On (holistic) modelling

A funny thing happened to me on my way to this forum. I met a bloke called John Farrands. It was in 1982, a long time ago really, but then I seem to have been coming to this meeting for a long time. Sadly, John Farrands died last year. During his illustrious career, he was the Chief Defence Scientist and later, the Secretary of the Department of Science and Technology. And in retirement, he became the Chairman of the Council of the Australian Institute of Marine Science, which was how I met him.

AIMS, like marine labs around the world, contained a bunch of marine biologists and a bunch of oceanographers, the one busily revealing the secret lives of corals and fish, the other busily uncovering the secrets of the ocean's currents, and both held together by a mutual love of the sea and the joys of field work. The oceanographers revelled in things they called models - huge mathematical structures built in homage to a god called Navier-Stokes - while the marine biologists enjoyed creating things they called theories - huge narrative structures built in homage to a god called Darwin. So it was basically a happy place, because each went his own way and ignored the other.

Unhappily, because science like art is not about increasing the sum of human happiness, John Farrands and I both stumbled independently on the problems this convenient division of labour had created, he from the outside, I from the inside. My revelation was that the narratives that my co-religionists were busily writing were often no more than biological 'Just So' stories (Gould and Lewontin 1979): they described in excruciating detail just how this coral or that fish got this shape or that colour, and thus helped to explain why the diversity of the coral reef was 'just so'. Diversity, of course, was the mantra in marine biology then, as it is in conservation now. It is worth noting in passing how both completely ignore Hutchinson's (1959) warning that explaining the how and what of diversity is far less important than explaining the why. Stephen Jay Gould (Gould 1989) might go even further and say that the how is of no importance whatsoever, and the what of only passing interest.

Along with many other theoretically inclined biologists, I thought that all this natural history, even when leavened with a dose of evolutionary theory, was basically a waste of time until we could describe what we saw in the context of what was possible - the contingent in the context of the universal. This led us to modelling in the sense of trying to build structures that could describe reality inside an envelope of possible realities (Casti 1989).

And this, of course, led me into direct conflict with the oceanographers. They, after all, were the keepers of the models in my lab; and what was I, an upstart biologist, doing not only treading on their turf, but starting to appropriate some of their jargon? Now it was true that I was appropriating some of their language and ideas, but not enough to become an honorary oceanographer - not enough maths, or at least not of the right sort. Instead I was fooling around with the then-newfangled idea of cellular automata (Bradbury, van der Laan, and Macdonald 1990) and the agent-based modelling being pioneered by my friends Paulien Hogeweg and Ben Hesper in Utrecht (Hogeweg and Hesper 1984). I was also using a funny computer language called Smalltalk based on a then-alien concept called the object oriented programming paradigm, instead of the imperative language Fortran. Why, at that time, most oceanographers did not even know that there was another language besides Fortran, let alone that languages came in flavours. They would have fainted if confronted with Lisp.

So there I was confronting my biological colleagues with all sorts of arguments about how to do biology which required of them, if they accepted them, to stop doing what they were comfortable with and start doing something new. This is never a recipe for winning friends and influencing people. And I was being confronted by the oceanographers who were thoroughly confused by this modeller manqué, who spoke like them, but was not of them.

Into this uproar walked our new Chairman, John Farrands. And we quickly found out that he was a hands-on sort of bloke, intensely interested in science and keen to take part in any intellectual debate. His first action was to ask me to put up or shut up, to explain just what I was on about. Unfortunately my reply only confused things more. I wrote a fairly philosophical piece about the place of modelling in science (Bradbury 1988). I should have known better - we all know how a roomful of Doctors of Philosophy, perhaps even this room, go quiet and look at their feet when the word philosophy is mentioned.

Anyway, I classified models three ways: in terms of function, structure and epistemology to produce a model space which was very sparsely populated indeed. In terms of function, I followed Pielou (1981) and argued that models can be used in four ways: for explanation, prediction, hypothesis generation and as standards of comparison. As for structure, I pointed to Hogeweg and Hesper (1985) who distinguished three sorts of models: variable oriented, event oriented and individual oriented models. Finally I championed West (1985) who talked about the five types of truth that models seek: Lockean or empiric; Leibnizian or analytic; Kantian or synthetic; Hegelian or dialectic; and Heisenbergian or pragmatic. I warned you this was philosophical!

