VNA: The question about mimetic forms concerns how
they arise. Do they arise gradually, through natural selection? or do they arise
suddenly, by chance?(and then, perhaps, get selected).
BB: Problem 1:
Surely if mimetic forms arose by chance, in particular individuals, this would
not explain how a particular mimetic pattern becomes established as a
species-wide trait, which after all is the real explicandum. A particular
mimetic pattern could not occur by CHANCE again and again in every member of the
species. The problem is to explain how the pattern becomes established as a
species trait.
VNA: I am not talking about the chance appearance of
mimetic forms in "particular" individuals, but about the sudden appearance of
large groups of mimetic forms, that look quite different from their parents.
Prof Boyd may reject the concept of "epochal evolution," but I accept it. This
is a concept of which, I've mentioned already, Nabokov seems to have had his own
version. For a very fine summary of the argument against gradualism, see
http://www.santafe.edu/projects/evca/Papers/evrevinno.html
BB: Problem 2:
Patterns like eyespots and other circular or linear markings can clearly be
generated by computer algorithms, but I would have thought that the mathematics
of combinatorial explosion would make it unlikely that a particular COMBINATION
of patterns would be coincident in otherwise unrelated species of, say,
Lepidoptera, without the selective pressure of natural selection.
VNA: I
have a friend mathematician Persi Diaconis whose speciality is studying
coincidences. Interesting side note: He is also quite a well-known performing
magician and he has taken a special interest in explaining (or debunking) the
apparently psychic abilities of other magicians and mindreaders by examining the
probabilities of chance patterns. As he says "our intuitive grasp of the odds is
far off. We are often surprised by things that turn out to be fairly likely
occurrences." The problem Prof. Boyd refers to his so well studied it has a
name. It is called "the birthday problem," and the main issue is not whether or
not many things are combined but the fact that the thing being represented by
the "mimic" is not specified beforehand. See Persi Diaconis and Fredrick
Mosteller, "Methods for Studying Coincidences," Journal of American Statistical
Association 84 (1989): 854. What may appear to be freakish luck to us is an
important part of how new useful forms get discovered. I think Nabokov was
trying to tell us that one should not try to explain it away. Most people, I
think, are irrational when it comes to thinking about luck, that is, as Diaconis
argues, most people don’t seem to have an intuitive sense of probabilities
(myself included: I have a special fondness for coincidences). It is trivial to
say that any one unspecified member of the 12,000 or so species of butterflies
will by chance resemble another unspecified species or an unspecified object in
nature. It would also be trivial to predict that someone's lottery ticket (a
combination of numbers) will match the winning number in a given drawing without
saying who will win. Although there is nothing magical about winning the
lottery, every winner cannot help but feel a bit favored by fortune. This is
because, as far as the lottery winner is concerned, he or she did prespecify the
winning number.
BB: Problem 3: If similarities of the order we find in
mimicry could be explained largely by spontaneous pattern-formation, would we
not expect there to be similarities, as marked and as frequent as those of
accepted mimicry, linking random features of random species, species that are
both phylogenetically and geographically unrelated? Does this in fact occur with
anything like the same frequency as mimicry...?
VNA: Yes. Contemporary
evolutionary biologists have found, for example, that the fact that many animals
have four limbs instead of, say, five or three is not indicative of common
ancestry. Four limbs represent a common configuration among mammals and birds
because the laws of pattern formation have the tendency to produce tetrapods. As
Brian Goodwin writes, "Tetrapod limbs are defined as the set of possible
forms generated by the rules of focal condensation, branching bifurcation, and
segmentation in the morphogenetic field of the limb bud. ... The idea of a
common ancestral form as a special structure occupying a unique branch point on
the tree of life ceases to have taxonomic significance. Now tetrapod limbs could
have arisen many times independently." See How the Leopard Changed its Spots:
The Evolution of Complexity (New York: Scribner, 1994), 155.
BB: Problem
4: If predator-prey relations play an insignificant part compared with
spontaneous pattern formation, would we not expect to find that there are cases
of elaborate visual mimicry where predators cannot see the pattern involved? For
instance, in night-flying moths would there not be proportionately as many cases
of elaborate mimicry of wing-patterns in the undersides of the wings (the upper
sides of the wings of course are often camouflaged to escape detection while the
moths rest by day) as there are on the wing patterns of day-flying butterflies,
even though in butterflies predators can be duped by the result and in the case
of night-flying moths predators like bats pay no attention to visual
detail?
VNA: Camouflage should not be considered mimicry. The
concept of natural selection works very well to explain why so many moths have
camouflage coloring. Moth wings are patterned, naturally having dots and lines.
They are more regular than tree bark. The wing patterns that are less noticeable
against tree bark are those that are most busy. A simple bold pattern would
stand out. Busy wing patterns and bark have relatively the same degree of
"information," as they say in theoretical physics. The salient point is that
camouflage wing patterns do not resemble bark. As H. Frederik
Nijhout points out, "there is no requirement that the elements of the pattern be
of a specific shape." See The Development and Evolution of Butterfly Wing
Patterns (Washington: Smithsonian Institution Press, 1991), 236. Because any busy wing
pattern of various configurations of dots and lines may be selected as
camouflage, natural selection might very easily and gradually evolve a large
number of various kinds of complicated wing patterns that would function as
camouflage. If natural selection had only one pattern that it could select for
fitness, for example a pattern that looked like the wing pattern of another
insect, then the chance that natural selection would find it would be relatively
low.