Joined: May 2002
A few recent posts from a new ISCID thread:
Most of the basic comments have already been made. Michael Francisco really should read the letters written in response to Berlinski's "A Scientific Scandal", particularly the response from Nilsson himself, and then see how many of his/Berlinski's claims are left standing.
I, for one, would really like to know why Berlinksi thought that the skull would have to be "reconstructed" when (1) eyes developed in the invertebrate (and therefore skull-less) chordate ancestors of fish, not in some kind of mythical blind fish, (2) skulls therefore developed around pre-existing eyes, not vice-versa, (3) the evolutionary model was of an invertebrate eye anyway, and (4) most of the camera eyes on the planet are in critters without skulls anyhow. This is basic biology that Berlinski misunderstands, and yet it is Berlinski who has the gall to go around accusing people of scandal.
The bit about the equations not being in the paper is really embarrassing for Berlinksi, as (1) some of them are, and (2) each of the others that are not is specifically referenced to previous literature either by Nilsson himself or in the optics literature.
I would also like to know why Commentary felt that publishing such an underinformed and misleading piece was appropriate.
Regarding Dawkins, RBH argues that even his referral to a "simulation" is ambiguous. There is, however, a bit somewhere where Dawkins refers to Nilsson and Pelger as undergoing random variations. Lesse, here are the quotes that Berlinski cites from Dawkins:
There is pretty clearly the implication of a stochastic simulation there I think. Dawkins let his imagination of what Nilsson and Pelger did overstep the bounds of what they actually did.
| [Their] task was to set up computer models of evolving eyes to answer two questions ... [:] is there a smooth gradient of change, from flat skin 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 attempt to simulate the internal workings of cells.
... Nilsson and Pelger began with a flat retina atop a flat pigment layer and surmounted by a flat, protective transparent layer. The transparent layer was allowed to undergo localized random mutations of its refractive index. They then let the model transform itself at random, constrained only by the requirement that any change must be small and must be an improvement on what went before.
The results were swift and derisive. A trajectory of steadily mounting acuity led unhesitatingly from the flat beginning through a shallow indentation to a steadily deepening cup, as the shape of the model eye deformed itself on the computer screen... And then, almost like a conjuring trick, a portion of this transparent filling condensed into a local, spherical region of higher refractive index.
... This ratio is called Mattiessen's ratio. Nilsson and Pelger's computer-simulation model homed in unerringly on Mattiessen's ratio.
What actually happened seems to be widely misunderstood. Here is my understanding (going from memory). Nilsson and Pelger started out with a common observation, that quantitative traits (traits that vary in an effectively continuous manner, like e.g. height, even though we all know inheritance is particulate at bottom) usually fall out in a distribution with a bell-shaped curve, i.e. a normal distribution.
See these lecture notes on Quantitative Genetics. Here is how particulate genes can add up to continuous variation with a normal distribution:
These distributions can be fully described by the mean and standard deviation, which makes a number of things simple. Namely, if you have selection acting on a continuously-varying trait of a population, and you have the heritability (h) of the trait, you can calculate how much the mean of the trait in the population will change with each generation. Nilsson and Pelger used these very simple fundamentals, making conservative assumptions about selection (1% IIRC), heritability, etc., and that's how they got their total number of generations.
Berlinski explains it well enough:
What is bizarre is that Berlinski appears to understand the above, but then begins to talk about the importance of random variations later on:
The chief claim of their paper now follows: to achieve the visual acuity that is characteristic of a "focused camera-type eye with the geometry typical for aquatic animals," it is necessary that an initial patch be made 80,129,540 times larger (or greater or grander) than it originally was. This number represents the magnitude of the blob's increase in size. How many 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 are required" to bring about the requisite transformation.
These steps, it is important to remember, do not represent temporal intervals. We still need to assess how rapidly the advantages represented 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 follows involves the multiplication of four numbers:
R = [h.sup.2] x i x V x m
Here, R is the response (i.e. visual acuity in each generation), h is the coefficient of heredity, i designates the intensity of selection, V is the coefficient of variation (the ratio of the standard deviation to the mean), and m, the mean value fur visual acuity. These four numbers 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 average value is spread over a population, and the mean or average value itself. Values are assigned as estimates to the first three numbers; the mean is left undetermined, rising through each generation.
As for the estimates themselves, Nilsson and Pelger assume that [h.sup.2] = .50; that i= 0.01; and that V = 0.01. On this basis, they conclude that R = 0.00005m. The response in each new generation of light-sensitive patches is 0.00005 times the mean value of visual acuity in the previous generation of light-sensitive patches.
Their overall estimate--the conclusion of their paper--now follows in two stages. Assume that n represents the number of generations required to transform a light-sensitive patch into a "focused camera-type eye with the geometry typical for aquatic animals." (In small aquatic animals, a generation is roughly a year.) It, as we have seen, the mean value of visual acuity of such an eye is [1.01.sup.1,829] = 80,129,540, where 1,829 represents the number of steps required and 80,129,540 describes the extent of the 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 to conclude at last that "the time required [is] amazingly short: only a few hundred thousand years." And this also completes my exposition of Nilsson and Pelger's paper. Business before pleasure.
