Looking for a Generic Model Structure for Resilience Assessment: A Case Study of Water Resilience in the Lisbon Region

Abstract

System Dynamics has a demonstrated potential as a model-based method for resilience assessment. In SD applications to societal resilience assessment, there is a need to start the modelling from somewhere, and generic structures might be of help. In this paper, we discuss the use of a small model that reproduces the emblematic system behaviors portrayed by the resilience literature as a starting point to conceptualize social ecological systems in resilience assessment projects. We illustrate it with a case study of a water resilience assessment project alongside a Lisbon civil society organization.

Full text

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Looking for a Generic Model Structure for Resilience Assessment:
A Case Study of Water Resilience in the Lisbon Region
Wang Zhao1, Igor Oliveira1, and Birgit Kopainsky2
1. European Master in System Dynamics, Department of Geography, University of Bergen, Bergen, Norway
2. System Dynamics Group, Department of Geography, University of Bergen, Bergen, Norway
Abstract
System Dynamics has a demonstrated potential as a model-based method for resilience
assessment. In SD applications to societal resilience assessment, there is a need to start the
modelling from somewhere, and generic structures might be of help. In this paper, we discuss
the use of a small model that reproduces the emblematic system behaviors portrayed by the
resilience literature as a starting point to conceptualize social ecological systems in resilience
assessment projects. We illustrate it with a case study of a water resilience assessment project
alongside a Lisbon civil society organization.
Keywords: Resilience; System Dynamics; Generic Structure
An applied resilience assessment case
Background
This paper builds on a three-month consulting engagement with a civil society organization in
Lisbon, Portugal, by two of its authors, in 2018. Initially, the client organization aimed to build
a resilience assessment tool that should be easy to use by multiple agents. It should be able
to continuously inform the entire Lisbon region society (roughly 3 million inhabitants over a
3,000 km² area) about how close to collapse the society is in every possible dimension. They
also had a special interest in water stress suffered by low income populations. The link
between these two dimensions was initially unclear to the client. The treatment of these cross-
scale interactions was a major issue we faced during the project.
The client organization had a view of resilience analysis as a type of risk analysis, inspired by
the OECD guidelines (2018a, 2018b, 2018c), which we incorporated to our theoretical
framework. They had already defined that the generalist tool would be an index, as it believed
indexes as an effective form of synthesizing complexity. Their theoretical background was
influenced by both Econometrics and the Complex Adaptive Systems paradigm.
The concept of resilience utilized here builds on an entire research tradition initiated by Holling
(1973), who characterizes resilience as the ability of a system to absorb changes of different
variables. More recent literature states that resilience research must be defined in terms of
“resilience of whom to what” (Carpenter, Walker, Anderies & Abel, 2001: 1).
When our consulting engagement with the Lisbonian civil society organization started, their
system of concern was defined as the Lisbon region society and the changes were not
specified, as the initial intention was to build a generalist societal resilience assessment tool.

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Later, we helped the organization redefine the boundaries of the project as the Lisbonian water
supply system resilience to changes in precipitation.
The specific problem to be modeled was later defined as the unknown vulnerability of low-
income populations to a projected decline of 20% in precipitation in the region by 2100
(Resccue, 2017). The client organization believed local low-populations were highly
vulnerable to this climate pressure, and this vulnerability could trigger structural change in the
Lisbonian society.
We envisioned a future connection between the generalist index and a future water supply
system model that could bridge the gap between their concern with societal resilience in
general and their more specific goals related to water. We proposed a conceptual structure
(Figure 1) where we would stick to their theoretical and methodological a priori for the Lisbon
Region Resilience Index. On the other hand, we would use System Dynamics for the water
resilience model. We will not detail the construction of the index here, to be able to focus on
the dynamic parts of the consulting project.
Figure 1. Conceptual model of the consulting project
We justified this to the client by showing that the need for dynamic tools had been mentioned
in the urban resilience assessment community. Constas, Cisse, Knippenberg & Downie (2016),
while comparing resilience assessment methods, most of them static and linear, refer to the
possibility of incorporating “dynamics among shock exposure, wellbeing, capacities, and path
or time dependence”. Sharifi (2016) also performs a review of the available resilience
assessment tools, and calls attention to the need for “accounting for cross-scale relationships,
capturing temporal dynamism, addressing uncertainties”.
Walker et al (2004) describe four basic components of resilience of social-ecological systems:
latitude, resistance, precariousness, and panarchy. The panarchy component is described as
the influence of cross-scale interactions on a system. It is an essential concept for this case
due to the interaction between a more general and a more specific resilience analysis. The
authors also define adaptability as the capacity of actors to influence resilience and
transformability as the capacity to (re)create systems after regime shifts.

