 568-580. doi: 10.1657/1938-4246-46.3.568.  Google Scholar

[23]

T. Säterberg, S. Sellman and Bo. Ebenman, High frequency of functional extinctions in ecological networks,, Nature, 7459 (): 468.   Google Scholar

[24]

Science, 329 (2010), 853-856. doi: 10.1126/science.1188321.  Google Scholar

[25]

Oikos, 118 (2009), 3-17. doi: 10.1111/j.1600-0706.2008.17053.x.  Google Scholar

[26]

Conservatin Biology, 25 (2011), 747-757. Google Scholar

[27]

The American Naturalist, 134 (1989), 664-667. Google Scholar

show all references

References:
[1]

Oikos, 117 (2008), 1227-1239. Google Scholar

[2]

Ecological complexity, 7 (2010), 494-499. doi: 10.1016/j.ecocom.2010.02.004.  Google Scholar

[3]

Proc. Natl. Acad. Scie., 106 (2009), 21484-21489. doi: 10.1073/pnas.0906910106.  Google Scholar

[4]

Annu. Rev. Ecol. Evol. Syst., 38 (2007), 567-593. doi: 10.1146/annurev.ecolsys.38.091206.095818.  Google Scholar

[5]

Journal of Theorethical Biology, 249 (2007), 307-313. doi: 10.1016/j.jtbi.2007.07.030.  Google Scholar

[6]

Physical Review E, 86 (2012), 021924. doi: 10.1103/PhysRevE.86.021924.  Google Scholar

[7]

Proc. Natl. Acad. Scie., 104 (2007), 11150-11154. doi: 10.1073/pnas.0701175104.  Google Scholar

[8]

Physica D, 224 (2006), 7-19. doi: 10.1016/j.physd.2006.09.027.  Google Scholar

[9]

The Open Ecology Journal, 2 (2009), 7-24. Google Scholar

[10]

Ecology Letters, 5 (2002), 558-567. doi: 10.1046/j.1461-0248.2002.00354.x.  Google Scholar

[11]

J. Anim. Ecol., 79 (2010), 811-817. doi: 10.1111/j.1365-2656.2010.01688.x.  Google Scholar

[12]

Journal of Theoretical Biology, 363 (2014), 332-343. doi: 10.1016/j.jtbi.2014.08.039.  Google Scholar

[13]

Chinese Physics, 16 (2007), 3571-3580. Google Scholar

[14]

Ecology Letters, 13 (2010), 442-452. Google Scholar

[15]

Ecology Letters 17 (2014), 350-359. doi: 10.1111/ele.12236.  Google Scholar

[16]

Proceedings of the Natinal Academy of Sciences of the United States of America, 108 (2011), 12337-12342. Google Scholar

[17]

Proceedings of the Royal Society B, 271 (2004), 2605-2611. doi: 10.1098/rspb.2004.2909.  Google Scholar

[18]

Ecology Letters, 10 (2007), 710-717. doi: 10.1111/j.1461-0248.2007.01061.x.  Google Scholar

[19]

Philosophical Transactions of the Royal Society. B, 365 (2010), 2071-2079. doi: 10.1098/rstb.2010.0015.  Google Scholar

[20]

, NCEAS interaction webs database,, Available from: , ().   Google Scholar

[21]

Networks and Heterogeneous Media, 7 (2012), 429-440. doi: 10.3934/nhm.2012.7.429.  Google Scholar

[22]

Arctic, Antarctic, and Alpine Research, 46 (2014), 568-580. doi: 10.1657/1938-4246-46.3.568.  Google Scholar

[23]

T. Säterberg, S. Sellman and Bo. Ebenman, High frequency of functional extinctions in ecological networks,, Nature, 7459 (): 468.   Google Scholar

[24]

Science, 329 (2010), 853-856. doi: 10.1126/science.1188321.  Google Scholar

[25]

Oikos, 118 (2009), 3-17. doi: 10.1111/j.1600-0706.2008.17053.x.  Google Scholar

[26]

Conservatin Biology, 25 (2011), 747-757. Google Scholar

[27]

The American Naturalist, 134 (1989), 664-667. Google Scholar

[1]

Juan Manuel Pastor, Javier García-Algarra, Javier Galeano, José María Iriondo, José J. Ramasco. A simple and bounded model of population dynamics for mutualistic networks. Networks & Heterogeneous Media, 2015, 10 (1) : 53-70. doi: 10.3934/nhm.2015.10.53
[2]

Fatiha Alabau-Boussouira. On the influence of the coupling on the dynamics of single-observed cascade systems of PDE's. Mathematical Control & Related Fields, 2015, 5 (1) : 1-30. doi: 10.3934/mcrf.2015.5.1
[3]

