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A scientific scandal
Commentary; New York; Apr 2003; David Berlinski;

IN SCIENCE, as in life, it is always an excellent idea to cutthe cards after the deck has been shuffled. One may admire the dealer, but trustis another matter.In a recent essay in COMMENTARY, "Has Darwin Met HisMatch?" (December 2002), I discussed, evaluated, and criticized theories ofintelligent design, which have presented the latest challenge to Darwin's theoryof evolution. In the course of the discussion I observed that the evolution ofthe mammalian eye has always seemed difficult to imagine. It is an issue thatDarwin himself raised, and although he settled the matter to his ownsatisfaction, biologists have long wished for a direct demonstration thatsomething like a functional eye could be formed in reasonable periods of time bymeans of the Darwinian principles of random variation and natural selection.Just such a demonstration, I noted in my essay, is what thebiologists Dan-Erik Nilsson and Susanne Pelger seemed to provide in a 1994paper.1 Given nothing more than time and chance, a "lightsensitivepatch," they affirmed, can "gradually turn into a focused-lenseye," and in the space of only a few hundred thousand years-a mere moment,as such things go.Nilsson and Pelger's paper has, for understand- able reasons,been widely circulated and widely praised, and in the literature of evolutionarybiology it is now regularly cited as definitive. Not the least of its remarkableauthority is derived from the belief that it contains, in the words of one ofits defenders, a "computer simulation of the eye's evolution."If this were true, it would provide an extremely importantdefense of Darwin's theory. Although a computer simulation is not by itselfconclusive-a simulation is one thing, reality another-it is often an importantlink in an inferential chain. In the case of Darwin's theory, the matter isespecially pressing since in the nature of things the theory cannot be confirmedover geological time by any experimental procedure, and it has proved verydifficult to confirm under laboratory conditions. The claim that the eye'sevolution has been successfully simulated by means of Darwinian principles, withresults falling well within time scales required by the theory, is thus a matterof exceptional scientific importance.And not just scientific importance, I might add; so dramatica confirmation of Darwinian theory carries large implications for ourunderstanding of the human species and its origins. This is no doubt why thestory of Nilsson and Pelger's computer simulation has spread throughout theworld. Their study has been cited in essays, textbooks, and popular treatmentsof Darwinism like River Out of Eden by the famous Oxford evolutionist RichardDawkins; accounts of it have made their way onto the Internet in severallanguages; it has been promoted to the status of a certainty and reported asfact in the press, where it is inevitably used to champion and vindicateDarwin's theory of evolution.In my essay, I suggested that Nilsson and Pelger's argumentsare trivial and their conclusions unsubstantiated. I also claimed thatrepresentations of their paper by the scientific community have involved aserious, indeed a flagrant, distortion of their work. But in a letter publishedin the March issue of COMMENTARY, the physicist Matt Young, whom I singled outfor criticism (and whose words I have quoted here), repeated and defended hischaracterization of Nilsson and Pelger's work as a "computer simulation ofthe eye's evolution." It is therefore necessary to set the matter straightin some detail.I hope this exercise will help to reveal, with a certainuncomfortable clarity, just how scientific orthodoxy works, and how it imposesits opinions on the faithful.HERE IN their own words is the main argument of Nilsson andPelger's paper:Theoretical considerations of eye design allow us to findroutes along which the optical structure of the eye may have evolved. Ifselection constantly favors an increase in the amount of detectable spatialinformation, a light-sensitive patch will gradually turn into a focused-lens eyethrough continuous small improvements in design. An upper limit for the numberof generations required for the complete transformation can be calculated with aminimum number of assumptions. Even with a consistently pessimistic approach,the time required becomes amazingly short: only a few hundred thousand years.And here is how they arrived at their conclusions. Thesetting is "a single circular patch of light-sensitive cells"-aretina, in effect-"which is bracketed and surrounded by dark pigment."A "protective layer" lies above these light-sensitive cells, so thatthe pigment, the light-sensitive cells, and the protective layer form a kind ofsandwich. Concerning the lightsensitive patch itself, Nilsson and Pelger provideno further details, indicating neither its size nor the number of cells it mightcontain.What they do assume, if only implicitly, is that changes tothe initial patch involve either a deformation of its shape or a thickening ofits cells. The patch can be stretched, dimpled, and pulled or pushed around, andcells may move closer to one another, like bond salesmen converging on acustomer.So much for what changes. What is the change worth? Assuming(reasonably enough) that an eye is an organ used in order to see, Nilsson andPelger represent its value to an organism by a single quantitative character orfunction, which they designate as "spatial resolution" or "visualacuity"-- sharp sight, in short. Visual acuity confers an advantage on anorganism, and so, in any generation, natural selection "constantly favorsan increase in the amount of detectable spatial information."There are two ways in which visual acuity may be increased inan initial light-sensitive patch: a) by the "invagination" of thepatch, so that it becomes progressively more concave and eventually forms theenclosed interior of a sphere; and b) by the constriction of the sphere'saperture (the two rounded boundaries formed as the flat patch undergoesinvagination). These changes may be represented on sheets of high-school graphpaper on which two straight lines-the x and y axes of the system-have beencrossed. On the first sheet, representing invagination, visual acuity movesupward on one axis as invagination moves to the right on the other; on thesecond sheet, visual acuity moves upward as constriction moves to the right. Thecurves that result, Nilsson and Pelger assert, are continuous and increasing.They do not hurdle over any gaps, and they go steadily upward until they reach atheoretical maximum.The similar shape of the two graphs notwithstanding,invagination and aperture constriction exercise different effects on visualacuity. "Initially, deepening of the pit"-i.e., invagination-"isby far the most efficient strategy," Nilsson