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A Conceptual Framework for Modelling
the Dynamics of Environmental Systems
Dr I Moffatt
University of Stirling
ABSTRACT
A conceptual framework for modelling the dynamics of environmental
systems is presented, It is argued that apparently stable systems can
evolve via bifurcation when critical thresholds are exceeded. When a
system is forced further away from equilibrium dissipative structures
emerge. These dissipative structures are characterized by stochastic,
non-linear feedback mechanisms which have the capacity to transform an
apparently stable environmental system into a relatively more complex
one which evolves. Some examples of these structures are simulated
using system dynamics and the implications for further research are
discussed.
INTRODUCTION
One of the major difficulties in building dynamic models of
environmental systems resides in resolving the paradox that these
systems are both stable yet evolve. Generally, model builders have
concentrated their efforts on understanding the dynamics of stable
systems. Whilst this research is well established it is clear that by
focussing attention on stable systems model builders have, by and large,
ignored the evolution of such apparently stable systems. This paper
outlines a conceptual framework which can simultaneously accommodate
both the dynamics of stable and developing environmental systems.
In the following section a brief definition and discussion of
environmental systems is offered. It will be argued that the study of
environmental systems transcends conventional disciplinary boundaries
and, through necessity, has to embrace both hard and soft systems
simultaneously, This discussion is then followed, in section three, by
presenting a conceptual framework for modelling the dynamics of
environmental systems. By drawing upon the extending the work of the
Brussels school (Prigogine and Stengers 1982) it is argued that an
apparently stable system can pass through a chaotic mode of behaviour
which, if driven further from a previous position of equilibrium, can
then undergo a radical transformation which has the potential for a new
qualitatively different system to emerge. These dissipative structures
are characterized by stochastic, non-linear feedback mechanisms and are
present, but latent, in many environmental systems. The fourth section
uses system dynamics and DYNAMO to simulate the various modes of
behaviour described in the conceptual framework for modelling
environmental systems, Finally, some of the implications of this
conceptual framework for further research into the dynamics of
environmental systems are discussed.
ENVIRONMENTAL SYSTEMS ARE HARD AND SOFT
According to Bennett and Chorley an environmental system can be defined
very broadly as an interdisciplinary study embracing ‘physical,
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biological, man-made, social and economic reality' (Bennett and Chorley
1978, p.21). Obviously, such a broad definition covers a whole host of
disciplines and it is, perhaps, useful to consider environmental systems
as the intersection of three sets namely the ecological; the economic
and socio-political systems, The study of ecological systems is
primarily concerned with the explicit elucidation of the structure and
function of a plant or animal community and its natural habitat. The
habitat can consist of both organic and inorganic material. Several
texts have shown that the structure and functioning of ecological
systems can be understood by use of computer simulation (Hall and Day
1977, Jeffers 1978). Whilst ecological studies are one important facet
of environmental science it would be misleading to suggest that all
environmental scientists are concerned solely with ecological
problems. Increasingly, societies economic activities are having a
major impact upon ecological systems. The misuse of ecological systems
for short term economic gain can have a major, if not catastrophic,
impact on the life support systems of this planet. If economic and
ecological systems are not integrated in a holistic manner then serious
repercussions may result from our short sighted negligence (Wilson and
Kirkby 1980).
The study of the inter-relationships between economic and ecological
systems do not, however, take place in a socio-political vacuum,
Increasingly, decisions made by socio-political institutions can have a
major impact on the environment. It is, therefore, essential that
environmental scientists consider the way in which material aspects of
our culture support a particular set of political ideas as opposed to
more ecologically sensible political philosophies and practices,
Pepper, for example, notes that 'the British Conservative Government in
1980-1 put so much research money into nuclear power rather than 'soft'
energy sources perhaps because of the power of the pro-nuclear lobby and
also because it wanted to break the political power of the coal-miners'
(Pepper 1984), In an attempt to explain the way in which vested
interests manipulate environmental decision making environmental
scientists need to consider critically the ethical principles and
political practices of these groups.
Clearly, an environmental system is a complex phenomena and it cannot be
studied in its entireity by adopting a purely ecological or economic or
socio-political perspective. To try and explain the dynamics of
environmental systems from any one or two perspectives is myopic. Yet,
to try and develop a conceptual framework which can accommodate all
three sets in an integrated, holistic dynamic framework is exceedingly
difficult. One of the reasons for this difficulty resides in the fact
that environmental systems are simultaneously hard and soft systems.
