|
|
|
||||||
|
|||||||
Feedback control systems are of fundamental and long-held interest in cybernetics and systems theory (Ashby, 1956; Riggs, 1970). The Daisyworld model (Watson and Lovelock, 1983) is an elegantly simple example of a feedback control system, apparently of a type not previously recognised (Saunders et al., 1998). It has remarkably broad application, has generated interest in the field of cybernetics (Andrew, 1996) and thus seems an appropriate launch platform for a research network. The Daisyworld Control System Daisyworld (Watson and Lovelock, 1983) was invented to demonstrate that a self-regulating system can emerge from physically realistic coupling between life and its material environment, without teleology (conscious foresight or planning on the part of unconscious organisms). In the model, the temperature of a hypothetical planet (Daisyworld) is stabilised by competition for space between two types of organism, one that warms its local environment by absorbing solar radiation (black 'daisies'), and the other that cools its environment by reflecting solar radiation (white 'daisies'). As the system is forced by increasing solar luminosity (as has been experienced by the Earth), the temperature of the planet is regulated by competition for space between the two phenotypes. When the solar luminosity is low, the black daisies are warmer than their white compatriots, they spread, and as they do so they darken and warm the planet. As the solar luminosity increases, the white daisies gradually take over, cooling the planet. As the sun brightens over a range that would heat a bare planet by over 60K, the daisies keep it within a few degrees of the optimum temperature for growth (the set point of the system). While both daisy types are present, the temperature of the planet actually decreases as the sun brightens (the system achieves negative steady state error). Daisyworld provides a template for a very effective type of feedback control system, which can be described in abstract form thus: A system variable is regulated by two effects that act in opposite directions on the variable and inhibit one another (Saunders et al., 1998). In Daisyworld, the variable is temperature, the warming and cooling effect are due to black and white daisies and they inhibit one another by competing for the same space. However, the basic template is more widespread, for example, it appears to be present in human physiology (Koeslag et al., 1997). This type of regulation has been termed "integral rein control" (Saunders et al., 1998), because it combines "integral control"1 with "rein control"2. It has considerable potential for technological application. The remarkable homeostatic behaviour of Daisyworld has already inspired numerous cross-disciplinary studies, which we now briefly summarise in terms of their relevance to systems theory. 1 "Integral control" involves feeding back a signal proportional to the difference between actual and desired outputs to a controller that responds until the difference vanishes, giving zero steady state error. Analytical studies of feedback control The mathematics of Daisyworld can be solved analytically (Saunders, 1994), and its structure can be simplified somewhat to give a general template for the control system (Koeslag et al., 1997; Saunders et al., 1998). It appears that the mechanism of glucose homeostasis in the human body is analogous to the Daisyworld temperature homeostasis (Koeslag et al., 1997). Blood glucose levels are regulated by the pair of hormones, insulin and glucagon, which appear to inhibit each other's secretion (Saunders et al., 1998). Other analogous physiological control systems also exist (Koeslag et al., 1999; Saunders et al., 1998). Analysis will lay the groundwork for further technological applications. Genesis and refinement of self-regulation Daisyworld provides a framework to explore the effects of evolution on system regulation. When organisms with no effect on their environment are allowed to mutate to alter their environment, self-regulation emerges (Lenton, 1998). Mutation of the environment-altering trait can also extend the range of self-regulation beyond that in the original model (Stöcker, 1995; Von Bloh et al., 1997). If the daisies optimum growth temperature adapts in response to the temperature prevailing in their environment this can impair environmental regulation (Robertson and Robinson, 1998; Saunders, 1994) but the energetic costs of and bounds on adaptation mean that it does not destroy self-regulation. Daisyworld has helped crystallise the notion that feedback to the environment can alter the forces of natural selection, which has been described as 'selective feedback' (Lenton, 1998) and as 'system-dependent selection' (Lansing et al., 1998). Effects of complexity and coupling on system stability Daisyworld has been developed to include a food web of many types of daisy, herbivores and carnivores (Lovelock, 1992). These ecological, multi-species Daisyworlds are remarkably stable when contrasted with conventional community ecology models that ignore coupling between life and its environment. They have provided a framework for exploring the effect of ecological interactions on ecosystem stability (Harding, 1999; Harding and Lovelock, 1996). This has yielded important results, in particular, that increasing food web complexity increases system stability when there is coupling to the environment (Harding, 1999). The effects of inter-specific competition (Cohen and Rich, 1999) and of including different population models (Maddock, 1991) have also been explored. Computer modelling of coupled feedback systems Daisyworld has generated much interest in the mechanisms by which the Earth's climate is regulated and the role of life in controlling the climate (Lenton, 1998; Lenton and Betts, 1998; McGuffie and Henderson-Sellers, 1997; Watson, 1999). This has led to new approaches in climate modelling, and the notion of the Earth as a system. 'Earth system science' is emerging as a new scientific field including the construction of computer models to help understand and predict the behaviour of the relevant coupled feedback mechanisms. 'Earth system analysis' brings humans into the equation and offers a methodology for action (Schellnhuber, 1999; Schellnhuber and Wenzel, 1998). Daisyworld inspired the TRIFFID dynamic vegetation model (Cox, 1998), which is now incorporated in the UK Hadley Centre's Earth system model of the climate and the carbon cycle. Earlier, "off-line" studies showed important self-beneficial effects of vegetation on climate akin to those in Daisyworld (Betts, 1999). Information Technology BT is interested in Daisyworld with a view to applying it to regulate Internet requests. These have been shown to have a deterministic pattern over time (Roadknight et al., 1999) as has real world solar forcing. The Daisyworld model has been subjected to different types of solar forcing: Linear, periodic, fractal and random walk. The forcing then begins to resemble web traffic in some respects. Measurements of the impact of these new types of forcing have been made, showing the differing effects of each type (C. Roadknight and T. M. Lenton, unpublished results). It is hoped that extensions of the Daisyworld model will help BT devise methods for converting traffic with fractal properties, into a stream of requests with a less variable distribution. A Time for Synthesis We suggest that the time is ripe for a synthesis of the aforementioned work and a greater dialogue with established systems theory. Improving cross-disciplinary communication between Daisyworld modellers and systems theorists has the potential to offer new insights to system theory and to speed progress in the relevant fields of natural science, by giving them a stronger theoretical basis. |
|||||||
|
|||||||
| Website maintained by James Dyke |
