ON DECONSTRUCTING COMPLEX ADAPTIVE SYSTEMS

 

doug cocks

(Talk to initial meeting of Complex Adaptive Systems Discussion Group in CSIRO Division of Wildlife and Ecology, Canberra, Mar 17 1999)

 

Introduction

Can I start with a couple of acknowledgements? I have enjoyed and profited from talking about biological and social systems with Mike Austin ever since he and Bruce Cook put together a dynamic simulation of inter-species competition in 1973, complete with oscillations, mode-locking and multiple equilibria. More recently, I have had some stimulating discussions with Franzi Poldy and Paul Walker and, most recently, Brian Walker lent me a set of CS Holling's collected papers which I have found useful in preparing this talk.

The reason I agreed to give this talk is that I have every intention, when I get around to it, of writing a book called something like The Learning Society. Because I believe social change can be usefully viewed in complex system terms, I reckoned that a commitment to talk to you tonight would prod me to start on the reading and thinking needed to write that book. In Future Makers, Future Takers, the book I have just finished, I explore three different strategies for managing Australian society over coming decades---economic growth, conservative development and post-materialism---but, on two grounds, I deliberately rejected the option of exploring a strategy called learning society: people are not ready to think in this way and the available thinking is too underdeveloped anyway.

Let me get straight down to tonight's business. The reason that Division of Wildlife and Ecology should set up a complex adaptive systems (CAS) discussion group is that doing so stands to significantly improve the Division's capacity and willingness to undertake research under the umbrella of a flourishing and, dare I say, fashionable paradigm. It is a way of looking at the world that promises new levels of understanding, perhaps even to the extent of qualitative prediction, of a family of systems that the Division sees as research prioriities. These include the tourist industry, regional land use systems, the national physical economy, social learning systems and the dynamics of particular ecosystems such as rainforest and rangelands. As well as in theoretical and applied ecology, this is a paradigm that has been claimed to be useful in disciplines as diverse as thermodynamics, oceanography, climatology, atmospheric chemistry, economics and evolutionary biology.

Continuing in didactic style, the initial aim of the discussion group should be to bring members to the point where they can freely discuss and interpret particular systems in the language of this paradigm. We have to learn how to talk the talk. A second aim should be to explore how to do research on complex adaptive systems. A third aim should be to share relevant research results, not necessarily our own. A fourth aim should be to explore how to operationally manage complex adaptive systems. Whether, as has been mooted, the group should plan to produce a practical Guide to the management of complex adaptive systems is a question which I think should only be taken up after the group has established iteslf and has a clearer idea of what such a manual might say to whom; and of what other collective projects might be contemplated.

Tonight I propose to make a small contribution to just the first of these aims and give a personal perspective on the vocabulary and scope of the complex adaptive systems paradigm. The reason that this is worth doing is that much of the terminology used in discussing complex adaptive systems is variable, woolly and ambiguous. If we are going to talk to each other about CASs with a minimum of misunderstanding, we need to be aware of the different ways in which the paradigm's vocabulary can be used. There is no CASyspeak dictionary as far as I know but that is not really what I am looking for. Something more along the lines of a CASyspeak equivalent of Fowler's Modern English Usage would be nice.

Before going on, you also have to realise that I have no shame. I admit to being confused by some of the CASyspeak vocabulary, to being plain ignorant of some of its terms and possibly plain wrong on others. This may encourage some of you to share your own puzzles with the group later. Those of you who have found the truth can use question time to demonstrate what a poor ignorant sod I am. I really and truly donít mind, specially if it makes you feel better. Just be a little bit careful though. I am not short of authority figures. Apart from CS Holling's early papers on resilience and stability in ecosystems (Holling 1973) and his recent chapter in the book Rights to nature (Holling and Sanderson 1996) I have picked up ideas recently from Bossel's (1998) Earth at a crossroads: Paths to a sustainable future and Edgar Dunn's (1971) Economic and social development: A process of social learning---a neglected tour de force in my opinion. I have also read a modest amount of the evolutionary economics literature including the 1982 seminal book by Nelson and Winter An evolutionary theory of economic change. On the other hand I retired wounded from a brush with the thermodynamics literature and there may be someone here who can crystallise the messages coming from that source.

