Biology and Philosophy 18: 463–476, 2003. © 2003 Kluwer Academic Publishers. Printed in the Netherlands.
Book Review
The Good, the Bad and the Impossible JAMES MACLAURIN Department of Philosophy University of Otago PO Box 56, Dunedin New Zealand E-mail:
[email protected]
A review of George R. McGhee, Jr., Theoretical Morphology: The Concept and Its Applications, Columbia University Press, New York, NY, 1999, 378 pp. (cloth), ISBN 0-231-10616-5. My own suspicion is that the universe is not only queerer than we suppose, but queerer than we can suppose. J.B.S. Haldane (1927) Philosophers differ widely in the extent to which they condone the exploration of the realms of possibilia. Some are very enamoured of thought experiments in which human intuition is trained upon the products of human imagination. Others are much more sceptical of the fruits of such purely cognitive explorations. That said, it is clear that human beings cannot dispense with modal speculation altogether. Rationality rests upon the ability to make decisions and that in turn rests upon the ability to learn about what is possible and what is probable. Thus, on pain of irrationality, we must have some means of exploring other possible worlds. Thankfully, intuition is not the only aid we have at our disposal. Science also is in the business of finding regularities, which hold counterfactually. Scientific theory tells us about the likelihood of particular outcomes flowing from particular processes given particular background conditions. Thus, it also tells us about the contents of other possible worlds. One consequence of the possibility of such inferences has been a theoretical interest, not just in the contents, but also in the geography of the domain of all possibly worlds. Metaphysicians, epistemologists and philosophers of language are very familiar with locutions such as “nearby possible worlds” (meaning possible worlds very similar to the actual world). Similarly, evolutionary theory tells us that there is little chance of us discovering an organism that is mammal-like in most respects except in having six limbs. It’s
464 not that we know such an organism to be impossible, but rather that we think it would be the product of an evolutionary history very different to the actual history of life on earth. Put another way, such organisms would be denizens of distant possible worlds. Clearly then, both biology and philosophy have ample motivation to be interested in the reasoning and evidence that supports such claims. Seemingly, in both disciplines there is a certain lure to this modal cartography, but ought we in fact to be convinced of its merits? Is it science or philosophy or not a good example of either? What sort of problems can it solve? What sort of problems will it create? How might we test its accuracy? In his excellent book Theoretical Morphology: The Concept and Its Applications (1999), George McGhee provides an admirable introduction to the complex theoretical landscape surrounding the exploration of possible biological form. The book aims to serve three purposes. First and foremost it is a thorough summary of the results of more that thirty years of theoretical morphology. While some of the examples will be familiar1 to many readers, most will be impressed by the tremendous variety and ingenuity2 of work in this little recognised and lightly funded area of theoretical biology. Along the way it also provides a useful primer for those unfamiliar with the methodology of modern theoretical morphology. The second aim of the book is to provide suggestions for further work and a plea for both graduate students and established researchers to help with the filling in of a rather daunting number of lacunae in the scope of current studies. Finally, if slightly patchily, the book addresses some of the philosophical issues canvassed above. It is perhaps a mark of the youthfulness of the discipline that the philosophical issues receive relatively little airplay. Indeed, I shall suggest in this paper that there is at least as much work to be done in this area as there is to be done in the investigation of as yet unexplored realms of morphological variation. One of the great virtues of McGhee’s book is that he sells with gusto the idea that theoretical morphology is a vibrant and important field of study. This is so for a variety of reasons. Firstly, one is inclined to think of the study of non-actual life forms as a new and perhaps outlandish scientific pursuit somewhat akin to exobiology (the study of hypothetical alien species). But the tradition in which McGhee writes is deep rooted in such venerable disciplines as biological taxonomy, developmental biology and evolutionary theory. Taxonomic systems serve many purposes and thus each is a compromise between competing theoretical imperatives (explanatory power, breadth of application, usability etc.). Part of this mix has always been the representation of biological diversity. That is why conservation biologists feel entitled to
465 employ taxonomy as a means of measuring that diversity. But, at least in one respect, to talk of the diversity of an assemblage of organisms is to make a claim about the extent to which those species are separated by possible but non-actual biological form. For the reasons just stated, taxonomic systems vary in the extent to which they implement this theoretical imperative (numerical taxonomy is a good example of a taxonomic system in which this notion of biological diversity is very much to the fore). Both developmental biology and evolutionary theory also seek to explain the development of morphology over time. But again, this explanation of evolutionary and developmental trajectory only makes sense if it is underpinned by a robust conception of the wider landscape of possible morphologies. Indeed, the idea of an evolutionary trajectory is more metaphor than science, unless one accepts that there is at least some truth underlying the