Victoria N. Alexander
NABOKOV AND INSECT MIMICRY (The final product of this research is a paper published in Nabokov Studies and can be found at http://www.dactyl.org/directors/vna/papers/InsectMimicry.pdf) [1]
"The mysteries of mimicry had a special attraction for me. Its phenomena showed an artistic perfection usually associated with man-wrought things.... When a butterfly has to look like a leaf, not only are all the details of a leaf beautifully rendered but markings mimicking grub-bored holes are generously thrown in. 'Natural selection' ... could not explain the miraculous coincidence of imitative aspect ..., nor could one appeal to the theory of 'the struggle for life' when a protective device was carried to a point of mimetic subtlety, exuberance, and luxury far in excess of a predator's power of appreciation. I discovered in nature the non-utilitarian delights that I sought in art" (Boyd 85-86)
--Vladimir Nabokov
Some believe Nabokov is implying here that there must be a creator responsible for some wonders of nature. (Paul Gant in his talk earlier this week made this assertion, for example.) Some assume this passage reveals his naiveté about Darwinism. I don't read it this way. I argue that Nabokov assumed there were some apparently teleological mechanisms in addition to natural selection that also guided the evolutionary process. And he was right. Recent research in evolutionary theory has uncovered a number of non-Darwinian mechanisms that limit (and thus seem to direct) the formation of biological structures.[2] Not everything is due to reproductive fitness.
My area of specialization as a narrative theorist is teleology, and more generally, causality. My understanding of telos, or final cause, differs from what I consider an oversimplified if not simply incorrect understanding held today by many postmodernists. (Jacqueline Hamrit mentioned Derrida's -- I believe flawed -- notion of teleology yesterday.) Telos does not produce "linear" sequential behavior directed at a goal. [3] As Henri Bergson (whom Nabokov most certainly read and seems to have admired) noted, to think of final causality this way is to turn it into "inverted mechanism," causality that conforms to classical reductionism, but played in reverse (Bergson 39). Throughout history, teleologists have been avid anti-reductionists. Many of the phenomena in nature that have been regarded as telic, when analyzed correctly, prove to be instances of the kind of self-organization that arises out of nonlinear systems.[4] Let me give you my working definition of final causality: A teleological explanation is only necessary if a purpose is fulfilled in a way that could not have been predicted by analyzing the initial conditions, or the starting point that led to the goal. In retrospect, however, it appears as if each stage in the process was a precondition for the advantageous or more complex property, quality, or event that eventually emerged. This is the very situation that nonlinear dynamics theorists now explain: they claim self-organizing systems are irreducible and hence unpredictable because effective factors (e.g., function or context) unaccounted for in the system's initial measure of energy are later generated by the dynamics. Thus one may say that these complex systems are capable of spontaneous increase in complexity or progressive behavior. At the same time, however, the degree of unpredictability is constrained by the dynamics that govern the system as a whole. Behavior, then, is directed as well as original. These two aspects, emergent lawfulness and ability to transcend laws opportunistically, make natural systems telic, that is, progressive or creatively organized toward goals. I know that's a lot for everybody to take in at first, so I will repeat these ideas throughout my talk. This meaning of final cause should become clearer as I go on.
I'm going to be looking at two forms of supposed mimicry that interested Nabokov: the viceroy species that is said to mimic the monarch species and the Kallima butterfly that is said to mimic a dead leaf. I argue the resemblance between the viceroy and the monarch was created not thanks to the gradual influence of predators' decisions but thanks to common laws of pattern formation, which make evolution seem teleological in the sense of constrained, directed, and predictable. We may say that the viceroy and the monarch are, as Nabokov thought, variations on a theme. The resemblance between the Kallima butterfly and a dead leaf, I also argue, did not arise by the gradual shaping influence of predators, but appeared suddenly. The dead leaf butterfly is, in some sense, an instance of freakish luck (which always makes it seem as if there is an interested deity intruding on reality's narrative and contriving improbable solutions to problems). The resemblance to a dead leaf may have come to have accidental functionality in some contexts, but this would not explain why the resemblance arose in the first place. I believe Nabokov understood the difference between fortuitous benefit and genuine adaptation.[5] Accidental functionalities make evolution seem teleological in the sense of anticipatory, inventive, and unpredictable.
I've divided my talk into three sections: First, Darwinian Evolution and gradual adaptation according to function. Second, Structural and Neutral Evolution and the existence of few archetypes in nature. Third, Teleology and the organization of nature in a way that seems designed.
