A Simple Matter of Complexity
Roger Lewin

New Scientist, 5 February 1994, pp 37-41

"The course of evolution is uncertain, but its patterns are not," observes Roger Thomas, a paleontologist of Franklin and Marshall College, Pennsylvania. "The most significant pattern in the history of life is the progressive net increase in complexity of structure and dynamics that has occurred in organisms and the ecosystems in which they participate." With this simple, straightforward statement, Thomas plunges headlong into one of the more contentious issues in biology: namely, the shape of the history of life on Earth. Does the evolutionary process inevitably generate ever more complex organisms and ecosystems as time passes? And if so, what is the nature of that increase?

Even to the casual observer, the answers to the questions seem self evident: Life started with single-celled organisms, progressed through primitive multicellular organisms, such as bizarre jawless fish and lumbering reptiles, and culminated (so far) in hot-blooded, sleek, and fleet-of-foot mammals, some of which are also endowed with large brains and even consciousness. Such a trajectory of change through time looks like the embodiment of increased complexity. Moreover, there appears to be an undeniable improvement of organisms through evolutionary time, for aren't mammals somehow "better" biologically than reptiles? So, when Dan McShea, a paleontologist at the University of Michigan, Ann Arbor, recently wrote, "Everybody seems to know that complexity increases in evolution," he seemed to be stating the obvious. Darwin believed it, as did most of his followers, with a few exceptions. Despite these skeptics, "increasing complexity is still the conventional wisdom," says McShea.

And yet, few topics provoke more emotion among biologists, not least because the putative increase in complexity is often conflated with the notion of progress. "Progress is a noxious, culturally embedded, untestable, nonoperational idea that must be replaced if we wish to understand the patterns of history," asserts Stephen Jay Gould, the eminent Harvard evolutionary biologist. The notion of progress has been taken to imply an evolutionary drive toward steady improvement, a march toward better and better life forms, culminating in Homo sapiens. These days, most biologists reject so anthropomorphic a sentiment. "It's acceptable to talk about complexity, but not progress," observes McShea. Michael Ruse, a philosopher of science at University of Guelph, Canada, makes the point more graphically: "Saying the word 'progress' in the company of serious evolutionary biologists is like saying 'fuck' at a vicars' tea party--it doesn't help the climb up the ecclesiastical pole."

The notion of increased complexity through evolutionary time has deep historical roots, and derives from the ancient idea of the image of an ordered world, with organisms arranged from the "lowest" to the "highest" forms. The ordering is to be found in Plato and implicitly in the sequence of creation in Genesis. Much later, in the eighteenth century, this ordering of nature became encapsulated in what was known as the Great Chain of Being, with the simplest form at the bottom of the chain and the most complex (humans) near the top, "a little lower than the angels." In those pre-Darwinian times, the chain was meant as a static description of each species' place in the world, not as a record of change over time. With the advent of Darwinian evolutionary theory, organisms came to be seen as the product of change over very long periods of time. The static order of the Great Chain of Being effectively became transformed in people's minds into a record of that evolutionary history, from simple to complex forms. An increase in complexity through evolutionary time seemed evident.

Despite biologists' long-held fascination with the notion of complexity and its trajectory of change through evolutionary time, few have actually tried experimentally to test the widespread assumption of inexorable increase. There is good reason for this reluctance, as Edward O. Wilson, of Harvard University observes: "It is not difficult to recognize complexity. The difficulty comes in how you measure it." George Gaylord Simpson expressed the same sentiment four decades ago: "It would be a brave anatomist who would attempt to prove that Recent man is more complicated than a Devonian ostracoderm." Comparing a cat with a clam, says McShea, many people will get the impression that there is "something more" going on in the cat. But, "is that 'something more' greater complexity or is it greater intelligence, greater mobility, or greater similarity to us? Hard to say."

