Contents lists available at ScienceDirect Agricultural Systems journal homepage: www.elsevier.com/locate/agsy Assessing both ecological and engineering resilience of a steppe agroecosystem using the viability theory R. Sabatier a,⁎ , F. Joly b,c , B. Hubert d a INRA, Université Paris-Saclay, UMR SADAPT, 16 rue Claude Bernard, 75005 Paris, France b Association pour le cheval de Przewalski: TAKH, Station Biologique de la Tour du Valat, Le Sambuc, 13200 Arles, France c ABIES/AgroParisTech, 19 avenue du Maine, 75015 Paris, France d INRA, UR Ecodéveloppement, Domaine Saint-Paul, 84000 Avignon, France ARTICLE INFO Keywords: Viability theory Dynamic modeling Rangelands Mixed-herd Resilience Mongolia ABSTRACT The high dependence of rangeland-based livestock farming systems to environmental uncertainty makes the resilience of these systems as important as production. Quantification of resilience is however difficult to con- duct in real systems due to their low reproducibility. In this study, we develop a modeling approach to quantify both engineering resilience (return time after a perturbation) and ecological resilience (magnitude of a per- turbation that a system can bear) of a mixed herd livestock farming system in Mongolian steppes. The model, build within the framework of the viability theory, captures the dynamics of the herd and its management. The system has the particularity to be impacted by agro-climatic events called dzuds that induce massive mortalities when harsh climatic condition and high stocking densities are met. Results show that (i) resilience non-linearly depends on herd composition and the level of underground biomass of the system, (ii) contrasted management strategies may be followed to cope with the risk of dzud and (iii) according to their herd composition most herders of the area can absorb climate shocks unless they compete for forage with other herders. Results are discussed regarding the impact of forage resource sharing on the resilience of these grazing systems. 1. Introduction A common issue in rangeland-based livestock farming systems is the high environmental uncertainty (i.e. unpredictability of environmental conditions) on which forage production and animal performances de- pend (Pickup and Smith, 1993). Due to the high unpredictability of environmental conditions, properties such as robustness, flexibility and resilience of the system become as important as more straight-forward dimensions such as the average level of production (Carande et al., 1995; Berkes et al., 2000; Vetter, 2005). However quantifying such properties in the real world remains a challenge. Studying the ability of a system to deal with uncertain events indeed requires studying the system over the long term and in a wide set of environmental condi- tions, which is hardly achievable in the field. Modeling approaches, therefore appear to be a good alternative to approximate such proper- ties. Models, by simplifying reality and making explicit the point of view given on the system are a powerful tool to capture complex be- haviors and asses non-trivial properties such as resilience. Especially, recent development of the mathematical framework of the Viability Theory (Aubin, 1991) made it possible to compute metrics such as ro- bustness (Anderies et al., 2004, Accatino et al., 2014, Sabatier et al., 2015b), flexibility (Sabatier et al., 2015a, Mathias et al., 2015), vul- nerability (Rougé et al., 2015) or resilience (Martin, 2004, Martin et al., 2011, Rougé et al., 2013) in a wide range of semi-natural systems such as forests, grasslands, savannahs or lakes. The viability theory is a mathematical framework that applies to the dynamics of state-control systems. It aims to look for the set of initial situations and management options that make it possible to maintain the system within a set of constraints through time. In the current study we intend to apply the viability theory frame- work to the quantification of two forms of resilience of a rangeland- based livestock farming system depending on highly variable environ- mental conditions. Holling (1996) indeed distinguishes two forms of resilience: (i) engineering resilience relates to the time that a system needs to come back to a steady state (or more generally to a desirable area) after a perturbation; (ii) ecological resilience relates to the mag- nitude of the perturbation that a system can absorb before shifting to another behavior. These two forms of resilience therefore characterize the ability of the system to recover after a perturbation (engineering resilience) or to absorb it (ecological resilience). We apply this approach to mixed-livestock farming systems of the steppe regions of Mongolia. These systems are particularly illustrative http://dx.doi.org/10.1016/j.agsy.2017.07.009 Received 18 January 2017; Received in revised form 3 July 2017; Accepted 12 July 2017 ⁎ Corresponding author. E-mail address: rodolphe.sabatier@agroparistech.fr (R. Sabatier). Agricultural Systems 157 (2017) 146–156 0308-521X/ © 2017 Elsevier Ltd. All rights reserved. MARK