NILSSON AND Pelger's work is a critic's smorgasbord.Questions are free and there are second helpings.Every scientific paper must begin somewhere. Nilsson andPelger begin with their assumption that, with respect to the eye, morphologicalchange comes about by invagination, aperture constriction, and lens formation.Specialists may wish to know where those light-sensitive cells came from and whythere are no other biological structures coordinated with or contained withinthe interior of the initial patch-for example, blood vessels, nerves, or bones.But these issues may be sensibly deferred.Not so the issues that remain. Nilsson and Pelger treat abiological organ as a physical system, one that is subject to the laws oftheoretical optics. There is nothing amiss in that. But while theoretical opticsjustifies a qualitative relationship between visual acuity on the one hand andinvagination, aperture constriction, and lens formation on the other, therelationships that Nilsson and Pelger specify are tightly quantitative. Numbersmake an appearance in each of their graphs: the result, it is claimed, ofcertain elaborate calculations. But no details are given either in their paperor in its bibliography. The calculations to which they allude remain out ofsight, if not out of mind.The 1-percent steps: in what units are they expressed? Andhow much biological change is represented by each step? Nilsson and Pelger donot say. Nor do they coordinate morphological change, which they treat assimple, with biochemical change, which in the case of light sensitivity is knownto be monstrously complex.Does invagination represent a process in which the patchchanges as a whole, like a balloon being dimpled, or is it the result of variouslocal processes going off independently as light-sensitive cells jostle with oneanother and change their position? Are the original light-sensitive cells thecomplete package, or are new light-sensitive cells added to the ensemble as timeproceeds? Do some cells lose their sensitivity and get out of the light-sensingbusiness altogether? We do not know, because Nilsson and Pelger do not say.Biologists commenting on Darwin's theory have almost alwaysassumed that evolution reflects what the French biologist Francois Jacob calledbricolage-a process of tinkering. Biological structures are put together out ofpieces; they adapt their function to changes in their circumstances; they getby. This suggests that in the case of eye formation, morphological change mightwell purchases less visual acuity than Nilsson and Pelger assume, the eye beingtinkered into existence instead of flogged up an adaptive peak. But if, say,only half as much visual acuity is purchased for each of Nilsson and Pelger's1-percent steps, twice as many steps will be needed to achieve the effect theyclaim. What is their justification for the remarkably strong assertion thatmorphological transformations purchase an optimal amount of visual acuity ateach step?Again we do not know, because they do not say.More questions-and we have not even finished the horsd'oeuvres. The plausibility of Nilsson and Pelger's paper rests on a singlenumber: 1,829. But without knowing precisely how the number 1,829 has beenderived, the reader has no way of determining whether it is reasonable or evenmeaningful.If nothing else, the number 1,829 represents the maximumpoint of a curve juxtaposing visual acuity against morphological transformation.Now, a respect for the ordinary mathematical decencies would suggest that thecurve is derived from the number, and the number from various calculations. Butall such calculations are missing from Nilsson and Pelger's paper. And if thecalculations are not given, neither are any data. Have Nilsson and Pelger, forexample, verified their estimate, either by showing that 1,829 1-percent stepsdo suffice to transform a patch into an eye, or by showing that such an eye may,in 1,829 1-percent steps, be resolved backward into an initial light-sensitivepatch? Once again, we do not know because they do not say.Still other questions suggest themselves. Although naturalselection is mentioned by Nilsson and Pelger, it is a force that plays no rolein their reasoning. Beyond saying that it "constantly favors an increase inthe amount of detectable spatial information," they say nothing at all.This is an ignominious omission in a paper defending Darwinian principles. Animprovement in visual acuity is no doubt a fine thing for an organism; but noform of biological change is without cost.Let us agree that in the development of an eye, an initiallight-sensitive patch in a given organism becomes invaginated over time. Such achange requires a corresponding structural change to the organism's anatomy. Ifnothing else, the development of an eye requires the formation of an eyesocket-- hardly a minor matter in biological terms. Is it really the case thatan organism otherwise adapted to its environment would discover that the costsinvolved in the reconstruction of its skull are nicely balanced by what wouldinitially be a very modest improvement in sensitivity to light? I can imaginethe argument going either way, but surely an argument is needed.Then there is Nilsson and Pelger's data-free way withstatistics. What is the basis of the mathematical values chosen for the numbersthey use in assessing how rapidly transformation spreads in a population of eyepatches? The