<<

Earth-Science Reviews - Elsevier Publishing Company, Amsterdam - Printed in The Netherlands

EVOLUTIONARY AND THE SCIENCE OF FORM

STEPHEN JAY GOULD

Mttseum of Comparative , Harvard University, Cambridge, Mass. (U.S.A.)

SUMMARY

A science of form is now being forged within evolutionary theory. It studies by quantitative methods, using the -machine analogy as a guide; it seeks to reduce complex form to fewer generating factors and causal influences. If a can be postulated for a structure, then its optimum form, or paradigm (RuDwtCK, 1961), can be specified on mechanical grounds. The approach of a structure to its paradigm provides the elusive criterion of relative efficiency that any science of adaptation requires. Physical laws and forces also specify that form be adapted to the requirements of size (surface/volume relation- ships) and space (close packing criteria). When we cannot establish paradigms on deductive criteria, an experimental approach to form is appropriate. Idealized models are favored over actual specimens because they can be built to test pre- determined factors. Paleontology need not remain solely a descriptive science based on observational methods, but may adopt the experimental techniques of explanatory procedures. It is inconceivable that each aspect of a complex form is the direct product of an individual genetic instruction. We can simplify, and thereby understand, the generation of apparent complexity by recognizing that physical forces directly influence shape and that a few simple rules can fashion some very intricate final products. These rules can be programmed; computers have simulated structures that bear remarkable correspondence to actual forms; the geometry of genetic instruction need be no more complex. The rules can be used to generate a range of potential form available to such structures as the coiled shell (RAuP, 1966). Actual forms fill only a part of the total spectrum; their basic adaptation may be grasped when we realize why unoccupied areas are not utilized. Among inductive studies of ontogeny and phylogeny, univariate techniques display trends and rates of change for single characters; they have been applied recently to the periodic growth lines of shells, providing thereby a paleon- tological input to . Bivariate procedures, as the inevitable story illustrates, have been plagued by errors of method. When properly applied, they serve well in the separation of and sexual dimorphs; they are the standard tool of quantitative description. Multivariate methods are based on the

Earth-Sci. Rev., 6 (1970) 77-119 78 s.J. GOULD more satisfactory premise that an organism grows and evolves as a set of inter- acting parts; interactions should be considered together, not abstracted as pairs. In the R-mode, these methods may detect interrelated character clusters, reduce the high dimensionality of a system to few interpretable directions of variation, and eliminate redundant variables. In the Q-mode, they provide an objective picture of phenetic differences among samples and specify how the measured characters produce these differences. The importance of a new methodology can be gauged by its impact on ideas of 's . A quantitative and functional science of form suggests that parallelism and convergence are dominant phenomena, not mere taxonomic nuisances. Early in their history, most phyla display great diversity at high taxonomic levels. These are not classic adaptive , but sets of competing in basic design. Early experimentation is followed by standardization of the best mechanical designs. These are often improved in similar ways by many independent lineages. Standardization and improvement provide invertebrate life with a history; the has not been a of endless ecological variation on a static set of basic structures.

THE SHAPE OF THINGS TO COME

Form and diversity are the two great subjects of . Although we now think of and adaptation where we spoke once of plenitude and design, it is only the terminology and not our concerns that have changed. Sys- tematics, the study of diversity, has been advanced by such thinkers as SIMPSON (1961) and MAYR (1963) to a level at which SYLVESTER-BRADLEY (1968) can justly christen a "science of diversity". Until recently, the study of form could make no such claim. It had, to be sure, its locus classicus -- D'ARcY THOMPSON (1917, second ed. 1942) -- but Thompson's treatise stood more as an awesome monument than a living work, its insights unnoted and its implications undeveloped. If paleontologists can now, as I believe, baptize a "science of form", it is because two approaches are beginning to unite under a common concept. The approaches are functional and quantitative; the concept is a mild mechanistic reductionism: an organism is a physical object subject to the laws of mechanics; its complexity can often be generated by a few, simple geometric instructions; its adaptation can be analyzed mechanically, often as an engineer would judge the efficiency of a machine built to perform a specific task i. In defending a concept that would seem crude or outdated in many physical sciences, I assert that alternative proposals offer no comparable access to the

1 I shall, if I may be permitted a literary barbarism, refer to this way of studying form as the quantifunctional approach. That it is, indeed, emerging as a fruitful strategy can be seen in the numerous papers of the recent Paleontological Society symposium entitled "Paleobiologieal Aspects of Growth and Development" (MACURDA, 1968).

Earth-Sci. Rev., 6 (1970) 77-119 EVOLUTIONARY PALEONTOLOGY AND THE SCIENCE OF FORM 79 evolutionary problem of form, to the question of adaptation. Just as experimental once needed Claude Bernard's determinism as a "specific conceptual tool" (COLEMAN, 1967, p.23), paleontology now requires a new strategy to found a science of adaptation. RUDWlCK understood this when he wrote (1961, p.450): "Although adaptation stands at the center of the modern debate on the mechanisms of evolutionary change, the problem of the recognition of adaptation in , or the inference of function from structure has received surprisingly little attention." And later (1964b, pp.34-35): "The detection of any adaptation in a fossil organism must be based on a perception of the machine-like character of its parts and on an appreciation of their mechanical to perform some function in the presumed interest of the organism." It is one of the ironies of history that the impact of evolutionary theory upon paleontology tended first to discourage the approach to adaptation we now advocate. Cuvier's functional was the first triumph of biological paleontology, but it "suffered a spectacular eclipse" with the acceptance of evolu- tion (RuDWlCK, 1964b, p.38). Speculative phylogeny, based on pure morphology (PANTIN, 1951) and the supposed "laws" of its evolutionary modification, marked the paleontological approach to the (GouLD, 1969b). HIS (1888, in COLEMAN, 1967; 1894), a great experimental embryologist, lamented the decline of functional studies and their replacement with a game of lineage building by "rigid morphological diagrams, abstracted by merely logical operations" (1888, in COLEMAN, 1967, p.175). Despite its later disenchantment with phylogenetic laws and parlor-room phylogenizing, paleontology has never dealt successfully with adaptation. Isolated men have had great insight -- Kovalevsky (STRELNIKOV and HECKER, 1968) and Dollo (GouLD, 1970) in particular. Neo-Lamarckists exploited the machine analogy (COPE, 1896, on kinetogenesis and JACKSON, 1891), but erred in assuming that mechanical optima implied direct mechanical pro- duction. The German school of experimental functionalists, particularly RICHTER (1929) and his followers (e.g., ZEUNER, 1933) studded the pages of Senckenbergiana and Paleobiologica with their work, but it had little outside impact and established no successful synthesis with modern evolutionary theory. Moreover, the worst features of speculative phylogeny are still with us, however reduced in frequency and impact, e.g., HOEEHAUS' suggested of comatulid pinnules with eurypterid walking legs (1963, p.460) -- as if a flexible structure built of hard parts could be constructed without jointing! But the conflict of functional and phylogenetic schools had no basis in necessity; any evolutionary theory must, in fact, deal with both questions. Yet since functional morphology had been the historical bailiwick of anti-evolutionists, it was degraded in the formulation of evolutionary theory. "The synthetic theory, despite its great verbal emphasis on function, tends to dissolve genuine adaptation into the non-morphological concepts of gene-pool, genetica[ fitness, adaptive zone, etc." (RuDWICK, 1964b, p.39). Our science of form must analyze adaptation

Earth-Sci. Rev., 6 (1970) 77-119 80 S.J. GOULD without contradicting modern views of ontogeny and phylogeny. Moreover, it should provide new insights into paleontology's unique domain, i.e., transspecific and major patterns in the history of life. This paper is written in the belief that such a science of form is now being forged.

