Thompson was more a brilliant reactionary than a visionary. He took Pythagoras seriously and worked as a Greek geometrician. He took special delight in finding the abstract forms of an idealized world embodied again and again in the products of nature. Why do repeated hexagons appear in the cells of a honeycomb and in the interlocking plates of some turtle shells? Why do the spirals in a pine cone and a sunflower (and often of leaves on a stem) follow the Fibonacci series? (A system of spirals radiating from a common point can be viewed either as a set of left- or right-handed spirals. Left and right spirals are not equal in number, but represent two consecutive figures of the Fibonacci series. The Fibonacci series is constructed by adding the previous two numbers to form the next: 1, 1, 2, 3, 5, 8, 13, 21, etc. The pine cone may, for example, have 13 left spirals and 21 right spirals.) Why do so many snail shells, ram’s horns, and even the path of a moth to light follow a curve called the logarithmic spiral?
Thompson’s answer was the same in each case: these abstract forms are optimal solutions for common problems. They are evolved repeatedly in disparate groups because they are the best, often the only, path to adaptation. Triangles, parallelograms, and hexagons are the only plane figures that fill space completely without leaving holes. Hexagons are often favored because they approximate a circle and maximize area within relative to the supporting walls (minimum construction for greatest storage of honey, for example). The Fibonacci pattern emerges automatically in any system of radiating spirals built by adding new elements at the apex, one at a time in the largest space available. The logarithmic spiral is the only curve that does not change its shape as it grows in size. I can identify the abstract Thompsonian forms as optimal adaptations, but to the larger metaphysical issue of why “good” form often exhibits such simple, numerical regularity, I plead only ignorance and wonder.
So far, I have only spoken to half the issue embodied in the problem of repeated perfection. I have discoursed on the “why.” I have argued that convergence never renders two complex organisms completely identical (a circumstance that would strain Darwinian processes beyond their reasonable power) and I have tried to explain close repeats as optimal adaptations to common problems with few solutions.
But what about the “how?” We may know what the fish of Lampsilis and the lure of the anglerfish are for, but how did they arise? This problem becomes particularly acute when the final adaptation is complex and peculiar but built from familiar parts of different ancestral function. If the angler’s fishlike lure required 500 entirely separate modifications to attain its exquisite mimicry, then how did the process begin? And why did it continue, unless some non-Darwinian force, cognizant of the final goal, drove it on? Of what possible benefit is step one alone? Is a five-hundredth of a fake enough to inspire the curiosity of any real item?
D’Arcy Thompson’s answer to this problem was overextended but characteristically prophetic. He argued that organisms are shaped directly by physical forces acting upon them: optima of form are nothing more than the natural states of plastic matter in the presence of appropriate physical forces. Organisms jump suddenly from one optimum to another when the regime of physical forces alters. We now know that physical forces are too weak, in most cases, to build form directly—and we look to natural selection instead. But we are derailed if selection can only act in a patient and piecemeal way—step by sequential step to build any complex adaptation.
I believe that a solution lies in the essence of Thompson’s insight, shorn of his unsubstantiated claim that physical forces shape organisms directly. Complex forms are often built by a much simpler (often a very simple) system of generating factors. Parts are connected in intricate ways through growth, and alteration of one may resound through the entire organism and change it in a variety of unsuspected ways. David Raup, of Chicago’s Field Museum of Natural History, adapted D’Arcy Thompson’s insight to a modern computer, and showed that the basic forms of coiled shells—from nautiloid to clam to snail—can all be generated by varying only three simple gradients of growth. Using Raup’s program, I can change a garden-variety snail into a common clam by modifying just two of the three gradients. And, believe it or not, a peculiar genus of modern snails does carry a bivalved shell so like a conventional clam’s that I gasped when I saw a snail’s head poking out between the valves in a striking close-up movie.