I have several points to make about Darwin. Number one, neither Nabokov nor I ever denied that natural selection is an active mechanism in evolution.[6] However, natural selection according to reproductive fitness is not responsible for all the shaping that goes on in evolutionary processes. In addition, Darwinian natural selection is supposed to work gradually. But evolutionary changes are often drastic and sudden. Nabokov knew this. In "Father's Butterflies," he compares the appearance of new species to the bursting of a bubble (218). This phenomenon is now understood as a form of "epochal evolution" (Crutchfield passim). Furthermore, many biological forms don't serve the function of reproductive fitness and never did. To assume that every biological structure has been chosen for reproductive fitness can be an absurd position in the extreme and worthy of a Candide-like critique. I think Nabokov recognized that some biologists were turning Darwin into a Dr. Pangloss figure.
About structural and neutral evolutionary theories, let me just mention first that structural evolutionary theory deals with the area of physics known as nonlinear dynamics. It is concerned with spontaneous pattern formation, and it is used to explain why nature favors relatively few structural archetypes. It limits the choices available for selection and helps explain why evolution seems directed or why some forms seem predetermined, as if Platonic. It turns out that these forms, called structural attractors, are not pre-existing like Platonic forms, but emerge out of local stochastic interactions. These new theories do not negate natural selection. They may be added to Darwinism to explain some phenomena that Darwin was not able to explain. Structural evolutionary biologists are revolutionary (to us) in the sense that they seek to uncover universal laws that constrain evolutionary processes. Their interest in physics makes them especially unlike the Darwinists in NabokovÌs day.
Regarding teleology, Nabokov was able to anticipate these "new" evolutionary theories because they are really not so new, but come out of the theoretical biology done by teleologists/teleomechanists in late 18th and early 19th centuries, which was all but forgotten after the success of On the Origin of Species.[7] We can think of teleology as an area of study that asks the question, What are the kinds of things that make nature's products seem designed?
I. Darwinism
On to the first section, Darwin assumed that "random variation" was the norm, so the task he set for himself was to explain why, instead of endless diversity and confusion in nature, there was so much order and sameness in the animal and plant kingdoms. He decided that among all the many possible forms only the fittest survive to reproduce. Reproductive fitness then, limits the number of structures in existence and is a cause of order in nature.
This 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, which makes them more regular than tree bark. The wing patterns that are least noticeable against tree bark are those that are most busy. A simple bold wing pattern of dots and lines would stand out against bark. But busy wing patterns and bark have relatively the same degree of "information" and thus fool the eye and blend together. The important point to understand is that camouflage wing patterns do not resemble bark in pattern or shape.[8] 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.
IMAGE (VICEROY)
Fig. 1. The Viceroy butterfly, Nymphalidae Limenitis archippus.
IMAGE (MONARCH)
Fig. 2. The Monarch butterfly, Nymphalidae Danainae Danaini
Danaus plexippus.
If we try to imagine how the viceroy might have come to resemble the monarch through natural selection, the story does not seem plausible. It did not seem plausible to Nabokov. According to the theory of Batesian mimicry, the ancestors of today's viceroy looked nothing much like the monarch. The monarch was bitter so birds didn't eat them much, and they had a reproductive advantage over more tasty (proto)viceroys. Then some viceroys were born that looked ever so slightly like monarchÛthough not enough to be considered mimicsÛand tended to be passed up by the predator population. Then the (proto)viceroys produced some offspring that looked more like monarchs, which lived to reproduce.
