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By Tim Lenton From the beginning, the science of Gaia was based on systems concepts such as feedback and homeostasis, adopted from cybernetics (control theory). Systems theory was fashionable in the 1970s, but somehow like flared trousers, it fell out of favour in the 80s. Then with the appearance of chaos theory, and later complexity theory in the 90s, systems started to get a look in again. Now in the new millennium we are all, it seems, declaring ourselves "Earth system scientists". But we must make sure that we really start to think in systemic terms rather than just rename our subjects. Systems theory has been maturing quietly and offers a host of principles and techniques to help us understand Gaia. Equally, study of Gaia is yielding new insights for systems theory. To try and foster this relationship, a research network in systems theory has been formed, entitled 'Daisyworld and Beyond'. This is being co-ordinated by Inman Harvey (Cognitive and Computing Sciences, University of Sussex) and myself, with help from Alister Hillman. We held our first workshop on 20-22 March 2001 at the University of Sussex and invited a mixture of researchers with an interest in systems, some familiar with and some new to Gaia science. The workshop used the Daisyworld model as a launch platform for considering regulation in complex feedback systems. The first day was devoted to synthesising our understanding of the Daisyworld control system, extracting general principles and considering how they could be applied elsewhere. The second day was focused on the development of new models to better understand the coupling of life and its environment. The meeting opened amidst a great snowfall, appropriate to the cold conditions when life starts on Daisyworld. The thermostat in the meeting room clearly wasn't built on Daisyworld principles because as the meeting progressed the heating became excessive. Luckily we had the benefit of teleology (conscious foresight) and were able to do something about this. Daisyworld, in contrast, was built to show that regulation of a planet, as envisaged in the Gaia hypothesis, does not demand teleology. We were honoured to have with us the inventor of the model, Jim Lovelock, who described its formulation over Christmas 1981. As it was impossible to represent the full complexity of the Earth system, Jim imagined a planet on which the environment was reduced to one variable, temperature, and this was affected by a simple property of life, its albedo (reflectivity to solar radiation). When stuck on how to represent life in a simple form, a paper serendipitously appeared in Nature describing the spread of plantains in a nearby Devon field, and it was a small leap to considering populations of black and white daisies. The model was formulated on one of the earliest personal computers. There was much knowing laughter when Jim recalled finding a bug in the first version. After fixing it, regulation emerged. Nearly twenty years of research have confirmed how stable the regulator is, leading Jim to speculate that Daisyworld may be one of a class of coherent models. Peter Saunders (Mathematics, King's College, London) argued that Daisyworld represents a new type of control system with what he calls 'integral control'. The key ingredients of integral control are counter-regulatory pairs of causative agents (e.g. warming and cooling daisies), two-way interaction between an affected variable (e.g. temperature) and the causative agents, and interaction (direct or indirect) between the causative agents (e.g. competition for limited space). Peter showed how the same principles that stabilise temperature on Daisyworld govern the regulation of blood glucose and blood calcium. He suggested that integral control is relatively easy to achieve in chemical systems, where regulation occurs at the intersection of reaction curves, but harder to achieve in physical systems. The intersection point in chemical-based systems (e.g. blood glucose) is often a thermodynamic property. Hence it is not subject to natural selection. This suggests that regulators will appear more readily and be harder to disrupt than one would assume from viewing regulatory systems as the product of natural selection. Where selection is operating, there is the danger of a system suffering the 'Esau effect' of sacrificing long-term benefit for short-term gains (named after the man who sold his birthright for a mess of pottage). Thus thermodynamic constraints make for a 'healthy' system, as does partitioning into sub-systems with some redundancy. For example, the human body can achieve the same effect (e.g. heating) in a number of ways. Healthy behaviour of a system is often counter-intuitive (e.g. cooling of Daisyworld as solar heating increases) and, conversely, an expected response is often a sign of something going wrong with a system. In this context, Peter suggested that the recent appearance of a distinct global warming signal is a cause for alarm. Subsequent discussion focused on thinking up other examples and applications of integral control. The basic principles of the Daisyworld thermostat can be applied to the temperature regulation of objects (e.g. satellites) using exchangeable dark and light panels or heat-sensitive (cold-dark, hot-pale) paint pigments. The mechanism of temperature regulation in a bee colony is similar and fulfils the criteria of integral control. An entertaining example of using counteracting effects simultaneously to achieve stability was Peter Saunders' tale of using the accelerator and the brake together when learning to ride a motorcycle. Suggested technological uses for integral control principles included the design of closed ecological life support systems (CELSS), and enforcing stability on unstable inputs (e.g. web requests). Chris Roadknight (BT Labs, Ipswich) has examined the performance of Daisyworld with a view to possible application in information technology. However, the model was found to deal poorly with chaotic input because the feedback in the system is so strong that it can overshoot. The original Daisyworld was a point model with no explicit representation of space. More recently, one- and two-dimensional variants of the model have been developed. 