These authors contributed equally to this work.

This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution license (http://creativecommons.org/licenses/by/3.0/).

In this paper, we deploy a complexity theory as the foundation for integration of different theoretical approaches to sustainability and develop a rationale for a complexity-based framework for modeling

“Most fundamentally, ecological and socio-economic systems are complex, adaptive systems, integrating phenomena across multiple scales of space, time and organizational complexity” [

The core theoretical foundations of sustainability, as a field of research and as a discipline, are still being developed, and a number of different, but mostly convergent theories—as argued in this paper—have emerged as theoretical frameworks for conceptualizing

Before we proceed, however, we must first clarify what we mean by “modeling”. The term “modeling”, as used in this paper, refers to both hard and soft systems’ analyses and models, that is: (1) whether explicit and coded into computer models and simulations, mathematical models,

Emerging theoretical frameworks for transitions to sustainability include: (1) resilience theory; (2) decoupling theory; (3) the multi-level perspective (MLP) on transitions to sustainability; and (4) behavioral change theories of sustainability. All these theories of sustainability proffer valuable perspectives in respect of how modeling and analysis can be used to help decision-makers negotiate the complexity of the challenge of transitioning to whole system sustainability. Systems and complexity theory has been deployed in all of these theories, but to varying extents. The differences between them are due to differences in their conceptual foundations and the complex systems’ properties they emphasize.

In this paper, we argue that the current theoretical approaches that seek to deal with the complexity of actualizing transitions to sustainability, do not fully appreciate the implications of complexity theory and hence remain restricted to modeling the

According to Loorbach and Rotmans [

The transition domains of our research foci could be considered as complex systems themselves;

The close and recursive relation between transitions and system innovations, which makes the complex systems approach an obvious choice;

As a unifying principle, the complex systems approach offers a framework for synthesizing different knowledge strands which is necessary for addressing transitions and system innovations.

Hence, we use complexity theory as a framework for integrating between different theories of transitions to sustainability. Note that the integrative role that complexity theory can play is as a “unifying principle”, and not as a “unifying theory”. We argue that this “unifying principle” can be actualized as a plural, open-ended framework that is articulated through a thorough consideration of complex systems’ properties.

Moreover, our framework is required to be able to help better understand and support transitions to sustainability, and hence, must match the adaptive management requirements for transitions adequately. These requirements are that adaptive management for transitions to sustainability are required to be “

The key question that we address in this paper is “

We go about addressing it in the following manner. Firstly, as pointed out by Chu

So instead of formulating a unified theory of complexity and applying it to the challenge of modeling sustainable development challenges, we adopt a different approach, that is; one that focuses on complex systems’

The reason complexity theory is important for understanding transitions to sustainability is that it can serve as a theoretical framework for integrating between different theories of sustainable development. We illustrate how in this paper. By themselves, these sustainability oriented theories separately emphasize and focus on different complex systems’ properties. We identify the key properties of complex systems that resonate with different theories of sustainability (see

We argue that, as a consequence of the strong resonance between complexity and sustainability theories, it is necessary (and possible) to formulate a complexity-based framework for modeling sustainability challenges. We use these points of resonance (

We argue that four key considerations are necessary to enable a complexity-based approach towards modeling sustainability and transitions to sustainability (see

The outcome is a high-level framework that can inform the modeling choices that are taken by researchers and decision-makers who are concerned with complex sustainability transitions. By way of example we illustrate how the framework can be used to make key choices that inform the selection of modeling techniques, that is; so that the key, requisite complex systems’ properties are addressed in the integrated modeling effort (see

In this section, we review the key concepts that underpin complexity theory, and the properties of complex systems.

“

In defining complexity theory as the “theory of the multi-agent system”, a very simple step is taken beyond conventional systems theory.

In dynamic systems theory, emergence is an outcome of

Moreover, in systems theory (and in particular, dynamic systems modeling), classical science methods and techniques are deployed to frame the conceptual model of the system, and to understand the “emergent” system behaviors (

Hence we argue that complexity theory is suited to help better understand how and why emergence occurs in integrated human-environment systems and that it has special relevance for the framing and analysis of questions of sustainability.

