Not-quite-endless Forms Most Beautiful, or Wormholes Through Morphospace


On Quintessence of Dust, associate professor of Biology Stephen Matheson (yes a Steve Steve), treats us to a fascinating trip through morphospace. He discusses a recent paper by Prusinkiewicz et al.titled Evolution and Development of Inflorescence Architectures, published in Science 8 June 2007:

In this paper, the authors not only show how, despite a multitude of possible forms, severe constraints are placed on biological diversity, but also show how the existence of ‘worm holes’ in fitness space link the various architectures. A beautiful story about scientific inquiry.

To understand the constraints on biological diversity, we analyzed how selection and development interact to control the evolution of inflorescences, the branching structures that bear flowers. We show that a single developmental model accounts for the restricted range of inflorescence types observed in nature and that this model is supported by molecular genetic studies. The model predicts associations between inflorescence architecture, climate, and life history, which we validated empirically. Paths, or evolutionary wormholes, link different architectures in a multidimensional fitness space, but the rate of evolution along these paths is constrained by genetic and environmental factors, which explains why some evolutionary transitions are rare between closely related plant taxa.

Well, read the rest of the story at Quintessence of Dust, it’s a fascinating story of science and provides us some useful lessons about Intelligent Design.

Matheson Wrote:

In my view, this is an extraordinary example of evolutionary thinking that drives a specific experimental analysis. The authors sought an encompassing developmental model precisely because they noted that the reality of common descent necessitates such a model. So if you’ve heard that evolutionary theory doesn’t make testable predictions or is of no use in modern biology, here’s one more demonstration of the falsity of those claims. “Design” considerations sure didn’t produce the key insight; on the contrary, the denial of common ancestry that is sadly typical in the ID camp would have precluded the authors’ approach.

Note that ID would be unable to make any positive prediction because its Designer (God) cannot be constrained.


See also Simulating the early evolution of plants, an earlier contribution by me on the evolution of tracheophytes

Niklas used computer models to mimic the early evolution of tracheophytes (ancient vascular plants). The architecture of the early spore producing tracheophytes can be mathematically simulated using relatively few parameters such as axial length, diameter, probability of branching, angle of branching, and the rotation angle. These parameters define the possible morphological variants or morphospace. In addition four very basic functions applicable to all plants can be defined. Namely interception of sunlight, exchange of water and gases and waste, stability, and reproduction. The fitness of these four functions can be evaluated rigorously using concepts of physics and chemistry.

The relevant finding was that

On stable landscapes, there are comparatively few morphologies capable of maximizing the performance of any of the four functions. However, when the number of functions to optimize increases, the number of optimal morphologies increases. In addition, the global fitness of these multiple morphologies decreases. This suggests that evolution may proceed easier when it has to optimize for multiple functions.

This ties back to evolution given multiple constraints and ID’s claims that such evolution will become more complicated. In fact, as the evidence shows, the existence of higher dimensional fitness functions, often simplifies evolution since it can provide ‘worm holes’ through which previous ‘islands’ of functionality can be connected.

Does anyone remember Gavrilets? Google… Holey Landscapes.… Soon…

What a beautiful piece of work. Thanks PvM.

In a previous thread I gave six examples of different types of limitations on natural selection. Well, here is a seventh. Natural selectin is limited to those regions of the fitness landscape to which the evolution of developmental pathways is possible, given historical constraints. The presence of such “wormholes” demonstrates that such pathways do exist and that they can be accessed through random mutations.

As the authors point out, this limitation not only helps to explain the solutions that are actually seen in nature, but it also helps in explaining what solutions might possibly arise in the future and what solutions might be extremely unlikely to ever arise.

So, once again, to a large extent it is the limitations of natural selection that have shaped the biosphere we see today. This is one of the most fundamental predictions of evolutionary theory. It explains the shape of the tree of life. It explains the lack of many seemingly possible solutions. It explains why those familiar with the evidence see no indication of intelligence, foresight or planning in the process of evolution.

But they’re still plants!! :)

Thanks to Stephen Matheson. He managed to write a very interesting posting about a very interesting paper which showed a variety of beautiful concepts of scientific inquiry. Something ID proponents would undoubtably call ‘just so stories’ because it is foreign to them

What a terrible terminology!

Wormholes creates new spacetime, and may or may not connect to global solutions of spacetime. But in this case the authors are describing connections between fitness spaces which connects through constrained channels by contingency. A more suitable analogy would perhaps been caisson locks.

The authors have predecessors of course. From at least 1997 there are papers referring to “wormholes” through shape space of deformable objects. In this case they have an algorithm that moves the model object through discontinuities in lower dimensional projections of shape space. Also not quite analogous to the previously postulated physical situation.

Still, one would like authors to check previous use before borrowing terminology.

PvM Wrote:

ID would be unable to make any positive prediction because its Designer (God) cannot be constrained. … Something ID proponents would undoubtably call ‘€˜just so stories’€™ because it is foreign to them

And undoubtedly IDiots will pop in and deliver their unconstrained “just so” design stories in 3 … 2 … 1 …

(Of course, in a derived sense it is more suitable. If “fitness space” in some measure matches a manifold for a localized system in spite of its discontinuities and contingencies, it probably does so locally.

So one could envision spaces establishing a smaller volume of a manifold as they evolve, making the analogy a closer fit. But it’s not the picture the illustrations give.)

To T. Larsson: the wormhole metaphor is perfect. Your confusion has less to do with the “borrowing” of “terminology” than it has to do with your failure to grasp the utility of the metaphor.

To PvM: thanks for the link! I’ve long been a Panda’s Thumb fan (it’s an original link at Quintessence of Dust), and I think I should start commenting more.

Catching up on old threads:

it has to do with your failure to grasp the utility of the metaphor.

I have explained why I think it is a bad terminology. If you have any objections, I would be happy to hear your motivation.

Torbjörn Larsson, OM: Catching up on old threads:

it has to do with your failure to grasp the utility of the metaphor.

I have explained why I think it is a bad terminology. If you have any objections, I would be happy to hear your motivation.

My “motivation” is my understanding of the difference between “terminology” and metaphor. The metaphor of a wormhole, as employed by Prusinkiewicz et al., is perfect as a metaphor. As I understand it, wormholes (cosmologically speaking) “offer a shortcut between two widely separated points in space.” (Paul Davies) The authors offer a wormhole as a metaphor, because they are depicting evolutionary trajectories that link seemingly widely separated points in morphospace. The trajectories are “shortcuts” that link fitness spaces that seem to be impossibly far apart.

I didn’t see anything in your criticism that reduced the utility of the metaphor. Sorry if I seemed rude.

Sheesh, I was sure I checked in on this thread after the last comment.

Anyway, my objection was that wormholes create new spacetime outside the original. They are a very specific type of shortcut, and the analogy isn’t reflecting this.

OTOH, caisson locks links separated points (over shorter distances), so I think that reflects the physical situation in an attempted analogy.

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This page contains a single entry by PvM published on October 1, 2007 10:06 PM.

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