  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.