Complexity is a very slippery term, and, as we will see, means different things to different people. Lacking a clear-cut, agreed-upon definition of the word, it is not surprising that biologists have been reluctant to stray experimentally into such uncertain territory. McShea is one of few who have had the courage to do so recently, as have George Boyajian, of the University of Pennsylvania, and Tim Lutz, of West Chester University. Working with several groups of vertebrates (McShea) and ammonites, Nautilus-like, shelled creatures (Boyajian and Lutz), none of the researchers saw evidence of an increase in complexity through time. To Thomas, these results were no surprise, not because he does not believe in the reality of increased complexity; rather, he says, McShea, Boyajian and Lutz were looking at the wrong things. Before exploring this further, it is worth looking more generally at how others have approached the issue of complexity at a basic level, in biological and nonbiological systems.

Working at an abstract level, mathematicians have attempted to quantify degrees of complexity embodied in a system, often with frustratingly paradoxical results (see box). Biologists, of course, are interested in organisms and groups of organisms, rather than the numerical systems that are the stuff of mathematics. A few biologists have tried to pin down criteria for measuring complexity, including counting the number of different anatomical parts, with only modest success. Is a cat more complex than a clam? It would be judged so by this criterion, but is it true in an absolute sense? And vervet monkeys seem more complex biologically than the trees they live in, but this view may be overlooking a subtle complexity of treeness.

There is a natural tendency not only to think of animals as more complex than plants but also to think of mammals as somehow more complex than reptiles. A lion seems a more advanced machine than, say, a Tyranosaurus, even though both are (or were) carnivores. Zebras are surely more complex in some way than hadrosaurs, even though both are (or were) grazers and social animals. But one thing that has become clear to biologists recently is that the modern world of mammals is just like the ancient world of the great reptiles. In both you can identify small and large carnivores, small and large herbivores, small and large insectivores, and so on. The same ecological niches are filled in both worlds, and with about the same number of species. Nothing to distinguish them there. But are mammals, with their higher metabolic rate, more complex than reptiles in a general sense, because they channel more energy?

One of the most respected attempts for developing an objective measure of complexity was made by John Tyler Bonner, of Princeton University. Count the number of different cell types in the organism, he suggested. In principle this gives a sense of the number of specialized functions an organism can perform, and that is a clue to complexity. It also has the virtue of considering the whole organism, not just one part. (It does leave out behavior, but the challenge is great enough when dealing only with morphology.) Bonner was able to show higher complexity in larger species by this measure, but he did not try to determine whether it increased through evolutionary time. That would, however, be a reasonable inference.

The notion of assessing the number of parts in an organism as a measure of complexity, as Bonner's approach embodies, finds considerable favour among biologists. This measure may be extended by looking at the irregularity of those parts. For instance, the spine of a fish is built from a chain of vertebrae, each of which is very similar to the next. In mammals, by contrast, the vertebral column is more complex, with considerable anatomical themes being played out as one travels from the cervical, through the thoracic, and on to the lumbar vertebrae. It was this possibility for an insight into the modification of complexity through time that attracted McShea in his research. He examined five groups of species--squirrels, ruminants, camels, whales, and pangolins--and in each asked whether the structure of the vertebral column had become more complex through evolutionary time, which stretched through some thirty million years.

McShea used a bank of six measures--such as thickness, length of spines, and so on--in his search for evidence of change in complexity through time. In some cases he did see indications of increased complexity, but he encountered decreases too, and stasis. "The overall impression is of no trend toward increased complexity," he concluded. "You see increased complexity no more frequently than decrease." Boyajian Tim Lutz came to a similar view with their study of ammonoids, which existed for 330 million years, before going extinct in company with the dinosaurs, sixty-five million years ago. The spiral-shaped shells of these creatures are constructed from multiple chambers, separated by walls, or septa. The structure of the septa are sometimes simple, sometimes complex. Although it is true that the most complex structures are to be found among the later species, and the simplest among the earliest, within any particular lineage there was no steady progression toward increased complexity. The pattern of change of structure through time was more or less random, with decreases just as likely as increases. "We don't see any direction to the change of complexity," says Boyajian.

As a side issue in their study, Boyajian and Lutz also asked whether greater complexity conferred any measurable survival advantage. Greater complexity is more expensive to produce than simplicity, so it seems reasonable to suppose that, where it occurs, such complexity is beneficial. But, again, there was no "common-sense" correlation. The average longevity for ammonoid genera was fifteen million years, with the anatomically more complex species doing no better (no any worse) than the simple ones. Apparently, the possession of greater anatomical complexity was neither beneficial nor detrimental to the species. The obvious question, then, is, Why bother to become more complex at all, ever?

