Part I Literature Review and Conceptual Framework
3.4 Dynamic System Framework
As already explained, dynamic models focus more on the processes and behaviours that cause change within a system, than on the structural components that make up a system. Overall, by considering interrelationships across time, dynamic models enable “the derivation of theorems concerning the values of variables, or changes in those values” (Kuenne, 1963, p.14). A dynamic model is therefore suited to investigating questions such as, “What are the implications over the next 50 years of substituting fossil fuels for biofuels or tax regimes aimed at reducing carbon emissions?”, or more generally, “What are the potential impacts on the biogeochemical cycles associated with, say, a continuation of current rates of economic growth?”
Dynamic modellers such as Forrester (1971a, 1971b), Ruth and Hannon (1997), Hannon
and Ruth (1994, 2001), Deaton and Winebrake (2000), and Sterman (2000) have outlined a number of reasons why dynamic modelling is of value – all of which are relevant to the core aim of furthering sustainability in relation to the biogeochemical cycles:
x Understanding the complexity of a system without being overwhelmed. Many systems
contain balancing and/or reinforcing feedback loops,41 time lags, interdependencies and
non-linear behaviours. Such complexity quickly overwhelms the unaided human mind, reducing the ability to envisage how a system might behave under change. Developing a dynamic model helps overcome this issue;
x Generation of new knowledge. Dynamic models enable exploration and experimentation through creation of simple ‘what if’ questions, in turn facilitating better understanding of the system including the identification of enablers and inhibitors as well as the behaviour of key processes and causal mechanisms;
x Discovery of patterns in details without losing the big picture. A dynamic model is as much about viewing the system as a whole, as it is about revealing underlying key processes or variables which may result in specific outcomes; and
x Assessment of future options. Dynamic models are primarily about understanding, but a good model may facilitate forecasting by revealing gaps in our knowledge of the system, as well as the potential result of future actions.
41 Balancing (i.e. negative) feedback loops counteract an initial change, while reinforcing (i.e. positive)
Based on these attributes, model building is an indispensable tool for both helping build comprehension and assisting in the selection of alternative actions. Any given model is, however, unlikely to address these two broad goals with equal aptitude. While a relatively broad and simple model is most useful in helping generate a general understanding of system behaviour across a variety of stakeholders, this may be inadequate for selecting among specific policy options where a relatively high degree of confidence in outcomes is required. In these regards, Costanza and Ruth (1998) provide a helpful overview of the modelling process, suggesting that it begins with the simplified, high generality models most suited to initial scoping of problems and consensus building. Once the research agenda is sufficiently defined, the modelling moves towards a more realistic, research stage, typically involving the collection of large amounts of historical data for calibration, testing and uncertainty analysis. Finally, high precision management models are developed, with the aim of considering specific
scenarios and management options.42
3.4.1 A Brief Overview of Dynamic Modelling Approaches
This thesis adopts System Dynamics as the modelling approach for investigating dynamics of the coupled economic and biogeochemical cycling systems. It is worth noting, however, that other dynamic modelling approaches exist. This section provides a brief overview of System Dynamics and alternative modelling approaches.
Statistical Models
Statistical models use independent variables to describe dependent relationships, obtaining an
indication of the relative influence of each of the variables (Bannock et al., 1992).
Econometrics, including regression analysis, may also be used to predict short-term future trends. Although advances in statistical models now allow for a great variety of model specifications, these models tend to require rich data sets and elaborate specification if they are to deal with multiple system feedbacks and spatial or temporal lags (Sterman, 1991;
42 Much earlier Meadows (1980) also suggested a three-stage approach to model building for social
decision making. At the first stage, where a problem may have never been studied or past studies are incomplete, models are targeted towards general understanding. Although quantitative precision is probably unattainable at this stage, the very process of building such models improves understanding via systematically asking questions and defining new conceptions. At the next stage, models are targeted more towards policy formulation. Broad policy choices are evaluated and compared to identify possible trade-offs or synergies. Then, during the final stage, with a basic policy direction already selected, the concern is generally with addressing a variety of questions concerned with detailed implementation of policies. At this stage, models tend to be highly detailed and accurate and involve the organisation and processing of many pieces of information.
Costanza and Ruth, 1998). Moreover, these models are typically based on observed historical trends and thus may not adequately capture the influence of alternative management schemes, emergent properties, limiting factors or thresholds if these are not represented by historic behaviour.
Optimisation/ Mathematical Programming Models
Optimisation models, including CGE models, may also be applied to study temporal dynamics. Optimisation models tend to breakdown a problem into three conceptual components: an objective to maximise or minimise, the activities or options available to achieve this objective, and any constraints or bounds that must abided (Meadows and Robinson, 2007). Rarely do complex systems, such as an economy or the biogeochemical cycles, however, maximise or minimise a single objective. Moreover, even though multi-objective optimisation may be constructed, these often become intractable in the modelling of complex systems.