In complexity theory, both

One definition of emergence simply describes situations where the conceptual or mental model of a system fails, and the behaviors that emerge from the system do not match the projections made by the model in use. That is, in this case, emergence is the “surprise” that couldn’t be predicted. Emergence is then the difference between the predicted ({L1}) behaviors and observed behaviors ({L2}) [

A second perspective defines emergence as a product of the accumulation of self-organization and disorganization within the system

And yet a third perspective on emergence states that emergence is a result of the “different ways of looking” [

Similarly, the notion of “self-organization” also enjoys multiple interpretations. In particular, self organization can firstly be attributed to multi-agent adaptation where the interdependencies, functions, controls and processes of a system undergo changes that either: (1) helps the system retain its overall identity (

As phenomena, both emergence and self-organization are defined in similar terms,

This duality, which is inherent in complexity theory implies that modeling complex systems requires going beyond merely understanding dynamic changes in the system but rather requires us to be able to understand the limits of the frameworks of analysis and methods of observation that are deployed. When this duality is acknowledged, a solely epiphenomenalist view of emergence is unsatisfactory.

Although there are similarities, complexity theory differs significantly from social structuration theory. In social structuration theory [

In complexity theory it is not just social structure that is emergent, but also whole system behaviors that are emergent. That is; the emergence of social structure is not the same as the emergence of systems behavior. This is especially the case when considering complex transitions to sustainability that involve considering the sustainability of SEEPP systems as a whole (

They are similar, however, as in complexity theory, emergence is also defined in terms of a duality,

Stable self-organization of complex systems are also a product of trade-offs that are made at the sub-system level. According to Richardson [

In order to better understand the “adaptive capacity” of a SEEPP system, we need to understand the full span of system configurations (

Lastly, complexity requires engaging with the “the logic of the Included Middle” [

Antifragility is the ability/capacity to harness volatility and uncertainty for gain, and not merely to withstand volatility and uncertainty and remain unchanged [

Complex systems also thwart attempts at defining their systems, agents and sub-systems in terms of hierarchies. Hierarchical taxonomies do not “fit” the behavior of complex systems, which can be fast-changing, non-linear and unpredictable. In complex systems,

In this section, we link complexity theory to emerging theories of sustainability transitions. The core theoretical concepts and complex systems’ properties underlying each theory are briefly summarized in this section, and compared in

Building on the definition tendered by Gunderson [

In resilience theory,

Resilience theory conceptualizes transitions between different social-ecological system regimes using the adaptive cycle (see

Adaptive Cycle and Complexity Theory [

Mapping conceptual foundations of complexity theory and complex systems’ properties to theories of transition.

Theories | Complex System Properties | Resilience Theory | Multi-Level Perspective (MLP) | Decoupling & Socio-Metabolic Flows | Behavioral Change |
---|---|---|---|---|---|

Primary Theoretical Concepts | Emergence | Resilience | Transition | Decoupled Growth | Social Change |

Secondary Theoretical Concepts/Properties | Self-organization;Antifragility Undecidability Heterarchy | Adaptability/Adaptive capacity; Transform-ability | Landscapes, regimes, niches framework | Socio-metabolic flows; Life cycle analysis; Material flows analysis | Values, beliefs, norms, behaviors framework |

Mapping key modeling themes to complex systems’ properties, and foundations of theories of transitions, to sustainability.