In a recent reappraisal of systems analysis Checkland has argued that
hard systems are a special case of the so-called soft-systems
methodology (Checkland 1984), A hard system can be characterized as
the search for an efficient means of reaching a clearly defined
objective or goal, once the goal or objective is clearly defined, then
systematic appraisal of alternative solutions to the problem, helped by
various techniques, enables the problem to be solved. A classic
example of this approach was the successful attempt by the American
nation to land a man on the moon. A soft systems approach provides a
way of tackling ill-structured problems without imposing on them the
means~end dichotomy which is characteristic of the hard systems
approach,
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In many cases the use of verbal models helps to clarify the
major interactions in a system without degenerating into arid polemic.
Alternatively, some simulation modelling of soft systems can ‘degenerate
into science fiction, in which fragmentary data are pushed far beyond
any limit of credibility’ (Coyle 1984, pp.599).
C: Customers
A: Actors
T: Transformation
W: Worldview
O: Owners
E: Ethics
Figure 1,
Paradigm 1
Hard systems
thinking
Decision-makers
who command
real world systems
External analysts
and engineers
Information into
advice to
decision-makers
Real world
problem is
systemic.
Methodology is
systematic
Optimization
is possible
Decision-makers/
clients
Power structures
and value systems
of the decision-
maker clients
Paradigm 2,
Soft systems
thinking
Participants who
debate the
differences between
the models and the
expression of the
problem situation
Those who choose
to take part:
analysts and/or
problem owners
Information into
specific learning
for the “actors”
Real world
problem is
problematical
Methodology is
systemic
Learning is
possible
“Actors” as defined
above, or the
analyst
As little as
possible compatible
with achieving
change in the
- problem situation
Hard and Soft Systems (After Checkland 1984)
The distinction between hard and soft systems is clearly illustrated
below (see Figure 1).
Despite the differences between these two
approaches to using a systems approach to either optimize or to learn
about a specific system of interest several researchers have failed to
grasp the significance of the soft methodology (Morgan 1981).
Often
they have attempted to apply the hard systems approach to problems which
are soft,
One of the results of this major methodological mistake has
been to ignore the interaction of clashing value systems found in soft
systems by assuming that the system model builders implicit values are
the only ones which are important.
Witness, for example, the heated
exchange over the value systems embedded in the World and Urban Dynamic
models (Forrester 1969, 1971;
Moffatt 1983),
If hard and soft systems
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are to be integrated in a coherent way then this problem of
incorporating dialectical changes within our models must be tackled.
Fortunately, the conceptual framework outlined in this paper is capable
of achieving this synthesis of hard and soft systems.
A CONCEPTUAL FRAMEWORK
In order to make progress in the dynamic modelling of environmental
systems it is essential that a framework is developed which can
incorporate both the hard and soft elements of these complex systems.
Furthermore, it is fundamentally important that the conceptual framework
can resolve the paradox that environmental systems are both stable yet
evolve. Generally, model builders have concentrated their efforts on
understanding the dynamics of stable systems. Whilst this research is
well established it is clear that by focussing attention on stable
systems model builders have, by and large, ignored the evolution of such
apparently stable systems, This section outlines a conceptual
framework which can simultaneously accommodate both the dynamics of
stable and developing hard and soft environmental systems.
Any dynamic model may be defined as a simplication of a real world
system which changes through time. This apparently straightforward
definition of dynamic models hides a bewildering richness of dynamic
behaviour (May 1976). This dynamic behaviour can be described as
synchronic or diachronic change (Huckfeldt, Kohfeld and Likens, 1982).
Synchronic change describes the way in which the elements of a system
alter through space-time within a fixed structure. Diachronic change,
however, describes the processes whereby the structure of a system is
transformed into another form. Most dynamic models of environmental
systems have examined synchronic structures but it is becoming
increasingly obvious that diachronic change must be examined if we are
to understand the complexities of the dynamics of environmental systems.
