Effects of limited volatiles release by plants in tritrophic interactions

Bruno Buonomo; Francesco Giannino; Stéphanie Saussure; Ezio Venturino; Bruno Buonomo; Francesco Giannino; Stéphanie Saussure; Ezio Venturino

doi:10.3934/mbe.2019166

Mathematical Biosciences and Engineering

2019, Volume 16, Issue 5: 3331-3344. doi: 10.3934/mbe.2019166

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Research article Special Issues

Effects of limited volatiles release by plants in tritrophic interactions

1.
Department of Mathematics and Applications, University of Naples Federico II, via Cintia, I-80126Naples, Italy
2.
Department of Agricultural Science, University of Naples Federico II, via Università, 100, I-80055Portici, Italy
3.
Norwegian Institute of Bioeconomy Research, Postboks 115, NO-1431 Ås, Norway; NorwegianUniversity of Life Sciences, P.O. Box 5003, NO-1432 Ås, Norway
4.
Dipartimento di Matematica “Giuseppe Peano”, University of Turin, via Carlo Alberto 10, Turin,I-10123 Italy

Received: 28 December 2018 Accepted: 10 April 2019 Published: 17 April 2019

We introduce a mathematical model to describe the tritrophic interaction between crop, pest and the pest natural enemy where the release of Volatile Organic Compounds (VOCs) by crop is taken into account. The VOCs may be considered as an indirect defence mechanism of the plant as they attract the pest natural enemies toward the attacked plants. The model dynamics is studied through qualitative analysis and numerical simulations. The factors that may enhance pest disappearance are identified. In particular, we show that VOCs may have a beneficial effect on the environment since their release may be able to stabilize the model dynamics. Specifically, for the parameter values that we have explored, this effect can arise only when both the phenomena of VOCs basic plant release and VOCs plant release due to pest attack are present.
- crops pests,
- volatile organic compounds release,
- mathematical model,
- stability,
- oscillations
Citation: Bruno Buonomo , Francesco Giannino , Stéphanie Saussure , Ezio Venturino. Effects of limited volatiles release by plants in tritrophic interactions[J]. Mathematical Biosciences and Engineering, 2019, 16(5): 3331-3344. doi: 10.3934/mbe.2019166

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Abstract

We introduce a mathematical model to describe the tritrophic interaction between crop, pest and the pest natural enemy where the release of Volatile Organic Compounds (VOCs) by crop is taken into account. The VOCs may be considered as an indirect defence mechanism of the plant as they attract the pest natural enemies toward the attacked plants. The model dynamics is studied through qualitative analysis and numerical simulations. The factors that may enhance pest disappearance are identified. In particular, we show that VOCs may have a beneficial effect on the environment since their release may be able to stabilize the model dynamics. Specifically, for the parameter values that we have explored, this effect can arise only when both the phenomena of VOCs basic plant release and VOCs plant release due to pest attack are present.

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