A modeler's guide to studying the resilience of social-technical-environmental systems
AA modeler’s guide to studying the resilience ofsocial-technical-environmental systems
Lea A. Tamberg , , Jobst Heitzig and Jonathan F. Donges , Institute of Environmental Systems Research, University of Osnabr¨uck, Barbarastraße 12,49076 Osnabr¨uck, Germany FutureLab Earth Resilience in the Anthropocene, Earth System Analysis, Potsdam Institutefor Climate Impact Research, Member of the Leibniz Association, Telegrafenberg A31,14473 Potsdam, Germany FutureLab on Game Theory and Networks of Interacting Agents, Complexity Science,Potsdam Institute for Climate Impact Research, Member of the Leibniz Association,Telegrafenberg A31, 14473 Potsdam, Germany Stockholm Resilience Centre, Stockholm University, Kr¨aftriket 2B, 114 19 Stockholm,SwedenE-mail: [email protected], [email protected]
16 September 2020 a r X i v : . [ phy s i c s . s o c - ph ] S e p odeler’s guide to resilience Abstract.
The term ‘resilience’ is increasingly being used in the domain of social-technical-environmental systems science and related fields. However, the diversity of resilienceconcepts and a certain (sometimes intended) openness of proposed definitions can leadto misunderstandings and impede their application to systems modelling. We propose anapproach that aims to ease communication as well as to support systematic development ofresearch questions and models in the context of resilience. It can be applied independently ofthe modelling framework or underlying theory of choice. At the heart of this guideline is achecklist consisting of four questions to be answered: (i) Resilience of what? (ii) Resilienceregarding what? (iii) Resilience against what? (iv) Resilience how? We refer to the answersto these resilience questions as the “system”, the “sustainant”, the “adverse influence”, andthe “response options”. The term ‘sustainant’ is a neologism describing the feature of thesystem (state, structure, function, pathway, . . . ) that should be maintained (or restored quicklyenough) in order to call the system resilient.The use of this proposed guideline is demonstrated for two application examples: fisheries,and the Amazon rainforest. The examples illustrate the diversity of possible answers tothe checklist’s questions as well as their benefits in structuring the modelling process. Theguideline supports the modeller in communicating precisely what is actually meant by‘resilience’ in a specific context. This combination of freedom and precision could help toadvance the resilience discourse by building a bridge between those demanding unambiguousdefinitions and those stressing the benefits of generality and flexibility of the resilienceconcept.
Keywords : resilience, modeling, socio-technical-environmental systems, complex systems,sustainant, adverse influence, response options
1. Introduction
Resilience is—literally speaking—the capacity of a system to deal with change. The conceptof ‘resilience’ is well-established in disciplines like psychology, ecology, social-ecologicalsystems and engineering sciences (Holling, 1996; Masten & Reed, 2002; Folke et al. , 2016)and is increasingly being applied in Earth system science (Rockstr ¨om et al. , 2009; Steffen et al. , 2015; Gleeson et al. , 2020). Its role as a boundary object or bridging conceptbetween different academic and non-academic fields has been emphasized (Baggio et al. , 2015; Turner, 2010). In recent years, it has also become an important idea in complex(adaptive) systems science (Fraccascia et al. , 2018; Lade & Peterson, 2019).In this interdisciplinary context, a vast number of definitions, concepts and related termshave been proposed to capture various aspects of resilience. For instance, the relation betweenterms such as ‘stability’, ‘adaptability’ and ‘transformability’ is intensely debated in thecontext of “resilience thinking” (Folke et al. , 2010; Cote & Nightingale, 2012; Walker &Salt, 2012; Curtin & Parker, 2014; Donges & Barfuss, 2017; Lade et al. , 2017). In fact,not even basic hierarchies between different notions have yet been consistently clarified. Forinstance, while stability is often seen as an aspect of the broader concept of resilience (Folke et al. , 2010; Ludwig et al. , 1997), other authors see both concepts as completely differentor even antagonistic aspects of a system (Holling, 1973), and yet others classify resilience asone of several “stability properties” (Grimm & Wissel, 1997) or aspects of stability (Orians,1974; Harrison, 1979). There is also a related discussion on whether a narrow or a broad odeler’s guide to resilience et al. , 2019; Hodgson et al. , 2015).Other authors, especially from the domain of social-ecological systems, explicitly advocatefor a broader understanding of the term (Folke et al. , 2010; Walker & Salt, 2012; Anderies et al. , 2006). Even though the theoretical treatment of these concepts is by far not completed,it has become increasingly clear that resilience has too many aspects to try assessing “the”resilience of a system as if it were a single measurable quantity.At the same time, many of the individual concepts tend to be hard to apply when itcomes to the analysis and modelling of real systems. This has several reasons including thementioned openness of definitions, lacking formalization, and missing estimation methods(Strunz, 2012; Brand & Jax, 2007; Hodgson et al. , 2015). Also, experience shows thatresearch questions based on abstract theoretical concepts often cannot easily be answeredwith pre-existing models that were not specifically developed for this purpose. Often, centralaspects of resilience theory are simply not represented in the model. For instance, a model inwhich the possibility of structural changes is not included does not fit to a research questionaddressing the adaptation capacity of a system. Another example would be the idea of learningincorporated in some concepts (Carpenter et al. , 2001). Obviously, this aspect of resiliencecannot be analysed in a system if no representation of learning processes or something similaris part of the chosen model.These considerations imply at least two complementary challenges for the modeller.First, the