Dynamical Systems
Dynamical Systems modelling shares a number of characteristics with Systems Dynamics. In particular, both modelling approaches are well suited to describing the evolution of systems
with time-dependent states via mathematical formalism of causal relationships.43 Recognising
that time is continuous, Dynamical Systems modelling relies predominantly on ordinary
differential equations to simulate such system states over time. Given that many different disciples are interested in the study of time-dependent systems, Dynamical Systems modelling has been employed in a great variety of applications, including applications from biology, chemistry, physics, finance, and industrial applied mathematics. Note, however, that solving mathematical problems comprised of numerous differential equations is often extremely difficult. Hence graphical and numerical solutions, applied either by hand or by computers, are often used to approximate solutions. Even with such techniques available, mathematical complexity remains a core challenge to the more widespread application of the approach for analysis of, and learning about, complex systems.
System Dynamics Models
System Dynamics is often described as a computer-aided modelling approach to policy analysis and design (e.g. Richardson, 2011). It is worth noting, however, that models constructed
43Relationships are connections that are postulated to exist between different elements of a system. In
turn, elements are generally visible or measurable system objects or flows. A relationship is deemed to
be causal if it incorporates some hypothesis about the mechanisms whereby one element directly
within System Dynamics programming languages are also frequently employed in problems that are not of a strict policy-orientation, for example design and engineering applications. Jay Forrester, at the Massachusetts Institute of Technology, developed System Dynamics in the
mid-1950s.44 At that time, Forrester was interested in understanding the success and failure of
corporations. Using General Electric as a case study, he showed, using hand drawn simulations, how employment issues at General Electric were the result of internal structures and not business cycles. In the late 1950s, Forrester and his team of graduate students developed the DYNAMO System Dynamics computer language. This was followed by
publication of Industrial Dynamics (1961), Urban Dynamics (1969), and World Dynamics
(1971). In 1972, following on from the notoriety received by World Dynamics, the Club of
Rome initiated the famous Limits to Growth (Meadows et al., 1972) study.
The Systems Dynamics approach relies specifically on finite differential equations to approximate solutions for differential equations along a path of successive ‘time-steps’. Although this results in some loss of information and precision, it significantly widens the scope of modelling exercises, enabling very complex systems to be represented within a computer simulation model, even by practitioners with no advanced mathematical training. Two popular graphical programming languages are now available for facilitating the construction of System Dynamics models, STELLA® and Vensim®. Both contain visual display and input and output features that enable users to easily grasp model structures, interactively run models and review results. As noted by Costanza and Ruth (1998), given the relative ease of use, these programmes constitute powerful tools for enquiry into the nature and dynamics of complex systems. A number of well-known practitioners advocate that System Dynamics models should be relatively simple and aggregate, and used primarily for the general understanding or policy-design stages of decision-making (see, for example, Meadows and Robinson (2007, p.38)). Nevertheless, array capabilities within the programming languages now allow for the modelling of systems that are highly disaggregate, for example, consisting of many different actors or spatial locations.
44 Forrester was also a pioneer of digital computing. During the 1940s he led the Whirlwind project, a
Cold War vacuum tube computer, which in a later form was the basis for the United States Air Force air defence system until the mid-1970s. During this time, he also created the ‘Multi-coordinate Digital Information Storage Device’ a key predecessor of today’s computer Random Access Memory (RAM). He is currently Professor Emeritus of the Sloan School of Management at the Massachusetts Institute of Technology.
3.4.2 Core Elements of the System Dynamics Approach
Aspects of the System Dynamics approach are presented and employed in the development of the DGES (Chapter 7), DGBCM (Chapter 8), and Ecocycle (Chapter 9) models. As an introduction, however, Table 3.1 provides a brief overview of some of the core concepts and
techniques of this approach.45 Like any model of a system, a System Dynamics model, is a
simplification of the system under consideration – in the end, the only full representation of a system is itself.
Table 3.1 Principal Concepts and Techniques of System Dynamics
Concept/technique Description
Causal loop modelling
A type of diagram used to represent the general pattern of elements and interrelationships (i.e. structure) of a system. Causal associations between two elements, or variables, are depicted by arrows. The variable at the tail of the arrow causes change to the variable at the head of the arrow. Causal loop modelling is often undertaken prior to the construction of a simulation to help clarify core components to include within the simulation model.
Feedback loops Systems are comprised of closed chains of causal relationships. This means
that the effects of a cause (e.g. a change in one variable) can be traced through a set of related variables back the the original cause. In general feedback loops are positive (reinforcing) or negative (counteracting or self- regulating).
Stocks Stocks are quantities within a simulation model that accumulate over time.
A stock therefore describes the condition of a system, and would continue to exist even if all relevant inflows and outflows to that stock ceased to exist.
Flows A flow is the change to a stock occurring over a defined period of time. For
example the number of births adding to a population stock during one year.
Converters Converters are auxiliary variables employed in functions that help to define
either other converters or flows.
45 Although many of these concepts are employed in other types of modelling, they deserve special