THE MECHANICS AND EXPERIMENTAL STUDY OF ADAPTATION IN FOSSILS

All changes in the extremities [of fossil ] are of course occasioned by mechanical conditions of movement and we really see that the problems set before the organism are solved by it exactly in compliance with theoretical mechanics. But a more exact, i.e., mathematical, investigation of this problem.., can only be made in the distant future.

Kovalevsky, 1873

The mechanics of adaptation It is often assumed that the detection of adaptation in fossils depends upon the observation of homologous structures in living relatives. Such a proposal replaces the search for an analytic science of adaptation with an empirical exercise in something close to pure observation. Although less satisfying intellectually, this technique would be a welcome expedient. But, as RUDWICK has noted (1961, 1964b), it has no foundation. It is by analogy, and not homology, that we argue from modern to fossil functions. Living relatives are important because their structures are often similar in design to extinct forms, not because they are linked to them in phylogeny. Moreover, in theory at least, the observation of modern analogs is merely a convenience; we should be able to infer adaptation from the structure of fossil alone (this is most obvious in functional studies of Problematica, e.g., YOCHELSON'S (1961) analysis of the hyolithid operculum). This point is vital, for the corollary to its acceptance is the guiding concept of adap- tational science -- the criterion of mechanical fitness: "Consequently the range of our functional inferences about fossils is limited not by the range of that happen to be possessed by organisms at alive, but by the range of our understanding of the problems of engineering" (RuDwICK, 1964b, p.33). The habit of treating problems in adaptation by analogy to simple machines has been part of morphology since Cuvier's time, but invertebrate paleontologists adopted a similar strategy only recently. To illustrate with three examples: (a) Jaw function and the mechanics of hinges and levers (e.g., OSTROM'S demonstration (1964) that a raised coronoid process and depressed articulation -- independently evolved in so many lineages -- increases the effectiveness of force by lengthening the moment arm of a 3rd lever). The of diductor musculature in has been elucidated in a similar way by SPJELDNAES (1957), JAANUSSON and NEUHAUS (1963) and ARMSTRONG (1968). On mechanical grounds, Spjeldnaes claims that the diductors of some strophomenids were not sufficiently strong to open the valves. They were aided, he suggests, by a

Earth-Sci. Rev., 6 (1970) 77-119 EVOLUTIONARY PALEONTOLOGY AND THE SCIENCE OF FORM 8 l ligamental attachment between the pseudodeltidium and chilidium; this would explain the negative correlation of diductor impression size and pseudodeltidial development among species.

Fig.l. Growth in the oyster Arctostrea to avoid transgression beyond the hinge line. Such transgression would prevent the shell from opening. Two solutions to the problem are shown. G marks the growing edge. (From CARTER, 1968.)

Carter has studied the hinge mechanics of Arctostrea, a Cretaceous oyster. As the shell arcs back in growth, it must avoid any transgression beyond the extension of the hinge axis, lest it lose the ability to open (Fig.l). Individuals approaching such a calamity either direct their growing edge away from the umbone or increase their rate of curvature to grow towards it in a closing spiral (Fig.l); "extreme specimens may actually fuse their shell into a complete 'circle'" (CARTER, 1968, p.466). The point is simple, but had been overlooked because we are not used to thinking in mechanical terms and have usually bypassed the subject of ostreid adaptation with a remark about extreme phenotypic variability. (b) The Reynolds number in aero- and hydrodynamics (KoKSHAYSKIY, 1967, on , fish and marine ). RUDWlCK (1961) noted that longitudinally grooved spines of the coralliform Prorichthofenia permiana could function in collecting food. Each spine is a fluted cylinder; the ridges increase eddying in the cylinder's wake and lower the critical velocity at which flow changes from laminar to turbulent. Eddying is needed to maximize the impact of food particles against the spine. (c) Streamlining and fin orientation in the swimming of fishes (HARRIS, 1936, 1938, and review in ALEXANDER, 1967). In pectinid clams, STANLEY(in press) had detected a strong correlation between swimming ability and a high width/length ratio. In wide shells, currents are expelled more directly backward to augment forward propulsion, the area of the mantle cavity devoted to water expulsion is enlarged and the shell dimension perpendicular to the direction of motion is increased relative to the parallel dimension, thus raising the aspect ratio, an index used by engineers to judge aerodynamic efficiency.

The function and relative efficiency of structures Structures that resemble simple machines or architectural designs are favored illustrations of evident adaptation. This principle is embodied in Benson's Mecha- nocythere (Fig.2). GRANT (1966b) compared spines of the Permian brachiopod

Earth-ScL Rev., 6 (1970) 77-11o 82 s.J. GOULD

Fig.2. The compleat ostracode, Mechanocythere. Drawn for Richard H. Benson by L. B. Isham and reproduced with the kind permission of Dr. Benson. "The purpose of this drawing", writes Dr. Benson (personal communication, 1969) "was to underline the mechanistic thinking that most zoologists use. I think the analogy is quite appropriate and scientifically reasonable, but I'm not sure that this is frankly admitted by most of our colleagues."

Waagenoconcha abichi to a snowshoe (to prevent sinking into mud). The radial ribs of many burrowing bivalves form a saw for slicing into (STANLEY, in press). The paradigm for an exchange system will fit a radiator as well as the cystoid dichopore (PAUL, 1968, p.709). PANTIN (1951, pp.138--139) called the "siliceous scaffold" of the hexactinellid sponge Euplectella "a marvellous com- bination of rigidity and lightness which recalls the geodetic construction familiar to aeroplane designers. No one has seen it alive in its natural . We judge the adaptation in this case because the structure is organized on a special plan which we know from experience has special mechanical properties." RUDWICK (1961 and later) formalized a method for judging adaptation. We specify the form of a structure that would fulfill a postulated function with efficiency; but since organisms must build from available material, the best possible form may only approach this theoretical ideal. The best possible or "paradigm" form is "the structure that can fulfill the function with maximal efficiency under the limitations imposed by the of the materials" (RUDWI¢I<, 1961, p.450). Although it has recently become fashionable to bandy the word "paradigm" in all kinds of functional arguments, Rudwick is quite explicit about its mechanical foundation. Its use should be restricted to mechanical criteria of design that are subject to quantitative tests of relative efficiency. In applying his method, Rudwick transforms a set of rival functional postulates to their paradigms and tests the approach of a fossil structure to each