coefficient of variation is the ratio of the standard deviation tothe mean. The standard deviation, one might ask, of what? No population figuresare given; there are no quantitative estimates of any relevant numericalparameter. Why is selection pressure held constant over the course of 300,000years or so, when plainly the advantages to an organism of increasing lightsensitivity will change at every step up the adaptive slope? Why do they calltheir estimates pessimistic (that is, conservative) rather than wildlyoptimistic?Finally, Nilsson and Pelger offer an estimate of the numberof steps, computed in 1-percent (actually, 1.00005-percent) intervals, that arerequired to transform their initial patch. At one point, they convert the stepsinto generations. But a step is not a temporal unit, and, for all anyone knows,each step could well require half again or twice the number of generations theysuggest. Why do Nilsson and Pelger match steps to generations in the way theydo? I have no idea, and they do not say.WE ARE at last at the main course. Curiously enough, it isthe intellectual demands imposed by Darwin's theory of evolution that serve toempty Nilsson and Pelger's claims of their remaining plausibility.Nilsson and Pelger assert that only 363,992 generations arerequired to generate an eye from an initial light-sensitive patch. As I havealready observed, the number 363,992 is derived from the number 80,129,540,which is derived from the number 1,829-which in turn is derived from nothing atall. Never mind. Let us accept 1,829 pour le sport. If Nilsson and Pelger intendtheir model to be a vindication of Darwin's theory, then changes from one stepto another must be governed by random changes in the model's geometry, followedby some mechanism standing in for natural selection. These are, after all, thecrucial features of any Darwinian theory. But in their paper there is no mentionwhatsoever of randomly occurring changes, and natural selection plays only aceremonial role in their deliberations.At the beginning of their paper, Nilsson and Pelger write oftheir initial light-sensitive patch that "we expose this structure toselection pressure favoring spatial resolution" (emphasis added), and laterthat "[a]s the lens approaches focused conditions, selection pressuregradually appears to ... adjust its size to agree with Mattiesen's ratio"(emphasis added). But whatever Nilsson and Pelger may have been doing to theirpatch, they have not been exposing it to "selection pressure." Thepatch does only what they have told it to do. By the same token, selectionpressures play no role in adjusting the size of their lenses to agree withMattiesen's ratio. That agreement is guaranteed, since it is Nilsson and Pelgerwho bring it about, drawing the curve and establishing the relevant results.What Nilsson and Pelger assume is that natural selection would track theirresults; but this assumption is never defended in their paper, nor does it playthe slightest role in their theory.And for an obvious reason: if there are no random variationsoccurring in their initial light-sensitive patch, then natural selection hasnothing to do. And there are no random variations in that patch, their modelsucceeding as a defense of Darwin's theory only by first emptying the theory ofits content.An example may make clearer both the point and itsimportance. Only two steps are required to change the English word"at" to the English word "do": "at" to "ao"and "ao" to "do." The changes are obvious: they have beendesigned to achieve the specified effect. But such design is forbidden inDarwinian theory. So let us say instead, as Darwin must, that letters are chosenrandomly, for instance by being fished from an urn. In that case, it will take,on average, 676 changes (26 letters times 26) to bring about the same two steps.Similarly, depending on assessments of probability, thenumber of changes required to bring about a single step in Nilsson and Pelger'stheory may range widely. It may, in fact, be anything at all. How long would ittake to transform a light-sensitive patch into a fully functioning eye? It alldepends. It all depends on how likely each morphological change happens to be.If cells in their initial light-sensitive patch must discover their appointedrole by chance, all estimates of the time required to bring about just thetransformations their theory demands-invagination, aperture construction, andlens formation-- will increase by orders of magnitude.If Darwin were restored to pride of place in Nilsson andPelger's work, the brief moment involved in their story would stretch on and onand on.FINALLY, THERE is the matter of Nilsson and Pelger's computersimulation, in many ways the gravamen of my complaints and the dessert of thisdiscussion.A computer simulation of an evolutionary process is not amysterious matter. A theory is given, most often in ordinary mathematicallanguage. The theory's elements are then mapped to elements that a computer canrecognize, and its dynamical laws, or laws of change, are replicated at adistance by a program. When the computer has run the program, it has simulatedthe theory.Although easy to grasp as a concept, a computer simulationmust meet certain nontrivial requirements. The computer is a harsh taskmaster,and programming demands a degree of specificity not ordinarily required of amathematical theory. The great virtue of