large variety of definitions and theoretical frameworks makes it necessary tocommunicate very precisely what is actually meant by ‘resilience’ in a particular studyto avoid confusion. In our view, a systematic approach to this required kind of meta-communication is needed to enhance the resilience discourse. Second, research questionsregarding resilience and the model(s) to answer them should be developed simultaneously inthe same structured process in order to ensure their compatibility. We believe that these twoconcerns—precise communication and compatible modelling—can be addressed together.In this paper, we develop an iterative approach to modelling that aims at easingcommunication as well as supporting research question refinement and model development inthe context of resilience. We propose a checklist of questions the modeller should answer inorder to communicate precisely about specific forms of resilience of a particular system ‡ and to guide the design of suitable models for studying these. Since, as we have seen,there is not one but many forms of resilience of a system, the checklist is designed toparticularly help narrowing down which precise form of resilience is to be studied, whatthe exact research question regarding this form of resilience is, and how a model should bedesigned in order to answer that question. In view of the ongoing theoretical debate, we takea neutral position regarding the definition of debated terms such as ‘resilience’, ‘adaptability’,‘stability’, ‘transformability’, etc. Instead, our checklist questions are formulated in terms ‡ This system could be of any kind, from purely physical to social-technical-ecological. The resilienceperspective is particularly promising for the latter; However, the guideline should be applicable to all domainsof systems modelling. odeler’s guide to resilience et al. , 2001), whodemand to answer the question “Resilience of What to What?” in order to avoid confusionwhen communicating about a system’s resilience. However, our guideline extends therequired precision by differentiating this question considerably. Also, we put less conceptualrestrictions on the possible answers to the questions. A similar extensive list of questionshas been proposed for a geographical context (Meerow & Newell, 2019). Their question setfocuses on “advancing a politics of urban resilience” and therefore differs significantly fromthe one proposed here which is designed for system modellers. However, their question setmay be seen as orthogonal to ours, each list allowing to refine the other as in a matrix structure.E.g., their questions about the “when” and “where” of resilience are helpful to pinpointthe spatial and temporal aspects of the four main structural components our questions willdistinguish: system, sustainant, adverse influence, and response options. Our guideline canalso be compared to a strategy proposed in ref. (Grimm & Wissel, 1997) for communicatingbetter on the term ‘stability’ in the domain of ecology. This strategy includes a checklistenforcing a precise definition of the “ecological situation” for which a stability statement ismade (Grimm & Wissel, 1997). Our checklist, though, is not restricted to ecology and leavesmore freedom to the modeller without demanding less precision.The paper is structured as follows. In Sect. 2, we present a proposed methodology forresilience modeling. By way of results, we then apply this methodology to two exemplaryapplication areas in Sect. 3, which is complemented by a third socio-technical system examplein the Appendix. The discussion in Sect. 4 concludes the paper.
2. A methodology for resilience modeling and research question refinement
The approach we propose can be seen as an iterative process, summarized in figure 1a. Westart from the assumption that in any particular research study, at least a basic, possibly onlymental, initial “model” of the system exists, as well as an initial, possibly only broadlydefined, research interest. While working through a checklist of guiding questions, moreprecise characterizations for an improved model and a more specific formulation of theresearch question will arise. Although initially, one may go through the guiding questions in astandard sequence, later iterations may require revisiting some of them in different order. Thisis because whenever the answer to one guiding question is modified, it may become necessaryto reconsider certain other guiding questions until the system model and research questionare consistent. Consistency is reached when the model suitably reflects the answers to allguiding questions without contradictions. If the specified research question suitably refinesthe original research interest and can be answered by the developed model, the model design odeler’s guide to resilience Research question on resilienceChecklist refines refines
Can the research question be answered with the model? effects answersworkingbasis
Model (a) overview of the iterative process
System? Sustainant? Adverse influence?
Response options?
Model Research question on resilienceChecklist (b) detailed view of the checklist components
Figure 1: Graphical representation of the modelling process when using the proposedguideline. Starting from a basic (mental) model and a broad research interest, the checklistwith four components helps to refine both until they are consistent.process is finished. Else, the research question must be revised or the modelling process hasto be iterated once more.In the following, the different questions in the checklist (see also figure 1b for anoverview) are presented and explained with the help of examples. Each of these questionsincludes a set of subquestions helping to be as precise as possible. The general idea is tospecify four different aspects of resilience in the context of a specific system:
Resilience ofwhat, resilience regarding what, resilience against what and resilience how?odeler’s guide to resilience What are the system boundaries and how sharp are they? What are the system’s parts and their interactions that appear relevant for answering the research question? With what aspects ofits environment does the system interact, through which kind of interfaces?