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We explained that their index would still have a rather static and discrete nature, while we
would use the System Dynamics model to understand the local water system and try to
connect it to the index, to be able illustrate some of the panarchical relationships involved.
This would allow for a prototypical dynamic risk analysis of water resilience in the Lisbon region,
especially when it comes to low income populations’ resilience to changes in precipitation.
The client then agreed with this approach.
Model building
The System Dynamics model was then built from documental analysis using reports and
datasets from government, research institutions, multilateral organizations and agents
involved in the water supply system. A water utility that controls most of the upstream and
downstream operations in the region provided data about the entire water cycle in the region,
besides tariffs and company debt (EPAL, 2018a, 2018b, 2017 and 2016). Other sources were
the national water regulator (SNIRH, 2018), a national public data portal (PORDATA, 2018),
OECD (2018d), CIES-IUL (2018), Structurae (2018), Jornal de Negócios (2001). One expert
interview with a member of a regional water board was conducted to clarify doubts about
idiosyncrasies of the local water system. Falkenmark (2003) and Folke (2003), as well as the
client mental model, inspired the model structure.
According to the slow vs fast variable approach in the resilience literature (Walker, Carpenter,
Rockstrom, Crépin & Peterson, 2012), resilience of socio-ecological systems is considered
compromised when the relationship between a key slow and a key fast variable in a system
moves away from a long-standing state, usually called an attraction basin, represented on a
phase diagram, like in Figures 4 and 5. When this happens, the system ceases to exist as
previously observed, generating a regime shift.
Walker et al. (2012) explain that the fast variable depicts a primary concern of system users.
In our case, water insecurity was a concern of both the client organization and the Lisbonian
population (DN, 2018). It had been cited in previous resilience assessments in the region
(Rockefeller Foundation, 2017). As highlighted by Walker et al (2012), fast variables often
represent access to goods or services. The slow variable is usually a stock that determines
how the fast variable reacts to external shocks. Walker et al. (2012) exemplify these shocks
with abrupt variations in rainfall, which is the same shock we investigated in this project.
The client organization’s experience working with local low-income populations to mitigate
water stress influenced the model structure, including the definition of the fast and slow
variables to be adopted: fraction of population water insecure (linking water price and income
distribution) and ‘water’ (the stock of water in the local water supply system, in cubic meters),
respectively.
One of the advantages of the approach by Walker et al (2012) is the ability to go beyond the
relationship between two populations of different species, which was the usual reductionism
in earlier resilience research since Holling (1973). In fact, May (1972), a key reference for
Holling’s seminal work, outlines that the predator-prey analogy is applicable to situations
where density-dependent responses to resources and predation is present as well as the
functional and numerical responses to resource density. The implication for this in Walker et

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al terms is that the slow and fast variables are not necessarily literal predator and prey
populations. In this consulting project, we identified functional, density-dependent responses
to water levels by both consumers (who adjust their consumption and potentially generate
social unrest) and the local government (who makes decisions about water infrastructure
expansion and tariffs).
The local water supply system is characterized by a strong dependency on one major reservoir
providing approximately 83% of the water to the region (EPAL, 2016), which made the
modelling easier, as we were able to reduce the water harvesting structure to surface water.
We modelled this reservoir as a proxy to the entire water system capacity and assumed this
simplification as a limitation of the consulting project.
The model generated by the consulting process (both Figure 2 and Figure 3) contains four
fundamental feedback loops, described in Table 1.
The local income distribution, water tariff subsidies and taxation structures were modelled to
be able to calculate the impact of these crises in the low-income household budget.
Figure 2 also contains five hypothesized relationships with the six components of the higher-
level resilience index (resistance, adaptability, innovation, economic pressure, disaster and
conflict). This means that changes in these six attributes, even when not caused by the water
system behavior, are taken into consideration.
Figure 2. Causal Loop Diagram containing cross-scale relationships with the resilience index

