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Impact of Volatile Mediated Indirect Defense Response of Plant and Herbivore Refuge in Tritrophic Cascade

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Abstract

Plants emit volatile secondary metabolites in response to the attacks from herbivorous insects and send signals to carnivorous enemies as reinforcement against the herbivores. Presence of higher carnivores, attracted by the released volatile blends, increases predation pressure on the herbivores. To reduce predation pressure, the herbivore adopts a refuge mechanism. Two natural phenomena are combined by proposing a volatile mediated model-based tritrophic system among the plants, herbivorous insects, and the natural carnivorous enemy, emphasizing the role of plant volatiles and herbivore refuge. In particular, we have highlighted the role of volatile mediated plant’s indirect defense mechanism on its fitness improvement under different ecological consequences, for example, considering different functional responses for herbivores (Holling type II) and carnivorous enemies (Holling type III) associating hiding behavior of herbivores (herbivore refuge) in a tritrophic interaction model. Numerical simulations and analytical treatments are conducted to validate our proposed hypothesis on the tritrophic interaction. Using Isocline method, we show the existence of the interior equilibriums. We illustrate sensitivity analysis of system parameters through Global Sensitivity Analysis using Latin Hypercube Sampling and Partial Ranked Correlation Coefficient. The high-dimensional Bendixson criterion is applied to show global stability of positive equilibrium. We observed two types of alternative states, transcritical bifurcation of limit cycle, and saddle-node bifurcation. High emission of volatiles promotes more stabilized dynamical behaviors, when all three species coexist, thus sustaining the ecological balance in the tritrophic interaction.

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Acknowledgements

We thank the anonymous reviewers and the editor for their insightful comments in improving the manuscript. This research of Ritwika Mondal was supported by DST/INSPIRE Fellowship/ 2015/ IF 150747. SS is supported by NPDF, SERB-DST, India, Award ID: PDF/2021/000585.

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Authors and Affiliations

  1. Department of Mathematics, Centre for Mathematical Biology and Ecology, Jadavpur University, Kolkata, West Bengal, 700032, India

    Ritwika Mondal & Dipak Kesh

  2. Department of Mathematics, Vivekananda College, Thakurpukur, Kolkata, West Bengal, 700063, India

    Debasis Mukherjee

  3. Cognitive Brain Dynamics Lab, National Brain Research Centre, NH-8, Manesar, Haryana, 122051, India

    Suman Saha

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  1. Ritwika Mondal
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Mondal, R., Kesh, D., Mukherjee, D. et al. Impact of Volatile Mediated Indirect Defense Response of Plant and Herbivore Refuge in Tritrophic Cascade. Differ Equ Dyn Syst (2024). https://doi.org/10.1007/s12591-024-00682-1

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