1. Introduction
Hundreds of millions of farmers worldwide are confronted with increasing uncertainty due to gradual changes and sudden fluctuations in external drivers associated with demography, climate, market prices for inputs and products, policies, and geo-political conflicts [
1,
2,
3,
4]. In order to maintain their livelihoods, and to secure the supply of food for a growing global population and the provision of other ecosystem services from rural landscapes, these agroecosystem managers have to minimize their vulnerability and should be able and willing to adapt to be resilient to changing circumstances.
Resilience and vulnerability are two attributes of socio-ecological systems that reflect their behavior in response to perturbations at a local, regional, or global level. Vulnerability represents the susceptibility to harm to the performance of a system from exposure to disturbances associated with environmental and social change [
5,
6], whereas resilience focuses on the capacity of the system to absorb disturbances and reorganize while undergoing change so as to still retain the same function and structure [
6,
7,
8]. These concepts have been useful in providing insight into the complexities of natural resource management in social-ecological systems. Their most salient application has been in the metaphoric sense, to illustrate the dynamics of systems development cycles (adaptive cycles), to show interrelations among scales within coupled social-ecological systems, and to indicate the necessity of preparedness for disturbances and adaptation at all hierarchical levels [
9,
10].
Disturbances differ in the intensity, duration, and frequency of the impact. Shocks denote sudden perturbations for a short period of time, whereas stresses affect a system uninterruptedly for longer time span (years) and with certain level of predictability [
11]. In agricultural systems, disturbances to farms negatively impact on system productivity and profitability. Disturbances can be classified [
8] as economic (input price increase, output price decrease, inputs availability, access to markets, and uncertainty on land tenure); climatic (weather shocks like extreme temperatures and precipitation rates); and management-related (plant pests, animal diseases, overharvesting, and overgrazing). In dairy farm systems, social, environmental, and economic domains are strongly linked to the animal and crop subsystems, where on-farm grassland or forage production is used as an alternative to reduce the external dependency of feeding and feeding costs, to recycle nutrients, and as source of income. Due to the complex interrelations among subsystems and the damage that these systems might suffer, it is relevant to identify the disturbance and to quantify the magnitude of the impacts in the social, economic, and environmental system domains.
Different theoretical models and practical approaches are available to understand and assess vulnerability and resilience in agricultural systems at different space and time levels [
11,
12,
13,
14,
15,
16]. Nonetheless, the challenge of quantitatively analyzing vulnerability and resilience at the farm systems level still remains. Such approaches could contribute to design of more resistant and resilient farms [
6,
11]. Multiple authors (e.g., [
12,
17]) have pointed out the need for approaches that use numerical analysis in the assessment of vulnerability and resilience.
Available quantitative approaches that make the concepts of resilience and vulnerability operational include dynamic systems analysis and the quantitative techniques, which support adaptive management. In dynamic systems analysis, ecological systems have been modeled in terms of differential equations that simulate the changes in slow and fast state variables. This method has been effective at demonstrating that ecosystems have multiple stable states and that they can collapse due to inappropriate too intensive management [
12,
18,
19,
20,
21,
22]. After such a regime shift to a degraded state, recovery to a desirable state might be difficult or impossible. The occurrence of over-use of systems or of their components has been attributed to the lack of feedback and correction mechanisms in the human dominated world, in particular in the socio-institutional and economic parts of systems [
23,
24].
Here we apply resilience and vulnerability in an illustration using quantitative farming systems models. Both dynamic and static quantitative representations of farming systems have been put forward in the literature. For instance, [
25,
26] developed a dynamic model of a dairy farm that is characterized by three state variables describing organic nitrogen, carbon, and inorganic nitrogen pools, respectively and grassland and cattle management that intervenes in the rates of change of the states. In contrast to these relatively simple, analysis-oriented models, [
27] presents a dynamic model of an arable farm with a large number of state variables describing soil-crop-atmosphere relations on different fields and their cross-field interactions, aiming at representativeness of reality. Static farming system models represent key elements of farming systems as balances of economic, social, and environmental indicators, aggregating changes over time periods of typically a year (see review by [
28]). Static farm models are generally far more tractable than dynamic farm models, but inherently lack dynamic feedbacks. Nevertheless, they may be applied in a semi-dynamic manner where the researcher re-initializes the model to mimic a disturbance. To our knowledge, such application is novel and may open up a new line of farming systems research.
The aim of this study was to present a quantitative approach to analyze and assess vulnerability and resilience in agricultural systems. The approach is illustrated through the analysis of these properties on family-based (FB) and semi-specialized (SS) dairy farms in Marcos Castellanos, Michoacán, Mexico, that undergo a shock disturbances in the form of a reduction in forage maize production. Alternative management options to strengthen system resilience (hereafter called ‘innovations’) are evaluated using a multi-objective farm-scale optimization model. This approach represents a way to operationalize and to reduce subjectivity and abstractness of the concepts of vulnerability and resilience.