Kaifa Wang, Yang Kuang. Fluctuation and extinction dynamics in host-microparasite systems. Communications on Pure & Applied Analysis, 2011, 10 (5) : 1537-1548. doi: 10.3934/cpaa.2011.10.1537
[4]

Miljana JovanoviĆ, Marija KrstiĆ. Extinction in stochastic predator-prey population model with Allee effect on prey. Discrete & Continuous Dynamical Systems - B, 2017, 22 (7) : 2651-2667. doi: 10.3934/dcdsb.2017129
[5]

Keng Deng, Yixiang Wu. Extinction and uniform strong persistence of a size-structured population model. Discrete & Continuous Dynamical Systems - B, 2017, 22 (3) : 831-840. doi: 10.3934/dcdsb.2017041
[6]

Thiago Ferraiol, Mauro Patrão, Lucas Seco. Jordan decomposition and dynamics on flag manifolds. Discrete & Continuous Dynamical Systems, 2010, 26 (3) : 923-947. doi: 10.3934/dcds.2010.26.923
[7]

Alexandre Caboussat, Allison Leonard. Numerical solution and fast-slow decomposition of a population of weakly coupled systems. Conference Publications, 2009, 2009 (Special) : 123-132. doi: 10.3934/proc.2009.2009.123
[8]

Giuseppe Bianchi, Lorenzo Bracciale, Keren Censor-Hillel, Andrea Lincoln, Muriel Médard. The one-out-of-k retrieval problem and linear network coding. Advances in Mathematics of Communications, 2016, 10 (1) : 95-112. doi: 10.3934/amc.2016.10.95
[9]

Tzy-Wei Hwang, Yang Kuang. Host Extinction Dynamics in a Simple Parasite-Host Interaction Model. Mathematical Biosciences & Engineering, 2005, 2 (4) : 743-751. doi: 10.3934/mbe.2005.2.743
[10]

Ling Xue, Caterina Scoglio. Network-level reproduction number and extinction threshold for vector-borne diseases. Mathematical Biosciences & Engineering, 2015, 12 (3) : 565-584. doi: 10.3934/mbe.2015.12.565
[11]

Nika Lazaryan, Hassan Sedaghat. Extinction and the Allee effect in an age structured Ricker population model with inter-stage interaction. Discrete & Continuous Dynamical Systems - B, 2018, 23 (2) : 731-747. doi: 10.3934/dcdsb.2018040
[12]

Jianfeng Feng, Mariya Shcherbina, Brunello Tirozzi. Stability of the dynamics of an asymmetric neural network. Communications on Pure & Applied Analysis, 2009, 8 (2) : 655-671. doi: 10.3934/cpaa.2009.8.655
[13]

Proscovia Namayanja. Chaotic dynamics in a transport equation on a network. Discrete & Continuous Dynamical Systems - B, 2018, 23 (8) : 3415-3426. doi: 10.3934/dcdsb.2018283
[14]

Wei Feng, Xin Lu, Richard John Donovan Jr.. Population dynamics in a model for territory acquisition. Conference Publications, 2001, 2001 (Special) : 156-165. doi: 10.3934/proc.2001.2001.156
[15]

Luca Gerardo-Giorda, Pierre Magal, Shigui Ruan, Ousmane Seydi, Glenn Webb. Preface: Population dynamics in epidemiology and ecology. Discrete & Continuous Dynamical Systems - B, 2020, 25 (6) : i-ii. doi: 10.3934/dcdsb.2020125
[16]

José Ignacio Alvarez-Hamelin, Luca Dall'Asta, Alain Barrat, Alessandro Vespignani. K-core decomposition of Internet graphs: hierarchies, self-similarity and measurement biases. Networks & Heterogeneous Media, 2008, 3 (2) : 371-393. doi: 10.3934/nhm.2008.3.371
[17]

Le Li, Lihong Huang, Jianhong Wu. Cascade flocking with free-will. Discrete & Continuous Dynamical Systems - B, 2016, 21 (2) : 497-522. doi: 10.3934/dcdsb.2016.21.497
[18]

Sergey Zelik. On the Lyapunov dimension of cascade systems. Communications on Pure & Applied Analysis, 2008, 7 (4) : 971-985. doi: 10.3934/cpaa.2008.7.971
[19]

Marina Dolfin, Mirosław Lachowicz. Modeling opinion dynamics: How the network enhances consensus. Networks & Heterogeneous Media, 2015, 10 (4) : 877-896. doi: 10.3934/nhm.2015.10.877
[20]

Winfried Just. Approximating network dynamics: Some open problems. Discrete & Continuous Dynamical Systems - B, 2018, 23 (5) : 1917-1930. doi: 10.3934/dcdsb.2018188

2019 Impact Factor: 1.053

Tools

Metrics

  • PDF downloads (11)
  • HTML views (0)
  • Cited by (3)

Other articles
by authors

[Back to Top]

Copyright © 2021 American Institute of Mathematical Sciences