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Mathematical model of livestock and wildlife: Predation and competition under environmental disturbances

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  • Laguna, M.F.
  • Abramson, G.
  • Kuperman, M.N.
  • Lanata, J.L.
  • Monjeau, J.A.

Abstract

Inspired by real scenarios in Northern Patagonia, we analyze a mathematical model of a simple trophic web with two herbivores and one predator. The studied situations represent a common practice in the steppes of Argentine Patagonia, where livestock are raised in a semi-wild state, either on the open range or enclosed, coexisting with competitors and predators. In the present work, the competing herbivores represent sheep and guanacos, while the predator is associated with the puma. The proposed model combines the concepts of metapopulations and patches dynamics, and includes an explicit hierarchical competition between species, which affects their prospect to colonize an empty patch when having to compete with other species. We perform numerical simulations of spatially extended metapopulations assemblages of the system, which allow us to incorporate the effects of habitat heterogeneity and destruction. The numerical results are compared with those obtained from mean field calculations. We find that the model provides a good theoretical framework in several situations, including the control of the wild populations that the ranchers exert to different extent. Furthermore, the present formulation incorporates new terms in previously analyzed models that help to reveal the important effects due to the heterogeneous nature of the system.

Suggested Citation

  • Laguna, M.F. & Abramson, G. & Kuperman, M.N. & Lanata, J.L. & Monjeau, J.A., 2015. "Mathematical model of livestock and wildlife: Predation and competition under environmental disturbances," Ecological Modelling, Elsevier, vol. 309, pages 110-117.
    • Handle: RePEc:eee:ecomod:v:309-310:y:2015:i::p:110-117
    DOI: 10.1016/j.ecolmodel.2015.04.020
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    References listed on IDEAS

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    1. Ilkka Hanski & Otso Ovaskainen, 2000. "The metapopulation capacity of a fragmented landscape," Nature, Nature, vol. 404(6779), pages 755-758, April.
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    1. Barlett, Trinidad Ruiz & Laguna, María Fabiana & Abramson, Guillermo & Monjeau, Adrian & Martin, Gabriel, 2024. "A new distributional model coupling environmental and biotic factors," Ecological Modelling, Elsevier, vol. 489(C).
    2. Li, Shangge & Jian, Jinfeng & Poopal, Rama Krishnan & Chen, Xinyu & He, Yaqi & Xu, Hongbin & Yu, Huimin & Ren, Zongming, 2022. "Mathematical modeling in behavior responses: The tendency-prediction based on a persistence model on real-time data," Ecological Modelling, Elsevier, vol. 464(C).
    3. Daza C., Y.C. & Laguna, M.F. & Monjeau, J.A. & Abramson, G., 2019. "Waves of desertification in a competitive ecosystem," Ecological Modelling, Elsevier, vol. 396(C), pages 42-49.

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