Key Modeling Themes | Complex Systems’ Properties | Resilience Theory | Multi-Level Perspective | Decoupling & Socio-Metabolic Flows | Behavioral Change |
---|---|---|---|---|---|

Emergence 1: Internal Dynamics | Uncertainty; |
Uncertainty; |
Uncertainty; |
Uncertainty; |
Uncertainty; |

Emergence 2: Perceptual | Multiple perspectives | Partial beliefs | Multiple levels | Systems perspective | Plural basis for values, beliefs, norms and behaviors |

Stability Conditions | Sub-optimization Principle; |
Basins of Attraction (Limits & Thresholds); |
Regimes = Stable Self-Organization; |
Sustainability = Decoupled Growth; |
Sustainability oriented values, beliefs and norms leading to sustainable individual and collective behaviors |

Transitions | Emergence and, non-linear change; |
Adaptive capacity; |
Regime change due to landscape pressures and niche evolution and innovation | Socio-metabolic flows; |
Sustainability based values and beliefs become normative and drive behavioral change |

Hierarchy | Heterarchy | Panarchy | Multiple levels: micro (niche), meso (regime) and meta (landscape) levels | Systems within systems, |
Agents and networks |

The multi-level perspective on transitions to sustainability is framed in terms of “socio-technical systems” (STS’s), which are in turn comprised of three theoretical “levels”. These levels can be described as follows [

The theory of decoupling proposes that sustainability should be orientated around strategies and actions to decouple growth (

Decoupling theory deploys material flows and life-cycle analysis as a means to understand how system limits and thresholds will evolve over time under different projected future scenarios (see

Behavioral change theories for sustainability emphasize that transitions to sustainability require behavioral change, which in turn requires changes in the

From a complexity theory perspective, behavioral change theories for sustainability essentially describes how agents, and groups and networks of agents influence system or regime level behaviors through

Note that a large number of the primary and secondary theoretical concepts accounted for in

In this conception of complexity, emergence is driven by interactions between sub-systems and agents within the system that can be uncertain and/or non-linear in nature. System dynamics (

This suggests that a

The fact that resilience theory acknowledges the existence of “partial beliefs” that govern how social-ecological systems are understood, implies that there will inevitably be conflicting understandings of social-ecological systems, and especially where decision-making over how to achieve sustainability is concerned. This is compatible with the notion of “perceptual emergence” described earlier in

Hence, the need for facilitated processes that are

Resilience theory essentially combines systems theory with the stable attractor concepts that were discovered and developed in chaos theory [

Here, stability occurs far away from equilibrium conditions, and is maintained through feedback mechanisms in the system that allow the system to correct within the amount of time required in order for the system to retain its “identity”

Moreover, from a complexity theory perspective, stability is achieved through making slight adjustments within the system [

Note that in both resilience theory and the MLP, whole systems (

In decoupling theory, resilience and stability are conceived in terms of decoupled system growth along the life-cycle of the system. That is, sub-optimization is contingent on closing socio-metabolic loops or improving the efficiency of resource use. The need for

In respect of stability conditions, the need for

In both human and environmental systems, agents also deploy strategies of self-organization to mediate exogenous pressures over which they have no control (e.g., species migration). In the case of environmental systems, environmental system thresholds and limits also dictate the extent to which a natural system can absorb pressures, and when limits are breached, the system enters transition and/or “flips” to another state [

In the MLP, regime transition is intimately dependent upon influences that emerge from the landscape and niche levels, which are ultimately direct drivers as well as complex processes that are in operation at different scales and levels. Modeling the sustainability of linked SEEPP systems requires that the notion of “

In respect of the decoupling theory and the MLP, material flows’ analysis and life cycle analyses hence provide the

In behavioral change theories, when the absorption of new values, beliefs and norms is high (

In summary, in respect of transitions, there is a need to understand the: (1)

In resilience theory, hierarchy is conceptualized as a “panarchy” of adaptive cycles. “Panarchy” is composed of many adaptive cycles operating at different scales, with significant cross-scale linkages [

Negotiating transitions to sustainability in multi-scale, multi-level and multi-agent SEEPP systems necessitates engagement across different levels of society. Decoupling theory is

Behavioral change can be non-linear

Where hierarchy is concerned, the need to accommodate heterarchy highlights the need to understand and act upon cross-scale, cross-sector and cross-institutional interdependencies (

