**2. Methods**

Modeling can be an important technique in analyzing and describing processes of desertification change in addition to furthering our understanding of the relationship between the socio-economic and ecological factors involved and their effects on desertification [21]. SD is a suitable tool for this challenge. SD is a modeling methodology grounded on the theories of nonlinear dynamical systems and feedback control developed in mathematics, physics, and engineering. SD states that the main, but easily overlooked, cause of the behavior of a complex system lies in its underlying structure of relationships, which includes feedback loops, non-linear relations, delays and decision rules. Formally, an SD model is a set of first-order ordinary differential equations that makes a stock-and-flow representation of the studied system; stock variables show the state of the system over

time, and flow variables represent the processes that change the stocks [19,22]. The main advantages of SD are [23,24]: (i) it improves system understanding, and develops system thinking skills, even from the first stage of its development as causal or sketch diagrams; (ii) SD models can incorporate empirical and process-based approaches, and help integrate interdisciplinary knowledge, (iii) the SD literature provides abundant information about related methodologies; and (iv) user-friendly software platforms allow easy access for non-modeler users.

In this paper, we stress the usefulnes of causal diagrams (see Sterman (2000) [22] for details). They are built by establishing the relationships between explanatory and explained variables. The polarity between the independent variables (*x*) and the dependent variables (*y*) can be (i) direct (+) when *x* and *y* move in the same direction, i.e., as *x* increases, *y* increases, or as *x* decreases, *y* decreases; or (ii) negative—or inverse—(−) when *x* and *y* move in the opposite direction, i.e., more *x* and less *y* or vice versa. The concatenation of the causal relationships between the variables gives rise to a network of feedback loops. The sign of the feedback loops illustrates their behavior: positive feedback is self-reinforcing and behind the explosive or exponential behaviour systems; negative feedback loops are self-correcting and represent the stable performance of the system. An even number of negative arrows or their absence gives rise to a positive feedback loop; an odd number of negative arrows gives rise to a negative feedback loop.

### **3. Results and Discussion**

Causal diagrams are very useful tools for channeling associative thinking that needs to be structured into a tangible hypothesis [25]. In this process of concreteness, operational variables, i.e., those that can be measured and have a real counterpart, coexist with ambiguous or imprecise concepts. This is the case of Figure 1A, where we show some of the relationships established in the exploitation of groundwater resources in NW China. As we can see, 'climate change' is a concept that allows us to reflect on the fact that snowmelt inputs are going to decrease. As the model becomes more concrete, we will have several options to make this idea fully functional. On the one hand, we will be able to develop a whole climate model that explains the dynamics of this snowmelt. On the other hand, we can implement different climate change scenarios that are reflected in different snowmelt volumes.

**Figure 1.** Causal diagrams to illustrate some of the elements of the oases dynamics in NW China. (**A**) Stabilizing behavior associated with negative feedback loops; non-linear relationship between water endowment and agricultural productivity. (**B**) Explosive behavior of a positive feedback loop.

The main idea that this diagram wants to convey is that feedback loops emerge from the various links between variables, which have different types of behavior associated with them. In this case, the loop is negative and has a stabilizing behavior. The water reserve will tend towards an equilibrium (which may be zero) whose value depends on various circumstances. For example, as the water table is deeper, the cost of pumping is higher and therefore discourages activity [26]. To what extent it discourages it will depend on the profitability per cubic meter, the cost of energy or the opportunity cost. It is also relevant to consider that the value of this balance is not irrelevant. When certain thresholds are crossed, processes, such as aquifer subsidence, marine intrusion, or desiccation of surrounding systems, can be triggered [27]. Note that the stabilization of the water reserve is associated with another equilibrium, that of the irrigated area.

In complex systems, such as socioecological systems, different types of loops coexist. In Figure 1B we show a positive one, which results in exponential growth (or decay) of the variables (typical behavior of the Anthropocene [28]). Indeed, as the profitability of a certain type of crop increases, in this case, cash crops, and the other alternatives are very unprofitable (i.e., low opportunity cost), more and more farmers opt for this alternative, which leads to an increase in the irrigated area. This leads to more profits and new farmland, leading to exponential growth in cash crop area. As it is easy to understand, this exponential behavior, towards infinity, cannot be sustained over time, but it allows us to see that, in isolation, there are parts of the system that for a time behave in a threatening way, putting the sustainability of the whole system at risk.

In addition to holistically understanding this structure, SD has specific tools to highlight the delays between cause and effect (e.g., farmers' decision-making time [29]), and the nonlinear nature of many of the system relationships (e.g., water productivity is not linear, but starts from zero, grows first exponentially and then linearly, and then saturates, reaching a maximum). These considerations, which lead us to more elaborate phases of the SD model, are what explain the counter-intuitive nature of the system in the face of certain solutions that try to alleviate water scarcity. Thus, for example, improving the efficiency of irrigation systems often leads to higher water consumption [30,31].