'Doctor Daisyworld', Werner von Bloh (PIK, Potsdam, Germany) introduced these. The one-dimensional model represents the latitudinal variation in solar forcing across the surface of a sphere. This leads to new regimes of behaviour as solar forcing increases. When black daisies appear they immediately cover an equatorial band, and regulate the temperature there, but the poles remain cold and uninhabitable. As the Sun gets brighter, daisies gradually spread to the poles, and when they fully cover the planet's surface, the global temperature is regulated. When luminosity gets too much, there is an abrupt transition in which life disappears from most of the planet's surface but hangs on at the poles (in the form of pale daisies). Ben Adams and Andy White (Mathematics, Heriot-Watt University, Edinburgh) have developed a similar one-dimensional model with just the original black and white daisy types. Interestingly, rather than co-existing in any region, the daisies form black and white stripes. This reminded other participants of a model of stripe formation by Alan Turing. However, the Turing model has two diffusion equations whilst the Daisyworld has only one (temperature diffusion). Thus it may offer a new mechanism for pattern formation. To fully represent spatial interactions of the daisies, a two-dimensional model is required. Werner von Bloh and colleagues have developed such a model using a 'cellular automata' approach. In essence, the world is represented as a giant grid. Each cell of the grid is either occupied or unoccupied by a daisy and there are common rules of interaction between the cells. This model is an even better regulator than the original Daisyworld. Even when the cells are progressively concreted over, the system continues to regulate until a fragmentation threshold is reached where the daisy areas become disconnected. Graeme Ackland and Michael Clark (Physics, Edinburgh University) have reproduced a similar model but have added curvature to the world (i.e. variation in solar forcing across it). They discovered that deserts appear and become self-sustaining beyond a critical size (about half the grid area). In contrast, the sides of a small desert can 'communicate' with each other and hence are eventually re-colonised. Interestingly, a glance at the surface of the Earth shows only large deserts persisting. What general lessons can be drawn from these studies? Discussion at the workshop focused on using that most intangible of quantities, entropy, as a basis for principles of system behaviour. In the spatial Daisyworlds, informational entropy (also a measure of biodiversity) was found to be greatest when regulation is not required and falls to a minimum at the most extreme forcing. It increases when regulation begins to break down (either through fragmentation or solar forcing). Thus when the system is regulating, it maintains an ordered, low internal entropy state. To do so it must be exporting radiative entropy to its environment (thus increasing disorder there). Many physical systems tend to maximise their entropy production or minimise their internal energy state. For example, Earth, Mars and Titan all tend to maximise their radiative entropy production. Peter Cox and Thomas Toniazzo (Hadley Centre, Bracknell) showed the results of applying a Maximum Entropy Production (MEP) principle to Daisyworld. On real planets, non-diffusive (e.g. turbulent) heat transport varies in a way that appears to maximise entropy production. In Daisyworld, non-diffusive heat transport is related to a 'q' parameter and is usually fixed. When it is allowed to vary in order to maximise entropy production, the range of regulation is extended. The original Daisyworld is found to be close to maximising entropy production in the region where black and white daisies co-exist. A new version of model that ignores the arbitrary 'q' parameter and uses the MEP principle to determine heat transport further extends regulation. Although new insights continue to emerge from work with the Daisyworld system, there is a need to develop new models to better understand the coupling of life and its environment. Daisyworld is limited in that the model is 'hard wired' with the local and global effects of life being identical. This makes it easy to see why the system is such a good regulator. Whatever is selected for at the individual level will automatically tend to be beneficial to life at a global scale. This was a favourite criticism of the late, great evolutionary biologist Bill Hamilton. Bill saw a way forward in extending community ecology models to include coupling of life to the environment. Peter Henderson (Pisces Conservation Ltd, Lymington) introduced 'Damworld', the model he developed with Bill to addresses the question of to what degree communities can become self-protecting? Dams were chosen as a ubiquitous example of life creating a new habitat (e.g. hot spring bacteria forming a pool). Dam building, dam destroying and neutral algal organisms are introduced to form a community that lives in the reservoir of water that gathers behind a dam. New species are added one at a time. Strong interactions are allowed with a few other species or weak interactions with many others. Typically the dam builds up and then the system oscillates. Growth of the dam is beneficial in that it supports a larger community. Clusters of species interaction emerge, but there is no evidence of compartmentalisation in the system. Tight cooperation is rare, because such combinations are too ruthless. Pete speculated that such teams are scarce on Earth probably because they share the same pathogens. It was found that some organisms act as stepping-stones on the way to a stable community. Pete and Bill used to entertain themselves by trying to think up "satan bugs" that would destroy their model systems. They found that it becomes harder to enter and disrupt a community as it gets larger, supporting a view that communities are defensive structures. An alternative, promising basis for new models is to use 'artificial life' techniques. The first such Gaian model was the 'Guild' model of Keith Downing (NTNU, Trondheim, Norway). This addresses the question of how inevitable is nutrient recycling? The model world is inhabited by 'agents', which have a genome that encodes for what to do with each of six different nutrient chemicals and encodes for the enzymes to transform them. The local environment of the agents is assumed to differ from the global. There are fluxes of the six chemicals through the model system. An optimal chemical composition ('Redfield') ratio is prescribed. Initially the world is seeded with 100 agents of identical genotype. Mutation can occur and the agents reproduce sexually allowing exchange of genetic material. High rates of