From the discussion of modeling themes held in the previous section, we distill and identify a set of requirements for our complexity-based modeling approach. We interpret these as a set of requisite elements (see below), which we position the proposed modeling framework around. We do not prescribe a single particular modeling methodology because mixed methods are more likely to be effective in addressing diverse and complex sustainability challenges. Rather the proposed framework informs how the selection of modeling methods should take place

Probability theory-based statistical methodologies and analyses are required for modeling the complexity of SEEPP systems. This is because non-linear feedbacks and other higher order effects reside mainly in the “line wings” of the probability distribution. When probability distributions are “linearized” (e.g., in maximum likelihood based statistical analysis), the line wings are omitted from analysis. Hence, the conditions under which non-linear and higher-order functions take effect are lost from analysis.

Moreover, models that are formulated using through “hindcasting” (e.g., maximum likelihood based statistics), rely on the notion that past trends remain continuous with future trends and no major “surprises” emerge (

Lastly, probability theory is fundamentally concerned with explanation, as conditionality is essential to assign probability to a particular proposition (

In summary, a probabilistic approach is required to accommodate uncertainty and non-linearity. Moreover, it is also required to be flexible and adaptive, so that it can accommodate learning, as well as a wide variety of possible endogenous and exogenous change effects.

Hierarchies in complex systems may change dynamically as the system evolves; as a result of changes in temporal, spatial changes, changes in scales of aggregation, or due to emergence. In that respect, modeling approaches are required where functions can rise to dominance within a networked hierarchy

Moreover, in respect of integration, both quantitative (e.g., statistics, data) and qualitative information (e.g., expert opinion, case studies and narrative analyses) must be integrated in modeling frameworks (e.g., such as behavioral analyses) [

In respect of integration, we need to understand how cross-scale and cross-sector influences, as well as intra-regime dynamics, critical limits and thresholds, combine with the processes that underlie behavioral change to facilitate transition in environments where there is incomplete knowledge and high levels of uncertainty and change (

In respect of inclusion, there is a need to accommodate multiple and diverse perspectives on issues related to: (1) how SEEPP systems integrate; (2) what actions/strategies for negotiating change should be taken (

Inclusive, participatory-based modeling approaches that accommodate multiple voices and narratives [

This extends agent-based modeling beyond computer-based modeling of rule-based agents within systems to the

In this section, we make explicit what considerations would be necessary for modeling transitions to sustainability, given the framework that we propose. Moreover, by way of example, we illustrate the usefulness of the framework: (1) in performing diagnostics of complex properties that a modeling technique (or a group of them) address (see

We propose a modeling framework that does not prescribe modeling techniques (e.g., scenario-making, soft systems analysis, dynamic systems models, agent-based dynamic systems models, Bayesian networks, agent-based Bayesian networks) but rather provides a framework in which these techniques can be complementarily deployed, or within which specific choices can be made to match particular techniques to particular properties of complex systems.

No one particular modeling technique can account for all the properties of complex systems, so we argue that a collection of equifinal and non-equifinal models are necessary in order to cater for multiple perspectives of the current status of regimes, as well as future projections.

In practical terms, the proposed modeling framework can be further elaborated and detailed as follows; it is required to be:

Probabilistic, in respect of:

Scenario-making and testing that deals with multiple futures, that is; multiple drivers exerted from the landscape level, as well as the multiple potential configurations of regimes [

Probability theory-based analytical frameworks are necessary,

Integrative, that is:

It must integrate between different systems, agents, scales, levels of description and decision-making options/variables.

It must be heterarchical so that it can integrate across scales and levels of description, and allow for the emergence of different configurations of controls, structures and processes as dominant drivers of whole system behavior.

Inclusive, that is:

It must accommodate multi-participant modeling processes, where stakeholders, decision-makers and researchers can jointly interrogate scenarios, interventions, adaptation strategies, narratives, and so forth.

In turn, this requires that

This is essential for decision-making,

It is also essential for generating strategies for self-organization in response to the need for systemic adaptation to exogenous pressures (e.g., global economic and climate change effects) and/or endogenous change effects (such as niche transitions to regime level).