a computer simulation is that if theset of objects is large, and the probability distribution and fitness functioncomplicated, the computer is capable of illustrating the implications of thetheory in a way that would be impossible using ordinary methods of calculation."Hand calculations may be sufficient for very simple models," asRobert E. Keen and James Spain write in their standard text, Computer Simulationin Biology (1992), "but computer simulation is almost essential forunderstanding multi-component models and their complex interrelationships."Whatever the merits of computer simulation, however, they arebeside the point in assessing Nilsson and Pelger's work. In its six pages, theirpaper contains no mention of the words "computer" or"simulation." There are no footnotes indicating that a computersimulation of their work exists, and their bibliography makes no reference toany work containing such a simulation.Curious about this point, I wrote to Dan-Erik Nilsson in thelate summer of 2001. "Dear David," he wrote back courteously and atonce,You are right that my article with Pelger is not based oncomputer simulation of eye evolution. I do not know of anyone else who [has]successfully tried to make such a simulation either. But we are currentlyworking on it. To make it behave like real evolution is not a simple task. Atpresent our model does produce eyes gradually on the screen, but it does notlook pretty, and the genetic algorithms need a fair amount of work before themodel will be useful. But we are working on it, and it looks both promising andexciting.These are explicit words, and they are the words of thepaper's senior author. I urge readers to keep them in mind as we return to theluckless physicist Matt Young. In my COMMENTARY essay of last December, I quotedthese remarks by Mr. Young:Creationists used to argue that ... there was not enough timefor an eye to develop. A computer simulation by Dan-Erik Nilsson and SusannePelger gave the lie to that claim.These, too, are forthright words, but as I have just shown,they are false: Nilsson and Pelger's paper contains no computer simulation, andno computer simulation has been forthcoming from them in all the years since itsinitial publication. Sheer carelessness, perhaps? But now, in responding to myCOMMENTARY article, Matt Young has redoubled his misreading and proportionatelyaugmented his indignation. The full text of his remarks appears in last month'sCOMMENTARY; here are the relevant passages:In describing the paper by Nilsson and Pelger..., I wrotethat they had performed a computer simulation of the development of the eye. Idid not write, as Mr. Berlinski suggests, that they used nothing more thanrandom variation and natural selection, and I know of no reference that saysthey did....The paper by Nilsson and Pelger is a sophisticatedsimulation that even includes quantum noise; it is not, contrary to Mr.Berlinski's assertion, a back-of-the-envelope calculation. It begins with aflat, light-sensitive patch, which they allow to become concave in increments of1 percent, calculating the visual acuity along the way. When some othermechanism will improve acuity faster, they allow, at various stages, theformation of a graded-index lens and an iris, and then optimize the focus.Unless Nilsson and Pelger performed the calculations in closed form or by hand,theirs was, as I wrote, a "computer simulation." Computer-aidedsimulation might have been a slightly better description, but not enough tojustify Mr. Berlinski's sarcasm at my expense....And here is my familiar refrain: there is no simulation,"sophisticated" or otherwise, in Nilsson and Pelger's paper, and theirwork rests on no such simulation; on this point, Nilsson and I are in completeagreement. Moreover, Nilsson and Pelger do not calculate the visual acuity ofany structure, and certainly not over the full 1,829 steps of their sequence.They suggest that various calculations have been made, but they do not show howthey were made or tell us where they might be found. At the very best, they havemade such calculations for a handful of data points, and then joined thosepoints by a continuous curve.There are two equations in Nilsson and Pelger's paper, andneither requires a computer for its solution; and there are no others. Usingprocedures very much like Nilsson and Pelger's own, Mr. Young has neverthelessdeduced the existence of a missing computer simulation on theoretical grounds:"Unless Nilsson and Pelger performed the calculations in closed form or byhand, theirs was, as I wrote, a computer simulation." But anotherpossibility at once suggests itself: that Nilsson and Pelger did not require acomputer simulation to undertake their calculations because they made no suchcalculations, their figure of 1,829 steps representing an overall guess based onthe known optical characteristics of existing aquatic eyes.Whatever the truth-and I do not know it-Mr. Young's inferenceis pointless. One judges a paper by what it contains and one trusts an author bywhat he says. No doubt Matt Young is correct to observe that"computer-aided simulation might have been a better description" ofNilsson and Pelger's work. I suppose one could say that had Dan-- Erik Nilssonand Susanne Pelger rested their heads on a computer console while trying toguess at the number of steps involved in transforming a lightsensitive patchinto a fully functioning