IDEAS home Printed from https://ideas.repec.org/a/eee/ecomod/v466y2022ics0304380022000266.html
   My bibliography  Save this article

Feasibility conditions of ecological models: Unfolding links between model parameters

Author

Listed:
  • AlAdwani, Mohammad
  • Saavedra, Serguei

Abstract

Over more than 100 years, ecological research has been striving to derive internal and external conditions compatible with the coexistence of a given group of interacting species. To address this challenge, numerous studies have focused on developing ecological models and deriving the necessary conditions for species coexistence under equilibrium dynamics, namely feasibility. However, due to mathematical limitations, it has been impossible to derive analytic expressions for equilibria locations if the isocline equations have five or more roots, which can be easily reached even in 2-species models. Here, we propose a general formalism to obtain the set of analytical conditions of feasibility for any polynomial population dynamics model of any dimension without the need to solve for the equilibrium locations. We illustrate the application of our methodology by showing how it is possible to derive mathematical relationships between model parameters in modified Lotka–Volterra models with functional responses and higher-order interactions (model systems with at least five equilibrium points)—a task that is impossible to do with simulations. This work unlocks the opportunity to increase our understanding of how parameters and their interconnections affect our conclusions of species coexistence as a function of model choice.

Suggested Citation

  • AlAdwani, Mohammad & Saavedra, Serguei, 2022. "Feasibility conditions of ecological models: Unfolding links between model parameters," Ecological Modelling, Elsevier, vol. 466(C).
  • Handle: RePEc:eee:ecomod:v:466:y:2022:i:c:s0304380022000266
    DOI: 10.1016/j.ecolmodel.2022.109900
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0304380022000266
    Download Restriction: Full text for ScienceDirect subscribers only