In these computer-drawn figures (they are not real snails, despite the similarities), a form (right) looking much like certain clams can be converted into a “snail” (left figures) simply by decreasing the rate at which the generating ellipse increases as the “shell” grows and by increasing the rate of translation of this ellipse down the axis of coiling. All these figures are drawn by specifying just four parameters.
PHOTO COURTESY OF D. M. RAUP
This closes my trilogy on the issue of perfection and imperfection as signs of evolution. But the entire set is really an extended disquisition on the panda’s “thumb,” a single, concrete object that spawned all three essays, despite their subsequent wanderings and musings. The thumb, built of a wrist bone, imperfect as a sign of history, constructed from parts available. Dwight Davis faced the dilemma of potential impotence for natural selection if it must work step by countless step to make a panda from a bear. And he advocated D’Arcy Thompson’s solution of reduction to a simple system of generating factors. He showed how the complex apparatus of the thumb, with all its muscles and nerves, may arise as a set of automatic consequences following a simple enlargement of the radial sesamoid bone. He then argued that the complex changes in form and function of the skull—the transition from omnivory to nearly exclusive munching on bamboo—could be expressed as consequences of one or two underlying modifications. He concluded that “very few genetic mechanisms—perhaps no more than half a dozen—were involved in the primary adaptive shift from Ursus [bear] to Ailuropoda [panda]. The action of most of these mechanisms can be identified with reasonable certainty.”
And thus we may pass from the underlying genetic continuity of change—an essential Darwinian postulate—to a potentially episodic alteration in its manifest result—a sequence of complex, adult organisms. Within complex systems, smoothness of input can translate into episodic change in output. Here we encounter a central paradox of our being and of our quest to understand what made us. Without this level of complexity in construction, we could not have evolved the brains to ask such questions. With this complexity, we cannot hope to find solutions in the simple answers that our brains like to devise.
2 | Darwiniana
4 | Natural Selection and the Human Brain: Darwin vs. Wallace
IN THE SOUTH transept of Chartres cathedral, the most stunning of all medieval windows depicts the four evangelists as dwarfs sitting upon the shoulders of four Old Testament prophets—Isaiah, Jeremiah, Ezekiel, and Daniel. When I first saw this window as a cocky undergraduate in 1961, I immediately thought of Newton’s famous aphorism—“if I have seen farther, it is by standing on the shoulders of giants”—and imagined that I had made a major discovery in unearthing his lack of originality. Years later, and properly humbled for many reasons, I learned that Robert K. Merton, the celebrated sociologist of science from Columbia University, had devoted an entire book to pre-Newtonian usages of the metaphor. It is titled, appropriately, On The Shoulders of Giants. In fact, Merton traces the bon mot back to Bernard of Chartres in 1126 and cites several scholars who believe that the windows of the great south transept, installed after Bernard’s death, represent an explicit attempt to capture his metaphor in glass.
Although Merton wisely constructs his book as a delightful romp through the intellectual life of medieval and Renaissance Europe, he does have a serious point to make. For Merton has devoted much of his work to the study of multiple discoveries in science. He has shown that almost all major ideas arise more than once, independently and often virtually at the same time—and thus, that great scientists are embedded in their cultures, not divorced from them. Most great id
eas are “in the air,” and several scholars simultaneously wave their nets.
