IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v153y2021ip2s0960077921008584.html
   My bibliography  Save this article

Statistical properties of mutualistic-competitive random networks

Author

Listed:
  • Martínez-Martínez, C.T.
  • Méndez-Bermúdez, J.A.
  • Peron, Thomas
  • Moreno, Yamir

Abstract

Mutualistic networks are used to study the structure and processes inherent to mutualistic relationships. In this paper, we introduce a random matrix ensemble (RME) representing the adjacency matrices of mutualistic networks composed by two vertex sets of sizes n and m−n. Our RME depends on three parameters: the network size n, the size of the smaller set m, and the connectivity between the two sets α, where α is the ratio of current adjacent pairs over the total number of possible adjacent pairs between the sets. We focus on the spectral, eigenvector and topological properties of the RME by computing, respectively, the ratio of consecutive eigenvalue spacings r, the Shannon entropy of the eigenvectors S, and the Randić index R. First, within a random matrix theory approach (i.e. a statistical approach), we identify a parameter ξ≡ξ(n,m,α) that scales the average normalized measures (with X representing r, S and R). Specifically, we show that (i) ξ∝αn with a weak dependence on m, and (ii) for ξ<1/10 most vertices in the mutualistic network are isolated, while for ξ>10 the network acquires the properties of a complete network, i.e., the transition from isolated vertices to a complete-like behavior occurs in the interval 1/10<ξ<10. Then, we demonstrate that our statistical approach predicts reasonably well the properties of real-world mutualistic networks; that is, the universal curves vs. ξ show good correspondence with the properties of real-world networks.

Suggested Citation

  • Martínez-Martínez, C.T. & Méndez-Bermúdez, J.A. & Peron, Thomas & Moreno, Yamir, 2021. "Statistical properties of mutualistic-competitive random networks," Chaos, Solitons & Fractals, Elsevier, vol. 153(P2).
  • Handle: RePEc:eee:chsofr:v:153:y:2021:i:p2:s0960077921008584
    DOI: 10.1016/j.chaos.2021.111504
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077921008584
    Download Restriction: Full text for ScienceDirect subscribers only