Let's start on tonight's task then---deconstructing the phrase complex adaptive system. In pre-post-modernist days I would probably have called this analysing complex adaptive systems, but there's progress for you.

System v environment

The concept of system has arisen as part of humanity's efforts to make sense of the world it finds itself in. By definition, systems are networks of isolable components or entities continuously interacting with each other according to their own behavioural rules or decision rules, eg a component's rules for transforming inputs into outputs or for transferring outputs of materials, energy or information between system components (most processes amount to some form of transformation or transfer). Once the concept is discovered of course, the world turns out to be full of 'systems'!

While components of any properly identified system interact with 'the rest of the world' (which means other systems), this interaction will be muted compared with the intensity of interactions between components within that system. While the act of putting a boundary around some part of the world and calling itís contents a system and everything else environment is ultimately arbitrary, there are those who argue that the biosphere at least is full of 'natural' systems formed by chunky sets of transformational processes that are comparably 'fast ' or 'slow'---ie which take similar times to experience significant change---or that take place at comparable spatial scales.

Studying systems rather than studying individual processes within systems is sometime interpreted as the difference between enlightened or holistic science and unenlightened or reductionist science. In fact this difference is blurry and the two approaches are complements rather than alternatives. Nevertheless, the study of complex adaptive systems is clearly non-reductionist for what that is worth.

Complex v simple

What is the difference between simple and complex systems? As Roger Pech pointed out at the Divisional scientists meeting, no-one is going to admit to studying a simple system. The reason, is probably that 'simple' sounds like a pejorative for 'easily understood'. Who wants to study a system that is easily understood? I will make the suggestion that simple systems are those which we believe can be adequately studied as 'black boxes', that is we study the relationships between inputs to the system and outputs from the system without worrying about what goes on inside the black box. Putting this another way, we study a simple system as a single multi-dimensional transformational process---which is getting very close to what a reductionist does. I am suggesting that complexity is in the eye of the beholder. Complex systems are those whose behaviour surprises us (Holling 1987), or, conversely, whose behaviour is difficult to predict. It is because a system of interest appears difficult to predict that we decide to go inside the black box and try to understand the interacting processes that are producing surprising behaviour. In short a system is complex when I declare it to be complex.

System behaviour

Before tackling the third and most problematic word of our three-word paradigm I want to make a few points about how complex systems behave over time, that is about their dynamic behaviour. Conversely, we can define a system that changes over time as a dynamic system.

The general reason why complex systems behave surprisingly and unpredictably is that they contain non-linear processes and multi-stage feedback loops. Spatial heterogeneity is a third common cause. In a linear process the rates of change of state variables are linear functions of the magnitude of the state variables. A step function, being discontinuous, is a good example of a non-linear process. A feedback loop is an arrangement where a change in some output or some state variable of some system component leads to a change to the inputs to that component. A lavatory cistern that uses a ballcock to slow the rate of inflow as the cistern fills is a good simple example of feedback. A state variable is simply any measure used to describe change in some system component over time.

A lavatory cistern that has no leaks and is full of water is in a state of static equilibrium where equilibrium means 'no tendency to change'. A cistern that has a small leak such that the cistern remains full only because inflow equals outflow is in a state of dynamic equilibrium.

A system that is stable or homeostatic is organised to counter any displacement from equilibrium by returning the system to equilibrium. I see no need to adopt Holling's confusing idea that a stable system is one that returns rapidly to equilibrium. A system that is resilient is organised to be able to counter what are judged to be large displacements from equilibrium. A non-resilient system is only organised to counter small displacements from equilibrium. I will return presently to what happens when a system is displaced beyond its resilience threshold or limit. Any system that has not been displaced beyond its resilience thresholds is in its equilibrium domain or stabilty domain.

A lavatory cistern that is 'disturbed' or 'perturbed' by pulling the chain begins to fill and return to equilibrium. It approaches equilibrium 'smoothly' in the sense that the water level keeps getting higher at a slowly decreasing rate. Suppose though that during filling the water level increased for a while then fell then increased again and then fell back again, although not so much this time, and, in this fashion, going through smaller and smaller falls in water level, eventually reached equilibrium. We would describe this as oscillatory behaviour. While we do not expect a lavatory cistern to oscillate towards equilibrium, this is very characteristic behaviour, following disturbance, of a somewhat more complex system containing multi-stage feedback loops.