One of the most famous of Merton’s “multiples” resides in my own field of evolutionary biology. Darwin, to recount the famous tale briefly, developed his theory of natural selection in 1838 and set it forth in two unpublished sketches of 1842 and 1844. Then, never doubting his theory for a moment, but afraid to expose its revolutionary implications, he proceeded to stew, dither, wait, ponder, and collect data for another fifteen years. Finally, at the virtual insistence of his closest friends, he began to work over his notes, intending to publish a massive tome that would have been four times as long as the Origin of Species. But, in 1858, Darwin received a letter and manuscript from a young naturalist, Alfred Russel Wallace, who had independently constructed the theory of natural selection while lying ill with malaria on an island in the Malay Archipelago. Darwin was stunned by the detailed similarity. Wallace even claimed inspiration from the same nonbiological source—Malthus’ Essay on Population. Darwin, in great anxiety, made the expected gesture of magnanimity, but devoutly hoped that some way might be found to preserve his legitimate priority. He wrote to Lyell: “I would far rather burn my whole book, than that he or any other man should think that I have behaved in a paltry spirit.” But he added a suggestion: “If I could honorably publish, I would state that I was induced now to publish a sketch…from Wallace having sent me an outline of my general conclusions.” Lyell and Hooker took the bait and came to Darwin’s rescue. While Darwin stayed home, mourning the death of his young child from scarlet fever, they presented a joint paper to the Linnaean Society containing an excerpt from Darwin’s 1844 essay together with Wallace’s manuscript. A year later, Darwin published his feverishly compiled “abstract” of the longer work—the Origin of Species. Wallace had been eclipsed.
Wallace has come down through history as Darwin’s shadow. In public and private, Darwin was infallibly decent and generous to his younger colleague. He wrote to Wallace in 1870: “I hope it is a satisfaction to you to reflect—and very few things in my life have been more satisfactory to me—that we have never felt any jealousy towards each other, though in one sense rivals.” Wallace, in return, was consistently deferential. In 1864, he wrote to Darwin: “As to the theory of Natural Selection itself, I shall always maintain it to be actually yours and yours only. You had worked it out in details I had never thought of, years before I had a ray of light on the subject, and my paper would never have convinced anybody or been noticed as more than an ingenious speculation, whereas your book has revolutionized the study of Natural History, and carried away captive the best men of the present age.”
This genuine affection and mutual support masked a serious disagreement on what may be the fundamental question in evolutionary theory—both then and today. How exclusive is natural selection as an agent of evolutionary change? Must all features of organisms be viewed as adaptations? Yet Wallace’s role as Darwin’s subordinate alter ego is so firmly fixed in popular accounts that few students of evolution are even aware that they ever differed on theoretical questions. Moreover, in the one specific area where their public disagreement is a matter of record—the origin of human intellect—many writers have told the story backwards because they failed to locate this debate in the context of a more general disagreement on the power of natural selection.
All subtle ideas can be trivialized, even vulgarized, by portrayal in uncompromising and absolute terms. Marx felt compelled to deny that he was a marxist, while Einstein contended with the serious misstatement that he meant to say “all is relative.” Darwin lived to see his name appropriated for an extreme view that he never held—for “Darwinism” has often been defined, both in his day and in our own, as the belief that virtually all evolutionary change is the product of natural selection. In fact Darwin often complained, with uncharacteristic bitterness, about this misappropriation of his name. He wrote in the last edition of the Origin (1872): “As my conclusions have lately been much misrepresented, and it has been stated that I attribute the modification of species exclusively to natural selection, I may be permitted to remark that in the first edition of this work, and subsequently, I placed in a most conspicuous position—namely, at the close of the Introduction—the following words: ‘I am convinced that natural selection has been the main but not the exclusive means of modification.’ This has been of no avail. Great is the power of steady misrepresentation.”
However, England did house a small group of strict selectionists—“Darwinians” in the misappropriated sense—and Alfred Russel Wallace was their leader. These biologists did attribute all evolutionary change to natural selection. They viewed each bit of morphology, each function of an organ, each behavior as an adaptation, a product of selection leading to a “better” organism. They held a deep belief in nature’s “rightness,” in the exquisite fit of all creatures to their environments. In a curious sense, they almost reintroduced the creationist notion of natural harmony by substituting an omnipotent force of natural selection for a benevolent deity. Darwin, on the other hand, was a consistent pluralist gazing upon a messier universe. He saw much fit and harmony, for he believed that natural selection holds pride of place among evolutionary forces. But other processes work as well, and organisms display an array of features that are not adaptations and do not promote survival directly. Darwin emphasized two principles leading to nonadaptive change: (1) organisms are integrated systems and adaptive change in one part can lead to nonadaptive modifications of other features (“correlations of growth” in Darwin’s phrase); (2) an organ built under the influence of selection for a specific role may be able, as a consequence of its structure, to perform many other, unselected functions as well.