Is there agency § in the system, meaning that parts of the system may exhibit targeted, intentional action?Following the usual linguistic convention, the question “Resilience of what?” refers tothe whole system of interest, not a specific system state as in (Carpenter et al. , 2001). Thelatter is covered in the next question of the checklist. Working out the mentioned aspects ofthe system is of course not a step only taken in the resilience context but in system modellingin general (Bossel, 2007; Voinov, 2010). The following questions are more focused on themodelling of resilience itself and build on the results of the first one, often making it necessaryto reconsider those in further iterations. Which feature or property of the system is supposed to be sustained or maintained in order tocall the system resilient? Its state or structure, its pathway? Some long-term equilibrium? Itsfunction, purpose, or utility for some stakeholder? Some quantitative or qualitative aspect ofthe system? What this “sustainant” is is no objective feature of a system but is normativelychosen by the observer from their perspective, which should be clearly communicated.Especially what the “function” or “purpose” of a system is can be seen differently fromdifferent perspectives (Cutter, 2016; Meerow & Newell, 2019).E.g., for different observers, the function of a forest could (among others) be to producewood, to enhance biodiversity, to provide a habitat, to serve for recreation, or to be beautiful.The model analysing the resilience of the forest regarding wood production would differcompletely from a model with biodiversity as the sustainant.Note that the neologism ‘sustainant’ is supposed to cover different ideas from theliterature about which system property the resilience of a system is related to. For instance,ref. (Carpenter et al. , 2001) demands the specification of a specific system state as an answerto the question “Resilience of what?” (while their “to what” refers to our “regarding what”).In contrast, ref. (Folke et al. , 2010) defines that a system is resilient if it essentially retains“the same function, structure and feedbacks”. The term ‘sustainant’ is not restricted to oneof these (or other) perspectives but leaves it to the modeller to clearly specify which systemproperty is of interest.Considering the normativity of the sustainant, it becomes clear that its choice can besubject to power relations, inequality, and competing interests. Many authors thereforedemand to consider the question “Resilience for whom?” to account for these aspects(Cretney, 2014; Cutter, 2016; Meerow & Newell, 2019). This question is located on a meta § Agency is originally a concept from sociology (Barker, 2002), meaning the capacity of individuals to actindependently and to make their own free choices. It is increasingly used in the context of resilience in social-ecological systems (Armitage et al. , 2012; Larsen et al. , 2011; Westley et al. , 2013). odeler’s guide to resilience threshold values for certain indicators that shall either not be exceeded ever or may onlybe exceeded temporarily. E.g., when modelling the development of the oxygen concentrationin an aquarium and choosing this system property as the sustainant, its restoration after adrop may be irrelevant if it was zero in between so that all fish have died. One could arguethat in this example, a better sustainant would be the fish being alive. However, this is aquestion of model boundaries. If the fish is not explicitly modelled but is only described as aconsumption factor in the water-oxygen system, the potential interest of the modeller in thefish staying alive leads to the definition of an acceptable range for the oxygen level. If themodeller does not care about fish survival but the general capacity of the system to restoreoxygen level, the sustainant can be defined without any threshold values.Such thresholds depend, as the choice of the sustainant itself, on the perspectiveand interests of the observer who has to define an acceptable range for the sustainant.Correspondingly, an acceptable recovery time should be defined.E.g., a fish stock may recover 50 years after a collapse; however, this is not relevant forsomeone aiming to evaluate the risks of investments into the fishery industry that is dependanton this resource on much shorter time scales. Again, the boundary choice (here only to modelthe fish population and describe the fishery as an external factor) leads to the populationsize being the chosen sustainant, specified by an acceptable recovery time motivated by theconcern for the fishery industry.As another example, consider a social network. A possible sustainant could be thatevery individual has at least one connection to another individual. This sustainant would be aproperty of the system’s structure. An appropriate recovery time could for instance considerhow long an individual can endure social isolation without developing mental illness.