implicit spatial analogy. So, all these venerable scientific disciplines would clearly benefit from a robust conception of what is now widely called ‘morphospace’. A second reason for giving theoretical morphology a good run for its money is that, in many ways, it is unlike other sciences. In A New Kind of Science (2002) Stephen Wolfram as controversially suggested that science in future will be more concerned with algorithms than laws. One wonders how this could be true of all science, but if there is any science of which this is clearly true, that science is theoretical morphology. One of the great success stories of this discipline is the discovery of algorithms that accurately chart the progress of both growth and evolution. So, if on closer inspection this discipline really is unlike those more concerned with laws and regularities, we might well ask whether or not it is thereby more successful and whether or not we need to broaden our philosophy of science to include this new type of enterprise. Finally, this discipline deserves much greater attention than it has hitherto received because of the great variety of problems in theoretical biology that would apparently be furthered by future successes in theoretical morphology. As McGhee notes, this is a fact that has been recognised by many involved in the relevant debates as is evident in the following quote from Stephen Jay Gould: I believe that the question of defining morphospaces and mapping their differential filling through time is so vital to our understanding of life’s history, particularly to the potential contribution of paleontologists. Yet relatively little has been done in this area. (1991: 422) Indeed, at times while reading Theoretical Morphology I found myself convinced that this fledgling discipline really is the next big thing. This is in part due to McGhee’s infectious enthusiasm for the subject. However, there
466 certainly is a great deal that we might hope to achieve through the employment of this research program. I shall return to these aspirations presently after a brief description of the theory and methodology behind theoretical morphology.
What is theoretical morphology? Theoretical morphology consists of two distinct programmes. These are the modelling of organic morphogenesis (ie. changes in shape during growth) and the analysis of possible organic form via the construction of theoretical morphospaces.3 A theoretical morphospace is an n-dimensional model in which each dimension corresponds to some aspect of possible biological variation4 (for example the shell aperture diameter in a mollusc or the tessellation pattern in which plant cells are packed together5 ). Once the morphospace is constructed it then becomes possible to generate hypotheses about why organisms have taken particular trajectories over both evolutionary and developmental time periods and about why particular regions within the space are densely or sparsely populated by known species. Theoretical morphology is importantly different from a variety of explanatory tools used in developmental and evolutionary biology. Dennett’s ‘Library of Mendel’ (1995) and the relatively recent notion of ‘ecospace’ (see for example Valentine 1995) are similar in obvious respects despite focussing upon different types of biological variation. However, in understanding the relationship between theoretical morphology and its sibling disciplines, there are two important distinctions to be kept in mind. These I will illustrate by comparing theoretical morphology with studies based on adaptive landscapes and studies based on morphometrics. Both enterprises employ a similar basic idea but to rather different purposes.
Theoretical morphology compared to the adaptive landscape Sewell Wright is famous, amongst other things, for the discovery of the concept of the adaptive landscape (1932). This is a hypothetical space traversed by evolving organisms which constantly climb its occasionally mobile fitness peaks. The adaptive landscape differs in many respects from a theoretical morphospace. Its dimensions are based on biological characteristics (except for the ‘height’ dimension which represents fitness), however, where it has many dimensions theoretical morphospaces typically have few. Also, the adaptive landscape was originally envisaged as a means of modelling genetic diversity rather than morphological diversity. But, McGhee notes,
467 philosophically the crucial difference between the two disciplines is that the adaptive landscape is, in effect, a highly successful thought experiment that has been used to justify a number of basic principles of evolutionary biology.6 Indeed, he endorses Dennett’s claim that ‘the idea of a fitness landscape . . . has become a standard imagination prosthesis for evolutionary theorists’ (1995: 190). Where Sewell Wright’s idea is qualitative and (at least by Popperian lights) largely philosophical, theoretical morphology is intentionally quantitative and at least putatively more scientific. Indeed, it is this quantitative approach that leads to the computational and representational limitations, which require that theoretical morphospaces have a relatively small number of dimensions. So, a theoretical morphospace is a representation of possible biological space whose dimensions correspond to biological characteristics. Moreover, if these models are to underpin biological explanations then they must be representations of real facts about the extent to which biological individuals or biological taxa (both actual and merely possible) differ from one another. But herein lies an important philosophical issue. The distance between two organisms within a theoretical morphospace depends upon which biological characteristics you choose to underpin the dimensions of that morphospace. Therefore, the inferences that can be drawn from facts about the occupation of a theoretical morphospace are also dependent upon the characteristics underpinning