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Transcribed, by permission, from Tuatara (1984) Vol. 27 (1): 26-48 Principia Botanica: By Michael heads
The word symmetry is often used in modern times to mean radial and even, as Weyl (1952) has noted, bilateral symmetry. The science of crystallography places no such restrictions on the idea of symmetry, and if development of general concepts of biological symmetry is desired we must likewise avoid any tendency to thing that radial/bilateral symmetry is the only important mode. The study of biological symmetry is obviously of great importance, but apart from work on phyllotaxis (leaf arrangement) it has been generally overlooked. For this reason biology has nothing to compare with te sophisticated work attained in the description and interpretation of crystal structure (Phillips 1971). This has had a crippling effect on the development of biology and on the flow of ideas between the sister sciences of biology and geology, in much the same way as has the lack of efficient concepts in biogeography. As one example of a general, fundamental problem of biological symmetry we can examine the question “why to components of organic structure so often possess symmetry based on five”? It is often observed that among flowers symmetry of five is the most frequent. It is less well known that sometime around 1510-1516 A.D. Leonardo da Vinci determined that in many plants the sixth leaf stands above the first (Richter 1939), this being perhaps the first reference to what later became well known as 2/5 phyllotaxy (the system consists of repetitions of five leaves in two turns of the axis). This is the most common of all patterns of leaf arrangement. In the animal kingdom symmetry based on five is manifest rather less obviously, be even so recurs with such frequency as to constitute a phenomenon of general interest. The radiolarians furnish many forms with pentagonal symmetry will come as no surprise to those familiar with these beautiful animals. Examples include the Pentaspheridae, the Pentinastrum group of general in the Euchitoniidae, and Cicorrhegma (Circoporidae) (Campbell 1954). The foraminiferan Pentellina pseudosaxorum exhibits a pattern of growth idetnifical to phyllotaxy in mode 2/5, sectors of growth being separated by a difference of five members (Van Iterson 1907; Croizat 1964a 440). The Priapulida, a group of burrowing marine worms, possesses dental armature arranged on its proboscis in pentagonal whorls (Nichols 1967). Echinodems, of course, sho a striking adherence to pentamerism. Since the time of the earliest known amphbians 360 million years ago, five has been the dominant number of digits in tetrapods, reductions from five (e.g. horses and birds) have been frequent, but increases occurring hardly at all, and then constituting abnormality. The “biological rule of five” is discussed only seldom (Nichols, 1967, has discussed it with reference to animals), but Croizat, in Chapters 7 and 8 of the Principia Botanica has subjected it to a thorough analysis. D’Arcy Thompson (1917) in a very influential work, unfortunately failed to realize that the key difference between the main modes of phyllotaxis is simply one of superposition. For instance in his fig. 327 “leaf” 1 is clearly superposed by “leaves’ 14, 9, 6, 4, in Fig. 327a, b, c, d respectively, leading to modes 5/13, 3/8. 2/5 and 1/3. In describing the obviously distinct appearances of the phyllotactic modes Thompson failed to mention this, noting instead that “the mathematical side of this very curious phenomenon I have not attempted to investigate”. This simple oversight led to over half a century of deep confusion, with many authors bent o analyzing the mathematics of this evidently very complex subject! As with the general problem of biological symmetry, the concept of superposition must be primarily biological rather than geometrical. Biological superposition cannot require, as does geometrical superposition, the presence of an exact perpendicular. The analysis of biological symmetry which utilizes essentially geometrical premises is similar in many respects to the analysis of plant morphology which begins with the given categories of leaf, stem and root or biogeography which begins with casual migrations. Utilizing the concept of superposition, the symbolism “2/5 phyllotaxy” refers to an important biological reality. Phyllotactic modes of ½ (two leaves per turn) and 1/3 (three leaves per turn) represent the morphological consequences of a meristem producing the minimum number of primordial (two and three) in the lowest modes of symmetry biradial and triradial. The minimum number of systems which can interact is, of course, two. Beginning with the two systems which themselves represent minimal symmetry, Croizat’s analysis shows that an immediate result of interaction between ½ and 1/3 symmetry is, in fact, 2/5 symmetry, or symmetry in fives. As with 2/5, the other common modes of phyllotaxis, 3/8, 5/13 etc., also produce between two and three leaves per turn i.e. ½ and 1/3 mark the basic symmetries. Croizat concludes that whenever a system of many primordial evolves by reduction of parts (e.g. by fusion) or by increase in number of parts, the system will tend to the minimal symmetries of ½ and 1/3, and their first “sum” 2/5. This tendency is responsible for the establishment, at the level of coelocanthid fishes, of the morphogenetic premise which led for example, to the five fingers of Homo and for the reduction of the ancestral strobile around five sectors of growth which led to modern pentamerous flowers. The genetic spiral, described by the developmental sequence of leaf primordial, is often assumed to have special significance for phyllotaxis. But by a constant, gradual displacement of primordial, phyllotaxis may pass easily from, say, mode ½ to mode 2/5. This is possible simply because both modes have two spirals of growing points (cyclosectors), just as modes 1/3 and 3/8 both have three. Thus the genetic spiral, while being descriptively useful, is interpretatively useless, since all phyllotaxies are composed of more than one cyclosector. The evolutionary history of echinoderms would furnish excellent material for a study of the inter-relationships of minimal symmetries. Biradial, pentaradial, and possibly archaic triradial forms exist. Current debate is concerned with whether or not this trimerous stage occurred in ecinoderm evolution (Philip 1979, Stephenson 1979), but unfortunately none of the students involved have related the problem to general concepts of biological symmetry. Modern studies of symmetry and ontongeny have rejected the traditional reliance on adapationist ‘explanations” of aspects of organic form. For instance Goodwin (1982a, b) interprets developing organisms as: “entities with an extensive range of morphological potential, describable in terms of probabilistic fields which collapse…into specific morphologies”. (1982b: 52). These concepts parallel those of Croizat on morphogeny vs. morphology very closely indeed, which is interesting as they have emerged from what are usually regarded as distinct areas fo study ontogeny and comparative morphology. For Goodwin the probabilistic field properties are a function of “general organizational principles”. (1982b: 53). As a consequence of this fundamental change of emphasis Goodwin has subjected the neo-Darwinian approach to a critical and severe analysis, and concluded: “Once it is recognized that there are principle so of organization and laws of form in biology, these time-independent properties of the living realm become once again central to the subject…. The realization that genes do not generate biological form leads to a rather different view of the evolutionary process in terms of the potential forms of the organisms and their appearance on the earth.” (1982a: 111-112). Thus Goodwin, Like Croizat, would place the emphasis on Darwin’s “laws of growth”, in contrast with the neo-Darwinists tradition of virtually ignoring them. Working with rather different subject matter from Goodwin, the Russian palaeobotanist Meyen (1973, 1978) has argued at length for a greater emphasis on the study of “general structural principles” (again corresponding to Darwin’s “laws of growth”) independent of phylogenetic considerations. Baas (1982), discussing the evolution of wood anatomy, criticizes “ridged adaptationist interpretations”, advocating the important role of “functionless trends imposed by correlative constraints…”. |