What is the concrete influence affecting the sustainant that shall be considered for this specificresilience analysis? Is it an abrupt but temporary disturbance (pulse), a shock, a constantpressure, noisy fluctuations, a perturbation, an abrupt but permanent shift in some feature,or a slow change? Does it originate in the system or in its environment? Does it affect thestructure, a parameter, or the state of parts of the system? In some cases, the influence that issupposed to be studied does not have a direct effect on modelled aspects of the system, butthrough an intermediate linked to the boundary interface of the system, making it importantto be precise about the actually modelled influence. Note that the term ‘adverse’ in ‘adverseinfluence’ is not necessarily meant as something undesirable. It only reflects that this influenceeffects the system in a way that weakens the sustainant. If the observer rates the sustainant assomething negative, the adverse influence on it can be seen as something positive (Donges &Barfuss, 2017; Dornelles et al. , 2020).Remark to the 2nd and 3rd question: Of course, a sustainant could be composed of odeler’s guide to resilience k E.g., one may be interested in the resilience of the climate system against a rise of CO concentration in the atmosphere (= single-influence) regarding the global mean temperature (=single-sustainant) or regarding the ensemble of temperature, precipitation, and wind maximaover the course of the year in each region (= multi-sustainant). Another example of interestmay be the resilience of a society against increasing abundance of misinformation and theshock of a pandemic (multi-influence) regarding trust in the government (single sustainant). Boundaries
Sustainant
Agency
Adverse influenceExternal Management
Interface
Environment
Endogenousreactions
System
Figure 2: Relations between terms such as ‘sustainant’ and ‘adverse influence’ as used in ourresilience modeling guideline
At which levels can or does a system react to adverse influences? Which types of reactionscan be observed? (One type could be the inherent stability behaviour of a system, bringing it k Folke et al. distinguish between specified resilience (“resilience of some particular part of a system, relatedto a particular control variable, to one or more identified kinds of shocks”) and general resilience (“resilienceof any and all parts of a system to all kinds of shocks, including novel ones”) and argue to concentrate on thelatter one in order to cope with uncertainty and trade-offs (Folke et al. , 2010). However, in a modelling context,specificity is crucial. It is inherent to the modelling process that decisions on what to represent in the modeland what not have to be taken. Therefore, our guideline asks to specify which sustainants and influences areconsidered. By choosing a multi-sustainant and a multi-influence, the risk of overlooked trade-offs can at leastbe reduced. odeler’s guide to resilience ¶ ? Which reactions are endogenous as a consequence ofthe system’s structure and rules? Which response options require external management oragency? In figure 2, some important terms used in the checklist are presented graphically. With the help of the checklist and the notion of ‘sustainant’, the research question can bespecified more precisely. Some possible types of research questions are: • Is the system “in general” resilient regarding the sustainant?
This might be a ratherqualitative question: Is the sustainant easily affected and does it recover in an acceptabletime range? • How much influence can the system bear without a change of the sustainant or witha recovery on a relevant time scale?
This corresponds to a quantified measure of thespecific form of resilience analysed, e.g., using metrics such as “basin stability” or“survivability” or variants thereof (Menck et al. , 2013; Mitra et al. , 2015; Hellmann et al. , 2016; Kan et al. , 2016). • How can the system be designed to be more resilient through its structure and internaldynamical rules?
Often, this is a question for general rules about how to build or fixcertain kinds of systems so that they show the desired resilience (Biggs et al. , 2015).To answer this question, the system model(s) must have a certain level of genericity thatallows for the comparison of different structural or dynamical changes. • What are resilience-promoting management strategies + In this case, the model shouldreflect the possibility to change structure, states, parameters and rules/cause-effectrelationships easily.2.6. Choosing appropriate modelling techniques
Answering the above guiding questions does not produce a complete model but a collectionof requirements that should be met by a more technical description. For this, our guidelinedoes not specify a single approach. In general, any mathematical or simulation techniquefrom differential equations over agent-based modelling to game-theoretical modelling may beused. Of course, the description resulting from answering the guiding questions will influencethis choice. For instance, if an important feature of a system is the social structure connectingpeople, choosing a network model appears natural. ¶ For instance, ref. (Elmqvist et al. , 2003) emphasizes the importance of “response diversity” regarding theresilience of desirable ecosystem states. + For instance, strategies such as the “sustainability paradigms” established in ref. (Schellnhuber, 1998) or themanagement of pathway diversity (Lade et al. , 2019) for agents outside the system (external agency). odeler’s guide to resilience
3. Application examples
In this section, we study two application examples to show how the proposed guideline canbe applied in the modelling process and for precise model communication (Tab. 1). Tohighlight the diversity of possible outcomes of this process, we will in each applicationexample formulate a series of different research questions and sketch corresponding modelversions. Each version is meant to be a potential result of one or more iterations of the aboveprocess. Note that the presented answers to the checklist’s questions are options amongstothers. As explained above, they heavily depend on the specific perspective and interests ofthe modeller.
As our first application, we use a paradigmatic and well-studied example from environmentaleconomics: a fishery (Perman et al. , 2003). The most elementary description of this system isa fish stock that is harvested by a fisher community. Traditionally, one would like to analyzethe ability of this system to maintain its harvested yield.
A very simple way to modela fishery system is by a single differential equation describing the change of fish populationsize via logistic growth and harvesting. In this case, the system description only has onevariable, the fish stock. There are two interfaces to the system’s environment. First, the fishpopulation, x , is influenced by ecosystem factors such as food supply, competition with otherspecies and climatic conditions. All these aspects are aggregated in the two parameters, theintrinsic growth rate r and the carrying capacity K . The second interface is the harvest of fishby human fishers, modeled as a subtractive harvesting term, e.g. a concave term controlled byan effort parameter h and elasticity α < : dxdt = rx (cid:18) − xK (cid:19) − hx α . (1)In this scope, the model does not reflect any agency—the harvest effort is a given for thischoice of boundaries. What is the sustainant?
