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Diversity in interaction strength promotes rich dynamical behaviours in a three-species ecological system

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  • Mohd, Mohd Hafiz

Abstract

Asymmetrical interactions are thought to have an important influence on multi-species competitive systems, and understanding this ecological process is a challenging task because of uncertain roles that asymmetrical interactions can have in maintaining species biodiversity. To address this problem, we employ a simple ecological model for multiple species with asymmetrical competitive strength and we analyse this model using the techniques from dynamical systems and bifurcation analysis. In particular, we examine the stability properties of steady states and also its bifurcation structures under parameter variation. We demonstrate that there exists threshold values for asymmetrical competitive strength, which correspond to transcritical and supercritical Hopf bifurcations. The occurrence of these bifurcations give rise to numerous dynamics in the model e.g. multi-species coexistence, species exclusion, alternative stable state communities and oscillatory dynamics among multiple species. Additionally, we observe the conditions under which co-dimension two (Gavrilov-Guckenheimer) bifurcation occurs as a result of the interaction between transcritical and Hopf bifurcations, which can lead to complex dynamics. We also investigate how diversity in interaction strength between multiple competing species causes counterintuitive observations: on one hand, asymmetrical interactions promote the maintenance of biodiversity through multi-species coexistence state and also coexistence via stable limit cycles (corresponding to oscillatory dynamics); on the other hand, we also observe that the occurrence of stable limit cycles can lead to destabilisation of multi-species communities.

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  • Mohd, Mohd Hafiz, 2019. "Diversity in interaction strength promotes rich dynamical behaviours in a three-species ecological system," Applied Mathematics and Computation, Elsevier, vol. 353(C), pages 243-253.
    • Handle: RePEc:eee:apmaco:v:353:y:2019:i:c:p:243-253
    DOI: 10.1016/j.amc.2019.02.007
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    References listed on IDEAS

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    1. Xia, Jing & Yu, Zhixian & Dong, Yucai & Li, Hongyan, 2016. "Traveling waves for n-species competitive system with nonlocal dispersals and delays," Applied Mathematics and Computation, Elsevier, vol. 287, pages 201-213.
    2. Andrew J. Davis & Linda S. Jenkinson & John H. Lawton & Bryan Shorrocks & Simon Wood, 1998. "Making mistakes when predicting shifts in species range in response to global warming," Nature, Nature, vol. 391(6669), pages 783-786, February.
    3. Mohd, Mohd Hafiz & Murray, Rua & Plank, Michael J. & Godsoe, William, 2016. "Effects of dispersal and stochasticity on the presence–absence of multiple species," Ecological Modelling, Elsevier, vol. 342(C), pages 49-59.
    4. Caplat, Paul & Anand, Madhur & Bauch, Chris, 2008. "Symmetric competition causes population oscillations in an individual-based model of forest dynamics," Ecological Modelling, Elsevier, vol. 211(3), pages 491-500.
    5. Mohd, Mohd Hafiz & Murray, Rua & Plank, Michael J. & Godsoe, William, 2017. "Effects of biotic interactions and dispersal on the presence-absence of multiple species," Chaos, Solitons & Fractals, Elsevier, vol. 99(C), pages 185-194.
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    1. Mohd, Mohd Hafiz & Md. Noorani, Mohd Salmi, 2021. "Local dispersal, trophic interactions and handling times mediate contrasting effects in prey-predator dynamics," Chaos, Solitons & Fractals, Elsevier, vol. 142(C).
    2. 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).
    3. Arellano-García, María Evarista & Camacho-Gutiérrez, José Ariel & Solorza-Calderón, Selene, 2021. "Machine learning approach for higher-order interactions detection to ecological communities management," Applied Mathematics and Computation, Elsevier, vol. 411(C).
    4. Aliyu, Murtala Bello & Mohd, Mohd Hafiz, 2021. "The interplay between mutualism, competition and dispersal promotes species coexistence in a multiple interactions type system," Ecological Modelling, Elsevier, vol. 452(C).
    5. Umar Sharif, Umi Syahirah Binti & Mohd, Mohd Hafiz, 2022. "Combined influences of environmental enrichment and harvesting mediate rich dynamics in an intraguild predation fishery system," Ecological Modelling, Elsevier, vol. 474(C).
    6. Park, Junpyo, 2021. "Evolutionary dynamics in the rock-paper-scissors system by changing community paradigm with population flow," Chaos, Solitons & Fractals, Elsevier, vol. 142(C).
    7. Acosta-Arreola, Jaime & Domínguez-Hüttinger, Elisa & Aguirre, Pablo & González, Nicolás & Meave, Jorge A., 2023. "Predicting dynamic trajectories of a protected plant community under contrasting conservation regimes: Insights from data-based modelling," Ecological Modelling, Elsevier, vol. 484(C).

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