It this story, the (proto)viceroy populations adapts toward a prespecified goal, the monarch population, that presumably remains stable, allowing the viceroy to catch up to it. As Nabokov argued in "Father's Butterflies," this is unlikely (225). The monarch population would also be undergoing random variation. As many of you know, Nabokov performed the viceroy-monarch taste test himself and found that both were bitter. Forty years later, a study by Jane Van Zandt and Lincoln Brower (using mockingbirds to taste test viceroys) verified NabokovÌs findings.[9] The Batesian theory of mimicry has now been discredited.[10]
The monarch and the viceroy resemblance arose, not due to function, but due to the laws of pattern formation. The viceroy-monarch pattern would appear even if selection were always random. In computer simulations of wing pattern development, variations of the monarch-viceroy-like pattern turn up frequently without selection.[11]
Common forms in nature are known as "structural attractors." (You've probably heard of "strange attractors" associated with the study of deterministic chaos.) The diffusion of pigment across a wing surface involves a number of variables, including timing and the size and density of pigment molecules, as well as the way the variables interact, with each other and with the wing surface. One can vary the parameters quite a bit and the same viceroy-monarch pattern will result. (This is an example of neutral evolution, that is, several different genotypes produce the same phenotype. Darwinian natural selection cannot "see" such genotypic difference and therefore cannot favor one over another.) If, however, the parameters vary beyond a certain threshold, the reaction-diffusion process will jump to another pattern, another attractor "basin." Attractors are notable in environments where selection is inconstant or random, and forms are not being pushed and pulled according to fitness. Attractors account for the existence of order when the natural tendency in nature is to vary randomly. In his comparison of speciation to the bursting of a bubble, one could say that Nabokov described something like an attractor basin. He noted that species can vary to a definite limit before they jump to another altogether different form ("Father's Butterflies" 218).
IMAGE (DEAD LEAF BUTTERFLY)
Fig. 3. Kallima paraletka, a "dead-leaf butterfly." Pictured here are the undersides of the wings, which are dull brown. The upper sides are boldly colored bright blue, orange, and black. Photo by Yves-Pascal Dion, 1998. Used by permission.
This is the dead leaf butterfly that so impressed Nabokov. It's quite good, isn't it? It turns out that this butterfly did not come to look like a dead-leaf, as Darwinists have thought, by gradual approximations. S½ffert had provided some evidence in the 1920s that the form appeared suddenly, pretty much as is (385-413). In the next section, I will mention some of the mechanisms that helped create this form, which we may also suppose is a natural attractor. Selection might help stabilize this form once structural mechanisms have found it, but natural selection could not create it by gradually turning a butterfly species that doesn't look like a leaf into one that does.
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 luck away by positing influential predators. Most people, I think, are irrational when it comes to thinking about luck, that is, most people donÌt 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 an unspecified object in nature. It would also be trivial to predict that someone's lottery ticket 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 that Fortuna must have been guiding the ping-pong balls just a little bit. This is because, as far as the lottery winner is concerned, he or she did prespecify the winning number, and the likelihood of a particular number being selected is significantly lower than an unspecified one and thus would seem to require some help, from a goddess that has recognized the lottery winnerÌs special fitness or deservedness, whatever that might be. [12]
The concept of "mimicry" as an underlying cause of a formÌs emergence makes no sense in Darwinian evolution because the advantageous form natural selection must select would have to be prespecified. We know that natural selection does not work this way. Selection works when it can choose any solution to a problem. Selection cannot be limited to one solution.
II. Structural
Evolution
Now I will move on to the next section, structural evolution. This is a ground plan, a butterfly wing pattern template, which was developed in the 1920s by German biologists who were interested in theoretical biology and the laws of biological form, not in Darwinian fitness. They came out of the teleomechanist tradition, which followed Immanuel Kant's brand of teleology. They argued that some similarities in butterfly wing patterns should be understood as "variations on a theme," a phrase from teleology. These themes are governed by inherent physical laws, and are not necessarily due to a common ancestor.
IMAGE (NYMPHALID
GROUND PLAN)
Fig. 4. The nymphalid ground plan. The spoke-like sections are called wing cells. Within each cell, pigment can diffuse in various ways, creating up to five distinct line segments (as in the marginal bands), spots (as in the ocelli), smudges (not shown) or other shapes (such as scalloped lines around the border ocelli). This illustration represents two alterative expressions of all possible elements. (Left from Schwanwitsch; Right from S½ffert.) Source: Nijhout, H. Frederik. The Development and Evolution of Butterfly Wing Patterns. Washington: Smithsonian Institution Press, 1991. p. 24. Used by Permission.
Nabokov analyzed wing pattern formation in terms of the way pigment diffused within individual wing cell sections (the little spoke-like compartments, See figure 4) not in terms of an overall wing pattern. He writes,
the classical conception of a row of ocelli eyecells as the result of a statically placed line or band having broken up into spots seems to me absolutely irrelevant to the understanding of the Lyc nid pattern. ... what we see is sic not the remnants of a definite band in a definite place, but this or that stage of a more or less coordinated longitudinal movement of spots ÷. In a word it is not a row of squares on a chessboard, but a shifting line of attacking pawns. (Boyd 282)
It is also important to note in regard to this issue that predators see overall patterns, but the mechanisms of pattern formation are local not global. Recent research has proven Nabokov right about "line" formation. [13]
Within each of these individual spoke-like cells, up to five elements can be expressed. Here are some of the basic variations that occur depending on how the pigment diffuses across the wing cell topology.