2. Conceptual Approach
The evolving nature of complex adaptive systems has been conceptualized as a continuous adaptive cycle [
29] of phases of growth, accumulation, restructuring, and renewal. The degree to which social-ecological systems can perpetuate these cycles depends on three general system properties [
30]. The first property is the ‘potential’ of a system, which is determined by the availability of options for future development that allow a system to continue functioning at a desired level for a predefined set of state variables after a disturbance. The other properties are the ‘controllability’ and ‘resilience’ of the system, which reflect the rigidity or flexibility for adaptation and change and determine the degree to which a system is affected by and can recover from a disturbance [
30].
The ‘potential’ of the system can be associated with two other ecosystem properties, buffer capacity and adaptive capacity [
19,
31]. We conceptualize buffer capacity as the ability of the system to continue performing at a similar performance level after a disturbance without structural changes in the number or diversity of components and processes in the system. In systems that are characterized by high diversity, the probability of the presence of redundant components and links is high, which supports the buffer capacity [
32] because links and flows can be redirected to support crucial system processes without compromising other vital functions. Adaptive capacity is defined as the ability to reconfigure and recover performance after new components have been introduced into the system.
Agroecosystems are coupled human-environment systems wherein the farmer, who participates in a larger socio-institutional network, manages part of the ecosystem with the aim to eventually harvest crop and/or animal products either for self-consumption or the market. The ecological part of the system can be either strongly dependent on biological processes such as nutrient cycling through animal manures and crop residues and pest suppression by natural enemies of crop pests, or more dependent on external inputs that can be imported from communal resources (e.g., food, feed, bedding for animals) or purchased on markets (e.g., seeds, fertilizers, pesticides, feeds). The concept of the ‘potential’ of the system is reflected in the ways the farmer can reconfigure crops, animals, resources, and management practices on his farm to reach a desired productive, environmental, and social outcome given the biophysical, socio-economic, and political environment in which he operates.
A disturbance can be a pest or drought or product price decline that can negatively affect the farming system performance. The farmer can respond by reconfiguring the farm with changes in for instance crop areas, animal numbers, amounts of inputs, selected market channels, or management practices to compensate for the effect of the disturbance. The available options for adjustment of the system with existing components and resources can be considered the ‘buffer capacity’. When the farmer decides to introduce new crops, animals, inputs, or practices the required adjustment and reconfiguration (both in the ecological system and in farm management) is expected to be considerably larger and is reflected in the ‘adaptive capacity’. This illustration of the concepts for an agroecosystem demonstrates that, besides the ecological (self-)organization, the farmer, his flexibility and skills, and his cognitive and managerial capacities will determine the chosen strategy of adaptation and the final effectiveness of reconfiguration, and thus agroecosystem resilience.
All possible combinations of values of state variables constitute the ‘window of opportunities’ or ‘solution space’ for a particular system [
33]. The potential of a system (P), resulting from buffer and adaptive capacity, can be derived from the size of the solution space, which defines the options for adjustment of the system. The solution space is delimited by the Pareto frontier (or Pareto surface when more than two performance criteria are included in the analysis), and for assessment of resilience we consider only options that perform at least as good as the existing system. The Pareto frontier can be established using multi-objective optimization, and the area (in 2 dimensions), volume (3 dimensions), or hyper volume (>3 dimensions) of the solution space can be calculated [
34], for instance, relative to a given reference point that represents the existing situation. This is demonstrated in
Figure 1, wherein only the portion of the solution space with improvements in two system states (productivity and environmental quality in this case) relative to the existing situation after a disturbance is depicted. The buffer capacity (area B in
Figure 1a) is estimated as the solution area corresponding to the reconfiguration of links and flows among the components that are already in the system. The adaptation capacity (area A in
Figure 1a) is estimated as the expansion of the solution area when new components are introduced in the system. The potential (P) is estimated as the sum of areas A and B.
Disturbances result in a deterioration of the performance of at least one of the state variables. This is visualized by the change in system state from point 1 to point 2 in
Figure 1a. The distance (here measured in unit of ordinate per unit abscissa) between these points represents the vulnerability (v) of the system to the disturbance. P represents the potential range of future development options that all differ in the degree of change that is needed to move from the disturbed state to a new, more desirable configuration. Which option will actually be realized (for instance, point 3 in
Figure 1a) depends on the ability to rebalance interactions and flows within the system, which have to be rebalanced through (self-)organization. This requires flexibility, learning, and experimentation. It can be expected that, in many cases, larger improvements in performance of state variables relative to the initial situation will also require larger adjustments in system configuration and organization. The distance between points 2 and 3 is the recovery (r) of the system. We propose to estimate the resilience as R = r/v, denoting the ability of a system to recover after a shock.
The size and shape of the solution space will change continuously since the system and its environment are subject to adjustments, for instance in bio-physical environment, or due to technological and socio-institutional innovations [
33]. For instance, declines in soil fertility resulting from erosion or invasion of the system by a new pest will reduce crop yields and productive farm performance; increased water infiltration and nutrient leaching due to enhanced precipitation associated with climatic change will affect the environmental impact of farming activities; changes in policy regimes and introduction of new taxation or subsidy schemes will alter the economic revenues from the agroecosystem. As a consequence, the vulnerability and resilience of the system should also be considered as dynamic properties. This is illustrated in
Figure 1b, which shows a sequence of disturbed and recovered system states.