Earth-Sei. Rev., 6 (1970) 77-119 EVOLUTIONARY PALEONTOLOGY AND THE SCIENCE OF FORM 83 of them. The confidence of a functional inference is directly related to the efficiency of a structural adaptation, i.e., to how closely it approaches the paradigm of that function. The method has many limitations. Some are substantive -- a structure may serve several functions and, in the resulting compromise, be unable to ap- proach any single paradigm closely. Others are methodological -- to show that a structure could have fulfilled a function does not prove that it did. Rudwick's demonstration that ventral spines of the Permian productid Prorichthofenia uddeni closely approach the paradigm for a protective grille (sufficient strength, uniform spacing and complete apertural coverage) may be considered a model for such arguments (1961, pp.464-465). I choose the following three examples to illustrate a few ways in which mechanical arguments foster a science of adaptation. (a) Since paradigms include several specifications, their identification may relate a number of structures otherwise seen as a set of separate problems. If long anterior spines of the brachiopod Acanthothiris serve as an early warning system (RuDwICK, 1965b), then their regular spacing, radial orientation and slender, cylindrical form are all explained. RVDWlCK (1964a) suggested that the zigzag commissure of many brachio- pods was evolved to prevent the entry of particles above a certain size while increasing the area available for intake (Fig.3). Other interpretations are those of WESTERMANN (1964a) for brachiopods and CARTER (1968) for Arctostrea. STANLEY (in press) supports Rudwick by mentioning that the zigzag commissure of tridacnid clams provides more area for zooxanthellae that inhabit the siphonal tissues without widening the gape. Rudwick's hypothesis explains the "graded" nature of zigzag strength. Since a brachiopod is hinged at the posterior margin, it gapes least here and most at the anterior border. Thus, in a plane perpendicular to the hinge axis, the amplitude of zigzags should decrease towards the hinge and dis- appear where the gape of the undeflected margin provides the same protection afforded by deflections at the anterior border (Fig.3). Moreover, since the geometry of zigzags provides less protection at crests and troughs (Fig.3), we can understand the repeated acquisition, in independent lineages, of accessory protection at these points. The Ordovician pentameracean Parallelasmapentagonum developed internal marginal diaphragms; the rhynchonellacean Sphaerirhynchia wilsoni and the Upper rhynchoporacean Rhynchopora nikitini evolved crestal spines (RuDwICK, 1964a), as did many uncinulid rhynchonellids (WESTBROEK, 1968); the Permian rhynchonellacean Uncinunellina jabiensis has crestal foramina that probably mark the site of protective setae. These requirements for protective devices are general and should explain structures in other groups. The entrance slit of a cystoid dichopore must exclude harmful particles, but not impede the current flow: the slits are often narrow to fulfill the first requirement and long to satisfy the second (PAUL, 1968). Ideally, the ratio of slit entrance length to exit length should exceed l, while the ratio of

Earth-Sci. Rev., 6 (1970) 77 119 84 s.J. GOULD

,

A

Fig.3. Brachiopod gapes in planes perpendicular (A and B) and parallel (C and D: at the anterior border of the shell) to the hinge axis for undeflected (A and C) and deflected (B and D) commissures. This is drawn to show the protection afforded by zigzags against the entry of large and potentially harmful particles. Note (B and D) that less protection is provided at crests and troughs of the zigzags. The line joining A and B passes through the point of compensation for B at which the gape of the undeflected margin affords the same protection provided by zigzags at the anterior border. Zigzags are not needed at smaller gapes and the margin is undeflected from here to the hinge. (From RUDWICK, 1964a.) areas should equal 1. This is often observed (PauL, 1968, p.715). Other cystoids developed a sieve-like entrance pore -- a better solution to the problem of protec- tion. (b) Mechanical analyses may prescribe modes of life and provide ecological information based purely on form (MUIR-WOODand COOPER, 1960; KAZMIERCZAK, 1967; GRANT, 1966a and 1968 on brachiopod spines). The posterior spines of some Silurian chonetids provide stability by equalizing the forward and backward turning moments of a brachiopod living free on the substrate with its ventral valve down and nearly horizontal (B/JGER, 1968). If the calyx is buoyant, a paradigm for normal crinoids requires a stem that is stiff near the root and flexible at the calyx (SEILACHERet al., 1968). Since the stem of Seiocrinus subangularis is flexible at the root and massive at the calyx, Seilacher et al. conclude that this crinoid attached to floating logs at the surface and grew downwards. (c) Paradigms establish a quantifiable criterion of relative efficiency for the comparison of adaptation. Comparisons are made between an organism and a theoretical ideal or between two organisms. When, in the former case, a structure fails to approach

Earth-Sol. Rev., 6 (1970) 77-119 EVOLUTIONARY PALEONTOLOGY AND THE SCIENCE OF FORM 85 its paradigm, it is either simply inefficient in the absence of competition -- the "sprawling" gait of early comes to mind -- or it may represent a com- promise among several requirements of performance. RUDWICK (1961) noted that the spines of Prorichtho['enia permiana do not form an efficient protective grille (they are too stout and disposed in an irregular thicket). Since they are not intrinsically debarred from fulfilling the paradigm -- the related species P. uddeni does satisfy it -- the spines of P. permiana are either simply inefficient or serve another function as well. "Every character that would have made the spines inefficient merely as a protective device would have made them highly efficient as a device combining the function of protection with that of collecting [food] particles" (RuDwICK, 1961, p.468). RUDWICK (1965a, b) interprets the marginal projections of three brachiopod homeomorphs as early warning systems to detect the approach of harmful objects. Ideally, the projections should extend upward and downward as well as outward, but cannot because the shell must be tightly sealed when the valves are closed; projections must extend in the same plane as the commissure. The intensity of zigzagging in the brachiopod commissure is limited by mounting resistence to water flow through the gape, even though more deflections would increase the area of intake (RuDWICK, 1964a). The ammonite shell does not optimize any one functional factor but represents a compromise among conflicting demands (RAUP, 1967). Throughout the , the greatest deterrent to a science of adaptation has been the lack of quantitative criteria for assessing the relative efficiency of similar structures. AGASSIZ (1860) argued against evolution by citing the complexity of eyes as the equal of anything evolved later. Today we evaluate such assertions to judge the adaptive reasons for specific pathways in the phylogeny of form. Using the physical principles of optics, CLARKSON (1966a, b, 1967) has inferred the range and acuity of vision in eyes of acastid and phacopid (see also BECKMANN, 1951). Certain acastids, for example, had 360 ° vision in a horizontal plane, but a very small vertical range. He finds that the angular separation of lens axes may be up to 15 greater in the horizontal than in the vertical plane. This produces vertical strips of vision. The trilobite will perceive uniform light intensity as a series of dark and light bands. A dark object moving horizontally across the field would temporarily occlude the bands. "A conception of the size, speed and direction of the moving object would be given by the changing pattern" (CLARKSON, 1966a, p.25). Fig.4 shows how a trilobite could sense a predator's approach by the progressive darkening of visual strips, bottom to top. Relative efficiency of burrowing in clams is correlated with basic form. Elongated shells dispense very little in burrowing because they oppose the substrate with a small surface area relative to volume and do not have to saw or slice their way in (STANLEY, in press).