To Gould, these results are just what would be expected of the evolutionary process. Evolution is driven by natural selection, and this is a local phenomenon, not a global trend. In other words, organisms, via natural selection, adapt to prevailing conditions, and these are just as likely to demand a decrease in complexity as an increase. To Thomas, however, McShea's results have another explanation. When a new group evolves, it undergoes an initial burst of change, an adaptive radiation that sees the establishment of evolutionary novelty in a proliferation of new species. Expressed graphically, the process of change through time is seen as an initial steep rise, followed by a plateau, where little further change occurs. "All the taxa included in his study lived long after the early radiation in which the main increase in mammalian complexity presumably occurred," says Thomas. In other words, McShea's study was effectively located on the plateau of the graph of change, where little change was inevitable.

But, as McShea himself says, everyone "knows" the world of nature is more complex now than it was 550 million years ago, when the first multi-cellular creatures evolved, and certainly more so than prior to

this event, when only single-celled organisms existed. So there has been an increase of complexity through time, even if it is not expressed as an arrow of change in all lineages. How is this to be explained? As the British evolutionary biologist John Maynard Smith puts it, "When you start simple, there's no way to go but up." In other words, even with random change, there is an inevitable drift toward more complexity, beginning, as life did, in the simplest possible form. As evolutionary time marches on, islands of greater complexity emerge stochastically against the background. And each new level of complexity provides new heights upon which chance changes can operate, like an evolutionary ratchet.

Competition is an important facet of natural selection, particularly competition between predator and prey. As a result of the continual struggle for existence, both predator and prey may be driven to develop ever more effective weapons and defenses. For instance, Geraat Vermeij, of the University of California, Davis, has documented a trend of thicker and stronger crab claws matched by increasingly effective defenses (such as thicker shells, the development of spines, and so on) in the snails the crabs feed on. Similar "arms races" can be seen in much of the world of nature, including insects, plants, and vertebrates. Species are driven to evolve new structures and behaviors, which may sometimes be manifest as increased complexity. And yet the species are no better off than they were, for they are running to stay in the same place for survival. With characteristic deftness, Leigh van Valen, of the University of Chicago, has labelled this the Red Queen effect.

In this view of evolution, increased complexity is seen to have arisen in at least two ways: first, as a stochastic drift, when the direction of change is constrained in one direction (towards the simple) and open in another (towards the complex); second, as a result of coevolution driven by competition. Thomas describes this overall pattern increased complexity in the history of life as "a long-term effect, not a law of evolution." In other words, complexity increases as a secondary effect of the evolutionary process, not as an inherent property.

Norman Packard, of the Prediction Company, Santa Fe, New Mexico, demurs from this "passive" explanation

of life's pattern. "Biological complexity has to do with the ability to process information," he says. Packard, a pioneer in the development of chaos theory and, more recently, complexity theory, has not yet developed specific measure of what he calls "computational capability." Nevertheless, he says, this capacity is seen in complex dynamical systems, such as certain computer models, and in living systems. "Increased computational ability is what drives the evolution of computer algorithms and living organisms." The computer algorithms, or programs, Packard refers to are allowed to compete with each other in some kind of "game," such as prisoners' dilemma. The programs are may "mutate" and accumulate changes through time. In all such programs, no matter the nature of the algorithm or the game, there emerges an ever greater complexity. "You start with the simplest possible strategy and you finish up with complex individual strategies and a complex interactive system," explains Packard. "It's simply the dynamics of the system that produces it, given the goal of playing the game." Sometimes some of the algorithms become simpler, not more complex, during the model's life, just as occurs in biological evolution. Nevertheless, "the system as a whole undoubtedly becomes more complex."

Packard's argument was developed from the realms of computer programs, but it resonates with a view expressed in a classic 1977 textbook on evolution, by Theodosius Dobzhansky, Francisco Ayala, G. Ledyard Stebbins, and James Valentine. They stated that the "ability to gather and process information" increased through evolutionary history, and, indeed, is a mark of progress. Ayala, speaking at a conference of "Evolution and Progress" some years ago in Chicago, said: "The ability to obtain and process information about the environment and to react accordingly, is an important adaptation, because it allows that organism to seek out suitable environments and resources and to avoid unsuitable one." Wilson also considers information processing as a measure of complexity: "There's no question that there has been a general increase in information processing over the last 550 million years, and particularly in the last 150 million years."