So far one can imagine different sustainants. An environmentalorganization could consider the system resilient if x > x min for some threshold x min . Inenvironmental economics, more importance is given to yield, y = hx α , which is what wechoose here as well. One could define a minimal yield y min and a maximal time t max that y may stay below y min because fishers have limited financial reserves. What is the adverse influence?
The sustainant can be challenged by an abrupt reductionof x due to, e.g., a fish pest or an invasion by an external fishing fleet. Since a reduced x means less yield, this effects the sustainant. What are the response options?
The only response “option” of the system is the built-inbasic dynamic stability that lets the stock converge to its unique stable equilibrium value x ∗ from whatever initial condition x (0) . Depending on parameters and perturbation size, x mayrecover fast enough to ensure that the drop in y does not last too long. odeler’s guide to resilience Research question : First of all, one can ask whether, given some value of h , equilibriumyield y ∗ = h ( x ∗ ) α is above y min . If so, the model can be used to find out by how much x may be reduced without exceeding the acceptable recovery time for y . With knowledge of theprobability distribution of such reduction events, one may also calculate the risk and expectedfirst occurrence time of a fishery breakdown depending on the value of h . In a more realistic model version, one couldargue that fishers could adapt their effort h to a changing y . This extension of the responseoptions makes it necessary to modify the model. Instead of treating h as an exogenousparameter, we need a new component representing the harvest decisions of the fishingcommunity. This could be done by specifying h (or the change dh/dt ) as a function f ofcurrent and past yield, y ( ≤ t ) .The modified model now includes agency since it models the fishers’ reaction tochanging yield. A research question could be: What is the optimal effort function f thatminimises the risk of collapse? The 2nd model would certainly lead to the insight thatunder certain conditions, h has to be reduced temporarily or permanently to ensure a longterm sustainable y . However, a fishing community is typically not a single entity but aheterogeneous group of fishers with individual interests. The model could thus reflect theresulting public good problem by including several agents i . This extension results in changeson all levels of the checklist. In contrast to the first and second model, we now need tomodel agents’ decisions on individual efforts h i . This could be done by assuming the samestrategy for all fishers, e.g., individual short-term profit maximization. However, a largediversity of other approaches is possible, usually introducing more heterogeneity. Sinceour original sustainant , overall yield, is indifferent to yield inequality between fishers, analternative sustainant could be that for a specific percentage of fishers, individual yield y i doesnot collapse below some y i, min for longer than some time ∆ t i, max . Or some welfare function W ( y , . . . , y N ) from welfare economics may be used to define a quantitative sustainant. The adverse influence would be the same as before but there would be several layers of responseoptions : The stock’s inherent convergence to equilibrium, the effort change of the agentsdue to their existing strategies, the change of these individual strategies, e.g. due to social orindividual learning, and the collective setting of rules by the community. One may then havea suitable model to answer—amongst others—the following research question : What rulesshould the community implement to maintain the sustainant?Obviously, the diversity of modelling options is extremely high when one decides toinclude the fishing community into the system scope in order to answer a research question onthis level. This is because much more simplification than in a non-human system is necessaryin order to control the complexity of the model. Especially the modelling of the agent’schoice strategies can become arbitrarily complex because humans are such complex systemson their own. Still more sophisticated approaches could also include the fish market, the socialstructure of the fishery community, multi-level governance institutions and processes etc. odeler’s guide to resilience might be necessary if fishers generate profit y i p − g ( h i ) (the new sustainant,with y i p being the sales and g ( h i ) the costs given by some function g ( . ) ) by selling their yieldto a market (an additional model component) whose price p may drop (adverse influence),to which they may react by jointly reducing their efforts h i to maintain a higher p or byredistributing income through taxation (response options). As an example of a much larger and more complex social-ecological system, let usfinally consider the Amazon rainforest: its hyperdiverse ecosystem and the human societiesinteracting with it. In view of climate change, a broad research interest lies in whether climateimpacts may cause a large-scale die-back of the forest via possible tipping dynamics (Lenton et al. , 2008; Lovejoy & Nobre, 2018).