Earth-Sci. Rev., 6 (1970) 77-119 86 S.J. GOULD

Fig.4. How a trilobite sensed the approach of a predator. At A, the predator darkens the bottom of a visual strip. As he advances towards the trilobite, he finally comes to darken the top of the strip at C. (From CLARKSON, 1966b.)

The dorsal valve of oldhaminid brachiopods supports a ptycholophous lophophore (STEHLI, 1956); the same is true of homeomorphic thecideaceans (RuDWICK, 1968a). Since the lophophore's efficiency is a function of its surface area, it must increase in complexity as the grows -- a standard example of size-required allometry (GouLD, 1966b). This is accomplished by budding new lobes which may arise from the medial side of the primary lobe as in thecideaceans or from the lateral side as in Bactrynium. "These alternatives, though topologically equivalent, are probably not equal in functional efficiency" (RuDWlCK, 1968a, p.355). Medial buds project in an anterior direction; lateral lobes project laterally. Since the gape of the valves is greatest at the anterior border and limited laterally, an unimpeded outflow of exhalent water is achieved more efficiently by medial budding. RUDWICK (1968a, p.356) suggests that this advantage may account for the longer range and greater diversity of thecideaceans vs. Bactrynium and the oldhaminids.

Physical laws and the interpretation of Jorm We have seen that structures are often explained by the physical character of specific mechanical analogs. We now emphasize another physical influence upon form -- its relation to the geometry and mechanics of size and space. The most pervasive physical influence upon form is size itself. Organic responses to decreasing surface/volume ratios are so ubiquitous that HALDANE (1965, p.476) defined comparative as "largely the story of the struggle to increase surface in proportion to volume" (THOMPSON, 1942; COCK, 1966; BONNER, 1968). I have reviewed the evolutionary implications of this principle elsewhere (GouLD, 1966b). It has been invoked recently by RUDWICK (1968a, b) to explain the development of brachiopod lophophores; by GOULD (1968) to suggest that doming in land snails could result from growth to maintain a constant foot surface/body volume ratio; and by PACKARD (1969) to interpret ontogenetic allometry in the squid Loligo in relation to requirements of streamlining and jet velocity at large sizes.

Earth-Sci. Rev., 6 (1970) 77-119 EVOLUTIONARY PALEONTOLOGY AND THE SCIENCE OF FORM 87

Other physical laws also relate size and form. When growth conforms to the power function, y = bx k high k-values limit maximal sizes because the y/x ratio increases continually with growth. This rule explains the decrease in k for height vs. length in large fluvial ripples as well as the inverse relation of size and intensity

. ,¢

2

lb is 2'o overoge width ot end of 7th whorl Fig.5. Inverse correlation of size and intensity of doming among three land snails of the subgenus P. (Poecilozonites). When k > l, height grows faster than length and doming results; the higher the k-value, the more intense the dome. If the doming rate of the small species (P. cupula) is projected to the size of the large species (P. nelsoni), a snail 20 times higher than wide would be produced. Thus, high k-values are size limiting. of doming (Fig.5) among three species of Pleistocene land snails from Bermuda (GOULD, 1966a). Among larvae of worker castes in army ants, minima always have higher k-values than maxima for leg-disk area vs. body length. If the slope for minima were extrapolated to the size of maxima, the leg disk would be longer than body length in some cases: a lower k-value for maxima is an obvious necessity (ScHNEIRLA et al., 1968, p.542). Close packing, an important law of space, determines the form of honey- combs and the hexagonal members of crowded coral colonies. It can also explain the distribution of brachiopod punctae (CowzN, 1966), trilobite eye lenses (CLARK- SON, 1966b), and echinoid plates (RAuP, 1968). The physical laws of size and space allow us to interpret structures as adaptations to their requirements, but they serve in other capacities as well: (a) Deviations can be spotted as anomalies that demand special explanation. Closest packing does not yield hexagons when plates differ in size (RAuP, 1968). Structural control of drainage can be seen in the deviation from hexagonal ordering that exists on land surfaces of uniform lithology (WoLDENBERG, 1969). Allometric growth, as predicted by the surface-volume criterion, does not always occur. Fish do not increase their gill surface area fast enough to keep a constant ratio with body volume in ontogeny (MUIR, 1969). (b) Their effects can be removed from complex systems to identify the factors not explained thereby. Many phylogenies illustrate size increase and must include responses to its requirements; we try to remove the influence of general size to recognize an adaptation to specific environments (GOULD, 1966a, pp. 1137-1139). So complex a structure as the ammonite is surely a mixture of direct genetic

Earth-Sci. Rev., 6 (1970) 77-119 88 S.J. GOULD

instruction and mechanical molding by contiguous structures. The latter must be identified to recognize the former (WESTERMANN, 1965, p.868; Raup, personal communication).

Adaptation in fossils, an experimental science The mechanical approach also has an inductive component. If the physicist tends to interpret form according to the natural laws he understands, the engineer will often with form to test its properties. If we advocate a reductionist methodology (though not a reductionist metaphysic) that views organisms as physical objects obeying physical laws, we must include the experimental approach of "basic" sciences among our acceptable procedures and not remain tied to the observational mode of traditional natural history. Experiments have been performed with actual specimens to test stability and streamlining (e.g., RICHTER, 1929 on Calceola). HALLAM(1968) conducted flow channel tests on specimens in the Liassic sequence Gryphaea arcuata -- G. mccullochii-- G. gigantea to show that evolution towards broader shells and looser coiling resulted in increased stability. KUMMEL and LLOYD (1955) constructed plaster casts of coiled to study streamlining in flume experiments. TRUEMAN (1941), analyzing body chamber/air chamber ratios, had concluded that the highly involute nautiloids were denser than water while evolute forms like Dactylioceras were equal to water in density. Kummel and Lloyd may have solved this enigma by showing that the superior streamlining of Nautilus compensates for its greater density. Idealized models can be varied in size and form to study the range and efficiency of specific adaptations. JEFFRIES and MINTON (1965) conducted such "feasibility experiments" on the Jurassic bivalve Bositra buchi. They tested alu- minum models to see if this clam could maintain its level by swimming upwards and sinking down between movements. Sinking would be sufficiently slow, they concluded, only if the animal were provided with a system of tentacles at the mantle edges. RUDWlCK (1961) suggested that the dorsal valve of Prorichthofenia could rotate back and forth to produce feeding currents. He built model brachiopods and suspended oil droplets in water to study currents produced by the rotatory motion. SHIELLS (1968) investigated the function of the flange in the Vis6an brachiopod Kochiproductus eoronus. He put flanged and unflanged models on a laminar flow table and placed permanganate crystals at regular intervals on the incurrent side. He let the crystals bleed into the area of study and photographed the resultant stream lines. The flange may act to check the velocity of incoming feeding currents, thereby trapping sediment on the lower flange and permitting the free inflow of food. OXNARD (l 968) plotted shoulder girdles on canoni- cal axes; the first axis produced a maximal separation between baboons and gibbons. To test his hypothesis that this axis expresses the functional differences between quadrupeds and non-quadrupeds, he modelled shoulder girdles in photo-