Survival has to do with gathering information about the environment, and responding appropriately. There is no doubt that brains have become ever more sophisticated in their ability to process this information--in other words, an increased computational ability. All complex dynamical systems in biology, from bacteria to people, have a degree of computational ability. "You don't have to have a brain to process information in the way I'm talking about it," says Packard, "but a brain puts you higher on the scale of computational ability." The phrase "higher on the scale" is instantly provocative to biologists, because, with Darwin cited as mentor, they are taught that "higher" and "lower" are value-laden terms, not meaningful biological labels. Biologists are also taught that higher and lower implies a progressive element in evolution, ascending the scale of nature from the simple to the complex--and that's anathema. As McShea said, biologists are willing to tackle the notion of complexity and accept that it has increased in the history of life in some ill-defined way, but to speak of "progress" is regarded as unwise. If evolution is held to be progressive, then it is all too easy to see it as being directed, following an arrow of improvement through time. And that is all too redolent of the Divine design of pre-Darwinian days.

Packard, a physicist, is not afraid to stray into this territory. "Intuitively, it seems reasonable that the task of survival requires computation," he explains. If this is true, then selection among organisms will lead to an inexorable increase in computational abilities, generating an arrow of change, not just a drift upwards. The fossil record shows a dramatic increase in average brain size with the evolution of mammals from reptiles, some 230 million years ago; a similar increase occurs when "modern" mammals evolve, 50 million years ago; primates are twice as "brainy" as the average mammal; within primates, apes are twice as endowed as monkeys, and humans boast a further three-fold increase. Humans stick out like a sore thumb, with our relatively enormous brain, but, says Packard, if we are left out of consideration, it is still accurate to say that computational ability has increased through time. "That's just what you'd expect," he asserts.

Gould concedes that some trends toward bigger brains can be discerned among the mammals, but argues that the overall pattern is nothing more than the inevitable drift from simplicity to complexity mentioned earlier. "You cannot suggest that what happens in some groups of six thousand species of mammals represents the thrust of evolution," he says. "Certainly, brains have had more effect than any other structure," Gould allows, but he goes on to say that this should not be conflated with increased complexity. "After all, next in effect are the bacteria. Effect has to be divorced from complexity."

Gould suggests that biologists are held in thrall by brain size increase through evolution because of a concern with human consciousness. "You can't blame us for being fascinated with consciousness," he says. "It's an enormous punctuation in the history of life. I view it as a quirky accident, but most people apparently don't want to look at it like that. If you believe there is an inexorable increase in brain size through evolutionary history, then human consciousness becomes predictable, not a quirky accident. Ours is a very `brain-centric' view of evolution, a bias that distorts our perception of the true pattern of history."

Many biologists are uncomfortable with talking about increase in brain size as a measure of increased complexity. "You'd like to think that being able to solve problems contributes to Darwinian fitness, wouldn't you?" says John Maynard Smith. "But it's hard to relate increased brain size to fitness. After all, bacteria are fit." Wilson, however, has no doubts, and is dismissive of the suggestion that a fascination with brain-size increase is the result of being "brain-centric": "Isn't that the ultimate politically correct mode of reasoning?" Packard is equally forthright about the reality of brain-size increase and the rejection of it for social rather than scientific reasons: "I don't impute a value judgement to computational superiority," he says.

The debate over brain-size increase as an inevitability of the evolutionary process echoes Darwin's ambivalence over progress in evolution. Darwin grew up in Victorian Britain, at the height of the nation's industrial and political prowess. Progress was the proper reward for effort in society, and this ethic became transferred to science, often expressed explicitly in texts on evolution, particularly on human evolution. "Darwin's doctrine of evolution...has been, and ever will be, the means of progressive evolution," wrote Henry Fairfield Osborn, director of the American Museum of Natural History in the early decades of this century. Darwin was not immune to this intellectual environment, and yet he saw that natural selection was a local, not a global, process. As a result, his writings are scattered with contradictory statements about the reality or otherwise of progress.