    File URL: https://libkey.io/10.1016/j.chaos.2021.111504?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Torres-Vargas, G. & Fossion, R. & Méndez-Bermúdez, J.A., 2020. "Normal mode analysis of spectra of random networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 545(C).
    2. Fredrik Liljeros & Christofer R. Edling & Luís A. Nunes Amaral & H. Eugene Stanley & Yvonne Åberg, 2001. "The web of human sexual contacts," Nature, Nature, vol. 411(6840), pages 907-908, June.
    3. Ugo Bastolla & Miguel A. Fortuna & Alberto Pascual-García & Antonio Ferrera & Bartolo Luque & Jordi Bascompte, 2009. "The architecture of mutualistic networks minimizes competition and increases biodiversity," Nature, Nature, vol. 458(7241), pages 1018-1020, April.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Cristina Fiera & Jan Christian Habel & Werner Ulrich, 2018. "Neutral colonisations drive high beta-diversity in cavernicole springtails (Collembola)," PLOS ONE, Public Library of Science, vol. 13(1), pages 1-12, January.
    2. Colton Brehm & Astrid Layton, 2021. "Nestedness of eco‐industrial networks: Exploring linkage distribution to promote sustainable industrial growth," Journal of Industrial Ecology, Yale University, vol. 25(1), pages 205-218, February.
    3. Benadi, Gita & Blüthgen, Nico & Hovestadt, Thomas & Poethke, Hans-Joachim, 2013. "Contrasting specialization–stability relationships in plant–animal mutualistic systems," Ecological Modelling, Elsevier, vol. 258(C), pages 65-73.
    4. Leto Peel & Tiago P. Peixoto & Manlio De Domenico, 2022. "Statistical inference links data and theory in network science," Nature Communications, Nature, vol. 13(1), pages 1-15, December.
    5. Courtney D. Corley & Diane J. Cook & Armin R. Mikler & Karan P. Singh, 2010. "Text and Structural Data Mining of Influenza Mentions in Web and Social Media," IJERPH, MDPI, vol. 7(2), pages 1-20, February.
    6. Fabio Saracco & Riccardo Di Clemente & Andrea Gabrielli & Tiziano Squartini, 2015. "Detecting early signs of the 2007-2008 crisis in the world trade," Papers 1508.03533, arXiv.org, revised Jul 2016.
    7. Timothée Poisot & Sonia Kéfi & Serge Morand & Michal Stanko & Pablo A Marquet & Michael E Hochberg, 2015. "A Continuum of Specialists and Generalists in Empirical Communities," PLOS ONE, Public Library of Science, vol. 10(5), pages 1-12, May.
    8. Sabine Dritz & Rebecca A. Nelson & Fernanda S. Valdovinos, 2023. "The role of intra-guild indirect interactions in assembling plant-pollinator networks," Nature Communications, Nature, vol. 14(1), pages 1-13, December.
    9. Matthew Eden & Rebecca Castonguay & Buyannemekh Munkhbat & Hari Balasubramanian & Chaitra Gopalappa, 2021. "Agent-based evolving network modeling: a new simulation method for modeling low prevalence infectious diseases," Health Care Management Science, Springer, vol. 24(3), pages 623-639, September.
    10. Singer, Alexander & Johst, Karin & Banitz, Thomas & Fowler, Mike S. & Groeneveld, Jürgen & Gutiérrez, Alvaro G. & Hartig, Florian & Krug, Rainer M. & Liess, Matthias & Matlack, Glenn & Meyer, Katrin M, 2016. "Community dynamics under environmental change: How can next generation mechanistic models improve projections of species distributions?," Ecological Modelling, Elsevier, vol. 326(C), pages 63-74.
    11. Sander, L.M & Warren, C.P & Sokolov, I.M, 2003. "Epidemics, disorder, and percolation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 325(1), pages 1-8.
    12. Roberto Cazzolla Gatti & Roger Koppl & Brian D. Fath & Stuart Kauffman & Wim Hordijk & Robert E. Ulanowicz, 2020. "On the emergence of ecological and economic niches," Journal of Bioeconomics, Springer, vol. 22(2), pages 99-127, July.
    13. , D. & Tessone, Claudio J. & ,, 2014. "Nestedness in networks: A theoretical model and some applications," Theoretical Economics, Econometric Society, vol. 9(3), September.
    14. Wanming Chen & Shengyuan Wang & Xiaolan Wu, 2022. "Growth Mechanism and Synchronization Effect of China’s New Energy Vehicle Enterprises: An Empirical Analysis Based on Moving Logistic and Kuramoto Model," Sustainability, MDPI, vol. 14(24), pages 1-17, December.
    15. Claes Andersson & Koen Frenken & Alexander Hellervik, 2006. "A Complex Network Approach to Urban Growth," Environment and Planning A, , vol. 38(10), pages 1941-1964, October.
    16. Laura Hernandez & Annick Vignes & Stéphanie Saba, 2018. "Trust or robustness? An ecological approach to the study of auction and bilateral markets," Post-Print hal-02005040, HAL.
    17. Chengyi Tu & Joel Carr & Samir Suweis, 2016. "A data driven network approach to rank countries production diversity and food specialization," Papers 1606.01270, arXiv.org.
    18. Ammar Alhmedi & Tim Belien & Dany Bylemans, 2023. "Habitat Modification Alters Food Web Interactions with Focus on Biological Control of Aphids in Apple Orchards," Sustainability, MDPI, vol. 15(7), pages 1-13, March.
    19. Wang, Xiangrong & Peron, Thomas & Dubbeldam, Johan L.A. & Kéfi, Sonia & Moreno, Yamir, 2023. "Interspecific competition shapes the structural stability of mutualistic networks," Chaos, Solitons & Fractals, Elsevier, vol. 172(C).
    20. Roland Pongou & Guy Tchuente & Jean-Baptiste Tondji, 2021. "Optimally Targeting Interventions in Networks during a Pandemic: Theory and Evidence from the Networks of Nursing Homes in the United States," Papers 2110.10230, arXiv.org.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:chsofr:v:153:y:2021:i:p2:s0960077921008584. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Thayer, Thomas R. (email available below). General contact details of provider: https://www.journals.elsevier.com/chaos-solitons-and-fractals .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.