Earth-Sci. Rev., 6 (1970) 77-119 EVOLUTIONARY PALEONTOLOGYAND THE SCIENCE OF FORM 89 elastic plastic and determined stress gradients by observing the patterns of polarized light passed through the model. When the baboon model is loaded as a quadruped, the stresses are well distributed. The gibbon model, loaded in the same way, concentrates the stresses in areas composed of very thin bone in actual scapulae. In pursuing an experimental technique, we are not limited to modern manipulation; many fossil situations possess the essential character of experiments even though no intervened. SEILACHER (1968, p.285) penned these remarks in showing, from the preferred direction of barnacle borings, that belem- nites usually swam forward even though their rostra were streamlined for "emer- gency" backward escapes: "Paleontology as a whole too often has an 'old- fashioned' appearance. The trend toward experimental work that marks the progress of so many other originally 'descriptive' sciences, seems to be blocked for paleontology. One cannot make experiments with organisms that became extinct hundreds of million ago. Still, isn't it an experimental approach if the belemnites' habits were tested through the reaction of its commensals? The fact that the actual test was made long before man's existence does not alter the principles of its evaluation," From other natural experiments conveniently per- formed by epibionts, SEILACHER (1960) and MEISCHNER (1968) inferred the life orientation of several ammonites from oyster overgrowths; MERKT (1966) observed how two Senonian ammonites infested by lopsided oysters, restored equilibrium by growing in a screw rather than a planispiral; the distribution of commensals that fed on inhalent currents allowed SCHUMANN (1967) to deduce the life position and current system of Mucrospirifer reidJbrdi, a brachiopod. Another class of natural experiments involves the regeneration and healing of damaged structures. Regeneration, a major tool of modern experimental , has been studied by URBANEK (1963) in graptolites and HOTTINGER (1963) in Fora- minifera. RUDWICK (1968b) and RUDWICK and COWEN (1968) examined the response of lyttonid brachiopods to injury of the dorsal valve. In arguing that ridges function to strengthen the carapace of ostracods, HENNINGSMOEN (1965, p.358) was greatly aided by the discovery of an individual that reinforced a healed crack with a supernumerary ridge "quite foreign to normal specimens".

GROWTH AND FORM -- THE REDUCTIONOF COMPLEXITY TO think that heredity will build organic beings without mechanical means is a piece of unscientific mysticism. Wilhelm His

A common strategy in the physical sciences suggests that complex situations be reduced to few controlling factors that can generate the system with minimal loss of information. It is inconceivable that each of several hundred echinoid plates, crinoid columnals, or radular teeth is a product of independent genetic

Earth-Sol. Rev., 6 (1970) 77-119 90 s.J. GOULD instruction; a few rules for the generation, growth and motion of structures, and the mechanical molding of parts by surrounding conditions can produce visually complex forms. These forms can be simulated by computers programmed with the appropriate rules; analytic explanation may supersede holistic marvelling. Ontogenetic development is often mediated by simple gradients; a spatially ordered set of structures may refer to the single factor of position in a gradient. "Cellular differentiation in the Hydra is controlled by a single factor varying quantitatively at different levels in the body column... Although the Hydra possesses 17 types.., they all arise from two basic stem cells. The differentia- tion of the stem cells is regulated by two conditions, (a) the position of the cells in a chemical gradient extending apico-basally along the body column, and (b) whether they reside in the inner cell layer or outer cell layer" (BURNETT, 1966, p.165). Regular variation of cusp number, form and position in mammalian molars has long been attributed to gradients or "morphogenetic fields" (see VAN VALEN, 1962 and GOULD and GARWOOD, 1969 for review). SEILACHERet al. (1968, p.279) write: "No matter how different crinoid stems may appear, their basic morphology can be discussed in terms of a few common growth gradients." They explain the thickening of stems at both ends by invoking two temporal gradients: one, the control of nodal diameter by size of the calycial generating area, produces wide proximal plates; a second countergradient, radial accretionary growth proceeding regularly through time, furnishes increased width in the oldest distal plates. In three excellent works that deserve to be better known, URBANEK (1960, 1963, 1966) attributes astogenetic and phylogenetic changes in monograptid zooids to "morphophysiological gradients". Phylogenetic novelties, he notes, are introduced proximally and spread distally in phylogeny. This he ascribes to increasing penetrance of a substance manufactured by the sicula and distributed in a gradient along the stipe (see URBANEK, 1960, pp.209-210). A second method attempts to generate organic shapes by specifying a simple set of geometric instructions that need not correspond to any biological substance or genetic command. D'Arcy Thompson's vector model of radial, transverse and tangential growth components and LlSON'S "matrix model" for the stacking of disks (1949 and defense in CARTER, 1967a) apply this strategy to the molluscan shell. RAUP (1961, 1966, 1967; RAUP and MICHELSON, 1965) has programmed computers to draw coiled shells by specifying only four parameters: shape of the generating curve, rate of increase in size of the generating curve, distance of the curve from the axis of coiling and rate of translation down the axis. In an early paper, RAUP asked (1961, p.608) if his parameters had "genetic reality"; I would argue that such a question, even though its answer could be yes, misconstrues the methodology, because the system is a formal one for the reduction of complexity, not for the identification of genetic factors. A third method, one more suited to the identification of instructions having a direct genetic basis, partitions the determinants of form into a set of actual

Earth-Sei. Rev., 6 (1970) 77-119 EVOLUTIONARY PALEONTOLOGYAND THE SCIENCE OF FORM 91 commands. With their computer simulation of the marine hydranth Podocoryne carnea, BRAVERMAN and SCHRAnDT (1966, p.169) wrote: "The ability of simple recursive rules to generate complex patterns suggests the possibility that genetic instructions of developing systems may, in part, be of a similar nature." The of many patterns in fossil feeding traces can be reduced to a few commands: "A model program for the Scolithus might consist of two commands. The first would be 'dig down vertically for n times your length', the second 'avoid crossing other burrows'" (SEILACHER, 1967, p.72). RAUP (in RAUP and SEILACHER, 1969) has programmed these instructions and drawn, by computer, some remarkable pictures that correspond in all important ways to actual feeding traces. To produce its curious dorsal valve, an oldhaminid brachiopod had to

Fig.6. Computer generated diagram simulating an echinoid ambulacrum. (From RAuP, 1968.)

