The results were swift and decisive. 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. The transparent layer thickened to fill the cup and
smoothly bulged its outer surface in a curve. And then, almost
like a conjuring trick, a portion of this transparent filling
condensed into a local, spherical subregion of higher refractive
index. Not uniformly higher, but a gradient of refractive index
such that the spherical region functioned as an excellent
graded-index lens. [...]
-- Richard Dawkins (1995). <River Out of Eden: A Darwinian
View of Life>, BasicBooks, p. 80-81.
And now a couple of excerpts from Nilsson and Pelger (N&P)
We have made such calculations by outlining a plausible
sequence of alterations leading from a light-sensitive spot
all the way to a fully developed lens eye. The model sequence
is made such that every part of it, no matter how small, results
in an increase of the spatial information the eye can detect.
The amount of morphological change required for the whole
sequence is then used to calculate the number of generations
required. Whenever plausible values had to be assumed, such as
for selection intensity and phenotypic variation, we deliberately
picked values that over-estimate the number of generations.
Despite this consistently pessimistic approach, we arrive at
only a few hundred thousand generations!
-- N&P p. 53.
[...]
Based on the principles outlined above, we made a model sequence
of which representative stages are presented in figure 2. The
starting point is a flat light-sensitive epithelium, which by
invagination forms the retina of a pigmented pit eye. After
constriction of the aperture and the gradual formation of a
lens, the final product becomes a focused camera-type eye with
the geometry typical for aquatic animals (e.g. fish and
cephalopods).
The changes in size and position of the aperture cause variations
in image brightness in the model sequence. To account for this
we have assumed that the receptor diameter is continuously
modified such that the photon catch per receptor, and thus the
signal to noise ratio, is kept constant throughout the sequence.
As the model is of arbitrary size, we have used a normalized
receptor diameter (d) which is 1 at stage 1 in figure 2.
-- N&P p. 56.
What N&P actually did was to construct a "model sequence" of several
intermediate structures. Figure 2 has eight such assumed intermediates.
The figure caption reads "Representative stages of a model sequence..."
so there may have been more than eight. Next they computed the number
of 1% steps in "visual acuity" required to traverse each stage in the
model sequence. They then used known relations between structure and
visual accuity to verify that the assumed model sequence always resulted
in a steady increase in visual acuity. The assumption then was that selection
would thus favor this path.
But Dawkins assessment:
The transparent layer was allowed to
undergo localized random mutations of its refractive index.
They then let the model deform itself at random, constrained
only by the requirement that any change must he small and
must he an improvement on what went before.
is a complete distortion of what was done. There were no random
mutations nor did the model deform itself at random.
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Brian Harper |
Associate Professor | "It is not certain that all is uncertain,
Applied Mechanics | to the glory of skepticism" -- Pascal
Ohio State University |
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