the dimensions of that space. From whence then, do we get these characteristics? This question brings me to the second explanatory enterprise, which is closely related to, but importantly different from, theoretical morphology. Theoretical morphology compared to morphometrics Morphometrics, inspired by the seminal work of D’Arcy Thompson (1917), is the study of actual biological form. It is an older discipline than theoretical morphology with a much larger literature, reflecting the wide variety of methodologies which can be employed in the description of morphology. One of these methodologies involves the construction morphospaces. However, crucially these are empirical morphospaces, which differ from theoretical morphospaces in that their dimensions correspond to actual biological characteristics. Indeed they are inferred from data using techniques such as Principle Components Analysis. One of the consequences of this is that adding to the original data set, in such studies, can alter the dimensions of the morphospace in question. This means that the inferences that can be made from such studies are very much tied to particular data sets. Hence, the crucial difference
468 between the two enterprises is that the empirical morphospaces employed by morphometrics do not support inferences about possible (but non-actual) biological form. That said, this still leaves us wondering just how it is that theoretical morphologists come up with the dimensions underpinning their morphospaces. The story is complex and philosophically intriguing. The aim of theoretical morphology is to represent possible biological form, but inevitably it is difficult to do this without at least taking actual biological form as guide to the dimensions of a theoretical morphospace. There are two reasons for this. First, one of the main aims of theoretical morphology is to use morphospaces to infer facts about the history and function of the characteristics possessed by actual organisms. Given this, characteristics chosen to underpin the morphospaces in question have to be ones that are relevant to the explanatory purposes of those studying the actual organisms. Secondly, while there is much debate over such issues, there is no recognised procedure for the determination of which biological characteristics to use in the development of a theoretical morphospace. This is an important issue given (as noted above) that there is considerable philosophical disagreement about the reliability of human intuitions as guides to the non-actual. In the absence of a clear or robust form of inference being used to generate the dimensions of theoretical morphospace, hypotheses about particular choices of characteristics to support theoretical morphospaces do not appear to be scientific (in the strict sense of being testable or indeed even in the sense of being arguments to the best explanation).7 This is so precisely because the dimensions of theoretical morphospaces are not supposed to reflect or correspond to actual biological form. Thus, we cannot test them for accuracy, nor can we easily invent a method of inference that will extract them from biological data (because this would just produce an empirical morphospace). An upshot of this is that readers of Theoretical Morphology: The Concept and its Applications are likely to be struck by the fact that studies using this methodology differ widely in the extent to which their choice of dimensions seems ‘obvious’ and thus not in need of further theoretical justification. As an example of a particularly ingenious morphospace whose dimensions are far from obvious, consider Thomas and Reif’s space of possible skeletons (Figure 1). It is clear that much of the debate in theoretical morphology concerns decisions about the characteristics that underpin the dimensions of theoretical morphospaces. Given that these appear untestable and therefore, to some extent the products of human intuition or imagination, this calls into question just how much such studies can tell us about possible (as opposed to
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Figure 1. Dimensions of Thomas and Reif’s skeletal theoretical design space (1993). 1) Topology: either internal (A) or external (B). 2) Material: either rigid (C) or flexible (D). 3) Number: either one element (T), two elements (V) or three or more elements (W). 4) Geometry: either rods (G), plates (H), cones (J), or solids (K). 5) Growth Pattern: either accretionary (L), unit/serial (M), replacement/moulting (Z), or remodelling (N). 6) Building Site: either in place (X) or in prefabrication (Y). 7) Conjunction: either in no contact (P), jointed (Q), sutured/fused , or imbricate (S). Artwork courtesy of R.D. K. Thomas.
470 actual) biological form. In effect, such inferences run the risk of becoming the biological equivalent of philosophical ‘conceivability’ arguments. That is to say that conclusions about the location and movement of organisms within morphospace might be rather more subjective than we would like. This appears not to be a concern shared by McGhee who seems happy that theoretical morphology really can tell us facts about the possibility (or impossibility) of morphologies in nature: The nature and shape of the hyperspace in a theoretical morphospace are determined by geometry, not by organisms. The dimensions of a theoretical morphospace exist mathematically pure and pristine in the absence of any measurement data. Such a morphospace can not only reveal what could be in nature (regardless of what nature has actually produced), it can also reveal what cannot exist at all. (McGhee 1999: 282) The extent to which this issue poses a problem for the theoretical morphology program, depends entirely upon what set of problems that we try and use it to solve and it is to that question that I shall turn in the final section of this paper. I shall argue that there are two types of problems to which we might apply this methodology.
