Mark Buchanan Ubiquity The Science of History Why the World is Simpler than we Think Weidenfels&Nicolson 2000

pg 120 Keywords: basic skeleton of co‑evolution: the nature of evolution of fitness landscapes - The essence of co‑evolution is that species interact - an evolutionary change in a single species could trigger an avalanche of co‑evolution that could affect anything from a few species to almost every single species in the ecosystem - the distribution of avalanches according to the number of species involved followed a power‑law form – co‑evolution - the ordinary evolutionary workings of ecosystems should lead inevitably to dramatic upheavals having no identifiable cause whatsoever - these games suggest that the global ecosystem rests in a critical state, and they hint ‑ but only hint ‑ that the mass extinctions may simply be the rare but expected and natural result of ordinary evolution - non‑equilibrium physics: underline one of the broader themes of this book: …we have seen that many things do indeed seem to be organised into critical states. But there is far more in non‑equilibrium physics than a fixation on the notion of self‑organised criticality might suggest - power laws and fractals and the same wild sensitivity in which a quite ordinary, run-­of‑the‑mill shock can trigger an upheaval out of all proportion to itself. What is more, as with the critical state, this sensitivity comes about naturally under an extremely broad set of conditions. These are the ubiquitous properties that arise again and again in things driven away from equilibrium, and in things in which history matters - these are the things that are making a new kind of science possible ‑ a theoretical science tuned to the context of the historical sciences Kauffman and Johnsen learned that by tuning their ecosystem ‑especially how rugged the landscapes were ‑ they could make its evo­lution become far more active and vigorous. When the landscapes for each species were rugged, but not too rugged, and when the influence of one species on the landscape of another was just right, they found that their ecosystem worked like the sand‑pile game. An evolutionary change in a single species could trigger an avalanche of co‑evolution that could affect anything from a few species to almost every single species in the ecosystem. Indeed, in running their game for a long time, they found that the distribution of avalanches according to the number of species involved followed a power‑law form. In the Kauffman‑Johnsen ecosystem, then, at least when it is properly tuned, there is no typical size for events. When one species evolves, it may be an isolated event, or trigger a million others to follow suit. What is more, the record of evolutionary events in this ecosystem game looked much like the record of the mass extinctions ‑ with long intervals of apparent quiet, punctuated by sudden bursts of activity. Kauffman and Johnsen had tuned their ecosystem to the critical point just as Fermi had his reactor. This game, to be sure, offers a vastly oversimplified view of co‑evo­lution in the real biological world. Even so, the principle of universality implies that for anything organised into a critical state, the effects of most details have no influence anyway. In 1993, as if to prove this point, Bak and Kim Sneppen ‑ both working then at the Niels Bohr Institute in Copenhagen ‑ found an even simpler game for co‑evolution that leads almost exactly to the same results. It is worth looking at their game in a little detail, for it is probably the most basic skeleton of co‑evolution conceivable. To see where it comes from, we need to think a bit more about the nature of evolution of fitness landscapes. Climbing uphill is just part of the story. Most real landscapes have some degree of ruggedness, with peaks of various sizes interspersed with valleys, and fitness landscapes are no different. As a result, it is unlikely that a population climbing into the hills will find its way to the highest of all peaks. Instead, it will almost certainly ascend towards one of the myriad smaller peaks, and then get stuck on top, as would any climber trying to ascend a rugged mountain without a map. Once there, a species cannot climb any higher without making a leap across to the closest higher peak. How long will it take a species to make such a leap? To do so, some members of the population need to traverse the intervening Death Valley of lower fitness. In each generation, the cloud will throw a few new variants into the valley. Being of lower fitness, the families of these variants will generally survive for only a generation or two. On rare occasions, however, a family might last four or seven, or even ten, generations. Eventually, on one of these occasions, an unspeakably rare string of genetic events, one in each generation, may lead a sequence of variants across the valley, and land a descendant on the Promised Land of the other nearby hill. Multiplying and climbing, this descendant and its offspring will then carry a population upwards to the higher peak. Evolutionary theory predicts