A multi-stage feedback loop is an arrangement wherein two or more state variables are coupled in a single closed feedback loop. In real-world systems it is commonly lags in the time it takes one state variable to respond to changes in another that cause overshoot followed by undershoot, ie cause oscillations. The business cycle is commonly attributed to the lag between a change in consumer demand and the production of goods to meet that demand.

Single-equilibrium systems v multiple-equilibria systems

We have now introduced sufficient terminology to make a very important distinction, namely between complex dynamic systems that have a single equilibrium state and stability domain and those that have multiple equilibrium states and stability domains. An equilibrium domain is simply all those system states from which the system is organised to move towards a particular equilibrium state. Let us call these single-equilibrium systems and multiple-equilibria systems.

I will try and create an example of a multiple-equilibria system around the case of a lavatory cistern. Imagine a lavatory cistern with an outlet valve that takes a long time to return to the cutoff position. As long as the outlet valve remains fully open there will be a period after emptying when the system is in a new state of dynamic equilibrium, one where water is rushing in at the same rate as it is rushing out. When the outlet valve finally closes, the system returns to a behavioural domain where it converges on the equilibrium state of being full. Thus our simple lavatory system has two stability domains and is a multiple-equilibria system.

Much 20th century science has been devoted to studying systems that have been identified as single-equilibrium systems. In ecology, for example, successional systems converging on a climax equilibrium are single-equilibrium systems. In economics, the orthodox model of a market economy where the rates of movement of all goods through all markets eventually stabilises is a single-equilibrium system.

However, in a number of disciplines in recent decades, single-equilibrium paradigms have, more and more, been judged to be unrealistic and attempts have increasingly been made to develop multiple-equilibria paradigms. You will all be familiar with state-transition models in ecology for example.

Behaviour of multiple-equilibria systems

What can we say about the temporal behaviour of (complex) multiple-equilibria systems?

The dynamics of multiple-equilibria systems are characterised by change from one equilibrium domain to another around critical threshold values for key state variables. These critical threshold values can be thought of as the boundaries at which the resilience of a system located in a particular equilibrium domain breaks down. Thermodynamicicsts who study systems near resilience boundaries talk of far-from-equilibrium systems.

Multiple-equilibria systems which are crossing domain boundaries can behave in various interesting ways, for instance in the type of trajectory thay take as they approach a new equilibrium. Another example. If a very small difference in the point where a system crosses between domains, perhaps too small to measure, leads fairly rapidly to radically different system behaviour we talk of chaotic behaviour. Chaotic behaviour superficially resembles random behaviour but is actually deterministic, meaning that it is obeying an unambiguous rule which, in principle, promises accurate prediction. Unfortunately it can be difficult to both determine the rule and to measure the system accurately enough to know if the correct values for state variables are being plugged into the rule.

If a boundary crossing leads to a rapid discontinuous change in system behaviour we talk of catastrophic behaviour. Walking towards the rim of the Grand Canyon with your eyes closed will precipitate catastrophic behaviour.

Next question---when can a system be said to no longer exist? Or, in ecological language, have stopped persisting? Is a savanna ecosystem that has lost all its perennial grasses the same system as it was before it lost them? Well, just as the mind creates systems out of something called 'everything' it is the mind that declares a system 'dead'. System death, or failure to persist, is a matter of definition. If I declare that a savanna ecosystem that has lost its perennial grasses is still a savanna ecosystem, then so be it. Just as a system is complex when I say it is complex, it is dead when I say it's dead. And if I am beginning to sound like the Red Queen, you are just imagining it.

In practice, a single-equilibrium system is likely to be regarded as persisting as long as it remains within its resilience thresholds and as having been resurrected as a new ecosystem once it crosses those thresholds. The more resilient a single-equilibrium system then, the more persistent or long-lived it stands to be. A multiple-equilibria system is likely to be regarded as persisting provided it is located in a domain from whence it can return, under apropriate stimulus, to its other domains. Putting this another way, an irreversible crossing into another domain is likely to be characterised as a failure to persist.

Within my limited knowledge, I could discuss further aspects of the behaviour and structure of complex single-equilibrium and multiple-equilibria systems. I could discuss the advantages of hierarchical organisation and types of connectivity and mode-locking and strange attractors and so on, but time is short and I still have not got to complex adaptive systems. So, let me do that right now.