From this broad researchinterest, one may derive the straightforward binary sustainant that Amazonia remains apredominantly forested area (rather than, e.g., a savannah). This is a sustainant regardingthe state of the system. As it is only a qualitative (and rather vague) state, an indicator for thesustainant is needed. A suitable candidate may be that the overall share of area that is coveredby forest, ≤ C ≤ , is above 1/2.A simple system model reflecting the ideas above would have as its sole variable theforest cover, influenced by climate conditions. If water availability is seen as the limitingfactor for vegetation growth which is most affected by climate, the relevant adverse influence is a potentially increasing aridity A . Following Menck et al. (2013), one could use a verysimple conceptual model, dC/dt = − δ C + 1 C>C ( A ) γ C (1 − C ) , (2)where the first term represents a decay at a rate δ > due to respiration and degradation,and the second is logistic growth at a basic rate γ > when C exceeds some minimal value C ( A ) that depends on A in a strictly monotonic fashion. This model has a stable fixed point of C ∗ = 1 − δ/γ (largely forest) as long as C ( A ) < C ∗ , and another stable fixed point of C = 0 (pure savannah) as long as C ( A ) > . If the system is already in the forest equilibrium, itis seemingly unaffected by changes in A that keep C ( A ) < C ∗ , since its responses to thosechanges are not detailed in the model. Once C ( A ) exceeds C ∗ , the system will die backtowards the savannah equilibrium.The only response option of the system to the slow parameter change of A is the inherentdynamic behaviour. Therefore, the model may be used to answer research questions suchas: If there were no other influences than an increase in aridity, would the Amazon rainforestbe resilient enough to survive predicted levels of global warming? How much can aridityincrease without a die-back? ∗ ∗ As the described model is extremely stylized and its quality mostly dependent on the quality of the function odeler’s guide to resilience In the first developed model, humanimpact on the Amazon rain forest is restricted to a slow increase in aridity due to climatechange. This is valid in order to answer research questions such as those formulated above.However, it is obvious that global warming is not the only way rainforests are threatened.Therefore, to get a more realistic picture of the risk to our sustainant, one would have toinclude other, often abrupt mechanisms on the system, such as droughts (Potter et al. , 2011),deforestation (Staal et al. , 2020), fire (Faria et al. , 2017), storms (Negr ´on-Ju´arez et al. , 2018)or soil poisoning by mining activities (Asner & Tupayachi, 2016). To formalize this, a multi-influence could be defined which includes slow aridity increase as well as sudden losses offorest land aggregating the mechanisms mentioned above ] . The resulting model would allowfor a large variety of research questions . Most interesting are those aiming at the interplaybetween the two different influences. For instance, one could analyse how an increase inaridity shrinks the basin of attraction of the forest state so that perturbations are more likely topush the system to the savannah state, as done in Menck et al. (2013). Building on this, onecould ask how much the size of shocks would have to be reduced by external management fora given level of climate change in order to avoid a collapse of the Amazon rainforest. When only regarding an aggregatedvariable such as tree cover, one ignores an important way in which ecosystems adapt tochanging climatic conditions: a change in the composition of different plant species (Jones et al. , 2014) and forest structure (R ¨odig et al. , 2018). Adding this process to the set of response options makes it necessary to change the system model significantly since manydifferent species (or groups of similar species with certain functional traits) or even individualtrees have to be considered. A possible way to represent them would be to introducedifferential equations for each of them †† . An important research question that can beaddressed when including this kind of adaptation response into the model is not only whetherit can help to sustain the forest state of Amazonia given a certain strength of the adverseinfluences (Sakschewski et al. , 2016). One may also further analyse the maximal rate ofchange that can be tolerated in terms of adaptation without causing a tipping of the system,reflecting that ecological processes leading to more adapted species compositions could betoo slow compared to the current rapidity of climate change. Outlook on further modelling approaches. C ( A ) , it should not be interpreted as a recommendation for answering the research questions but as an easilyunderstandable example for the kind of models suitable for this purpose. ] Of course, on could also argue that deforestation is a process that also happens slowly on a long timescale, notonly as abrupt shocks. For simplicity, this is ignored in the description of this application example, although itcould be included by defining differentiated adverse influences for slow baseline deforestation and more abruptevents. †† However, ecological forest modelling also offers a wealth of much more sophisticated models designed forthe study of species shifts in forests under changing climatic conditions and/or direct human impact, especiallyin rain forests (Shugart et al. , 1984; K¨ohler et al. , 2003; Fischer et al. , 2016; Botkin et al. , 2007) odeler’s guide to resilience • As the Amazon rainforest interacts with the atmosphere via different feedbackmechanisms (Shukla et al. , 1990; Cowling et al. , 2008), modelling this couplingwould give a more realistic insight into the dynamics of regional ecological and climateconditions (Zemp et al. , 2017). A new adverse influence would have to be defined onthe level of the regional or global climate system (e.g. CO concentration). • Including socio-economic systems in the scope of observation would allow for theconsideration of agency in the system (M¨uller-Hansen et al. , 2019). For instance, onecould be interested in the design of rules ensuring a sufficiently low level of deforestationdespite economic shocks.