IMAGE (MAJOR THEMES)
Fig. 5. There are two, mutually exclusive, major themes in wing patterns, the intervenous stripe (top left), and the ground plan (top right). Major variations of the ground plan elements are shown in the lower left. Further variations on one of the elements are shown lower right. Variations can be attributed to differences in the reaction-diffusion process during individual development or across species. Source: Nijhout, H. Frederik. The Development and Evolution of Butterfly Wing Patterns. Washington: Smithsonian Institution Press, 1991. p. 209. Used by permission.
The so-called eyespot is one of the most likely forms produced in a reaction-diffusion process. Functionality and preferential fitness may become a factor later on down the line -- but fitness is not necessary to explain its existence or its prevalence.
IMAGE (DEAD LEAF GROUND PLAN)
Fig. 6. The form of a dead-leaf butterfly (Lepidoptera: Ditrysia: Papilionoidea: Nymphalidae: Nymphalinae Kallima inachis) is achieved with relatively few modifications of the elements of the ground plan (fig. 4). In the upper wing, reduced eyecells (ocelli) and the left half of the ocelli border have moved to the center, connecting with a merged version of the central symmetry system. Together the ocelli border and the symmetry system form a single line down the center that looks like a leaf vein. Source: S½ffert, F. "Zur vergleichende Analyse der Schmetterlingszeichnung." Biologisches Zentralblatt 47 (1927): 386.
You can see that the ground plan of the dead leaf is distorted because the entire wing is stunted. The result is a symmetrical shape and the main line here tends to end up dead center. Now compare the dead-leaf ground plan (fig. 6) to the normal ground plan (fig. 4). What were called eyespots in other contexts now look like "grub-bored" holes. Change of context makes new interpretations possible. I'd like to compare this to what Juliette Taylor said about mistranslation and puns: the meaning of the pigment changes. The effect is like that of a pun. This is a very important point, I think, because this is one of the ways in which chance can have real effects even in an entirely deterministic universe. [14] I think we have to be careful, by the way, not to say that Nabokov rejected determinism, as Brian Boyd argued at the beginning of this symposium. I doubt Nabokov believed that nature can defy its own physical laws. What Nabokov rejected was classical determinism, that is, reductionism. I think Nabokov would have whole-heartedly accepted today's determinism, which includes nonlinear dynamics and quantum mechanics.
III. Teleology
Now we have come to the
third and final section of my talk, teleology. I make a distinction between two
kinds of telic processes that I think you will find helpful in understanding
Nabokov's attitude toward mimicry. Remember at the beginning of my talk I said
there are two aspects that make evolution seem teleological. One is inherent
directedness. The other is accidental functionality. It so happens that
throughout history teleologists have divided into two camps whose interests
reflect these two aspects. The first camp says that inherent design
(pattern/orderliness) in biological systems is created by internal automatic
principles. These teleologists may be associated with Aristotle and Kant (and I
would argue, Emerson, though many would disagree), as well as with contemporary
structuralists. They were interested in variations on themes, like the monarch
and the viceroy. The second camp is associated with Christianity and the idea
of Divine Providence. This camp says that design (pattern/orderliness) in
biological systems suggests a Designer external to the system, who actively
limits, guides, and controls things according to His (sometimes arbitrary) idea
of fitness. (Think also of a meddlesome author of a contrived novel.) These
teleologists would have been interested in the dead leaf mimic. An analogy may
help further clarify the difference between these two groups. If the first
group (teleomechanists, structuralists) can be associated with the following
sequence of numbers:
3, 6, 9, 12, 15, 18, 21, 24,
27,
the Second group (Christians, authors of contrived fiction) can be associated with this sequence:
14, 23, 28, 33, 42, 51, 59, 68.
The sequence
3, 6, 9, 12, 15, 18, 21, 24, 27, 30 is governed by a rule that can be
discovered by examining the sequence itself. What is the rule? Add 3 to each
number to get the next. Once you discover this rule, you can predict every new
number in the sequence. This sequence may be compared to the laws that govern
pattern formation; you can discover the laws by examining the process of
pattern formation itself. The sequence 14, 23, 28, 33, 42, 51, 59, 68
is also governed by a rule. Can any one tell me what it is? Any New Yorkers?