Complex deterministic systems

Complex single-equilibrium systems and multiple-equilibria systems are examples of a class of systems called machine systems or deterministic systems. This means that such systems behave over time as though their components are under the control of one or more sets of unchanging behaviour rules or if-then decision rules---something like a computer program that tells system components how to behave, ie how to respond to signals from the environment or from other system components. In the case of a multiple-equilibria system it is useful to think of the system switching from one set of unchanging behaviour rules to another set of unchanging behaviour rules as the system crosses from one domain to another, ie there is a set of unchanging behaviour rules specific to each domain. When we do research on complex deterministic systems we are basically hoping to identify the system's behavioural rules because, if we were to be successful, we would then be able to predict system behavior subject to given signals from the system's environment.

Complex adaptive systems

Complex deterministic systems can be contrasted with complex adaptive systems. Other terms in the literature that may or may not be exactly equivalent to complex adaptive systems are complex stochastic systems, complex learning systems and complex evolving systems. It might also be useful to coin the term complex non-adaptive systems as a synonym for complex deterministic systems.

The essential difference between these two is that the behaviour rules or 'programs' controlling the temporal behaviour of a complex adaptive system's components are not unchanging. When components of complex systems actively change their behaviour rules or have them changed passively we describe this as adaptive behaviour.

Note that in that last sentence I am distinguishing two types of adaptive behaviour. The first is endogenous adaptive behaviour where a system essentially re-programs itself. The second is exogenous adaptive behaviour where an outside agent takes one program out of the system and puts another in, so to speak. The obvious name for systems exhibiting endogenous adaptive behaviour is creative or active learning systems but I do not have a name for systems exhibiting exogenous adaptive behaviour. The Poldy-Foran ASFF model is a good example of exogenous adaptive behaviour because the modeller imposes different behavioural strategies on the system till one that reaches some target is identified. Perhaps, in-house, we could call them Poldy-Foran systems! So, summing up, complex adaptive systems exhibit adaptive behaviour in the form of active learning or passive re-programming.

It is widely accepted I think that the only systems that can exhibit adaptive behaviour are systems containing biological organisms as components, ie bio-systems. A deterministic system may be a bio-system but an adaptive system must be a bio-system.

Beyond deconstruction

This completes my quick and dirty deconstruction or analysis of the term complex adaptive system. This tree-figure (Fig 1 Types of systems) traverses a number of the distinctions I have made. It opens the way to a variety of interesting questions and concfepts which I do not have time to pursue tonight:

Examples of interesting ideas

Cultural v genetic adaptation (sociogenesis v phylogenesis)

Innovation v mutation

Adaptation v mal-adaptation

Adaptation v adaptability

Examples of interesting questions

Question: Are the separate domains of a complex non-adaptive system appropriately called equilibrium domains or stability domanis or something else?

Question: Is fragile the opposite of resilient? Why not unstable?

Question: Is a self-organising system the same as a homeostatic system? hierarchical system?

Question: Is there a clear distinction between exogenous and endogenous adaptive systems?

Question: Should we be recognising a class of complex deterministic multi-domain systems that are not equilibrium-seeking?

A challenge to finish with

Let me finish with a question which is also a challenge. While it is at least possible in principle to build predictive models of complex deterministic systems, I do not believe it is possible to build predictive models of the future behaviour of real-world complex adaptive systems. It may however be possible to build simulation models which mimic the past behaviour of some such systems. Am I right?

References

Bossel H, 1998, Earth at a crossroads: Paths to a sustainable future, Cambridge University Press, Cambridge.

Dunn ES, 1971 Economic and social development: A process of social learning, Johns Hopkins, Baltimore.

Holling CS and Sanderson S,1996, Dynamics of (Dis)harmony in Ecological and Social Systems, in Hanna S and Maler K-G (eds) Rights to nature: Ecological, Economic, Cultural and Political Principles of Institution for the Environment, Island Press, Washington.

Holling CS, 1973, Resilience and stability of ecological systems, Annual Review of Ecology and Systematics, Vol 4, 1-23.

Holling CS, 1987, Simplifying the comples: The paradigms of ecological structure and function, European J. Operations Research, 30, 139-46

Nelson RR and Winter SG, 1982, An evolutionary theory of economic change. Belknap, Cambridge, Mass.