__- DYNAMIC MOP
SYNCHRONIC a DIACHRONIC
locally stable
or new system
metastable
i: i iv
unstable dissipative
structure
|
| 7
|____,t bifurcation chaos
Figure 2. Various modes of behaviour in dynamic models,
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In figure 2 a conceptual framework which attempts to integrate both
synchronic and diachronic structures is illustrated. Beginning with
systems which are locally stable, emphasis is placed on those systems
which are in dynamic equilibrium (i.e. whose macroscopic state variables
do not fluctuate through time although the microscopic elements may, in
fact, change). Included in this class of local stability is the
concept of stable cyclical oscillations in the behaviour of a system.
As an open environmental system is driven further away from locally
stable locations by either exogenous or endogenous change then unstable
behaviour is exhibited. An obvious manifestation of such change is a
demographic system collapsing to extinction or increasing exponentially.
Apart from the obvious forms of instability a more interesting case is
that of bifurcation. Several workers have noted that primary
bifurcation or the hystersis phenomenon can be exhibited in a variety of
environmental, biological and chemical systems (Oldfield 1983). By
forcing a system beyond a threshold of stability the system can achieve
anew locally stable state. Alternatively, these primary bifurcations
can be developed so that the trajectory of the system changes in a more
complex manner. As the system moves away from one position of dynamic
equilibrium further bifurcations are possible until chaotic behaviour is
observed even in systems with deterministic equations (May 1970).
Chaotic behaviour is observed in many dynamic system models which have
one, or more, feedback loops. These non-equilibrium systems,
especially when interacting with the outside world may also form the
genetic phase for the formation of new structures. These new
structures are termed self-organizing or dissipative structures. They
may appear locally stable but are, as Prigogine and Stengers write
‘essentially a reflection of the global situation of non-equilibrium
(processes) producing them’ (Nicholis and Prigogine 1977). Unlike
bifurcation and chaotic behaviour in dynamic models of environmental
systems these dissipative structures are generated by a mix of
deterministic and stochastic elements. It is important to realise that
such stochastic perturbations may be very small in any environmental
system but can alter fundamentally the entire system of interest.
Furthermore, these structures are created and maintained in open systems
by a continuous influx of energy or matter (Peacocke 1983). In this
way the dynamics of environmental systems can exhibit diachronic as well
as synchronic change.
SOME EXAMPLES
Numerous examples could be given to illustrate the use of this new
conceptual approach to modelling the dynamics of environmental
systems. Three examples (population growth using a logistic equation;
a dynamic version of Christaller's theory of central places; and the
environmental management implications of dynamic models) are described
briefly below. In each example, there is a wide range of dynamic
behaviour implicit in these relatively simple models.
When a population is composed of single generations with no overlap
between successive generations then the population growth occurs in
discrete steps. In such circumstances it is convenient to model these
systems of interest as difference equations (May 1974), The logistic
equation (S-shaped curve) is probably the simplest form of non-linear
equation used in ecological studies. There are various ways of writing
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the logistic equations but a discrete version could be written as follows
Ap rn (i = Bo (equation 1)
where p is the number of people, L is the upper limit or carrying
capacity on this number and r(1-P/L) is the rate at which new people
are recruited into the system. This difference equation can be
modelled using system dynamics to produce a variety of dynamic
behaviour. When 0< r<_1 then the system coverges monotonically
towards L. Oscillating convergence towards L is observed when l< r<
2. If, however, the condition 2<_r< 2.57 a series of stable limit
cycles of period 2" can develop. When r > 2.57 then the logistic
equation model enters into chaotic behaviour. As the name implies,
chaotic behaviour is unpredictable. Any value of r which falls into
this regime can generate trajectories that may settle into a stable
limit cycle of any integral period or may never settle into a finite
cycle (Kohfeld and Salert 1972,) in Figure 3.
re -B Let0.pie-S 1 fe 2°56,L*10,p 55-5
i
stable limit cycle
dynamic equilibrium ~
=
TIME TIME
re 2-t.L=10.po=°5 q f= 3.L= 10.poe 01
stable limit cycle chaos
& poverty - \ Hy
ra \/
| | i
| i
i |
|
TIME TIME
Figure 3
Various modes of behaviour in a simple difference equation — see text
for explanation
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As is well known, Christaller's (1933) theory of central places showed
three different hexagonal lattices depending on the marketing, transport
or administrative principles (k = 3, 4 and 7 respectively). Each of
these sets of hexagonal patterns appear to be time-less, optimized
spatial configurations. It was, however, clear to Christaller that
these static patterns represented ‘only a snapshot of the existing world
in continuous change; the stationary state is only fiction whereas
motion is reality' (Christaller 1933, 84), In the past decade several
researchers have attempted to provide a dynamic version of Christaller's
pioneering work (Moffatt 1974; White 1977, 1979).