recycling evolve and the abundance of elements in the environment is regulated close to the 'Redfield' ratio requirements of the organisms. Recycling can be expressed in terms of the cycling ratio of nutrient through primary producers to that coming in and out of the system. Cycling ratios are typically ~25 and sometimes as great as ~100. Peter Zvirinsky (EPFL, Lausanne, Switzerland) has made a two-dimensional grid version of Guild, called the metabolising agents ('MAG') model. This uses the 'Swarm' tool for multi-agent simulation developed at the Santa Fe Institute. In this extension of Guild there is a random rain of nutrients in, random leaching of nutrients out, and the 'agents' have a gene for vision that determines how good they are at 'seeing' available resource. Similar regulation emerges as in the original, non-spatial Guild model. We were able to watch this happening live at the workshop. In the real world, systems are driven by free energy. Hence Keith is developing a 'Guild II' model with abstract chemistry, entropy and energy. The model is populated with cells whose interiors constitute the local environment. A Gaian regulatory index is introduced to measure the success of the systems. The preliminary results showed regulation in over 20 cases out of 100. This is remarkable given that the systems are running on relatively little free energy, supplied in chemical form. In the real world, most ecosystems run on abundant free energy from sunlight. Practical applications can also make good use of artificial life techniques. For example, it proves hard to build an intelligent network using classical control theory, because it is too rigid. Hence Chris Roadknight and colleagues are exploring the use of biological principles of adaptive control. They set 'microbial' agents the task of dealing with requests coming from a network. The agents formed a layered structure of dealing with tasks that resembles a microbial mat. Ultimately this approach will also be designed with the capacity to defend a network from aggressive attack. Models of abstract life on abstract worlds are not everyone's cup of tea and Ric Colasanti offered an incisive critique from an ecological perspective. The workshop moved on by relating the emerging understanding from abstract worlds to studies of the real world. Richard Betts (Hadley Centre, Bracknell) presented the results from using a general circulation model of the climate to explore climate-vegetation feedback. Many areas of forest on Earth today were found to be self-sustaining in that they maintain the climatic conditions in which they can persist, just as the daisies do in Daisyworld. Richard went on to classify the responsible properties of vegetation and resultant feedbacks. The low surface albedo (black daisy effect) created by forest is found to have an important climate warming effect in high-latitude regions with heavy snowfall. Interestingly, it is not just a property of the individual trees, because it is enhanced by internal reflection between different trees in a forest. Evaporative cooling (white daisy effect) is more important in low-latitude regions. Enhanced precipitation is beneficial to forests everywhere, and enhanced cloud cover can have beneficial cooling effects in tropical regions. The Amazon rainforest is often given as the archetypal example of a self-regulating ecosystem. However, Peter Cox showed that the latest coupled climate-carbon cycle model predicts that the Amazon climate regulator will collapse later this century, as a consequence of climate warming and drying, leaving the region as an arid semi-desert and adding more carbon dioxide to the atmosphere. Peter Henderson's direct experience from fieldwork in the Amazon emphasised from a different perspective that the rainforest is not the stable, homogeneous place always assumed. On a longer timescale, the effects of vegetation on the global carbon cycle generate self-limiting (regulatory) negative feedback. By amplifying the rate of silicate rock weathering and the consequent removal of carbon dioxide from the atmosphere, land plants maintain a low atmospheric carbon dioxide level that limits the rate of photosynthetic carbon fixation. Some of my own work with Werner von Bloh shows how this negative feedback generates Daisyworld-like regulation of global temperature and is predicted to extend the life span of the plant biota. The mechanism may be an example of a more general principle of 'biotic plunder' - homeostasis of the environment toward an impoverished but habitable state - introduced by Toby Tyrrell (Southampton Oceanography Centre). However, the short-term loss in question is a small price to pay for the long-term gain. Richard Betts set all this in the context of the debate over whether life may have just been lucky in surviving for so long on the Earth. Richard argued that the very presence of life 'loads the dice' in favour of the system finding a regulatory trajectory. The closing discussion centred on the realisation that there are a number of different forms of selection operating in the real world and in the model systems that had been considered. Whilst natural selection is clearly important, other types of selection can also determine system behaviour, for example, in the distributed control observed in social insect colonies (e.g. ants using pheromone trails). This posed a semantic problem, especially for the evolutionary biologists present who often take "selection" to mean just "natural selection". New terms are clearly required to describe different types of selection. The danger at present is that differences of language are obscuring our search for a common understanding. The proposition that the same general principles operate across a variety of systems is central to 'complexity theory'. However, some of these principles may be too general to contribute much to our understanding of Gaia. For example, observing maximum entropy production does not distinguish systems with life from those without. When asked if complexity theory has much to offer Gaia, Jim Lovelock was sceptical, suggesting that Gaia-type mechanisms do operate at a smaller scale than the global, but that a critical mass (number of organisms) is required for them to work. Daisyworld embodies Einstein's advice (quoted by Graeme Ackland) that "everything should be as simple as possible, but no simpler". As we try to move beyond Daisyworld to better understand systems, this should be our guiding principle. |
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