Some of the science behind Ecobuttons

Ecobuttons: A bit of science for you!

Our world is made up of complex systems. From earthquakes to our economy, from our human language, to the very evolutionary networks that lie behind our very origins. All of these systems are based on the same kind of power laws, they all rely on interacting components that when connected in the right way produce something more than the sum of their parts; what’s more, within these complex systems you have arrived at a state where even a small trigger can create a very large change in the system as a whole.

Over the decades, many models have been created to show how ecosystems can be thought of as complex systems in this way. Ecosystems are created largely from the connections that exist between different species (or different nodes), and researchers have shown how this process of co-evolution actually works using various computer models. But models using piles of sand and networks of light bulbs have also been popular in showing how complexity works! Imagine an idealised grain of sand landing on top of an existing sand pile, sometimes the sand grain landing might have only an extremely localized effect, but, at other times, the fall of an extra grain of sand on the network may trigger a large-scale rearrangement of the sand; but after this rearrangement has occurred there will still be a complex network of critical states, it will just be in a different pattern.

How can we tell that a particular system is complex? One of the most influential workers in the field of complex systems and especially on its relation to evolutionary biology is Stuart Kauffman who initially worked with what are called Random Boolean Networks. Without getting into too much detail here, what we can see from Boolean networks is that as the total number of nodes in a network (Kauffman was using light bulbs), and the number of other nodes each node is connected to, we see distinctive changes of behaviour in the system. Basically we see a phase transition occurring (just like the phase transition which occurs when water transforms into ice at a certain temperature); in this case it is a phase transition between order and chaos. If the number of connections between each node is under a certain critical threshold value then the system is highly ordered, and nothing very interesting happens. If the number of connections rises above the critical value we see a system behaving chaotically, which is also useless for our purposes. But when the number of connections is at that critical value, at the very edge of chaos, then we see very interesting behaviour indeed. An intermediate behaviour, a kind of self-organizing criticality. States that systems settle down into are called attractors, in the self-organizing state of a complex system the same attractor is reached no matter what the initial conditions, I.e. no matter how the initial nodes were connected.

But what has this got to do with ecosystems? Actually there are many implications for biology and ecology from the work that has been done on complex systems. It is possible that in many cases the networks of species that are present in complex ecosystems are, through a process of co-evolution, pushing themselves from either extreme towards the interesting region of self-organized criticality in the phase transition on the edge of chaos. As one popular science writer has noted “Simply by each individual acting to maximise its own evolutionary fitness, the whole ecosystem evolves towards the edge of chaos. This is exactly analogous to the sand pile model. In which the addition (or removal) of a single species from the network corresponds to the addition (or removal) of a single sand grain from the pile; it is also essentially the same as the light bulb model… complex systems naturally evolve towards the phase transition at the edge of chaos.” (Gribbin, 2004). Bak and Sneppen, and later, Amaral and Mayer have created virtual ecosystems, based on ‘games theory‘, which show the dynamics of ecosystems in action and bare striking resemblance to what actually occurs in nature- here we get self-organized states where small changes in the system can cause large changes in the system as a whole. (These works are explored in more detail in Gribbin, 2004)

What’s more, we can go further then this and not just look at ecosystems as being closely intertwined with the physical environment. Indeed, using James Lovelock’s Gaia theory, we can come closer to seeing how the biological and physical worlds can be thought as part of one single network which obeys the same underlying, deeply simple rules. These two worlds should be thought of as being interconnected just as their various components, or nodes are. Beyond the unfortunate quasi-mystical undertones that the theory has (I cannot stress just how much this activity will avoid bringing about such representations), this is genuine science, and does help us in understanding how the world works at a very fundamental level. According to this theory, “the behaviour of life on Earth alters the physical landscape (where ‘physical’ includes things like the composition of the atmosphere) as well as the biological landscape, and both these changes affect the overall fitness landscape, with feedback a key component of the interactions.”

One way that Kauffman has demonstrated how important networks are in emerging complex systems is by using buttons. Yes, everyday buttons like the ones we all have hidden away at the backs of drawers at home. Starting with the buttons spread out on the floor, with no button connected to any other button, we must first choose a pair of buttons at random and tie them together while leaving them in their original positions. We then repeat that process a few times, and if we come across a button that is already connected to another button we just use the thread to connect it to another button as well. After a while, we will start to see some structure in the mass of buttons. Increasingly we do come across buttons that are connected to another button already, perhaps two… To tell how interesting a network has become we can lift up a sample of the buttons and see how many connections they each have with others. The buttons are examples of nodes, the clusters of buttons are known as components. The number of buttons in the largest cluster is a measure of the current complexity of the system. What we should find is that at first the size of the largest cluster at first grows slowly but that when the number of threads (of connections) approaches and then exceeds half the number of buttons the size of the largest cluster rapidly increases.

Soon after this we will find that a supercluster has formed- a network where the great majority of buttons are interconnected in one component, after which the growth rate tails off, more threads usually just connecting buttons that are already connected. Although the network has now stopped changing very much it is now without doubt a complex system. Notice how this compares with what was said earlier with regard to Boolean networks- once the number of threads reaches a certain critical value (exceeds half the number of buttons) the system quickly switches from a very boring state to another state with which there is a lot of structure but with little scope for further change. It is right on the edge of chaos, the switching point between the two states, where the interesting activity happens. It seems that in the real world living systems regulate themselves to keep themselves at this edge of chaos; and we can see how when we start to look at processes such as far from equilibrium dynamics. But we need not go into this now- all we need to think about now is what would happen if Kauffman’s buttons represented species in an ecosystem…

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