What shall we do with theoretical morphology? There are many possible purposes to which we might put theoretical morphology. Some items of the following list are discussed by McGhee. Some of the more speculative items on the list I have added as my own contribution to McGhee’s list of projects worthy of further research: (1) Theoretical morphology has already led to a better understanding of growth in living organisms. This is the fundamental purpose of that branch of theoretical morphology, which undertakes the modelling of organic morphogenesis. (2) A second key use of theoretical morphology is in the formulation and testing of adaptationist8 hypotheses. (3) Chapter seven gives a fascinating sample of theoretical morphology’s contribution to the investigation of evolutionary trends in morphospace. (4) McGhee (p. 208) suggests that theoretical morphology might one day shed light on the “great Cambrian disparity debate”. One of Stephen Jay Gould’s most famous claims is his attack on the idea that natural selection produces a cone of increasing diversity. In a succession of works, Gould (1989, 1991, 1993, 1995) advanced the thesis that biological disparity is in fact, lower now than it was directly after the Cambrian explosion.
471 Debate has raged ever since, as to how we might measure disparity in an effort to test the original claim. (5) Theoretical morphology might aid in making operational the idea of the adaptive landscape (see for example McGhee 1999: 57). (6) Theoretical morphology might allow us to better understand the nature of biodiversity and thus aid in the performance of conservation biology. (7) Theoretical morphology might solve a problem identified by Sally Fergusson (forthcoming) concerning evolutionary explanation. She notes that we think of traits as standing in need of evolutionary explanation because of their complex functionality. However, if the function referred to can only be spelled out in teleological terms, then the whole idea of providing an evolutionary explanation begins to look circular. Using Theoretical morphology may provide a means of avoiding this problem (because it allows us to focus upon the explanation of pattern rather than process).9 (8) Finally, theoretical morphology might allow us to sort life into the actual, the non-actual and the impossible and, thereby, it might help us to better explore the fundamental constraints on living systems. As I noted above, some of these suggestions are very speculative, so it would add little to further speculate about the likelihood of their success. However, in one sense this list is importantly heterogenous. So I think it will be useful to separate these enterprises into two distinct categories. Up to now I have addressed some of my comments to the construction of “a theoretical morphospace” and others to the construction of “theoretical morphospace”. McGhee does the same. “A theoretical morphospace” refers to a hypothetical space with a limited number of dimensions that can be represented graphically and used to evaluate hypotheses about the histories of particular traits within particular lineages. This is the ‘bread and butter’ of theoretical morphology. By contrast “theoretical morphospace” (at least in the context of some of the explanatory enterprises mentioned above) refers to a very different beast. This is the totality of morphospace. It has many (perhaps uncountably many) dimensions and houses within it all possible biological form. It is akin to what Daniel Dennett has called the Library of Mendel (1995) and it is the manifold to which Richard Dawkins refers when he writes: The actual animals that have ever lived on Earth are a tiny subset of the theoretical animals that could exist. These real animals are the products of a very small number of evolutionary trajectories through genetic space . . . each perched in its own unique place in genetic hyperspace. Each animal is surrounded by a little cluster of neighbours, most of whom have never existed, but a few of who are its ancestors, its descendants and its cousins. Sitting somewhere in this huge mathematical space are humans
472 and hyenas, amoebas and aardvarks, flatworms and squids, dodos and dinosaurs. (1987: 73) For convenience sake I shall mark this distinction, by calling these two types of model “partial theoretical morphospace” and “total theoretical morphospace” respectively. Obviously, there are many partial theoretical morphospaces but only one total theoretical morphospace. In the list of projects just mentioned, projects 1, 2, 3 and 7 are clearly to be investigated using partial theoretical morphospaces, while 4 and 8 seem more likely to be investigated using total theoretical morphospaces. 5 and 6 could be investigated using models of either type. In what remains of this paper I shall argue that this difference has considerable significance for the sort of hurdles that these projects will have to overcome and so ultimately for the likelihood of their success.