Then I argued that this 4 x 5 x 3 space is quite sparse. Not only do most sorts of models not exist, but scientists spend most of their lives in one or two little corners of this universe. And, perhaps more importantly, these corners are disjunct in the sense that the different disciplines who claim modelling as a key tool are in different corners that are not even very close to each other. Thus, the computational fluid dynamics (CFD) models beloved of oceanography are explanatory/variable oriented/Kantian models, while the models of the theoretical biologists are often hypothesis generating/ individual oriented/Heisenbergian in tone.

Now this analysis confused my Council, especially Ray Steedman, the famous oceanographer, who was further agitated by my heretical assertion that cellular automata had been shown to perform as well as traditional Navier-Stokes equations in modelling ocean currents (Wolfram 1984). Perhaps, like many physicists, he confused the tools with the reality, assuming that models of the world are in some way the world itself. Not so John Farrands, who, in a good-natured way, called my analysis 'picaresque' (which, according to the Shorter Oxford, means 'of or pertaining to rogues, knaves or urchins') and dubbed me 'the young Lenin' as much for my bolshie tendencies as for my tendency, during argument, to jut, or was it lead, with my chin?

This smorgasbord of modelling potential led to a pig-out of actual modelling when I later convened a workshop on modelling the outbreaks of the crown-of-thorns starfish, Acanthaster planci, on the Great Barrier Reef (Bradbury 1990). By this time, I think, John Farrands, the physicist, was quite intrigued by all this biologising, because he obligingly opened the workshop, not as the standard eminent worthy, but by actively joining the debate with a paper, 'On modelling' (Farrands 1990). If that paper threw down the physicist's gauntlet, then this, my paper today, is the biologist picking it up. It is the paper I now know I wanted to write for John Farrands, but hadn't then learned enough about science. But it is a response as a work-in-progress, because I also want to argue that our ideas about modelling have undergone such tremendous change in the last few years that only the brave or foolhardy would say that there is not more change in store.

To understand this point, we need to look at what we did then, almost a decade ago, and contrast it to what we are doing now.

When we modelled the crown-of-thorns outbreaks in 1988, I think we made as many models as their were participants in the workshop. There were simple narrative models in the 'Just So' tradition. There were simple visualisations of the data and simple models based on transition matrices. There were CFD models of the hydrodynamics of the ocean currents, alone or tweaked to allow the tracking of neutrally buoyant particles, and there were diffusion-reaction-transport models borrowed from chemistry. There were population dynamics models of the starfish-coral interaction in several flavours: stochastic, deterministic, age-structured and as metapopulations. There were agent-based models, catastrophe theory models, cellular automata models, and adaptive hypothesis generating grammar theory models. Finally there were models based on nonlinear signal processing theory and optimality theory.

What there wasn't was a grand unified model of the whole phenomenon. The best we could do then was a narrative model to wrap it all up at the end.

Afterwards we congratulated ourselves for being stunningly avant-garde (which, in hindsight, we were), and for pushing back the frontiers of knowledge (which, again in hindsight, we did). But there were some who said: 'So what? What changed?'. In our euphoria, we dismissed these criticisms as sour grapes. But now I think perhaps we won the battle, but not the war. And in the small hours, I worry that perhaps science, after all, is only about winning battles.

But both our critics and I are wrong, even if science itself is just a litany of ever more interesting, ever more clever lies (Bradbury 1977). I can see now that we did do something important. We showed and we learned that there is no universal modelling paradigm that can be applied to all phenomena. It really is 'different strokes for different folks'. This, of course, was where the Club of Rome modellers (Meadows et al. 1972) came unstuck a decade earlier with their systems dynamics approach - they tried to use the one tool for everything because they needed to model everything.

We learned that modelling is both an art and a science: science in its construction, but art in its freedom of choice. Good models above all are graceful and elegant in their harmony with their natural phenomena. And grace, elegance and harmony are not words found in most scientific tracts.

Fast-forward to today. A bunch of small, but perfectly formed, models of different parts of a phenomenon was acceptable a decade ago because they were, collectively, better than any single grand model of the whole. We could compute them, visualise them, predict with them. But any synthesis was limited to some sort of narrative. Today, because of a huge change in our perspective on the world, this is no longer enough. That change is, of course, the development of the concept of ecologically sustainable development (ESD) and its acceptance as a central part of the global public policy agenda.