I can only think that Berlinski would have been far less confused if he had made the connection between the population genetics equation and the Gaussian distribution that describes the variation in typical biological traits.
|Nilsson and Pelger assert that only 363,992 generations are required to generate an eye from an initial light-sensitive patch. As I have already observed, die 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 at all. Never mind. Let us accept 1,829 pour le sport. If Nilsson and Pelger intend their model to be a vindication of Darwin's theory, then changes from one step to another must be governed by random changes in the model's geometry, followed by some mechanism standing in for natural selection. These are, after all, the crucial features of any Darwinian theory. But in their paper there is no mention whatsoever of randomly occurring changes, and natural selection plays only a ceremonial role in their deliberations.|
We could go into more detail about the equations (I have the pdf of the paper from JSTOR) if people really want to, but it's pretty clear that Berlinski never even got this far in his understanding of the calculations.
Berlinski's various recent papers in Commentary are online here (sometimes just excerpts). Here is A Scientific Scandal.
I've been thinking of doing this for some time. Here is a brief summary of the calculations and reasoning of Nilsson & Pelger (N-P) in a step-by-step fashion. Hopefully this will be helpful for Mike.
The first step is to set up a model of the evolutionary sequence from light-sensitive patch to camera eye. This is the portion of the inquiry where the existence of a "gradual route" to a camera eye is investigated. Studies of the variations in eyes in the animal kingdom (e.g., Darwin 1859, Salvini-Plawen and Mayr 1977) already indicated that such a route existed.
Nilsson and Pelger (1994) begin by arguing that the whole eye series can be seen as a continual improvement in visual acuity, specifically spatial resolution. They argue that the various uses of eyes, i.e. "measuring self-motion, detection of small targets, or complicated pattern recognition", are all fundamentally dependent on the information-gathering capacity possible with a given spatial resolution.
The eye cup
NP therefore begin by calculating how optical resolution changes as (1) the light-sensitive patch curves inward and becomes cupped and (2) as the aperture narrows. Both of these changes improve resolution by narrowing the angle at which light can strike the retina. Nilsson calculated in a 1990 paper (referenced in NP 1994) that the most efficient (in terms of minimal morphological change) way to increase resolution at first is to deepen the pit. Once the pit depth equals the pit width, however, it becomes more efficient to increase resolution by constricting the aperture. Although some further improvement of resolution is gained by deepening the pit, the returns diminish rapidly (Figure 1a).
The eye aperture
The disadvantage of narrowing the aperture is that fewer and fewer photons are able to enter the eye. For reasons of optics, the fewer photons that are available, the less "signal" there is relative to the "noise". There is therefore an optimum aperature width, below which further narrowing cuts off too much light. This optimum width depends on light intensity, so the authors calculate it for several orders of magnitude of intensity (Figure 1b, and equation 1).
From here, the only way to further improve resolution is via a lense. All along, as the eye pit has deepened, it has been filled with "vitreous mass" (transparent cells) derived from the initial protective surface layer of the light-sensitive spot. A lense can be developed simply by varying the density of the vitreous mass. N-P cite Fletcher et al. (1954) for the calculations. Spatial resolution improves very rapidly with morphological change at this stage (Figure 1c).
Quantifying the amount of morphological change
In order to quantify the amount of morphological change, N-P constructed graphical models of various stages in the process (Figure 2) and decided to calculate the number of 1%-change steps in-between each stage. As an example, it takes 70 1% steps in order for a structure to double in length (due to the compounding of change think compound interest -- it takes only 70 steps rather than 100 in order for doubling to occur). They admit that there is some subjectivity in deciding *how* to measure morphological change, but they decide on the following as simple measures:
length of straight structures
"arc length of curved structures"
"height and width of voluminous structures"
changes in radius of curvature use the arc length of the inside and outside of the curved structure
changes in lens refractive index above the starting point of 1.34
With this method they came up with 1829 1% morphological steps for the evolutionary sequence. They note that in actual evolution, some of the changes could happen simultaneously (e.g., lense development and aperture narrowing could occur together), but because they are being pessimistic, they restrict the steps to happen in series.
Calculation of the number of generations
Nowhere up to this point have the authors made *any* consideration of selection or the number of generations required. All of the preceding work served simply to establish that (1) a gradual route of continual improvement from eyespot to camera eye actually existed and (2) to quantify how much morphological change this entails. Knowing this, N-P can use a simple population genetics equation for continuous traits to calculate how many generations it would take for this set of transformations to occur. Here is the equation:
R = h^2 * i * V * m
h^2 = heritability (genetically determined proportion of the variance in the phenotype)
i = intensity of selection
V = the coefficient of variation in the continuous trait (std. dev./mean), assuming the variation in the population has a normal distribution (a common situation)
m = the mean
R = response in 1 generation
The values they use:
h^2 = 0.5 (a common value for heritability -- half of the variation due to genes, half to environment; only the genetic component can be inherited & retained by selection)
i = 0.01 (deliberately low; selection coefficients of 0.3-0.5 are commonly found, e.g. in peppered moths)
V = 0.01 (also low; if the mean adult human male is 6 feet tall, a V=0.01 value would mean that 95% of the male population had height of 6 feet +/- 1.44 inches).
When these variables are plugged in, one gets:
R = 1.00005m
...which means that the change per generation is only 0.005%.
N-P note that 1829 1% steps amounts to morphological change by a factor of 1.01^1829 = 80,129,540. Instead of height doubling (x2), imagine height being multiplied by 80,129,540 (keep in mind, of course, that in our actual example a number of different traits are being modified).
The Time Estimate
As the change per generation is 1.00005, the number of generations (n) can be calculated via:
1.00005^n = 80,129,540
If we assume one generation per year (and many animals reproduce much faster than this), we get a pessimistic time for the origin of the eye of ~364,000 years, which is a geological eyeblink.
Edited by niiicholas on June 11 2003,03:32