that the time required to make such a jump becomes very large very quickly as the distance to the next peak grows. In other words, if a species faces a short jump, it might make it in a reasonable time. If it faces a long one, then forget it ‑ it will be hung up on that peak for aeons. Bak and Sneppen used this insight to great effect. They reasoned that each species, after climbing into the hills, will inhabit a local peak and be prevented from moving to a higher peak by some intervening gorge. The width of the gorge reflects just how difficult it is for the species to evolve further, and how long it will take to do so. The widths of these gorges ‑ one for each species ‑ are crucial, since nothing can happen until some species makes a leap. So Bak and Sneppen focused entirely on these numbers, and ignored everything else. I To visualise the state of an ecosystem through their eyes, imagine a string of sticks with lengths equal to the width of the various gorges the species are facing. Just to butcher reality a bit further, Bak and Sneppen supposed that the lengths of these sticks can only be between O and 1. The ecosystem evolves by two rules. Since short leaps are so over­whelmingly more probable than long leaps, the first species to jump will almost always be the one facing the narrowest gorge. When this species does jump, it will find itself on a new peak, and so face a new gorge, which will be either broad or narrow ‑ no one can tell. So, rule number one: find the species with the shortest stick, and replace it with another having random length between O and 1 (Figure 15). This rule captures how species evolve by themselves. The essence of co‑evolution is that species interact. For simplicity, Bak and Sneppen supposed that each species interacts with its two nearest neighbours. When one species evolves, it disturbs the fitness landscapes of its neighbours. Having been on peaks, they suddenly find themselves off peaks, and so rapidly evolve to reach new peaks, where they face new gorges. Hence, rule number two: after you have replaced the shortest stick with another of random length, also replace the sticks to its lett and right with new sticks of random length. To play the game, you begin with a random assortment of short and long sticks, representing an ecosystem in some state. You repeat the procedure again and again. What happens? At first, there are plenty of short sticks. But since the shortest stick and two others get replaced each time, the average length of the sticks increases. Eventually, as it turns out, all the sticks come to have lengths or greater. At this point, the ecosystem has reached a relatively steady state, with all the species facing wide gorges. The ecosystem has now to wait a very long time for the next evolutionary jump. Somewhere in the line, however, there is a shortest stick. Wait long enough, and the specie 1' corresponding to this stick will jump to a new peak. This single evolutionary jump replaces the stick for one species and its two neighbours by new random sticks. All three sticks might in fact be fairly long, in which case the ecosystem will again be locked into a long‑lasting situation. But there is a good chance that one of the three new sticks will be much shorter than 23. If so, then the specie corresponding to this stick, facing a narrow gorge, will leap again very quickly. So you replace this stick and its neighbours with new sticks. Once again, one of the new sticks will probably be quite small, and lead to a further evolutionary jump very quickly. In this way, an avalanche of evolution will run through the ecosystem until finally, by chance, al the sticks once again have lengths greater than 3. At this point, the avalanche has stopped, and with all species again facing wide gorges, there is another long wait until the next burst of activity. So the Bak‑Sneppen ecosystem evolves into a state in which all the species face fairly large barriers to further evolution. At the same time, even a single evolutionary step made by one species can destabilise the situations of other species, and can trigger rapid chain reactions of evolution that sweep through most of the ecosystem before things again settle down. Although obscured by more details, the Kauffman‑Johnsen game has essentially the same character. Both suggest that the ordinary evolutionary workings of ecosystems should lead inevitably to dramatic upheavals having no identifiable cause whatsoever. Could this be the real cause of the mass extinctions? Not surprisingly, biologists have criticised both games for all kinds of reasons. They are indeed terrific oversimplifications of biological reality. As we have seen earlier, this is not necessarily an argument against the validity of a model in the light of the principle of universality. There are, however, some very real shortcomings of both these games. If you look at the preceding discussion, for example, you will find that neither model ever mentions the word 'extinction'. Indeed, they are models for co‑evolution in the absence of extinction. When a species hops from