eyeball, their work could also be represented ascomputer-- aided.MATT YOUNG is hardly alone in his lavish misreadings. Themathematician Ian Stewart, who should certainly know better, has made virtuallythe same patently false claims in Nature's Numbers (1995). So have many otherprominent figures.3 But misreadings are one thing, misrepresentations another.More than anyone else, it has been Richard Dawkins who has been responsible foractively misrepresenting Nilsson and Pelger's work, and for disseminatingworldwide the notion that it offers a triumphant vindication of Darwinianprinciples.In a chapter of his 1995 book, River Out of Eden, Dawkinswrites warmly and at length about Nilsson and Pelger's research.4 Here is whathe says (emphasis added throughout):[Their] task was to set up computer models of evolving eyesto answer two questions ... [:] is there a smooth gradient of change, from flatskin to full camera eye, such that every intermediate is an improvement? ...[and] how long would the necessary quantity of evolutionary change take?In their computer models, Nilsson and Pelger made no attemptto simulate the internal workings of cells.... Nilsson and Pelger began with a flat retina atop a flatpigment layer and surmounted by a flat, protective transparent layer. Thetransparent layer was allowed to undergo localized random mutations of itsrefractive index. They then let the model tramform itself at random, constrainedonly by the requirement that any change must be small and must be an improvementon what went before.The results were swift and decisive. A trajectory of steadilymounting acuity led unhesitatingly from the flat beginning through a shallowindentation to a steadily deepening cup, as the shape of the model eye deformeditself on the computer screen.... And then, almost like a conjuring trick, aportion of this transparent filling condensed into a local, spherical region ofhigher refractive index.... This ratio is called Mattiessen's ratio. Nilsson andPelger's computer-simulation model homed in unerringly on Mattiessen's ratio.How very remarkable all this is-inasmuch as there are nocomputer models mentioned, cited, or contained in Nilsson and Pelger's paper;inasmuch as Dan-Erik Nilsson denies having based his work on any computersimulations; inasmuch as Nilsson and Pelger never state that their task was to"set up computer models of evolving eyes" for any reason whatsoever;inasmuch as Nilsson and Pelger assume but do not prove the existence of "asmooth gradient of change, from flat skin to full camera eye, such that everyintermediate is an improvement"; and inasmuch as the originallight-sensitive patch in Nilsson and Pelger's paper was never allowed to undergo"localized random mutations of its refractive index."And how very remarkable again-inasmuch as there are nocomputer "screens" mentioned or cited by Nilsson and Pelger, noindication that their illustrations were computer-generated, and no evidencethat they ever provided anyone with a real-time simulation of their paper whereone could observe, "almost like a conjuring trick," the "swiftand decisive" results of a process that they also happen to have designed.And yet again how very remarkable-inasmuch as Nilsson andPelger's "computer-simulation model" did not home in unerringly onMattiessen's ratio, Nilsson and Pelger having done all the homing themselves andthus sparing their model the trouble.Each and every one of these very remarkable asseverations canbe explained as the result of carelessness only if one first indicts theirauthor for gross incompetence.FINAL QUESTIONS. Why, in the nine years since their workappeared, have Nilsson and Pelger never dissociated themselves from claims abouttheir work that they know are unfounded? This may not exactly be dishonest, butit hardly elicits admiration. More seriously, what of the various masters ofindignation, those who are usually so quick to denounce critics of Darwin'stheory as carrying out the devil's work? Eugenie Scott, Barbara Forrest,Lawrence Krauss, Robert T. Pennock, Philip Kitcher, Kelly Smith, Daniel Dennett,Paul Gross, Ken Miller, Steven Pinker-they are all warm from combat. Why havethey never found reason to bring up the matter of the mammalian eye and thecomputer simulation that does not exist?And what should we call such a state of affairs? I suggestthat scientific fraud will do as well as any other term.[Footnote]
1 "A Pessimistic Estimate of the Time Required for an Eye to Evolve," Proceedings of the Royal Society, London B (1994) 256, 53-- 58. In my essay I twice misspelled Susanne Pelger's name, for which I apologize.

[Footnote]
2 A graded-index lens is a lens that is not optically homogeneous; the figure of 1.52 is "the value close to the upper limit for biological material."

[Footnote]
3 Among those who, by contrast, have raised (on the Internet) points similar to my own, I would single out especially Brian Harper, a professor of mechanical engineering at Ohio State University.
4 A version of the same material by Dawkins, "Where D'you Get Those Peepers," was published in the New Statesman (July 16, 1995).

[Author note]
DAVID BERLINSKI is the author of A Tour of the Calculus, The Advent of the Algorithm, and Newton's Gift. His new book, Secrets of the Vaulted Sky, is forthcoming from Harcourt later this year.




John Landon
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