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Sensitivity analysis led to the identification of key variables that later inspired scenario analysis
(precipitation, % of EU funding to infrastructure expansion, time for government to perceive
water gap, aggressiveness of infrastructure expansion, implementation speed of the ongoing
national tariff system centralization). The identification of these leverage points, depicted
within a second CLD in Figure 3, was considered useful by the client organization as they are
now able to direct their campaigning efforts to these points.
Figure 3. Causal loop diagram including exogenous variables and leverage points
Table 1 below contains the four feedback loops within the model and a corresponding
description of their meaning.
Feedback loop
Description
B1: Water deficit control by
capacity expansion
Whenever policy makers detect the need for more water in
the system, they tend to increase harvesting capacity by
building infrastructure.
B2: Debt control by tariff
adjustment
The public utilities that supply water usually run on debt.
Soaring debt stimulates water tariff increase by regulators.
R1: Deterioration of societal
resistance by water costs
Of the three types of costs related to water, two of them
(interest paid by utility companies and expansion costs) are
charged from the population through taxation. One is
charged directly via water tariffs. The higher these
household expenditures are, the more people will become
water insecure, which might generate broader societal

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crises and trigger more capacity expansion (B1) by
lowering the threshold utilized by authorities to decide on
infrastructure construction.
R2: Thriving water operations
The water utilities’ business relies on tariffs to keep running.
Table 1. Feedback loops
A public hearing was organized, and three other prominent local civil society organizations
provided feedback on the entire project during a three-hour session along with a dozen
interested citizens. A final hand-in session was provided to the client, to ensure continuity.
Model-based resilience analysis
Based on sensitivity analysis, we defined four scenario runs (Table 2) that were the basis for
resilience analysis.
Scenario
Description
Base case
Precipitation projections from base climate scenario by Resccue (2017)
showing a 20% decline until 2100. Other variables as observed in the
present or recent past, depending on data availability.
Pessimistic
precipitation
A 60% decline in precipitation until 2100. Exaggeration is made explicit for
model analysis purposes.
Pessimistic
without EU
A 60% decline in precipitation until 2100 and absence of European Union
funding for infrastructure projects.
Tariff
centralization
Strong country-wide water tariff centralization which would bring the Lisbon
region closer to the tariffs currently practiced in the driest and most
expensive regions of Portugal. We used a positive exponential growth curve
that would affect the tariffs by a 1.8 multiplier in 2100, which is close to the
median tariff in the country. This centralization process is already happening
in reality, but at a slow pace due to policy resistance (DN, 2012).
Table 2. Scenario runs
By running this model, it is possible to observe two types of water crises, shown in Figure 4:
expansion-driven crises (generated by B1, amplified by R1) and price-driven crises (generated
by B2). Price-driven crises occur when water becomes too expensive for an important fraction
of the population. Expansion-driven crises happen when government makes disproportionate
infrastructure investments that are indirectly paid by low-income population through taxation.
In both types of crises, the fast (‘fraction of population water insecure’) and the slow (‘water’)
variables leave their usual value range (the so-called attraction zone or regime). This happens
in three out of four scenarios that were analyzed: pessimistic precipitation, tariff centralization
and pessimistic precipitation without the currently available EU funding for infrastructure.

