Towards scientifically based management of extensive livestock farming in terms of ecological predator-prey modeling

Grassland production systems have important impact on food supply and in the economy of several countries. In the specific case of Uruguay, located at the Pampa biome, extensive livestock farming represents 80% of the country land use and beef produced in those systems is 90% of the national meat production. Precision livestock production (PLP) or the manipulation of livestock activity taking into account the different components of agroecosystems to improve production has acquired growing importance in recent years within an "ecological intensification" new paradigm. In particular, there has been an increasing interest in applying mathematical.modeling to support PLP. Here we develop an integral ecological approach to PLP by modeling the dynamics of the combined grass-animals system as a predator-prey dynamical system or Predator-Prey Grassland Livestock Model (PPGL). The model involves two variables, the grass height and the individual liveweight of animals, as well as the nonlinear interaction between them: animal performance (liveweight) is linked with grass consumption, which depends on forage availability, which in turn is affected by the grazing pressure. To check the PPGL model internal coherence we studied the long-term evolution for its two variables and found oscillations which capture the general observed dynamics both for grass and animal liveweight. From a mathematical point of view this behavior is robust since we show that it corresponds to a frequency locked limit cycle (i.e. forced oscillations). Regarding the quantitative performance of PPGL, the model is able to reproduce known empirical data from extensive grassland farm systems in Uruguay, like the pasture growth rate with a logistic function. Simulations for Basaltic soils of Uruguay resulted in a total production of 3972 kg thy matter. ha(-1).year(-1), with an annual distribution of 20%, 14% 31% and 34% for autumn, winter, spring and summer, respectively. Results for animal liveweight variation, presented a as expected high dependence on stocking rate and on initial grass allowance. Winter simulations with low initial grass height (5 cm) and high stocking rate (1 animal-ha(-1)) results in a liveweight loss of 0.02 kg.animal(-1) .d(-1), whereas spring and summer presented the highest liveweight gain (0.655 kg.animal(-1). d(-1)). An annual optimal stocking rate of 0.8 Gross Unit. ha(-1) for native grassland is supported by short and long-term simulations. (C) 2017 Elsevier Ltd. All rights reserved.