ESD wants now what the Club of Rome tried to deliver more than twenty years ago: a holistic view of the dynamics of the world's coupled biophysical and socioeconomic systems. ESD is where ecology meets economics, and it wants to be able to predict the outcomes of current global behaviour and to explore possible futures.

But we now know that grand Club of Rome models don't work, and that elegant little models are too limited. As Lenin himself said in 1902: 'What is to be done?'

Lenin was talking about bringing on the revolution in the context of a decaying social order. We are talking about bringing on a modelling revolution in the context of intense technological change. The two greatest changes that impact on us here are the availability of data and the computational power to process those data. A little more than a decade ago, I was managing a massive logistical exercise to acquire base line data for understanding Acanthaster outbreaks (Bradbury et al. 1986). It required a one-year survey of 230 coral reefs (about 10% of the total in the Great Barrier Reef) and needed 12,000 nautical miles of steaming and 3000 km of underwater survey. It took 35 man-years of effort and cost about a million dollars. And all the data had to be processed on a single VAX mini-computer! Today, there exist hundreds of continental and regional biophysical datasets at resolutions of hundreds of metres or even better (Bradbury and Shrestha 1995). Today we have the metadata and directories to help us find and access those data, and we have high performance computers (HPC) millions of times more powerful than VAXs, the scientific workhorse of the eighties (Malafant and Radke 1995). And, critically, we have a host of new scientific visualisation tools that can bring the most arcane models to life (Casti 1997; Kaufmann and Smarr 1993). We are truly in 'model heaven'.

But most importantly we are developing new holistic modelling paradigms suitable for attacking ESD issues. These paradigms acknowledge both the mistakes and successes of the past, and take full advantage of the availability of data as well as computation and visualisation tools. Rather than complete modelling solutions in themselves, in the Club of Rome tradition, they are modelling frameworks (Gault et al. 1987; Malafant and Fordham 1995). They 'outsource' much of their work to other software systems, and concern themselves with protocols and methods for bolting together different sorts of individual models, each themselves tightly adapted to the peculiarities of the piece of the action they are interested in. They use modern database systems and the internet to access data often remotely and often in real-time, they use HPC routinely and often remotely, they use the power of scientific visualisation tools not only to present their results more effectively, but also to allow for interaction with the user. Instead of striving for prediction of the future, they strive for exploration of possible futures. Instead of striving for global optimisation or equilibrium, they strive for user interaction by confronting him with tensions - physically inconsistent or socially unacceptable futures - and involving the user in the resolution of those tensions. They allow us to anticipate and understand risk in complex situations, and discover new options for action. They answer Lenin's question for ESD.

Modelling frameworks like these are a radically new way of confronting complexity without reducing it. They deserve the epithet 'holistic', and perhaps can help reclaim that honourable, historic and scientifically useful word from the New Age slough into which it has sunk (Bradbury, van der Laan, and Green in press).

So let me finish with a little more philosophy (eyes may be cast towards feet at this point). In 1931 Kurt Gödel (1931) augured an end to mathematics with his incompleteness theorem, arguing that there were mathematical propositions, call them models, that were undecidable. We might say, in the light of that, that the trouble with the Club of Rome and system dynamics was that it could never provide the answer no matter how big and how sophisticated its grand model got. It was necessarily incomplete. In 1970 Richard Levins (1970), the theoretical ecologist, took this argument squarely into the modelling realm in a prescient paper entitled 'Complex systems'. He said: 'Since there are no universally optimal models a theory must be a cluster of models which fit together in different ways. ... A theorem is then called robust if it is a consequence of different models, and fragile if it depends on the details of the model itself. The search for robustness leads to the proposition that truth lies at the intersection of independent lies.'

I said earlier that science is a collection of ever more interesting, ever more clever lies. Our question now surely is: Just how interesting are our bunch of clever little lies? That, I think, is a question John Farrands would have liked, and I challenge you with that question as we begin this conference.

This paper is dedicated to the memory of John Law Farrands, AO. Born Melbourne, 11 March 1921. Died Melbourne, 14 July 1996.

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