Partial and total theoretical morphospaces Theoretical morphology is at it’s best when it is used for the evaluation of hypotheses concerning the evolution and development of particular traits in particular organisms or clades (roughly projects 1, 2, and 3 above). Such work can be addressed using partial theoretical morphospaces with small numbers of dimensions. On my initial reading of this book I was struck by the somewhat unflattering thought that this was just adaptationism with pictures. I now think that perhaps it is, but that the pictures are crucial. One of the main advantages of theoretical morphology as a tool in adaptationist reasoning, is that it makes plain that such reasoning is always defeasible. That is because it forces us to think of these inferences as hypotheses about a limited number of dimensions (i.e. characteristics). Gould and Lewontin’s original attack on adaptationist reasoning (1979) alleged that it abstracts away from important features of evolution and development. The great virtue of theoretical morphology is that it makes that abstraction visible. Indeed, it makes it central to the discussion. Having said this, the analysis of functional significance using theoretical morphology is at its best when the number of variables in play is low. Towards the end of the book (in Table 11.1) McGhee provides a comprehensive list of taxa that have not yet been subject to studies by theoretical morphologists. It is clear both from this list and from the wider description of the discipline afforded in the book, that the problem here is not just time and money. The beauty of branching and accretionary growth systems is that they can be modelled using a relatively small number of parameters. This is clearly not the case for many of the as yet unstudied clades such as the arthropods
473 and the mammals. Of course, one might happily model for example a ball and socket joint, but this is a far cry from the creation of a partial theoretical morphospace with which one might provide a convincing model of the fitness affecting characteristics of an elephant. Far be it from me to suggest (on the basis of a conceivability argument!) that such a model is therefore impossible. Rather my point is just that a rise in the number of parameters in play worsens the signal to noise ratio affecting resulting inferences concerning fitness and adaptation. In other words, theoretical morphology makes vivid the inverse relationship between the complexity of the system under study and the reliability of adaptationist reasoning about that system. Finally, I turn to the examination of scientific investigation using total theoretical morphospaces. Chief amongst these (and the only one that receives a significant amount of attention from McGhee) is the problem of defining “biological disparity” in a way that would allow us to evaluate Gould’s claims about the propensity of natural selection to increase disparity over evolutionary time periods. Clearly we want to answer the question – What does natural selection do? It doesn’t make things like us (it just happened to in this world). It doesn’t enhance long-term fitness (at least not if it’s true that the ultimate fate of all species is to go extinct). One plausible answer to the question is that, as Darwin supposed, natural selection increases biological diversity. That is not to say that it produces more species, but rather than it produces more varied species. This phenomenon is what Gould calls an increase in disparity. According to Gould (1989), the trouble with this hypothesis is that it turns out that when you measure the system and do the math, the claim comes out false. This argument began a debate that is still raging some fourteen years later and whose present state might best be summarised by the claim that – actually nobody has yet worked out how to measure the system and do the math. Might theoretical morphology help? McGhee certainly thinks so. Indeed, he provides a (rather confusing) argument (pp. 207–208) to the effect that the trouble with present efforts in this area is that too any people are trying to solve the problem using methodology based on empirical morphospaces when they should be focussing their efforts on theoretical morphology. I think there are several reasons to be cautious in this investigation. First and foremost, we cannot really model, and thus cannot really draw inferences from total theoretical morphospace. Even if there are only countably many dimensions in such a space, it seems unlikely that we will ever be able to martial such a massive amount of data for the purposes of creating a theoretical morphospace. It is thus very important that we do not slide from inferences made using partial theoretical morphospaces into conclusions that could only be justified by knowledge of total theoretical morphospace.