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Figure 4. Phase diagram including four scenarios
Figure 4, obtained from four different model runs corresponding to the four above-mentioned
scenarios, contains the same definition of axes as proposed by Walker et al (2012) in Figure
5: fast variable on the y axis, slow variable on the x axis.
Figure 5. Walker et al (2012) illustration of a regime shift
Figure 5 is an illustration from Walker et al (2012) showing minor disturbances in the system
that are successfully absorbed. The system state could move along the two branches of the
Z-like curve in the graph. Vertical lines are exogenous disturbances or perturbations. There is
an unstable equilibrium point in the middle of the dotted part of the curve (where there is a
two-direction arrow). In this case, the system state (which is a point with slow and fast variable
as its two coordinates) is on the upper branch and will possibly get perturbed by external
disturbance. If it falls on the dotted line but still to the right of the unstable equilibrium, it will
go back to the upper branch, indicating the perturbation is absorbed. However, if it falls on the
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dotted line and to the left of the unstable equilibrium, it will go to the lower branch, which is a
regime shift.
Comparing Figures 4 and 5, it is possible to understand that only one of the scenarios in Figure
4, namely ‘pessimistic precipitation without EU funding’, contains disturbances that are
important enough to be interpreted as causes of a regime shift. Although the price-driven
crises in the tariff centralization scenario are important, they do not drive the current system
to a definitive collapse.
Figure 6 shows that the price-driven crises would happen first (in the tariff centralization
scenario), while the expansion-driven crises seem to be far away in terms of time horizon. The
base run scenario, which is based in historical data (variables like precipitation, water
company finance, cost of capacity expansion, income distribution) corrected by base
scenarios of climate models (a 20% decline in rainfall until 2100), does not show any crisis.
Figure 6. ‘Fraction of population water insecure’ over time
Briefly after the communication of these analyses to the client, they began using it to
communicate risks. For instance, they now understand that tariff centralization can trigger
price-driven crises and abrupt expansion due to strong precipitation decline and disruption of
the EU funding schemes can generate expansion-driven crises. By knowing the potential
pathways to collapse, it became easier to communicate their agenda to stakeholders.
Another interesting result of this project is the possibility to illustrate water crises influenced
by panarchical aspects, such as the strength of economic pressures (one of the components
of the resilience index proposed by the client). Figure 7 shows that the 2012 economic crisis
(and its effect on income) would have to be much stronger to generate a regime shift in the
regional water supply system, which is in line with the findings on Figure 6 showing that the
Lisbonian water system is far from collapse when the base case conditions are observed. This
analysis is possible by changing the initial value of ‘economic pressure’ on the model, which
impacts ‘fraction of population water insecure’ positively by pushing the income levels of the
entire Lisbonian population lower while maintaining the same income distribution. The sine
wave representation on Figure 7 was adopted by the client for communication purposes.
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Figure 7. Illustration of a water system threshold as compared to economic pressure as a
disruption element, adopted by the client
Toward a generic structure
Throughout the consulting project, it became clear that we were spending excessive time and
energy in model conceptualization. Due to difficulties in boundary definition that are inherent
to projects with a cross-scale ambition, we had unfruitful interactions with our client as every
new structure was added from documental analysis. A broader understanding of the main
feedback mechanisms in the water model was only achieved towards the end of the three-
month project, which constrained our capacity to transmit system understanding capabilities
to the client and to civil society in general.
We realized then that a better use of generic structures, such as canonical situation models
(Lane & Smart, 1996), could have helped us perform a more effective intervention. Even the
process of negotiating a clear focus on water could have been easier if we had the capacity
to illustrate the type of dynamics we would be able to capture when focused on water. As
demonstrated by Lane and Smart (1996), canonical situation models can be used as
precursors to specific application models and serve as a general theory of structure and
behavior in specific domains, in this case, regional resilience assessment.
This is consistent with a need for operationalization in the context of resilience assessment,
noticed in both the resilience research community and the resilience-related system dynamics
literature.
Demand to operationalize resilience research
From the resilience research perspective, the demand for a well-developed and practical
resilience framework has persisted for long. Walker et al. (2002) suggested a participatory
framework for analyzing social-ecological resilience, defining a procedure in work-steps for
carrying out such analysis. Anderies, Walker and Kinzig (2006) analyzed 15 case studies on
intervening social-ecological systems (SESs) and found the traditional optimal-control
centered top-down approach would not work. This paper suggested two reasons why it has
not been replaced by resilience-based theories, one of them is that “there has not been an
alternative theory or framework to replace it”. The study then pointed out that such a theory
could generalize findings from one SES to another, noted that “many papers about resilience
theory are either mainly descriptive or are combinations of ecological and economic theory
applied to specific systems with particular nonlinearities”, and proposed that a generic
structure could play an important role in bridging existing resilience theories and analyzing
results from multiple cases.