Appli-cation Ver-sion System Sustainant Adverseinfluence Response options
Fishery 1 fish stock,total harvest total yield populationdecline convergence tostable equil. stock2 + totalfishing effort total yield + lowering of effort3 + individualfishers fishers’minimal yield + fishers’ strategicinteraction4 + externalmarket income-basedwelfare metric + price drop + output reduction,taxationAmazonrainforest 1 tree-coveredarea
C C > / slowly risingaridity convergence tostable equil. C C
4. Discussion
The guideline proposed above has been developed to support research on and communicationabout resilience in the field of complex systems at large and social-technical-environmentalsystems in particular. As the application examples show, the presented checklist is not a strict odeler’s guide to resilience et al. , 2015), resilience is the resistance and/orrecovery of a system’s state, where resistance is the “instantaneous impact of exogenousdisturbance on system state” and recovery “captures the endogenous processes that pull thedisturbed system back towards an equilibrium” (Hodgson et al. , 2015). This interpretationcan be the result of a specific set of answers to our checklist’s questions: The sustainant isthe system’s state, the adverse influence is some exogenous disturbance aiming at changingthis state and the response options are both the capacity of the system to stay unchangedin state (or only change slightly) despite this disturbance (=resistance) and the capacityto develop back to the original state after the state has been perturbed (=recovery). As asecond example, consider the forms of resilience used in “resilience thinking”: persistence,adaptability and transformability (Folke et al. , 2010). A model with a specific system stateas the sustainant can be used to study persistence, while adaptability requires the model toinclude the possibility to change the system’s structure or rules. If one would like to examinethe transformability of a system, it is obvious that the chosen sustainant would have to bea more abstract property, such as system function, since a system undergoing a generaltransformation of structure and feedbacks (e.g. according to ref. (Folke et al. , 2010) achange of its stability landscape) can by definition not be resilient regarding for instance itspathway. These examples of resilience theory show how different answers to our checklist canbe used to cover different abstraction levels of resilience, reaching from a simple “bounce-back” conception to the broader perspective of transformation.Several avenues for future research present themselves. First, the conceptualizationalong the dimensions of system, sustainant, adverse influence, and response options maybe used in some kind of “resilience study intercomparison project” in the spirit of the odeler’s guide to resilience et al. , 2014)or similar activities. Furthermore, our questions may help defining consistent types of“resilience metrics” which might take different mathematical forms to deal with these variousdimensions, e.g., in a way similar to basin volume-based metrics proposed by Menck et al. (2013); Mitra et al. (2015); Hellmann et al. (2016); Kan et al. (2016) or the quantifiersfollowing Hodgson et al. (2015). For example, one type of novel resilience metric might bea real-valued function f that maps a combination of four indicators—one for the current state x of the system, one for the acceptable threshold θ of the sustainant, one for the strength σ of potential adverse influences, and one for the allowable recovery time T —to the probability p = f ( x, θ, σ, T ) that the system will return to acceptable levels of the sustainant within theallowable time after suffering in the specified state an adverse influence of the given strength.Our avoidance to choose a specific theoretical resilience framework could be understoodas a capitulation to the exhausting but important process of concept formation. However, onecould also interpret this guideline as an attempt to build a bridge between two different viewson the concept of resilience: As already mentioned in the introduction, some authors stress theimportance of a clearly specified concept in order to facilitate formalization and measurementwhile others value resilience as a transdisciplinary bridging concept and boundary object,e.g. for catalysing discourses on sustainability transformations. As our guideline demandsmaximum precision from the user while giving maximum freedom regarding the type ofsustainant, adverse influence and response options, it connects elements from both views.A modeller can examine the system for its adaptability or resistance by choosing appropriateanswers to the checklist questions. However, in contrast to merely naming these terms, aconscientious application of the guideline will clarify and define their meaning in a specificcontext. Overall, the proposed approach may help to contribute to the development of a unifiedtheoretical framework on resilience of complex systems. Acknowledgments
The idea for this work was developed during a “Studienkolleg” working group on “The Earthas a complex system” funded by the German National Academic Foundation (Studienstiftungdes deutschen Volkes). The work was carried out as part of the bachelor program onApplied Systems Science at Osnabr¨uck University together with the COPAN collaborationat the Potsdam Institute for Climate Impact Research. J.H. and J.F.D. are supported by theLeibniz Association (project DominoES), the European Research Council (ERC) under theEuropean Union’s Horizon 2020 Research and Innovation Programme (ERC grant agreementNo. 743080 ERA). L.A.T. is supported by the German National Academic Foundation. Weacknowledge further support by Deutsche Forschungsgemeinschaft (DFG) and the OpenAccess Publishing Fund of Osnabr¨uck University. We thank Frank Hilker, J¨urgen Kurths,Steven J. Lade, Marc Wiedermann, Nico Wunderling, Vivian Z. Grudde, Bastian Grudde,Adrian Lison, Florian Schunck, and Sascha Haupt for valuable comments and discussions.
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Power grids have often been studied regarding various forms of stability, robustness, andperformance (e.g., Menck et al. (2014); Plietzsch et al. (2016); Hellmann et al. (2016);Nitzbon et al. (2017); Wienand et al. (2019)), many of which can naturally be seen as
EFERENCES et al. (2013)). Therefore, this kind of system isa good example to illustrate the proposed framework, even though it is only interacting withthe environment but has no major environmental component itself. A basic starting modeldescription for a power grid could be that electricity producers and consumers are connectedby power transmission lines. The broad research question is to analyze if the grid is easilydisturbed by changing conditions.