5. Discussion
Socio-ecological systems are highly conditioned by the human capacity to reduce vulnerability by controlling disturbances and managing adaptive capacity [
8,
32]. These systems are dynamic and strongly influenced by external factors and internal components and the interaction of biotic and abiotic variables involved. Farmers, technicians, and governments interfere intentionally in this dynamic and in the direction of changes by decision-making. The exploration of alternatives might support planners and policy-makers in the definition of policies, technicians in the search of solutions and innovations, and farmers in the implementation of changes all aimed at increasing or improving the adaptability of the systems.
By applying the presented framework to vulnerability and resilience assessment, these concepts lose abstractness by showing concrete and numerical changes that quantify and explain farm performance, and potential effects of both disturbances and a broad range of possible responses. The outcomes of the vulnerability assessment showed that both dairy farm systems were able to absorb the effects of the shock disturbance of reduced on-farm maize productivity. The vulnerability was assessed as the magnitude of the change of the performance indicators between the farm before and after the disturbance. Vulnerability was larger for the SS farm than for the FB farm, in particular in terms of profitability and to a lesser extent OM balance (
Figure 2). The FB farm depended less on on-farm produced maize (and thus had a larger reliance on externally sourced feeds), which resulted a better capacity to absorb the effect of on-farm forage maize production reduction than for SS in our scenario. This scenario is valid under the current system delineation of the farm that considers markets and product prices external to the system. However, in the actual situation, the impact on profitability will also depend on the changes in maize fodder prices that could occur when the disturbance affects not only the farm under study, but reduces maize productivity at a larger scale.
The set of alternatives obtained during the exploration process showed the capacity of the farms to adjust their subsystems to the disturbance by reconfiguring their resources and diversifying the farm´s production. The buffer capacity was larger for SS than for FB due to its higher diversity of available resources and greater deficiencies in baseline farm performance including factors such as poor herd structure and low milk production and crop productivity. The adaptive capacity increased after inclusion of the new management practices of forage barley cultivation after maize and manure application by enhancing the possibilities for mitigating the negative effects of the disturbance on the objective variables. The potential P of the SS farm was larger than that of FB, mainly for minimizing the N balance, which was the indicator that improved the most after implementation of the alternative of management. Both farms could adjust their management by reconfiguring and adjusting the management of already available resources. For maximizing profitability, SS had to intensify by increasing milk production and productivity, and sales of products (milk and maize forage). On the other hand, FB had to intensify its milk production and to diversify its sales, adding maize forage, although this implied increasing the external dependency of feedstuffs. More diversity in land-use at farm and landscape levels can lead to higher resilience against disturbances, offering more alternatives to manage the impacts [
8] and to stabilize economic returns [
41].
Generating multiple collections of snap-shots to create a timeline of changes in system performance and windows of opportunities, as done in our framework, can make the analysis with a static bio-economic model semi-dynamic. However, the inherent limitations of static models remain—i.e., the importance of the system state for the response to disturbance is not addressed—and the dynamics and feedbacks cannot be incorporated directly. Nevertheless, that analytical framework can be readily coupled to more complex dynamic and event-driven models. Another limitation of the illustration presented here is that it only comprised the scales of field and farm, whereas larger landscape and community studies would also be useful and relevant to assess the influence of cooperative decision-making and of policies and institutions [
42,
43,
44]. Possible extensions include the evaluation of scenarios of change in the external drivers such as climatic change, demographic change, and changes in socio-institutional conditions (prices and policies), cf. [
33].
To illustrate our concept, we only considered a single shock disturbance to assess vulnerability, one alternative to analyze resilience, and three objective variables. Nevertheless, due to the many factors and interactions between subsystems the analyses revealed to contain rich complexity, which would be difficult to assess with simple conceptual models as it is commonly proposed [
8,
11,
19,
32]. While conceptual models support the analysis by understanding the structures and functions of the systems under assessment, model-based quantitative analysis can enrich the analysis by demonstrating links between subsystems and considering social, economic, and environmental performance of systems after disturbance.
6. Conclusions
We presented a framework for quantitative analysis of vulnerability and resilience of farming systems, based on a multi-objective explorative whole-farm model that quantified buffer and adaptive capacities of the two case study farms. The results express vulnerability and resilience in terms relevant for farm assessment, thus reducing abstractness of the notions and providing leverage points for on-farm adaptation. Yet, generating meaningful analyses requires a close collaboration between farmers and researchers to gather relevant and accurate information to build the conceptual models, to define the objectives, to parameterize the simulation model, and to identify the salient disturbances and alternative practices in order to increase the buffer and adaptive capacities.
The results of the study show how a system reconfiguration can play a role in reducing the impact of disturbances and in increasing the potential capacity of agricultural systems. However, taking advantage of system resilience may require considerable change in practices and will draw on the skills, motivation, and learning capacity of the farmer.