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There have been multiple attempts in finding an operational framework for resilience. From
the perspective of homeland security, Kahan, Allen and George (2009) proposed an
operational framework for resilience by identifying key objectives and principles of resilience,
with the aim of bringing different theories about resilience into a same framework. Extensive
effort has been made on clarifying frequently-used concepts, while one constraint of this
framework is the lack of support to quantitative analysis. Ganin et al. (2016) proposed an
approach to quantitatively measure the resilience of complex systems that consist of large
number of interdependent nodes. Advantage of this work is that it supports quantitative
analysis of hyper-complex networks. However, additional effort is needed to make its
measurement applicable to researches on social-ecological systems, since they are using a
different set of concepts for components of resilience. Similar attempts were done by Alderson
et al. (2015), in which the resilience of a supply chain system was quantitatively analyzed in
terms of the speed at which operation cost grows after the system’s losing a number of
components, and Munoz and Dunbar (2015), in which a simulation-based approach close to
system dynamics was adopted and resilience was also measured in terms of recovery after
impact.
As literature showed us so far, a framework that allows for quantitative applications of
resilience theory to social-ecological systems is still missing. The demand for a tool for not
only conceptual but also analytical assessment of resilience persists. Such a tool, while
capable for communicating with resilience researchers, needs also to be easy to understand
and applicable to a wide range of SESs.
Demand to analyze resilience using System Dynamics
From the system dynamics perspective, there have been multiple attempts in recent years to
apply system dynamics to resilience assessment, mostly from a model analysis perspective,
such as in Bueno (2012) and Herrera (2017).
Bueno (2012) used a single-stock model with three flows, namely ‘regular flow in’, ‘regular flow
out’, and ‘disturbance flow’ as a core stock-flow structure to test the system’s stability.
Although stability would not necessarily be equal to resilience from many perspectives, it still
reflects a way to capture the dynamic system. A more complex model used in the same paper
is an aging chain as a second-order material delay, where one of the stocks representing a
population was studied as the variable of interest. Herrera’s (2017) operationalizes resilience
analysis, allowing policy testing in terms of five fundamental resilience characteristics. His
study was based on an interacting three-stock model, of which the three stocks are ‘Standing
biomass’, ‘Deer population’ and ‘Predator population’.
However, a starting point for modeling a system of interest and subsequently studying its
resilience is still missing. The authors make such argument based on dividing the question
‘how to assess a system’s resilience’ into two sub-questions:
● How to model a system in a way that variables and relations important to resilience
analysis are included?
● How to assess the resilience based on this model but also in line with established
resilience theories?

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Most SD-based resilience literature focus on the second question: they assume that a model
for has already been built. However, in many cases, as in the consultancy project done by two
of the authors, the system of interest has not yet been modeled. A first step of such a project,
might therefore be to model the system for subsequent assessment of resilience. Generic
structure is a tool that could help a lot in this situation, by guiding the model conceptualization
and standardizing the subsequent model-based resilience assessment, which is a part of
model analysis.
From a specific case to a generic structure
Our attempt to search for a generic structure that fits resilience assessment, could be
interpreted as a three-step process:
1. Summarize the core mechanism of a model for resilience assessment in a specific
situation, make them into a set of core components, and clarify the core dynamics;
2. Look at other widely-accepted system dynamics generic structures, simplify these core
components to a similar level of simplicity;
3. Validate the proposed generic structure against both the literature on resilience
assessment and possible situations where this generic structure may be applied, to
ensure the generic structure’s ability in generalization.
By following this procedure, we intended to increase the chances that the generic structure
obtained would be sufficiently valid, simple, and general. These three features are rooted in
the expectations people have when searching for generic structures to start their building of
specific models.
A feature of the model built for the case in Lisbon is the interplay of two stock-like variables,
namely the fast variable and the slow variable, which are ‘fraction of population water insecure’
and ‘water’ in the model. Although ‘fraction of population water insecure’ is not a stock, it is
understood as the relationship between two stocks, determined by the income levels of the
local population and the water-related costs they incur. As analysis of interaction between ‘fast’
and ‘slow’ variables is a key feature of resilience studies (Walker et al, 2012), a generic
structure for system dynamics-based resilience assessment should provide favorable
conditions for such analysis. A two-stock model would be a promising choice for such a use.
Two-stock models are not a recent innovation in system dynamics studies. For example,
Moxnes (2004) used a simulator based on a simplified 2-stock system dynamics model to
reveal decision makers’ misperceptions of basic dynamics in renewable resource
management. Many other applications of two-stock models could be found in previous system
dynamics studies. Swart (1990) studied the predator-prey model of two stocks and found it
capable of reproducing many of the phase-plane graphs, including the classical Lotka-Volterra
behavior, as shown in Figure 8. These behaviors were also paid attention to by Holling in his
1973 work, as shown in Figure 9.