and Pelger write; "butwhen the pit depth equals the width, aperture constriction becomes moreefficient than continued deepening of the pit." From this, they concludethat natural selection would act "first to favor depression andinvagination of the light-sensitive patch, and then gradually change to favorconstriction of the aperture."THE RESULT is a pin-hole eye, which is surely an improvementon no eye at all. But there exists an aperture size beyond which visual acuitycannot be improved without the introduction of a lens. Having done all that itcan do, the pin-hole eye lapses. Cells within the light-sensitive sphere nowobligingly begin to thicken themselves, bringing about a "localincrease" in the eye's refractive index and so forming a lens. When thefocal length of the lens is 2.55 times its radius-the so-called Mattiessenratio-the eye will have achieved, Nilsson and Pelger write, the "idealsolution for a graded-index lens with a central refractive index of 1.52."2Thereafter, the lens "changes its shape from ellipsoidto spherical and moves to the center of curvature of the retina." A flatiris "gradually forms by stretching of the original aperture," whilethe "focal length of the lens ... gradually shortens, [until] it equals thedistance to the retina ... producing a sharply focused image." Theappearance of this spherical, graded-index lens, when placed in the center ofcurvature of the retina, produces "virtually aberration-free imaging overthe full 180 degrees of the visual field."The same assumptions that governed invagination and apertureconstriction hold sway here as well. Plotted against increasing lens formation,visual acuity moves smoothly and steadily upward as a graded-index lens makesits appearance, changes its shape, and moves to center stage. When thesetransformations have been completed, the result is a "focused camera-typeeye with the geometry typical for aquatic animals."One step remains. Nilsson and Pelger now amalgamateinvagination, constriction, and lens formation into a single"transformation," which they represent by juxtaposing, against changesin visual acuity, changes to the original patch in increments of 1 percent. Theresulting curve, specifying quantitatively how much visual acuity may bepurchased for each 1-percent unit of change, is ascending, increasing, andstraight, rising like an arrow at an angle of roughly 45 degrees from its pointof origin. Transformations are "optimal" in the sense that they bringabout as much visual acuity as theoretically possible, with the "geometryof each stage [setting] an upper limit to the spatial resolution of theeye."It is the existence and shape of this fourth curve thatjustify their claim that "a light-sensitive patch will gradually turn intoa focused-lens eye through continuous small improvements in design"(emphasis added). This is not the happiest formulation they could have chosen.HOW MUCH does the initial light-sensitive patch have tochange in order to realize a focused camera-type eye? And how long will it taketo do so? These are the questions now before us.As I have mentioned, Nilsson and Pelger assume that theirinitial light-sensitive patch changes in 1-percent steps. They illustrate theprocedure with the example of a flat one-foot ruler that also changes in1-percent steps. After the first step, the ruler will be one foot plus 1 percentof one foot long; after the second step, it will be 1-percent longer than thelength just achieved; and so forth. It requires roughly 70 steps to double aone-foot ruler in length. Putting the matter into symbols, 1.01^sup 70^~= 2.Nilsson and Pelger undertake a very similar calculation withrespect to their initial light-sensitive patch. But since the patch is athree-dimensional object, they are obliged to deal with three dimensions ofchange. Growing in steps of 1 percent, their blob increases its length, itscurvature, and its volume. When all of these changes are shoehorned together,the patch will have increased in magnitude along some overall (but unspecified)dimension.The chief claim of their paper now follows: to achieve thevisual acuity that is characteristic of a "focused camera-type eye with thegeometry typical for aquatic animals," it is necessary that an initialpatch be made 80,129,540 times larger (or greater or grander) than it originallywas. This number represents the magnitude of the blob's increase in size. Howmany steps does that figure represent? Since 80,129,540 = 1.01^sup 1,829^,Nilsson and Pelger conclude that "altogether 1,829 steps of 1 percent arerequired" to bring about the requisite transformation.These steps, it is important to remember, do not representtemporal intervals. We still need to assess how rapidly the advantagesrepresented by such a transformation would spread in a population of organisms,and so answer the question of how long the process takes. In order to do this,Nilsson and Pelger turn to population genetics. The equation that followsinvolves the multiplication of four numbers:R=h^sup 2^*i*V*mHere, R is the response (i.e. visual acuity in eachgeneration), h is the coefficient of heredity, i designates the intensity ofselection, V is the coefficient of variation (the ratio of the standarddeviation to the mean), and m, the mean value for visual acuity. These fournumbers designate the extent to which heredity is responsible for visual acuity,the intensity with which selection acts to prize it, the way its mean or averagevalue is spread over a population, and the mean or average value itself. Valuesare assigned as estimates to the first three numbers; the mean is leftundetermined, rising through each generation.As for the estimates themselves, Nilsson and Pelger assumethat h^sup 2^=.50; that i = 0.01; and that V= 0.01. On this basis, they concludethat R = 0.00005m. The response in each new generation of light-sensitivepatches is 0.00005 times the mean value of visual acuity in the previousgeneration of light-- sensitive patches.Their overall estimate-the conclusion of their paper-nowfollows in two stages. Assume that n represents the number of generationsrequired to transform a light-sensitive patch into a "focused camera-typeeye with the geometry typical for aquatic animals." (In small aquaticanimals,'a generation is roughly a year.) If, as we have seen, the mean value ofvisual acuity of such an eye is 1.01^sup 1,829^ = 80,129,540, where 1,829represents the number of steps required and 80,129,540 describes the extent ofthe change those steps bring about; and if 1.00005^sup n^ = 1.01^sup 1,829^ =80,129,540, then it follows that n = 363,992.It is this figure-363,992-that allows Nilsson and Pelger toconclude at last that "the time required [is] amazingly short: only a fewhundred thousand years." And this also completes my exposition of Nilssonand Pelger's paper. Business before pleasure.


John Landon
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