Earth-Sol. Rev., 6 (1970) 77-119 92 s.J. GOULD follow only two rules: keep a minimum distance from other lobes and bud a new lobe when the previous one reaches a limiting length that is specified by the shell edge (RuDWICK, 1968b). Objections are often raised to describing a shell in this way because it adds a theoretical dimension to what should be "pure" observation. Rudwick's reply to this argument is worth quoting: "The 'facts' of conventional static description are as theory-loaded and interpretive as the terms of a dynamic morphology would be; the difference is that the theory with which they are loaded is... simply false" (1968b, p.38). RAoP (1968) generated echinoid ambulacral patterns (Fig.6) by specifying only a rate of plate supply, a gradient of meridional growth and an initial plate shape. D'ARcY THOMPSON (1942) believed that many aspects of form, even in advanced organisms, are directly produced by physical forces acting upon flexible material. Although everyone accepts the argument for oysters and barnacles (STRAUCH, 1968), Thompson's fine insight has been widely ignored in the holistic thinking of most paleontologists. The ammonite suture and the echinoid test are among the marvels of invertebrate form, yet much of their complexity is probably fashioned by physical forces. WESTERMANN (1965) noted strong correlations of suture form with whorl cross section and coiling pattern; he assumed that many features of the suture pattern are a secondary consequence of conch shape. We need to specify only the type of material and a few points of suspension to produce some remarkably intricate folding patterns in a curtain 1. Moss and MEEHAN (1968, p.437) regard the complex ontogeny of an echinoid test largely as the "passive, secondary and mechanically obligatory" result of the growth of soft body tissues. Raup using a similar theme, has focussed on the growth of individual plates: "The basic question will be to what extent coronal morphology in echinoids (plate patterns, in particular) is under direct genetic control and to what extent it is mechanically inevitable, given basic conditions of development, and therefore is under indirect genetic control" (RAuP, 1968, pp.50-51). Since the growth of plates is peripheral and concentrated in areas of low counter pressure, their shape is fashioned by close packing among units of diverse size on surfaces of varying curvature. Moreover, both plate shape and the number of plate columns in ambulacral areas can be simulated by soap-bubble arrays. Bubbles are deposited one by one at the narrow end of a V-shaped trough: the trough's width determines when a single string of bubbles passes to a double array with zigzag boundaries. In echinoids, these transitions are not mediated by predetermined width but by the rate of plate supply relative to meridional growth. This rate is low in Bothriocidaris and high in multicolumned echinoids. Raup has extended these methods far beyond the simple insight that a

1 I thank A. Seilacher (via D. M. Raup) for the metaphor.

Earth-Sci. Rev., 6 (1970) 77 119 EVOLUTIONARY PALEONTOLOGY AND THE SCIENCE OF FORM 93 % % \

o

o ¢~ o ¢~ • • •

ii J. ~ n I- I- I- I-

e... TRANSLATION [~ E,

az,,6 o

o

ccJ

%

% /

Earth-Sci. Rev., 6 (1970) 77-119 94 s.J. GOULD

?i~i~i~zl i~i! © O/

- \

;pOdO!q3oJ:

---.

_o s s'~ (M) ~o~ uo=suodx 3

S

is~ ....

Earth-Sci. Rev., 6 (1970) 77-119 EVOLUTIONARY PALEONTOLOGY AND THE SCIENCE OF FORM 95 complicated form can be produced by a few simple instructions. In his study of the coiled shell, he varies three parameters in a systematic fashion to generate the spectrum of all geometrically possible forms (Fig.7); the fourth parameter is held constant in assuming a circular generating curve. The range of actual shapes does not fill the theoretical cube (Fig.8), and each major occupies a characteristic region on it. "In the empty regions we are presumably dealing with forms which are geometrically possible but biologically impossible or functionally inefficient. The correct explanation of such empty regions may provide keys to the ultimate inter- pretation of the morphology of actually-occurring shell forms" (RAUP and MlCHELSON, 1965, p. 1294). The requirement of adequate hinging imposes an evident constraint upon bivalve growth, limiting it largely to areas of high whorl expansion rate, in which reasonable sizes can be attained without whorl overlap. Moreover, a bivalve encounters the problem of umbone interpenetration even before the danger of overlap is reached. Raup's analysis -- his "theoretical morphology" -- provides a common explanation for the many devices evolved by clams to avoid interpenetra- ting umbones (STASEK, 1963): umbones are offset and coil each other in Glossus; interumbonal growth is prevalent in arcids; very high whorl expansion rates obviate the problem in pectinids; umbones are very small but do interpenetrate in species of Solen, Ensis, and Tellina; one valve is flattened to a lid in highly coiled chamids, ostreids and rudists. Clams are not found in regions of high translation rates, for here the relative size of the opening becomes very small (Fig.7). The opening must accommodate the adductor musculature. Muscular strength is proportional to cross-sectional area; if the opening is relatively small, it will not be able to house an adequate musculature and also provide enough space for other vital organs (RAuP, 1966, p.1187). Clams with high rates of translation are strongly inequivalve; one valve becomes a light cap that can be manipulated by small muscles. Snails, on the other hand, are common in areas of low expansion rates. A univalve, for protection, must keep its aperture relatively small; limpets, of course, are protected by their substrate and do not challenge this explanation (RAUP, 1966). In addition, the requirements of shell strength favor snails in regions of overlapping whorls (Fig.7). Again, the exceptions are among forms that receive support by adhering to a substrate: vermetids to rocks (KEEN, 1961; MORTON, 1965), some vermiculariids to coral (GouLD, 1969a) and many siliquariids to sponges (GouLD, 1966C). Among ammonoids, high whorl expansion rates are disadvantageous for several reasons (RAuP, 1967): carbonate efficiency is low, stability is too high for effective manoeuvering, buoyancy would require a very short body chamber, and the aperture would be poorly oriented. The restriction of ammonoids to a small

Fig.& Cube of theoretically possible forms for the coiled shell. The three parameters of Fig.7 are used as axes. Actual shells occupy only a small volume of potential shapes. (From RAUP, 1966.)

