I’ve just been directed towards P. Z. Myer’s Pharyngula blog in which, during the course of a dissection of Fodor and Piattelli-Palmarini’s book

*What Darwin Got Wrong*, Myers has the following to say about D’Arcy Thompson and*On Growth and Form*:*D’Arcy Wentworth Thompson was wrong.*

*Elegantly wrong, but still wrong. He just never grasped how much of genetics explained the mathematical beauty of biology, and it's a real shame — if he were alive today, I'm sure he'd be busily applying network theory to genetic interactions.*

[Sorry, must stop you there. Not even Fodor and Piattelli-Palmarini called their book

*Darwin Was Wrong*. I suspect they wanted to, but could not justify it even to themselves. D’Arcy Thompson’s book is over 1000 pages long. Is it*all*wrong? Simple answer: of course it is not. Take a look at this, for example. I know; this is simply rhetoric. It’s just that I still believe it matters to find the right words, rather than sound bites.]*Let's consider that Fibonacci sequence much beloved by poseurs. It's beautiful, it is so simple, it appears over and over again in nature, surely it must reflect some intrinsic, fundamentally mathematical ideal inherent in the universe, some wonderful cosmic law — it appears in the spiral of a nautilus shell as well as the distribution of seeds in the head of a sunflower, so it must be magic. Nope. In biology, it’s all genes and cellular interactions, explained perfectly well by the reductionism [Mary] Midgley deplores [in her review of F&P-P].*

*The Fibonacci sequence (1, 1, 2, 3, 5, 8…each term generated by summing the previous two terms) has long had this kind of semi-mystical aura about it. It's related to the Golden Ratio, phi, of 1.6180339887… because, as you divide each term by the previous term, the ratio tends towards the Golden Ratio as you carry the sequence out farther and farther. It also provides a neat way to generate logarithmic spirals, as we seen in sunflowers and nautiluses. And that's where the genes sneak in.*

*Start with a single square on a piece of graph paper. Working counterclockwise in this example, draw a second square with sides of the same length next to it. Then a third square with the same dimensions on one side as the previous two squares. Then a fourth next to the previous squares…you get the idea. You can do this until you fill up the whole sheet of paper. Now look at the lengths of each side of the squares in the series — it's the Fibonacci sequence, no surprise at all there.*

*You can also connect the corners with a smooth curve, and what emerges is a very pretty spiral — like a nautilus shell.*

*It's magic! Or, it's mathematics, which sometimes seems like magic! But it's also simple biology. I look at the whirling squares with the eyes of a developmental biologist, and what do I see? A simple sequential pattern of induction. A patch of cells uses molecules to signal an adjacent patch of cells to differentiate into a structure, and then together they induce a larger adjacent patch, and together they induce an even larger patch…the pattern is a consequence of a mathematical property of a series expressed on a 2-dimensional sheet, but the actual explanation for why it recurs in nature is because it's what happens when patches of cells recruit adjacent cells in a temporal sequence. Abstract math won't tell you the details of how it happens; for that, you need to ask what are the signaling molecules and what are the responding genes in the sunflower or the mollusc. That's where Thompson and these new wankers of the pluralist wedge fail — they stop at the cool pictures and the mathematical formulae and regard the mechanics of implementation as non-essential details, when it's precisely those molecular details that generate the emergent property that dazzles them…*

*There is nothing in this concept that vitiates our modern understanding of evolutionary theory, the whole program of studying changes in genes and their propagation through populations. That's the mechanism of evolutionary change. What evo-devo does is add another dimension to the issue: how does a mutation in one gene generate a ripple of alterations in the pattern of expression of other genes? How does a change in a sequence of DNA get translated into a change in form and physiology?*

*Those are interesting and important questions, and of course they have consequences on evolutionary outcomes…but they don't argue against genetics, population genetics, speciation theory, mutation, selection, drift, or the whole danged edifice of modern evolutionary biology. To argue otherwise is like claiming the prettiness of a flower is evidence against the existence of a root.*

