T(w)o patch or not t(w)o patch: A novel additional food model
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| Format: | Preprint |
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2023
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| _version_ | 1866929478902480896 |
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| author | Verma, Urvashi Banerjee, Aniket Parshad, Rana D. |
| author_facet | Verma, Urvashi Banerjee, Aniket Parshad, Rana D. |
| contents | A number of top down bio-control models have been proposed where the introduced predators' efficacy is enhanced via the provision of additional food (AF). However, if the predator has a pest dependent monotone functional response, pest extinction is unattainable. In the current manuscript, we propose a model where a predator with pest dependent monotone functional response is introduced into a ``patch" such as a prairie strip with AF, and then disperses or drifts into a neighboring ``patch" such as a crop field, to target a pest. We show the pest extinction state is attainable in the crop field and can be globally attracting.
The AF model with patch structure can eliminate predator explosion present therein and can keep pest densities lower than the classical top-down bio-control model. We provide the first proof of the global stability of the interior equilibrium for the classical AF model.
We also observe ``patch-specific chaos" - the pest occupying the crop field can oscillate chaotically, while the pest in the prairie strip oscillates periodically. We discuss these results in light of bio-control strategies that utilize state-of-the-art farming practices such as prairie strips and drift and dispersal pressures driven by climate change. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2310_17003 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | T(w)o patch or not t(w)o patch: A novel additional food model Verma, Urvashi Banerjee, Aniket Parshad, Rana D. Populations and Evolution Dynamical Systems A number of top down bio-control models have been proposed where the introduced predators' efficacy is enhanced via the provision of additional food (AF). However, if the predator has a pest dependent monotone functional response, pest extinction is unattainable. In the current manuscript, we propose a model where a predator with pest dependent monotone functional response is introduced into a ``patch" such as a prairie strip with AF, and then disperses or drifts into a neighboring ``patch" such as a crop field, to target a pest. We show the pest extinction state is attainable in the crop field and can be globally attracting. The AF model with patch structure can eliminate predator explosion present therein and can keep pest densities lower than the classical top-down bio-control model. We provide the first proof of the global stability of the interior equilibrium for the classical AF model. We also observe ``patch-specific chaos" - the pest occupying the crop field can oscillate chaotically, while the pest in the prairie strip oscillates periodically. We discuss these results in light of bio-control strategies that utilize state-of-the-art farming practices such as prairie strips and drift and dispersal pressures driven by climate change. |
| title | T(w)o patch or not t(w)o patch: A novel additional food model |
| topic | Populations and Evolution Dynamical Systems |
| url | https://arxiv.org/abs/2310.17003 |