Adaptive, that is:

Modular: “cut and paste” style modeling frameworks (

Evolutionary: near real-time and real-time modeling capabilities are required in order to allow for models to be able to be linked to real-time databases.

Heterachical modeling frameworks are required, so that it accommodates emergence

Moreover, as illustrated in

Each modeling technique that is used can be assessed by evaluating the extent to which it services the two dimensions of

Note that both soft and hard systems considerations must be made when considering whether a particular modeling technique fulfils the requirements of

When considering whether Bayesian networks and systems dynamics models are probabilistic in how they address “emergence and self-organization” (see

Bayesian networks would be considered probabilistic because they directly model whole probability distributions that preserve non-linearity

Systems dynamics models would be considered probabilistic because they help assess how multiple futures may unfold, and specifically account for non-linear interactions (albeit not in a formal probability distribution). So in this case, systems dynamics models are probabilistic in a “soft systems” sense.

Similarly, when considering whether Bayesian networks and system dynamics models are probabilistic in how they address “stability, degeneracy and sub-optimization” (see

Again, Bayesian networks are probabilistic in that they directly model the whole probability distributions to assess stability conditions and trade-offs, and multiple potential stability regimes, while.

Systems dynamics models are probabilistic in the soft systems sense

That is, in both cases, self-organization can be assessed, but only with Bayesian networks are they assessed within a probability theory-based formalism.

Accordingly, both techniques can be used to assess “adaptive capacity”, but unless agent-based formalisms are employed, then agency is indirectly modeled through the process of deciding on model constraints and configuration.

Where Bayesian networks and systems dynamics models differ, for example, is that Bayesian networks are heterarchical (

As illustrated in

Taken together, the collection of modeling techniques that are applied to the particular sustainability challenge that is being addressed can then be accounted for in terms of the span of complex systems’ properties they address. More importantly,

Mapping properties of complex systems, and requirements for modeling transitions to sustainability, to selected modeling techniques.

Requirements for modeling transitions to sustainability | ||||||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

Probabilistic | Integrative | Inclusive | Adaptive | |||||||||||||

X | X | X | X | X | X | X | X | X | X | X | X | X | X | |||

Modeling techniques | ABN | BN | ASD | SD | ABN | BN | ASD | SD | ABN | BN | ASD | SD | ABN | BN | ASD | SD |

Properties of complex systems | ABN | BN | ASD | SD | ABN | BN | ASD | SD | ABN | BN | ASD | SD | ABN | BN | ASD | SD |

Multi-agent | X | X | X | X | X | X | X | X | ||||||||

Emergence & self-organization | X | X | X | X | X | X | X | X | X | X | X | X | X | X | X | X |

Stability, degeneracy and sub-optimization | X | X | X | X | X | X | X | X | X | X | X | X | X | X | X | X |

Adaptive capacity | X | X | X | X | X | X | X | X | X | X | X | X | X | X | X | X |

Undecidability | X | X | X | X | X | X | X | X | ||||||||

Heterarchy | X | X | X | X | X | X | X | X | ||||||||

Non-linearity | X | X | X | X | X | X | X | X | X | X | X | X | X | X | X | X |

Anti-fragility & creative capacity | X | X | X | X | X | X | X | X |

ABN: Agent-Based Bayesian Networks; BN: Bayesian Networks; ASD: Agent-Based Systems Dynamics Models; SD: Systems Dynamics Models. The different colors in

Evaluating different modeling techniques within the proposed modeling framework. (Each color corresponds to a particular modeling technique and indicates what envelope or “footprint” of complex systems’ properties are addressed by it. It helps differentiate between the usefulness of different modeling techniques that were evaluated in

In summary, the proposed modeling framework allows a research group to decide on a set of modeling techniques that fit a particular, context-specific sustainability challenge, by framing them within the broader context of what complex systems’ properties are necessary to address in respect of the specific sustainability challenge being modeled.