Earth-Sci. Rev., 6 (1970) 77-119 96 s.J. GOULD region among possible forms "does not appear to represent the optimization of any single functional factor but rather is a geometric region which minimizes several geometric problems faced by the ammonoid" (RAuP, 1967, p.64). Consider carbonate efficiency: whorl overlap should not be extensive lest the ratio of shell/ internal volume become too great. An evolute shell, on the other hand, must deposit the whole generating curve. Carbonate efficiency may explain the rarity of evolute forms but not the concentration of ammonoids in their region, for the carbonate optimum (low W and high D) is occupied by no actual shells. Low whorl expansion rates yield very unstable designs since the center of lies too near the center of buoyancy (TRUEMAN, 1941). Techniques that generate idealized forms by few parameters are also useful in the following situations: (a) The explanation of departures from idealized form: receptaculitids and many colonial bryozoans approach the Fibonacci pattern of growth in multiple spirals radiating from a common point. They do not achieve it because intercalated spirals emerge at various points along the surface. If the size of plates or zooids is limited, then the entire structure, as it grows, will eventually acquire holes unless additional spirals are intercalated (J. Foster, personal communication, 1969). Like- wise, the bivalve lunule can be seen as a "space-filler" for a hole produced in the generation of an ideal clam (CARTER, 1967b; but see alternate interpretation of SEED, 1968). (b) "Mistakes" can be programmed as an experimental approach to the study of normal and abnormal variation. In their computer simulation of verte- brate limb morphogenesis, EDE and LAW (1969, p.248) noted that "slight changes in the instructions produce dramatic changes in shape which are comparable with those found in mutant embryos". Both SEILACHER (1967) and RUDWICK (1968b) use simulated errors to explain individual variants (Fig.9 is an oldhaminid dorsal valve produced by the imposition of a single, simple error; forms like this have been found in nature). Both Seilacher's worms and German tractor drivers made the same mistakes in trying to cover an area completely (for exploiting food and destroying airfields respectively). The error sets up a test situation for proposed rules; it may be difficult to identify the rules if they are never broken. To end this chapter on a methodological note: RAUP (1966) recognizes two potential explanations for the restriction of molluscan orders to certain regions of his cube, (1) phylogenetic accident (insufficient time or chance failure to populate the entire cube) or (2) functional, usually mechanical, necessity. Raup claims that "to draw this former conclusion is to disregard the question and thereby to ignore the possibility of a rigorous functional explanation" (1966, p.1190). Testing the functional hypothesis is the best approach because its rival cannot be proven. In trying to apply the functional postulate, we might be stymied, but this would be the strongest potential support available for the idea of phylogenetic accident. In fact, we have not been stymied, rather stimulated.

Earth-Sci. Rev., 6 (1970) 77-119 EVOLUTIONARY PALEONTOLOGY AND THE SCIENCE OF FORM 97 standard 1

i i ii:.iiiii !ill

standard~7 ...... :~ii::ii:~i i] :i f lobe width W./ ~---"~-" Icritical d ~lobe length K A 'front' F

10/ '

Fig.9. A. An oldhaminid dorsal valve generated by the specification of a few simple rules. Lobes are of standard width, separated by a standard distance, limited in length by the shell edge and budded when a previous lobe reaches a critical length. B. The left part of the drawing shows an aberrant dorsal valve produced by the following modifications in the rules of 9A: left lobe 8 does not grow to its limiting length and left lobe 10 fails to branch off the next sub- median bud. The right part of the drawing shows an actual aberrant specimen similar in growth pattern to the idealized model at left. (From RUDWICK, 1968b.)

QUANTITATIVE STUDIES OF ONTOGENY --- THE INDUCTIVE APPROACH

Functional inference and the inductive method As evolutionists, we ask two questions about form: where did it come from (a request for antecedent states in ontogeny and phylogeny), and what is it for. Although these questions are distinct in logic, we consider both when an analysis of antecedent states illuminates the function of a terminal product. I argued previously that the deductive study of ontogeny can suggest functional insights; inductive investigations based on the measurement of actual specimens have the same potential.

Earth-Sci. Rev., 6 (1970) 77-119 98 s.J. GOULD

In the ontogeny of .[oordi, a rhipidistean fish, the paired fins moved back and decreased in relative size while the caudal fin enlarged and de- veloped pronounced upper and lower lobes (THOMSON and HAHN, 1968). Eusthenop- teron either swam slowly and continuously by sculling or darted rapidly and periodically by strong lateral motion of the caudal fin. The relatively small caudal fins of juveniles indicate "a more continuously active existence in which very high speeds were less important than high maneuverability" (THOMSON and HAHN, 1968, p.212); they may have fed on large plankton and small pelagic organisms. The size of their prey increased as they grew and they came to feed on other fishes. Now they lay in wait or stalked their new and less numerous prey to capture it by rapid and sudden motion. "The maturing Eusthenopteron foordi took up a life in which very fast swimming speeds must be used, if only for short periods at a time... The whole body architecture reflects this change in locomotor pattern" (THOMSON and HAHN, 1968, p.212). In calycial plates of the Devonian crinoid Protothylacocrinus esseri, a gradient of relative growth passes distally from the infrabasals to the top of the calyx; the anal and radianal grow fastest of all. This rapid growth is needed to support the massive, chimney-like anal sac (KESL1NG, 1968). A rapid and discontinuous change in shape is usually related to a new mode of life; slow, gradual, and persistent changes are often a response to the mechanical requirements of increased size. The adult form of Bositra buchi, a Jurassic bivalve, is attained gradually with only a small increase in shell thickness and little change in outline; hence JEFFRIES and MINTON (1965) argue that this clam never became a bottom dweller but remained pelagic throughout life. In addition, they attribute a I mm mortality peak, usually ascribed to unsuccessful settlement, to difficulties in the transition from ciliary to muscular swimming; this transition is size-required (GouLD, 1966b, p.590). In several brachiopods with zigzag commissures, RUD- WICK (1964a) notes that the paradigm slit is approached gradually in ontogeny and attained only at adult sizes. He suggests that brachiopods must reject particles above a certain absolute size. In young brachiopods, the gape is small, and harm- ful particles are excluded without the added protection of a zigzag commissure. In another interpretation, increased deflection is a size-imposed requirement to keep the intake surface/body volume ratio sufficiently high for adequate feeding.

Bivariate studies of ontogeny Bivariate studies of ontogeny have been impeded by such recurrent mistakes in method as the fitting of several lines to curved data and the misinterpretation of parameters in growth equations (WHITE and GOULD, 1965). Another common error lies in the assumption that unchanged shape implies unchanged adaptation, regard- less of the size range over which it is displayed. THOMSON and HAHN (1968), for example, suppose that the isometric relationship of anterior to posterior skull roof divisions in Eusthenopteron foordi suggests that this mechanism functioned at

Earth-Sci. Rev., 6 (1970) 77-119 EVOLUTIONARY PALEONTOLOGY AND THE SCIENCE OF FORM 99 equal efficiency in juvenile and mature fish. COLBERT (1948), on the other hand, correctly notes that the constant head length/body length ratio maintained during phyletic size increase of ceratopsian is a special adaptation; for the head of large animals is relatively shorter than that of small animals with the same structural design (see STmqL, 1962, on similarity criteria in scaling). Functional differences are inferred by Ruowlc~ (1968a) because two brachiopods of very disparate size possess a similar "oldhaminid" dorsal valve. The Gryphaea story has been plagued by such errors. They date to Trueman's claim that a phyletic increase in coiling rate could be inferred from a set of histo- grams that showed a progressive increase in whorl number up the stratigraphic sequence. Whorl number is a function of size; the Gryphaea sequence is charac- terized by progressive increase in size. More whorls may only reflect this general enlargement; an intensified coiling rate must be measured by increasing whorl number at a common size -- as in VAN VALEN'S (1968) proposal. HALLAM (1959, 1962) denied that any increase in coiling rate occurred; PHILW (1962) affirmed Trueman's original claim. Both used the same method: they constructed ontogenetic plots of right valve (R) vs. left valve (P) length

p R A [3 Fig.10. A. Gryphaea shell and its measurements. Adapted from HALLAM(1959). B. Ide- alized plot to show that a higher slope need not imply a greater intensity of coiling.