In the 1970s a dynamic model of interacting urban centres, combining
both stochastic and deterministic elements, was developed in an attempt
to describe the evolution of a central place system (Allen and Sanglier
1978, 1979a, 1979b, 1981). Using a modified logistic equation in which
the natural carrying capacity L (equation 1) of a particular place can
be increased by its potential employment capacity as used in the
familiar Lowry model (Lowry 1964). Unlike the previous example,
however, each population centre is in competition with other centres of
activity located elsewhere. Furthermore, each central location is able
to act as a focus of production and consumption for the inhabitants of
the central place and those in the immediate hinterland. By
incorporating non-linearities and stochastic processes into this dynamic
model a qualitatively more realistic evolution of central place patterns
has been produced. Preliminary empirical work indicates that this
model is sufficient to describe correctly the evolution of tertiary
employment and residential structure in the Bastogne region of Belgium,
1947-70 (Allan et al 1981).
In the previous two examples it is clear that even in the case of some
simple, non-linear dynamic models there is a very sharp transition from
stable to unstable or chaotic behaviour as a parameter exceeds a
eritical threshold value. Within the range of a critical threshold
value it is possible to optimize some aspect of the behaviour of the
modelled systen. In this way it may be possible to develop simple
models which may be used for environmental management and planning
(Moffatt 1984). It is, however, very clear that if simple dynamic
models are to be used in environmental management and planning then
there is an urgent need to develop rigorous methods to determine
sensitive parameters before policies emanating from these models are put
into practice.
Apart from the technical problems involved in using dynamic models of
environmental systems for management or planning purposes there are also
deeper ethical considerations to be taken into account. O'Riordan
(O'Riordan 1981) notes that the environmental ethic exists to change
people's outlook on the world, their values and behaviour and not just
to shift public policies and redirect particular decisions. One way of
addressing ethical issues involved in environmental management and
planning is to use a simple dynamic model of structural conflict in the
environment. In the case of advanced industrial societies three
different attitudes towards the environment can be discerned. The
conservative approach suggests that the market mechanism will solve
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environmental problems when they arise. The liberals, however, suggest
that such problems can be eradicated only if further funding is given to
environmental management. Finally, the radicals argue that a
fundamental shift in attitudes to the environment is required to resolve
the problems. These three different attitudes have been built into a
dynamic model which incorporates a dissipative structure. This
dissipative structure is triggered by stochastic peturbations in a
non-linear feedback loop. The result of triggering this dissipative
structure can reveal the ways in which conflicting values can lead to
different forms of social evolution which are either antagonistic to, or
in harmony with, the environment.
CONCLUSION
This paper has described the nature of environmental systems as the
interaction of ecological, economic and socio-political sets. One of
the problems in studying environmental systems resides in the fact that
they are both hard and soft. Furthermore, in attempting to model the
dynamics of these systems it is clear that both synchronic and
diachronic change must be considered. The conceptual framework
outlined in the paper incorporates hard and soft systems as well as
synchronic and diachronic change.
By drawing upon the notion of dissipative structures it is possible to
portray the dynamics of environmental systems as cyclic phenomena moving
from stability, into instability, bifurcations, chaos and into
dissipative structures. These latter structures can radically
transform the behaviour and structure of the entire system of
interest. These revolutionary changes are embedded in complex systems
and are triggered by low probability stochastic changes which cause
fundamental shifts in the structure and function of hitherto apparently
stable systems.
Whilst this conceptual framework for modelling the dynamics of
environmental systems is tentative it is clear that several
environmental systems do in fact exhibit these modes of behaviour.
Several examples of the dynamics of environmental systems have been
discussed using the method of system dynamics simulation. These
examples include stable but oscillating predator-prey relationships;
the chaotic behaviour of urban dynamics and dissipative structures
illustrating the emergence of a more ecologically sane society as a
result-of dialectical conflict in a model of an environmental system.
Obviously, much more detailed empirical and theoretical research needs
to be undertaken in order to comprehend the dynamics of environmental
systems. Nevertheless, the conceptual framework described above offers
environmental scientists a new and useful way of understanding and
changing environmental systems as they unfold around us.
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