The rule governing this sequence cannot be discovered by examining the sequence
itself. It represents the stops on the Lexington Avenue subway line in New
York.[15]
The rule is found outside the sequence and is imposed upon it. I
associate this kind of thinking with the dead leaf mimic: the interpretation of
its form as a leaf is imposed upon it by a predator (or, if not, only the
lepidopterist) who is not a part of the process that actually causes the
pattern to form. As I say, I associate this second kind of teleology with the
idea of the deus ex machina and with contrived fiction.
It involves the kind of unpredictability that is associated with accidental
functionality.
This brings me to the idea
of funny coincidences in Nabokov's Plots.
÷it dawned on me that this
Was the real point, the contrapuntal theme;
Just this: not text, but texture; not the dream
But topsy-turvical coincidence,
Not flimsy nonsense, but a web of sense (Pale Fire 342)
You all know that John Shade begins to suspect that there is an afterlife when he hears about Mrs. Z who, like he, saw a fountain during a brief and aborted visit to the other side. He feels that this is too unlikely to be a mere coincidence and so must be indicative of a common truth. When Shade later learns Mrs. Z had seen a mountain, not a fountain, he appreciates the coincidental misprint. He feels that some thing or someone seemed to be making "ornaments/of accidents." Apparently, whether or not there truly is a God or an afterlife is not as interesting to Nabokov as the fact that it is suggestive coincidences that give the impression life is like a novel written by an omniscient and somewhat playful author. This is teleology of the second type.
Why is chance so important to the belief in an external supernatural Creator (whose role is very like that of an Author of fictional worlds)? Science is only interested in resemblances that are indicative of a common cause. For instance, why many galaxies have spiral shapes: the processes that have formed them obey the same laws of pattern formation. Science is not interested in what might be called poetic resemblances, those that are merely coincidental, for instance, the fact that there is a "big dipper" and a "little dipper" in the stars. Since science doesn't care about such coincidences, only a superstitious belief can step in to provide an explanation: the stars are intentionally designed by a god with a partiality for patterns and a desire to entertain us mortals. In his fiction, Nabokov satirizes the tendency to see any purpose, divine or otherwise, as a cause of what is truly a mere coincidental resemblance (or an initially nonutilitarian resemblance formed by similar physical laws).
In "The Vane Sisters," there is a man who pours through the pages of books in search of clever misprints such as when "Hither" is given as "Hitler" and coincidentally makes some new perverse sense. Why would anyone care about such things? Nabokov claimed such typos illustrated "the chance that mimics choice, the flaw that looks like a flower" (622). I think this is how we ought to understand many cases of insect "mimicry."
Victoria N. Alexander
Dactyl Foundation for the Arts & Humanities
64 Grand Street
New York, NY 10013
Santa Fe Institute
1399 Hyde Park Road
Santa Fe, NM 875
alexander@dactyl.org
Works Cited
Bergson, Henri. Creative Evolution. Trans. Arthur Mitchell. Mineola, New York: Dover Publications, 1998.
Boyd, Brian and Robert Pyle, eds. Nabokov's Butterflies. New York: Beacon Press, 2000.
Crutchfield. James P. "When Evolution is Revolution: Origins of Innovation." Evolutionary Dynamics: Exploring the Interplay of Selection, Neutrality, Accident, and Function. Eds. J. P. Crutchfield and P. Schuster. New York: Oxford University Press, in press.
Nabokov, Vladimir. "Father's Butterflies." Nabokov's Butterflies. Eds. Brian Boyd and Robert Pyle New York: Beacon Press, 2000.
---. Pale Fire. 1962. New York: Vintage, 1989.
---. "The Vane Sisters." The Stories of Vladimir Nabokov. 1959. New York: Knopf, 1995.
Nijhout, H. Frederik. The Development and Evolution of Butterfly Wing Patterns. Washington: Smithsonian Institution Press, 1991.
Schwanwitsch, B. N., "On the groundplan of the wing-pattern in nymphalids and certain other families of rhopalocerous Lepidopetra." Proceedings of the Zoological Society of London, ser. B, 34: 509-528 (1924).
S½ffert, F. "Zur vergleichende Analyse der Schmetterlingszeichnung." Biologisches Zentralblatt 47 (1927): 385-413.