    File URL: https://libkey.io/10.1016/j.ecolmodel.2022.109900?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. Jacopo Grilli & Matteo Adorisio & Samir Suweis & György Barabás & Jayanth R. Banavar & Stefano Allesina & Amos Maritan, 2017. "Feasibility and coexistence of large ecological communities," Nature Communications, Nature, vol. 8(1), pages 1-8, April.
    2. Yacine, Youssef & Loeuille, Nicolas, 2022. "Stable coexistence in plant-pollinator-herbivore communities requires balanced mutualistic vs antagonistic interactions," Ecological Modelling, Elsevier, vol. 465(C).
    3. Theresa Wei Ying Ong & John H. Vandermeer, 2015. "Coupling unstable agents in biological control," Nature Communications, Nature, vol. 6(1), pages 1-9, May.
    4. Fort, Hugo, 2018. "On predicting species yields in multispecies communities: Quantifying the accuracy of the linear Lotka-Volterra generalized model," Ecological Modelling, Elsevier, vol. 387(C), pages 154-162.
    5. Benjamin Kerr & Margaret A. Riley & Marcus W. Feldman & Brendan J. M. Bohannan, 2002. "Local dispersal promotes biodiversity in a real-life game of rock–paper–scissors," Nature, Nature, vol. 418(6894), pages 171-174, July.
    6. Novoa-Muñoz, Francisco & Gómez-Fuentealba, Nelly & Osorio-Baeza, Florencia, 2021. "Lotka–Volterra model applied to two sympatric species of Liolaemus in competition," Ecological Modelling, Elsevier, vol. 439(C).
    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. Menezes, J. & Moura, B., 2022. "Pattern formation and coarsening dynamics in apparent competition models," Chaos, Solitons & Fractals, Elsevier, vol. 157(C).
    2. Yang, Ryoo Kyung & Park, Junpyo, 2023. "Evolutionary dynamics in the cyclic competition system of seven species: Common cascading dynamics in biodiversity," Chaos, Solitons & Fractals, Elsevier, vol. 175(P1).
    3. Clenet, Maxime & El Ferchichi, Hafedh & Najim, Jamal, 2022. "Equilibrium in a large Lotka–Volterra system with pairwise correlated interactions," Stochastic Processes and their Applications, Elsevier, vol. 153(C), pages 423-444.
    4. Fort, Hugo & Grigera, Tomás S., 2021. "A method for predicting species trajectories tested with trees in barro colorado tropical forest," Ecological Modelling, Elsevier, vol. 446(C).
    5. Huang, Wenting & Duan, Xiaofang & Qin, Lijuan & Park, Junpyo, 2023. "Fitness-based mobility enhances the maintenance of biodiversity in the spatial system of cyclic competition," Applied Mathematics and Computation, Elsevier, vol. 456(C).
    6. Tenorio, M. & Rangel, E. & Menezes, J., 2022. "Adaptive movement strategy in rock-paper-scissors models," Chaos, Solitons & Fractals, Elsevier, vol. 162(C).
    7. Bazeia, D. & Bongestab, M. & de Oliveira, B.F. & Szolnoki, A., 2021. "Effects of a pestilent species on the stability of cyclically dominant species," Chaos, Solitons & Fractals, Elsevier, vol. 151(C).
    8. Menezes, J. & Barbalho, R., 2023. "How multiple weak species jeopardise biodiversity in spatial rock–paper–scissors models," Chaos, Solitons & Fractals, Elsevier, vol. 169(C).
    9. Han, Jia-Xu & Wang, Rui-Wu, 2023. "Complex interactions promote the frequency of cooperation in snowdrift game," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 609(C).
    10. Dai, Hui & Wang, Xiaoyue & Lu, Yikang & Hou, Yunxiang & Shi, Lei, 2024. "The effect of intraspecific cooperation in a three-species cyclic predator-prey model," Applied Mathematics and Computation, Elsevier, vol. 470(C).
    11. Stiadle, Thomas I. & Bayliss, Alvin & Volpert, Vladimir A., 2023. "Cyclic Ecological Systems with an Exceptional Species," Applied Mathematics and Computation, Elsevier, vol. 443(C).
    12. Mohd, Mohd Hafiz & Park, Junpyo, 2021. "The interplay of rock-paper-scissors competition and environments mediates species coexistence and intriguing dynamics," Chaos, Solitons & Fractals, Elsevier, vol. 153(P1).
    13. Fort, Hugo, 2020. "Making quantitative predictions on the yield of a species immersed in a multispecies community: The focal species method," Ecological Modelling, Elsevier, vol. 430(C).
    14. Damijan Novak & Domen Verber & Jani Dugonik & Iztok Fister, 2023. "Action-Based Digital Characterization of a Game Player," Mathematics, MDPI, vol. 11(5), pages 1-35, March.
    15. Erik Brockbank & Edward Vul, 2021. "Formalizing Opponent Modeling with the Rock, Paper, Scissors Game," Games, MDPI, vol. 12(3), pages 1-20, September.
    16. Zhong, Linwu & Zhang, Liming & Li, Haihong & Dai, Qionglin & Yang, Junzhong, 2022. "Species coexistence in spatial cyclic game of five species," Chaos, Solitons & Fractals, Elsevier, vol. 156(C).
    17. Bazeia, D. & Bongestab, M. & de Oliveira, B.F., 2022. "Influence of the neighborhood on cyclic models of biodiversity," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 587(C).
    18. Park, Junpyo & Chen, Xiaojie & Szolnoki, Attila, 2023. "Competition of alliances in a cyclically dominant eight-species population," Chaos, Solitons & Fractals, Elsevier, vol. 166(C).
    19. Park, Junpyo, 2022. "Effect of external migration on biodiversity in evolutionary dynamics of coupled cyclic competitions," Chaos, Solitons & Fractals, Elsevier, vol. 158(C).
    20. Verma, Tina & Gupta, Arvind Kumar, 2021. "Evolutionary dynamics of rock-paper-scissors game in the patchy network with mutations," Chaos, Solitons & Fractals, Elsevier, vol. 153(P1).

    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:ecomod:v:466:y:2022:i:c:s0304380022000266. 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: Catherine Liu (email available below). General contact details of provider: http://www.journals.elsevier.com/ecological-modelling .

    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.