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Figure 8. Phase plane behaviors produced with 2-stock system dynamics model of predator
and prey in Swart (1990)
Figure 9. Possible behaviors of a two-population system in phase plane, from Holling (1973)
The last question is whether a two-stock generic structure is capable of resilience assessment.
This question has two aspects. First, from a structural perspective, can the core component
and mechanisms of interest in a resilience assessment be represented in this generic structure?
Second, from a behavioral perspective, does the behavior shown by this generic structure
represent components of resilience, namely, latitude, resistance, precariousness, and
panarchy (Walker et. al 2004)? In the next section, after presenting the generic structure, these
concerns will be addressed.
A preliminary generic structure
We departed from a two-stock structure as the interplay between two variables is aligned with
both the resilience tradition and the SD-based approaches to resource management.

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Figure 10. Preliminary generic structure for resilience assessment (stock-and-flow diagram)
As resilience assessment is mostly applied in social-ecological systems, the authors believe
that the core dynamics herein should include both the natural aspect and the societal aspect,
that could be manifest as physical capital, financial capital, population or any other cumulative
variable that expresses societal development. Although it is arguable what specific dimensions
both aspects should cover, it would be less controversial that ‘levels’, or ‘stocks’ are needed
to capture the state of both aspects.
Both main stocks in Figure 10 have their own dynamics. Natural resources, which here stands
for a certain category of natural resources that regenerate, will stop by Max Resource Capacity
if there is no consumption, where net growth rate i.e. Regeneration is zero. Max Regeneration
Rate could be achieved when Natural Resources’ stock level is at half of Max Resource
Capacity.
Physical capital, for example, is positively dependent on available natural resources for its
development and will depreciate if natural resources are not relatively sufficient. Natural
resources utilized by societal activities such as physical capital development are including but
not limited to those for population growth and infrastructure construction, which means
demographic and economic dynamics are drivers of physical capital development that can be
modelled depending on the context in which the model-based resilience assessment project
is performed.
The interaction in a social-ecological system could therefore be abstracted as an interplay
between two subsystems centered on single stock, which enables further analysis of the
structure.

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Analysis of the generic structure
Analysis in this section is carried out on both structural and behavioral dimensions. Structural
analysis discusses the realistic implications of the proposed generic structure to ensure the
narrative it tells is aligned with processes and mechanisms that a resilience assessment will
care about. Behavioral analysis shows the dynamic behavior generated by the generic
structure and validates it against how a social-ecological system in the real world would
behave.
Structural analysis
Figure 11. Preliminary generic structure for resilience assessment (causal loop diagram)
The interaction between human activities and natural resources is represented by loop B2, in
which consumption of natural resources by physical capital reduces natural resources and in
turn limits societal activities’ development.
Loop
Interpretation
R/B0
Loop R/B0 represents the self-regeneration of natural resources. For a great amount
of types of natural resources are able to regenerate but only within a certain growth
rate, the parameter max resource capacity is introduced to control the upper limit of
its stock.
R1
Loop R1 represents the development of physical capital, its reinforcing polarity is in
line with the persistent expansion of human communities. However, this loop is
controlled by the relative sufficiency of natural resources, therefore would not show
a behavior of exponential growth.
B1
Loop B1 represents the self-depreciation of physical capital. It is assumed that all
ongoing human-built infrastructures are destined to depreciate, and only with
ongoing regeneration can the collective activities maintain a certain level.

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Depreciating is also influenced by sufficiency of natural resources. By separating
Regeneration and Depreciation, flows influencing physical capital are treated
separately, not like the case for natural resources, which leaves more room for
extensions such as policy structures.
The interaction between loop R1, B1, and B2 may be seen as a competition for dominance.
The human society’s basis for expansion drives R1 but could be balanced by B1 - higher
depreciation of its own or B2 - higher depreciation due to insufficient natural resources.
In this interaction natural resources function as an anchor but still has its own dynamics. For
a regenerating type of resources, if depleted too much in a short period of time, it may collapse
without regenerating again.
For example, water resource as a type of natural resource is regenerated through rainfall but
its total amount is limited by the reservoir, and water resource is key to the society in that
region. Therefore, we may argue that the generic structure is applicable in this case.
Furthermore, structures of policy interventions can be identified and added to this generic
structure (not shown in the diagram).
To avoid the reductionism posed by the use of ‘Physical Capital’ in Figure 11, a further
generality of this generic structure could be achieved by replacing the natural resources and
physical capital variables with the slow vs fast variable (Walker, Carpenter, Rockstrom, Crépin
& Peterson, 2012; also discussed earlier) approach as in Figure 12.
Figure 12. Proposed generic structure following the slow vs variable approach
By comparing the final generic structure (Figure 12) to the Lisbon water model, we realize that
the generic structure could have facilitated our initial conceptualization efforts with the client,
as we could have started from a holistic understanding from the beginning instead of eliciting
each relationship. Even the problem definition could have been made easy if we had proposed
the definition of key variables within the proposed generic structure.