one peak to another, it does not go extinct; it simply changes phenotype. The avalanches are simply avalanches of evolutionary activity. One might well argue, however, that if a hundred species are forced to adapt to new fitness peaks during some evolutionary upheaval, some will not make it and will instead go extinct. If the upheaval involved a thousand or ten thousand species, a correspondingly larger number would go extinct. This would lead to a power law for extinctions, as well as for evolutionary avalanches. This is hardly a watertight argument, but it is certainly plausible. All in all, these games suggest that the global ecosystem rests in a critical state, and they hint ‑ but only hint ‑ that the mass extinctions may simply be the rare but expected and natural result of ordinary evolution. pg 126 Evolutionary Thinking A few chapters ago, I quoted the biologist Francis Crick who had concluded from personal experience that 'most mathematicians are intellectually lazy'. I imagine that Crick would say much the same thing about Bak, Sneppen and anyone else who sees anything other than utter nonsense in the results of the simple ecosystem made of sticks. Then again, Crick may have a rather extreme view on what does and does not count as 'real' science. He and the philosopher Daniel Dennett once argued about the merits of theoretical simplification in science, specifically attempts to model the workings of the brain. One modern effort to do this is based on neural networks ‑ simple mathematical networks of interacting 'neu­rons' which, like real neurons, fire when stimulated in the right way by other neurons in the network. The neurons in these models have little else in common with real neurons. They are theorists' neurons, and because they are simple, theorists can learn things about the properties of networks of interacting neurons that they could never learn if each single neuron was far more complicated. Crick objects to the entire spirit of this approach. 'These people may be good engineers,' Dennett recalls him saying, 'but what they are doing is terrible science! These people willfully turn their backs on what we already know about how neurons interact, so their models are utterly useless as models of brain function.' I suspect that few biologists, physicists or scientists of any kind would cling to this kind of position for very long. Newton would never have understood the earth's motion around the sun had he not ignored every last detail about the earth except one ‑ that its mass is affected by gravity. He didn't worry that it has a core and a mantle, or that each day, because of the tides, oceans of water slosh back and forth on the surface. He didn't worry that, strictly speaking, the exact position and mass of every last tree on the planet should come into his calculations. Newton assumed that none of this would make much difference, and he was right. Even all that sloshing water does not alter the length of the year by a single minute. pg 131 When it comes to the mass extinctions, everything leads to spreading confusion. In view of Newman's game, there is no way to know for sure whether the mass extinctions were triggered by external or internal shocks. One of the aims of current research in this area is to explore these games further, to see if subtle differences in their mathematical signatures can be detected in the fossil record, and so settle the matter. But even if Newman's game prevents us from making a bold final conclusion about the mass extinctions, it serves to underline one of the broader themes of this book. We have seen that many things do indeed seem to be organised into critical states. But there is far more in non‑equilibrium physics than a fixation on the notion of self‑organised criticality might suggest. Technically speaking, Newman's game does not organise itself into a critical state; nevertheless, it does show power laws and fractals and the same wild sensitivity in which a quite ordinary, run-­of‑the‑mill shock can trigger an upheaval out of all proportion to itself. What is more, as with the critical state, this sensitivity comes about naturally under an extremely broad set of conditions. These are the ubiquitous properties that arise again and again in things driven away from equilibrium, and in things in which history matters. And these are the things that are making a new kind of science possible ‑ a theoretical science tuned to the context of the historical sciences. In geophysics and biology, these ideas are already making themselves felt. But history has a far wider reach, and, in particular, has its fingers on almost every human activity. With the conceptual tools we have gathered so far, we can now begin asking what they imply about the nature of the human world. Unfortunately, it is not often easy to put precise numbers on social changes. Political revolutions and waves of new fashion affect us all, but cannot easily be measured with the same precision as fluctuations in a magnet, or vibrations in the earth's crust.

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