Differentiation between iteration of the checklistfor one model version or several as here for didactic reasons
What is the system?
The historically earliest and also most simple model of a power gridis a graph with edges representing high-voltage transmission lines and nodes representingtransformers to lower voltage levels, aggregating consuming and producing subsystems notfurther defined. The interface to the environment of the system is the production/consumptionof every node. Each transmission line has a certain capacity. It is assumed that productionand consumption are always balanced. This reflects the fact that the model does not includemechanisms to match electricity offer and demand, such as a market. The model is non-dynamic, the electricity transport is calculated with static power flow equations basicallyrepresenting Kirchhoff’s laws. This can be used as a base model to address the next questionsof our framework.
What is the sustainant?
From the perspective of a society maintaining a power grid,the function and sustainant of such a system can be seen as enabling all power transmissiondesired by producers and consumers. This is a binary sustainant: Either everyone’stransmission demand is met or not.
What is the adverse influence?
In this model, the sustainant can be challenged by a new(but still balanced) production and consumption pattern that may lead to line overload. Sinceour base model treats production/consumption as part of the environment rather than as part ofthe system, this influence is seen as an external influence on the system at this point, affectingthe system by the input or consumption status of nodes.
What are the response options?
Since the model does not include any agency, the onlyresponse option is that the power flow adjusts automatically to shift load from overloadedlines to others as a consequence of Kirchhoff’s laws.The model is suitable for answering the very specific research question : “Can thegrid transmit all desired production/consumption or not?” for a specific state, as well asderiving from that: “Which production/consumption patterns’ transmission demands can beserved?” or “How must the grid be designed to serve the transmission demands of a specificproduction/consumption pattern?”.
Answering the questionsmentioned above will not be very satisfying since production/consumption of nodes usuallychanges often over time and there may occur situations in which it can be necessary to reduceproduction/consumption of some nodes for some time to avoid line overload. Therefore,
EFERENCES research question could be: “If a reduction is necessary, which reduction patternshould be applied?” For this question, the sustainant must be refined.The new sustainant could be the fulfillment of each consumer node’s demand. In orderto call the overall system resilient, for each node, the delivered power needs to be within anacceptable range after the reduction.To study the resilience of the power grid regarding this new sustainant, the current systemmodel is insufficient. It has to be extended with the critical demand of each consumer node.The adverse influence is then a continually changing production/consumption pattern on thenodes.Additionally, the system model is equipped with a first response option to these patternchanges: an algorithm that specifies which nodes’ production or consumption gets reducedhow and under which conditions.The new research interest can then be addressed by varying the reduction algorithm.
In reality, of course, rules exist that deal withadverse influences which exceed the reaction capacity of the reduction algorithm or influencethe sustainant in another way than only a changed infeed/consumption pattern. It maytherefore be helpful to define an extended influence , a multi-influence that consists of thewell-known pattern changes as well as line tripping and generator failures. As a consequence,the system model has to be extended with the information whether a node or edge is activeor not. A new interface to the environment is their activation/deactivation (Plietzsch et al. ,2016).The new research question could then be: Is the system’s reaction resilient (regardingthe sustainant defined in the last version) in cases where the chosen reduction algorithm fails?To study this reaction, it is necessary to model the decisions taken in system operation (byengineers and software) in certain contingencies ( response options ). If the research interest is not to determine whetherthe reaction of a specific system is resilient but rather which kind of management decisionsmake it resilient (exploration instead of prediction/evaluation), the model has to be extendedby a set of additional response options that can be chosen in certain contingencies. E.g.,the network operator could build additional lines, the government could introducing networkfees, taxes or subsidies to incentivise changes in production or consumption, and electricitycompanies could change their pricing schemes and production locations.This system model would not be purely deterministic or stochastic since the agents’decisions are not modelled, only their decision options. Therefore, the model would havegame-theoretical traits.
In more recent considerations on the resilience of powergrids, frequency stability has become an important aspect due to an increasing producervolatility caused by larger shares of renewable energy sources. Therefore, a suitableextension of the sustainant is the following: At every node, the frequency must not leave
EFERENCES et al. , 2016). Adding this aspect to the already consideredsustainant, we obtain a “multi-sustainant”. To answer any research question regarding thisnew sustainant, the electricity transport on the network has to be modelled representingdynamics of frequencies and phases on short time scales. Technically, this could be doneby replacing power flow equations by so-called “swing equations,” the power flow wouldthen be a result of these new equations. The adverse influence would then be extended by thechange of frequency at a specific node.
Outlook on further modelling approaches
The presented ways of how to answer thechecklist when studying the resilience of a power grid are by far not complete. In orderto get an idea of the vast number of other possibilities, consider these further aspects: • The net operator could define the purpose of the network (and, in their perspective, thesustainant) as generating profit. A corresponding model would have to include a powermarket which could produce internal fluctuations as an adverse influence inside of thesystem boundaries (Heitzig et al. , 2017). ••