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As we demonstrate in Table 3, departing from the proposed generic structure could helped us
focus on the key feedback processes that drive the problematic behavior. It could have helped
prevent both reductionism and excessive detail.
Generic
structure
loops
Lisbon
model
loops
Comment
R/B0 & B1
B1
Water as a natural resource regenerates through rainfall and the
consequent harvesting by the water supply system. Depreciation
of the water infrastructures limits harvesting. These are two
fundamental mechanisms that were reduced to one in the Lisbon
model. The use of a generic structure could have prevented
reductionism.
B2
B2
Consumption erodes natural resources' stocks and generates a
need for further investments.
R1
R1
More physical capital, here represented by the water system
capacity, leads to more developments as it supports demographic
and economic growth.
none
R2
The reinforcing mechanism that describes the successful water
business would probably not be present in an initial model based
on the generic structure, which seems correct as this mechanism
is less relevant to describe the problem.
Table 3. Feedback loop comparison
Behavioral analysis
Behavioral analysis in this section is conducted by first contrasting the behaviors generated
by the generic structure with the ones from the Lisbon case. Then, we analyze the ability of
the proposed generic structure to depict the main components of resilience according to
Walker et al (2004).
1) Compliance with the behaviors from the Lisbon case
Behavioral analysis shows convincing dynamic behavior generated by the generic structure.
a) Equilibrium

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b) External Shock and Recovery
c) External Shock and regime shift
Figure 13. Behavior generated by the generic structure.
In the Lisbon case scenarios, we observe the three behaviors in Figure 13. The generic
structure could have helped us visualize these three possible behaviors much earlier in the
project and continuously build the structure in more detail.
Behavior (e) on Figure 9 could only be reproduce by Swart (1990) with the use of a nonlinear
function, which we avoided in our proposed generic structure. Our structure is capable of
reproducing all behaviors in Figure 9 except (e).
2) Capability to reveal resilience components
Walker et al. (2004) describes four basic components of resilience: latitude, resistance,
precariousness, and panarchy. We list their definitions as following and demonstrate the way
they are represented in the generic structure.
Component
Definition
Latitude
The maximum amount a system can be changed before losing its ability
to recover (before crossing a threshold which, if breached, makes
recovery difficult or impossible)
Resistance
The ease or difficulty of changing the system; how “resistant” it is to be
changed

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Precariousness
How close the current state of the system is to a limit or “threshold.”
Panarchy
Because of cross-scale interactions, the resilience of a system at a
particular focal scale will depend on the influences from states and
dynamics at scales above and below. For example, external oppressive
politics, invasions, market shifts, or global climate change can trigger
local surprises and regime shifts.
Table 4. Definitions of the four components of resilience made by Walker et al. (2004).
Furthermore, Walker et al. (2004) visualized the first three components in Figure 14, and the
last one – panarchy in Figure 18. In Figure 14, a three-dimensional topography is used to
represent a stability landscape – a set of all possible states of the system – with two basins of
attraction. A black dot is used to represent the system’s current state. Three components of
resilience, namely latitude, resistance, and precariousness are visualized as:
● Latitude (L): “the positions of the thresholds (edges) between basins” (Walker et al.,
2004);
● Resistance (R): “depths of basins, a measure of how difficult it is to move the system
around within the basin” (Walker et al., 2004);
● Precariousness (Pr): a system’s “position within a basin relative to the edge” (Walker
et al., 2004).
Figure 14. Basins of attraction from Walker et al. (2004)
The proposed generic structure is able to present a system’s resilience in a similar
visualization and supports the analysis of latitude, resistance, and precariousness. Taking the
output obtained from a simulation of the proposed generic structure as an example:

19
Figure 15. Latitude illustration from generic structure output
Latitude can be measured as the diameter of the zone in which after a perturbation a system
will still be able to recover. This diameter could be different in different direction, indicating
perturbation on different component of the system.
Figure 16. Precariousness illustration from generic structure output
Precariousness can be measured as the distance between a system’s current state at the
edge of a recoverable zone.
Figure 17. Resistance illustration from generic structure output