Wallace stated the hard hyper-selectionist line—“pure Darwinism” in his terms—in an early article of 1867, calling it “a necessary deduction from the theory of natural selection.”
None of the definite facts of organic selection, no special organ, no characteristic form or marking, no peculiarities of instinct or of habit, no relations between species or between groups of species, can exist but which must now be, or once have been, useful to the individuals or races which possess them.
Indeed, he argued later, any apparent nonutility must only reflect our faulty knowledge—a remarkable argument since it renders the principle of utility impervious to disproof a priori: “The assertion of ‘inutility’ in the case of any organ…is not, and can never be, the statement of a fact, but merely an expression of our ignorance of its purpose or origin.”
All the public and private arguments that Darwin pursued with Wallace centered upon their differing assessments of the power of natural selection. They first crossed swords on the issue of “sexual selection,” the subsidiary process that Darwin had proposed in order to explain the origin of features that appeared to be irrelevant or even harmful in the usual “struggle for existence” (expressed primarily in feeding and defense), but that could be interpreted as devices for increasing success in mating—elaborate antlers of deer, or tail feathers of the peacock, for example. Darwin proposed two kinds of sexual selection—competition among males for access to females, and choice exercised by females themselves. He attributed much of the racial differentiation among modern humans to sexual selection, based upon different criteria of beauty that arose among various peoples. (His book on human evolution—The Descent of Man (1871)—is really an amalgam of two works: a long treatise on sexual selection throughout the animal kingdom, and a shorter speculative account of human origins, relying heavily upon sexual selection.)
The notion of sexual selection is not really contrary to natural selection, for it is just another route to the Darwinian imperative of differential reproductive success. But Wallace disliked sexual selection for three reasons: it compromised the generality of that peculiarly nineteenth-century view of natural selection as a battle for life itself, not merely for copulation; it placed altogether too much emphasis upon the “volition” of animals, part
icularly in the concept of female choice; and, most importantly, it permitted the development of numerous, important features that are irrelevant, if not actually harmful, to the operation of an organism as a well-designed machine. Thus, Wallace viewed sexual selection as a threat to his vision of animals as works of exquisite craftsmanship, wrought by the purely material force of natural selection. (Indeed, Darwin had developed the concept largely to explain why so many differences among human groups are irrelevant to survival based upon good design, but merely reflect the variety of capricious criteria for beauty that arose for no adaptive reason among various races. Wallace did accept sexual selection based upon male combat as close enough to the metaphor of battle that controlled his concept of natural selection. But he rejected the notion of female choice, and greatly distressed Darwin with his speculative attempts to attribute all features arising from it to the adaptive action of natural selection.)
In 1870, as he prepared the Descent of Man, Darwin wrote to Wallace: “I grieve to differ from you, and it actually terrifies me and makes me constantly distrust myself. I fear we shall never quite understand each other.” He struggled to understand Wallace’s reluctance and even to accept his friend’s faith in unalloyed natural selection; “You will be pleased to hear,” he wrote to Wallace, “that I am undergoing severe distress about protection and sexual selection; this morning I oscillated with joy towards you; this evening I have swung back to [my] old position, out of which I fear I shall never get.”
But the debate on sexual selection was merely a prelude to a much more serious and famous disagreement on that most emotional and contentious subject of all—human origins. In short, Wallace, the hyper-selectionist, the man who had twitted Darwin for his unwillingness to see the action of natural selection in every nuance of organic form, halted abruptly before the human brain. Our intellect and morality, Wallace argued, could not be the product of natural selection; therefore, since natural selection is evolution’s only way, some higher power—God, to put it directly—must have intervened to construct this latest and greatest of organic innovations.
The Panda's Thumb: More Reflections in Natural History Page 4