474 Perhaps though I am being too pessimistic. Might we not make some progress on problems such as Gould’s using large partial theoretical morphospaces (i.e., partial theoretical morphospaces in which the number of dimensions is very large)? There are two problems with such a suggestion. First, if we learn about the occupation of a partial morphospace (one that includes some but not all the possible dimensions), does this tell us anything about the occupation of morphospace as a whole? The answer to this is – yes it does. It tells us about morphospace in just the same way that learning where I am in space tells you something about where I am in the space-time manifold. However, prima facie, facts about the occupation of partial morphospaces do not appear to tell us about the relative extents to which different organisms occupy total morphospace. Thus, it seems they will not settle the argument concerning changes in disparity. One might call this the tip of the iceberg problem. This is clearly a problem on which, even now, there is still much work to be done. Secondly, I noted above that theoretical morphology lacks a clear procedure by which its practitioners could work out which biological characteristics should be chosen as the basis of a particular theoretical morphospace. This is not problematic if theoretical morphology is being employed for the purposes of broadly adaptationist reasoning, as discussed at the beginning of this section. What is being claimed in such studies is that, if we model some set of biological characteristics then we do (or don’t) find interesting patterns in the partial theoretical morphospace so produced. That different patterns might have been produced had we chosen to model the same organisms using different parameters, just seems to provide us with more evidence about which characteristics have historically affected the fitness of the organisms in question. In short, we shouldn’t worry if we decide that there is no fact of the matter as to which set of parameters was the right one to choose. The same cannot be said for the investigation of biological disparity. If the generation of a large partial theoretical morphospace is inevitably the result of human imagination or human intuition, then it seems that there will be no way in principle to settle disagreements about which biological characteristics ought to provide the basis for such a model. Thus, if the two models give different solutions to Gould’s problem there will be no way to say which is correct. The only way (and this is not a new suggestion) to solve Gould’s problem is to find some independent means of determining which biological characteristics matter for the purposes of evaluating Gould’s claim. That project appears to be beyond the scope of theoretical morphology.
475 In conclusion Theoretical Morphology: The Concept and its Applications is a work well worth reading for anybody interested in philosophy of biology, evolutionary biology or developmental biology. It is an enthusiastic and scholarly summary of an exciting new scientific discipline whose scientific application and philosophical implications are potentially very far-reaching. I conclude by making the same recommendation to philosophers that McGhee makes to biologists – There is so much to be done! Notes 1 See for example the comprehensive discussion of the work of Raup (1966) and many others
on mollusc morphology. 2 See for example the fascinating work on possible skeleton morphologies by Thomas and Reif (1993). 3 Also known as ‘hypothetical morphospaces’. 4 Hereafter I shall call these ‘biological characteristics’. However, I do not mean to imply that they need be characteristics of actual organisms. 5 See for example Niklas (1997). 6 These include the idea the natural selection is a satisficer rather than an optimiser as well as the idea that large mutations are more likely to be deleterious than small ones. 7 Note: I do not mean by this to suggest that theoretical morphology is a sort of pseudoscience. Many sciences involve creative or intuitive thinking, particularly in the so-called ‘context of discovery’. Nonetheless, as I shall argue shortly, this particular facet of theoretical morphology is one that should be added to McGhee’s list of fruitful topics for further research, because it has important ramifications concerning the type of projects that can profitably be addressed by the discipline. 8 I use this term in its non-pejorative sense to refer to investigations of the relationship between the current function of a trait and its selective history. 9 Note: Actually this would not solve Ferguson’s problem, as she is particularly concerned with the explanation of cognitive traits. However, her argument strategy generalises to morphological traits and thus evolutionary arguments concerning those traits might benefit from the appropriate application of theoretical morphology.
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476 Gould, S.J.: 1993, ‘How to Analyze Burgess Shale Disparity – A Reply to Ridley’, Paleobiology 19, 522–523. Gould, S.J.: 1995, ‘A Task for Paleobiology at the Threshold of Majority’, Paleobiology 21(1– 14). Gould, S.J. and Lewontin, R.: 1979, ‘The Spandrels of San Marco and the Panglossian Paradigm: A Critique of the Adaptationist Programme’, Proceedings of the Royal Society of London B 205, 581–598. Haldane, J.B.S.: 1928, ‘On Being the Right Size’, in Possible Worlds, and other Papers, Harper & Brothers, New York/London. Niklas, K.J.: 1997, The Evolutionary BIology of Plants, Chicago University Press, Chicago. Raup, D.: 1966, ‘Geometric Analysis of Shell Coilling: General Problems’, Journal of Paleontology 40, 1178–1190. Thomas, R.D.K. and Reif, W.E.: 1993, ‘The Skeleton Space: A Finite Set of Organic Designs’, Evolution 47, 341–360. Thompson, D.W.: 1917, On Growth and Form, Cambridge University Press, Cambridge. Wright, S.: 1932, ‘The Roles of Mutation, Inbreeding, Crossbreeding and Selection in Evolution’, Procedings of the sixth International Congress of Genetics 1, 356–366. Wolfram, S. (2002). A New Kind of Science, Wolfram Media, Champaign, IL. Valentine, J.W.: 1995, ‘Why No New Phyla after the Cambrian? Genome and Ecospace Hypotheses Revisited’, Palaios 10, 190.