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Resistance can be measured as the amount of change in a system’s state in response to a
certain perturbation, or in another word, how hard to change a system’s state. This can be
related to resilience analysis in the SD literature, notably by Herrera (2017), who uses variance
analysis to determine the importance of such change.
Figure 18. Illustration of panarchy from Walker et al. (2004)
As mentioned above, the only component of resilience not depicted in Figure 14 is panarchy
(Pa). Figure 18 from Walker et al. (2004) shows the influence of a system’s state on scales
above and below the focal scale (i.e. the system’s own scale).
Figure 19. Demonstration of panarchical relationships modelling
Panarchy can be modeled with the proposed generic structure, benefited from the extendibility
of System Dynamics models. As shown in Figure 19, by extending the generic structure to
more focal scales using almost the same structure, panarchy can also be analytically studied.
Discussion: Generalization for Resilience Assessment
First, it is important to recognize a limitation of this research by acknowledging the argument
by Holling (1973), who argues that stability analysis is not a synonym of resilience analysis.
This is, in fact, still a weakness in SD-based resilience analyses as in Herrera (2017). Only by
observing the persistence (or not) of the system structure or the emergence of new structure
we can really detect resilience change first hand.

21
Nevertheless, stability analysis has an important role in the prospective, risk-analytical nature
of resilience studies. In most cases, it is not enough to observe concrete signs of structural
change in order to assess resilience risk, as it might be the case that this change is not
happening yet, but the underlying processes that will lead to change are. As in the Lisbon
consulting case, modelers are called to help a group of actors improve their capacity to
understand and gradually foresee structural change.
In this sense, we had in mind the objective of conceiving a simple structure able to replicate
all or at least most of the system behaviors described in Holling (1973), shown in Figure 9. We
consider the slow vs fast variable approach (Walker et al., 2012) to be a more competent
simplification than the classic two-population reductionism in Holling (1973) exactly because
it provides structure-related insight by demonstrating relationships between two key variables.
The phase diagrams in Figure 9 may be interpreted, considering contemporary research, as
relationships between fast and slow variables.
The use of such structure has a potential to increase systems understanding speed and quality,
which are two related aspects of resilience assessment projects, as project calendars are
usually very compressed. Like in the Lisbon case study, systems understanding is often an
implicit objective of clients and sponsors. Our client benefited directly from knowing the
feedback loops, the sensitive parameters, the scenarios. They helped the client create more
effective narratives to engage with stakeholders. However, it took us too long to show them
the value of knowing all that, partly because it took us too long to have a model to illustrate
the analytical potential of what we were building together. This could have been avoided using
a generic structure.
Attempts to utilize the proposed generic structures in multiple dimensions that interact among
each other could be especially useful to deal with the panarchy aspect of resilience
assessments. In the Lisbon consulting case, civil society organizations have already
manifested their interest for the inclusion of interactions between the water system, the ageing
population and the housing market. This could allow for a more bottom-up approach to the
generalist resilience assessment once envisioned by the client organization, replacing the use
of top-down resilience assessment tools like econometric indexes and indicator panels.
Figure 20. Conceptual structure of a future Lisbon region resilience assessment using SD
Every model has its limitations, and the limitation of generic structures lies in the type of
situation they try to capture, as they are constrained by core assumptions. Recalling May

22
(1972), we believe that social-ecological systems that fulfill the following assumptions could
be modeled and subsequently assessed by the proposed generic structure:
● The slow variable is self-regenerating within a certain limit;
● The fast variable is dependent on the sufficiency of the slow variable.
Conclusions
This research was a first step into finding a generic model structure for resilience assessment
projects. We developed a structure that satisfies both the needs we observed from a concrete
case and the needs that are described in literature.
We also identified some of its potential limitations: it seems to fit prospective risk assessments
but not the detection of emerging structural change, which would be a more literal definition of
resilience assessment. Moreover, it seems to be suitable to cases where the May (1972)
conditions (presence density-dependent and functional responses) are met, which means
potentially not every case.
More applications of the proposed generic structure and consequent critical research is
needed to determine its generality when applied to different resilience assessment contexts
and projects. As consultants, we intend to utilize it in our next resilience assessment projects
and encourage other practitioners and researchers to explore it.

23
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