For instance, Darwin wrote to Alpheus Hyatt, an American biologist, saying, "After long reflection I cannot avoid the conviction that no innate tendency to progressive evolution exists." And yet, toward the end of the Origin of Species he wrote, "And as natural selection works solely by and for the good of each being, all corporeal and mental endowments will tend to progress towards perfection." Proponents of both sides of the progress/no-progress debate are therefore able to adduce Darwin's words in support of their position, by selective quotation. McShea, who embarked upon his study of the literature and the experimental detection of progress, expected to find evidence in its favour, but failed. Now, he is left pondering the following question: "Why do we want to find progress in evolution, rather than find if it is there." He wonders whether it is a device "to justify our position on the top of the biological heap."

Gould takes a similar view: "There is a profound unwillingness to abandon a view of life as predictable progress," he says, "because to do so would be to admit that human existence is nothing but a historical accident. That is difficult for many to accept." In other words, the reality of evolutionary progress gives meaning to life.

Complexity, in its varying degrees, is a property of all of the natural world, not just of living organisms. For instance, a crystal lattice clearly displays a different state of complexity than gas molecules in the air. What is the difference? The paradoxical answers that some proposed measures come up with for such comparisons illustrate the problem of quantifying complexity, even in systems that seem relatively tractable to description.

Claud E. Shannon, of Bell Telephone Laboratories, New York, was among the first to propose a measure of complexity, four decades ago. His approach was based on the very reasonable assumption that the amount of information processed by the system in question reflects its complexity. Unfortunately, Shannon's measure produced answers that, to biologists at least, were plain wrong. In comparing two strings of letters, bbbbbbbb with lofigwq, for instance, the first would be judged less complex than the second by Shannon's approach. The orderliness of bbbbbbbb seems to reflect a low information content, whereas the randomness of lofigwq embodies a large information content, because nothing is predictable in the sequence. As Seth Lloyd, of the California Institute of Technology, points out, "By this measure, a chimpanzee typing 650 pages of random alphanumeric characters would in short order produce a work not only as long as but more complex than James Joyce's Finnegan's Wake." Literary scholars would surely disagree, as would biologists, who view order, not randomness, as an expression of complexity.

The same problem befell the notion of algorithmic complexity, devised three decades ago by Raymond J. Solomonoff, of the Zator Company, Cambridge, Massachusetts, Gregory J. Chaitin, of the City University, New York, and Andrei Kolmogorov, of the Mathematics Institute, Moscow. Applied to numbers, the measure says that the longer the algorithm, or computer program, that is necessary to generate those numbers, the more complex is the set of numbers. If natural systems can also be transformed into number set, a similar assessment can be made. The structure of a crystal lattice, for instance, might be represented by a series of one's and zeros, such as 101010101010101. Measured by algorithmic complexity, such a structure would be viewed as simple, because it can be described by the brief algorithm "print 10 n times." By contrast, the random distribution of molecules in the air, represented by one's and zeros, will itself be random. The simplest algorithm describing the string of one's and zeros will be the string itself, thereby clocking up a high level of complexity on this scale. Again, disorder, not order, equates with complexity with this measure.

"Thus both Shannon's information content and algorithmic information content fail to capture our intuitive understanding of the concept of complexity," says Lloyd. What is required is something that values intricacy over randomness. Several scholars have worked toward this, including Lloyd himself. For instance, Charles H. Bennett, of the IBM Thomas J. Watson Research Center, New York, developed something he called logical depth. The approach assesses the difficulty of constructing a system, without being diverted by the unpredictability of randomness. The measure is, however, difficult to apply to natural systems. In collaboration with his colleague Heinz Pagels, Lloyd extended this approach, and developed a measure of complexity based on the amount of information processed during the evolution of the system, biological or physical. The measure involves assessing the amount of informational and thermodynamic effort involved in assembling the system, and, says Lloyd, "thus avoids ascribing high complexity to things such as random sequences of letters that carry much information but are easy to handle." Although more logically satisfying to biologists, the Lloyd/Pagels' measure is impossibly hard to apply to organisms more complex than the simplest of bacteria.