OK (hello, me again), I think I’d go along with just about all of this, apart from a suspicion that there is probably a better term for ‘wankers of the pluralist wedge’. Indeed, it is precisely how this self-organization is initiated at the biomolecular/cellular level that I have explored, both in phyllotaxis and in developmental biology generally, in my book

*Shapes*(OUP, 2009) (alright, but I’m just saying). Yet there seems to be a big oversight here. Myers seems to be implying that, because genetic signals are involved, phyllotactic patterns are adaptive. I’m not aware that there is any evidence for that. In fact, quite the contrary: it seems that spiral Fibonacci phyllotaxis is the generic pattern for any meristem budding process that operates by some reaction-diffusion scheme, or indeed by any more general process in which the pattern elements experience an effective mutual repulsion in this cylindrical geometry (see here). So apparently, in phyllotaxis at least, the patterns and shapes are not a product of natural selection. Possessing leaves is surely adaptive, but there seems to be little choice in where they go if they are to be initiated by diffusing hormones. In his review of F&P-P, Michael Ruse puts it this way: ‘The order of a plant’s leaves may be fixed, but how those leaves stand up or lie down is selection-driven all of the way.’So sure, there is absolutely nothing in this picture that challenges Neodarwinism. And sure, we should say so. But it does imply that, in the case of plants, an important aspect of shape determination may lie beyond the reach of natural selection to do much about. And this surely suggests that, since the same processes of morphogen diffusion operate in animal development, there might equally be aspects of that process too that have little to do with natural selection. Myers alludes to the case of spiralling mollusc shells: well yes, here too it appears that the basic logarithmic-spiral shape is going to be enforced by the simple maths of self-similar growth, and all evolution can do is fine-tune the contours of that spiral. That, indeed, is what Myers has said, though appearing to think he has not: the pattern is an inevitable consequence of the maths of the growth process. So no, it’s not magic. But it’s not in itself adaptive either. And correct me if I’m wrong, but I believe that was basically D’Arcy Thompson’s point (which is not to deny that he was unreasonably suspicious of adaptive explanations).

*that*is less commonly recognized. Ian Stewart argued the same point in

*Life’s Other Secret.*Anyone wishing to argue that such constraints undermine the case for natural selection happening at all is of course talking utter nonsense (and not even Fodor and Piattelli-Palmarini go that far). But it’s an interesting issue, and I’m made uncomfortable when people, through understandable fear of creationism’s malign distortions, want to insist that it’s not.

## 2 comments:

No evolution expert I, yet it seems strange to label some feature of a complex organism "not adaptive" just because it can be generated by something that can be understood, approximately, as akin to a relatively simple finite automaton. Becoming a multicellular organism at all is an adaptation, I suppose, so in at least that minimal sense the structure of a leaf is adaptive.

More than that, to implement a relatively more complex algorithm that would not be related to the Fibonacci sequence may be more costly for a complex organism, so the adaptation is that for a given environment a simple process is good enough, and better, because less costly, than more complex processes that might well have been tried over the millenia. If one could prove that more complex alternatives have never been tried, and found less successful, perhaps one might say that a simple process is not adaptive, but proving such a negative is difficult, perhaps ultimately impossible.

I've displayed enough ignorance, I suppose. I'm curious whether it makes enough sense for a reply.

Peter,

My view is pretty much as you say: I suspect that the default setting of Fibonacci spirals is "good enough", if all the plant needs is to space leaves comfortably around the stem, and that the cost of altering this deep-rooted structure is too great to permit any tinkering. I hope to be able to say something a bit more definitive on that shortly. The point would then be that natural selection imposes only a very generalized aspect of the morphology, or to put it another way, other factors rather tightly constrain what selection can do. In other cases, such as butterfly wings, it appears that the adaptive gains are sufficient to justify rather more drastic tinkering with the options that a self-organized patterning process can offer. What I'm interested in is how natural selection interacts with the constraints imposed by the physics and chemistry. Myers seemed to imply that, if genes are involved, then natural selection can get to work more or less unencumbered.

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