Mathematical model of livestock and wildlife: Predation and competition in a disturbed habitat

M. F. LAGUNA; G. ABRAMSON; M. N. KUPERMAN; J. L. LANATA; J. A. MONJEAU

ECOLOGICAL MODELLING

ELSEVIER SCIENCE BV

Lugar: Amsterdam; Año: 2015 vol. 309 p. 110 - 117

0304-3800

Inspired by real scenarios in Northern Patagonia, we analyze a mathematical model of a simple trophicweb with two herbivores and one predator. The studied situations represent a common practice in thesteppes of Argentine Patagonia, where livestock are raised in a semi-wild state, either on the open rangeor enclosed, coexisting with competitors and predators. In the present work, the competing herbivoresrepresent sheep and guanacos, while the predator is associated with the puma. The proposed modelcombines 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. Wefind that the model provides a good theoretical framework in several situations, including the control ofthe wild populations that the ranchers exert to different extent. Furthermore, the present formulationincorporates new terms in previously analyzed models that help to reveal the important effects due tothe heterogeneous nature of the system.