Modeling the impact of adaptative stocking strategies on dry rangeland

Toyo Vignal, Mathematics, University of Edinburgh, Edinburgh, United Kingdom, Toyo Vignal and Jonathan Sherratt, Mathematics, Heriot-Watt University, Edinburgh, United Kingdom, Mara Baudena, Institute of Atmospheric Science and Climate, National Research Council of Italy, Turin, Italy, Angeles Garcia Mayor, Copernicus Institute of Sustainable Development, University of Utrecht, Utrecht, Netherlands

Background/Question/Methods
Half of the world's livestock lives in (semi-)arid regions, where an important proportion of the population relies fully or partially on animal husbandry for survival. However, overgrazing can lead to land degradation and subsequent socio-economic crises. Sustainable management of arid rangeland requires suitable stocking strategies and has been the subject of intense debate in the last decades. Our goal is to understand how different stocking strategies interact with the environment and which ones provide both ecological and economic resilience. We describe the rangeland dynamics through a simple mathematical model consisting of a system of coupled ordinary differential equations: one for livestock density and one for vegetation density. We assume that the livestock density is limited by forage availability only, which is itself limited by water availability, hence rainfall. We test different management strategies, namely non-adaptive and adaptive destocking rates. In adaptive strategies, the destocking rate tracks forage availability and answers with varying sensitivity.
Results/Conclusions
The model is very simple and does not take into account spatial-temporal variability in rainfall, plants' phenologies nor market constraints. However, it still gives theoretical insights on the impact of different destocking strategies on the environment. We find that:
1) For all destocking strategies, there exists a threshold before a catastrophic collapse of the system: even gradual changes in the management can lead to abrupt and irreversible land degradation.
2) This threshold occurs at the maximal sustainable livestock density. Because the climax coincides with the tipping point, it is riskier to be at maximal productivity.
3) Higher reactivity of the destocking rate to available biomass i.e. increased opportunism in times of high vegetation and conservatism in times of low vegetation, makes the system both more resilient and potentially more profitable. In particular, with a highly adaptive destocking rate, the collapse is not more likely to occur than in the absence of livestock.
The first two results emphasize the need for adapted dry rangeland management strategies, in order to prevent an irreversible land degradation resulting from the conflict between profitability and sustainability. The third point offers a theoretical suggestion for such a strategy.