As the authors of [

Hyperstructures are “scientifically legitimate explanations of complex systems” [

We hence refer to the collection of models that are used to “understand and explain” complex socio-ecological/social-ecological and/or socio-technical systems (

For example, where global climate change is concerned, no single model is definitive. Hence, a collection of “global climate models” (GCMs) is required to ensure rigor and robustness of projections. As a collection of hyperstructures, where models are underlaid by differing sets of assumptions and techniques, GCMs can be used to cross-verify equifinality, and to obtain deeper understanding of non-equifinal outcomes in different scenarios (

Moreover, the challenge of ensuring shared understanding is paramount. In this respect, Baas and Emmeche state that, “(t)he point is to combine the notion of emergence and hierarchy into the notion of hyperstructure [

Accordingly, the modeling framework we propose

Model formulation and implementation process.

The proposed complexity-based modeling framework is an open framework (

The model formulation and implementation process that we propose is shown in

Evaluate potential modeling techniques in terms of their complex properties envelope (or “footprint”), and select a range of techniques that cover all potential complexities, or a specific set of complexities.

Use specific techniques to formulate models of sub-systems and/or whole systems.

Verify, validate and accredit models where necessary.

Run models, observe system trajectories and determine set of potential system outcomes.

Trace system outcomes back to the complex system properties (and the interdependencies associated with them) that drive possible equifinal and non-equifinal future system outcomes.

In this way, we can enable a complexity-based understanding of transitions to sustainability, that is; through understanding what behaviors manifest as a result of complex system properties, and the interdependencies associated with these properties at a systems level.

Moreover, each phase is supported through powerful visualizations and graphical aids. Through using powerful visualizations of complex systems’ properties and behaviors to understand transition trajectories to sustainability, high levels of “shared understanding” can be engendered amongst researchers of different disciplines, stakeholders, decision-makers and policy-makers. This shared understanding of transitions itself—e.g., through scenarios, forecasts, system constraints, key drivers of system evolution such as functions, controls, processes, and complex systems’ properties and behaviors—can serve as a strong basis for inclusive, transparent and representative learning, participation, negotiation and coordination between different sectors, stakeholders and decision-makers. This is especially important where the negotiation of sub-optimization system profiles, as well as resolving undecidables is concerned.

Furthermore, in respect of the need for a plurifocal approach (see

Where equifinal models are concerned—

Where non-equifinal models are concerned the approach allows for divergent outcomes to be assessed and/or evaluated and cross-compared within a complexity-based framework where complex systems’ properties, and their impacts, are understood.

That is, the modeling framework enables a plurifocal approach (multiple system configurations, multiple system drivers and multiple futures), which is also rigorous in addressing an “envelope” of complex systems’ properties that are essential for understanding and negotiating transitions to sustainability. These “properties”, and how they are framed, also help shift the focus of modeling towards understanding complex properties and the interdependencies associated with them instead of an exclusive focus on “parts” and “mechanisms”.

The proposed modeling framework can be used to assess the extent to which different modeling techniques address complex systems’ properties that are important for understanding complex transitions to sustainability. The framework: (1) elucidates and visualizes which complex systems’ properties are addressed by particular modeling techniques; (2) allows for gaps to be identified; and (3) can allow for adaptively managing models and modeling techniques as real-world transitions unfold.

The authors would like to acknowledge the National Research Foundation (NRF), which provided the funding for a postdoctoral fellowship under which this research was conducted. In addition, the authors would like to acknowledge the support of the School of Public Leadership in the Faculty of Economic and Management Sciences, Stellenbosch University, South Africa. This research is dedicated to the memory of the late Professor Paul Cilliers, whose contribution to the field of complexity remains a major source of inspiration to many students, academics and intellectual across the world.

Camaren Peter is the lead author of this paper. It was conducted under the supervision and guidance of Mark Swilling, who hosted the NRF Fellowship under which Peter conducted the research presented in this paper.

The authors declare that no conflict of interest exists in respect of the submitted manuscript. Although this research builds upon previous research conducted during the course of Ph.D. studies, the research submitted in this paper is substantively new and represents a significant advancement of previous arguments.