(Fig. 10A). The argument arose because Philip fitted the points by an arithmetic curve of the form: P = aR + b, while Hallam used the power function: P -- bR a. Both assumed that increased coiling would be demonstrated by a progressive increase in slope for stratigraphically higher samples. That this is not so is shown in Fig.10B, where specimens on line 1 (lower slope and higher stratigraphic position) are more tightly coiled than those of line 2 at any size common to both samples. (It is irrelevant that the curves would intersect at some size never reached by Gryphaea.) In other words, the y-intercept, or some other measure of position, must be considered as well as the slope (WHITE and GOULD, 1965; COCK, 1963, 1966). I have calculated (Table I) the P/R ratio at common sizes of R -- 20 and 30 mm from the equations given by Hallam and Philip. Hallam's data show in- creased coiling up the sequence; Philip's data display no stratigraphic trend; both indicate an increased coiling rate in ontogeny. Ironically, Hallam's data support Philip's conclusion, while Philip's data uphold Hallam! BURNABY (1965)

EarthoSci. Rev., 5 (1969) 77-119 lO0 S.d. GOULD

TABLE I

P/R RATIOS CALCULATED FROM DATA OF HALLAM (1959) 1 AND PHILIP (1962) 1

Stratigraphic level From Hallam's data From Philip's data

at R at R at R at R -- 20 mm 30 mm 20 mm 30 mm

Higher (Bucklandi-Gmuendense Zone) 2.25 2.83 2.23 2.8 l Lower (Angulata Zone) 1.97 2.52 2.49 2.77

1 HALLAM (1959) gives one equation for each of the stratigraphic levels. The figures for PHILIP (1962) are mean values for four subsamples in the Angulata Zone and 3 in the Bucklandi-Gmuen- dense Zone. has helped to clarify the situation and I do not doubt that his conclusion (that his samples from higher stratigraphic levels are less tightly coiled) is correct. Finding no significant difference in slope among samples, Burnaby used a common a-value to compute the value of log b for each sample. He then took the value of log b as an invariant measure of the tightness of coiling since the difference between log b for any two lines of the same slope is the same at any size. But b and a are not independent (WHITE and GOULD, 1965), and even insignificant differences in a can produce very large distinctions in b when the value y = 1 is a distant extra- polation from the actual size range of data. And yet, the greater irony, as HALLAM (1968) has shown so well, is that Trueman's story is but a small part of the evolution of Gryphaea in the British LiPs. No matter what happened in the lower LiPs -- and PmLIP (1967), using new information, has again reasserted Trueman's claim, this time to HALLA~'S potential satisfaction (1968, p.125) -- the dominant trend throughout the LiPs was towards decreased intensity of coiling. May this be a fitting end to what had become a barren debate. Most bivariate work in fossil invertebrates has been taxonomic in nature. Ontogenetic changes are the basis for classification of some common fossil groups -- turritellid gastropods for example (ALLISON, 1965). Some authors are now including quantitative data on ontogenetic allometry as a standard part of species descriptions (SORYAY, 1968 on Senonian inoceramids from Madagascar). Allometric studies often lead to the elimination of names incorrectly established for juvenile stages. NYHOLM (1961) had recognized several "genera" as ontogenetic stages of the Recent foraminifer Cibicides lobatulus; REYMENT (1966a), on this basis, was able to synonymize names in three other "genera" with single species of Cretaceous and Paleocene Cibicides. SHAW (1959) reduced four species of the trilobite Proliostracus to one, claiming that differences in propor- tion were due to ontogenetic change. By plotting trends of ontogenetic allometry in the Lower Carboniferous blastoid Orbitremites, JOYSEY (1959) showed that

Earth-Sci. Rev., 6 (1970) 77-119 EVOLUTIONARY PALEONTOLOGY AND THE SCIENCE OF FORM 101

"O. mccoyi" is a juvenile O. ellipticus and "O. companulatus" a young O. orbi- culatus. WELLYHOVER (1968) and THOMSON and HAHN (1968) have questioned species of pterodactyls and rhipidistean fishes respectively. Russian work on this theme is reviewed in NEVESSKAYA (1967). The basic problem underlying this work is one of standardization. To compare two species, they must either be studied at a common age, size or develop- mental or else the allometric trends of ontogeny must be recognized and removed. Eccentricity of the apical system is an important character in the classifi- cation of spatangoid . In Den&aster from the west coast of the United States, RAUP (1956) found that eccentricity increases with length in samples of small specimens but decreases among large individuals. Many previous workers would have regarded these opposing trends as evidence for a large taxonomic distinction, but Raup showed that the relationship of eccentricity to length over the entire size range is non-monotonic, increasing to a maximum and then de- creasing. He was then able to compare samples by removing the effect upon eccentricity of mean sample differences in length. Bay forms are less eccentric than open coast samples. Turbulence is stronger in the latter environment, and increased eccentricity allows the sand dollar to bury more deeply without obscuring the madreporite. (Dendraster feeds with its anterior third buried.) A popular subject for allornetric study of late has been sexual dimorphism. The theme, again, is synonymization of species; the method involves bivariate plotting and the recognition that ontogenetic stages of two supposed species are identical before the onset of sexual maturity. Dimorphism has been detected in fossil ostracods by LUNDIN (1964), SANDBERG (1964), and REYMENT(1966b); in the Frasnian brachiopod Cyrtospirifer by VANDERCAMMEN (1959); in the gastropod Pachymelania by KOTAKA and UOZUMI (1962); and in the trilobites Norwoodella halli and Welleraspis lata by Hu (1963, 1964). Good cases among ammonoids are documented by MAKOWSKK(1962), WALLISER (1963) on goniatites, LEHMANN (1966), PALFRAMAN (1966, 1967), and WESTERMANN (1964b). According to WESTERMANN (1964b, p.69), sexual dimorphism is so prevalent and unrecog- nized among ammonoids that most named species are "monosexual parataxa". I detect two new and fruitful trends in the bivariate study of ontogeny: (a) The search for new characters beyond the linear features of gross morphology. RAUP (1960) has measured the c-axis orientation of crystalline calcite in echinoid plates with regard to plate size and position. The counting of growth periodicities in shell microstructure will be discussed at the end of this chapter. (b) The study of complex growth patterns in their own right without gross oversimplification to such models as the logarithmic spiral or simple power function. BURNABY (1966) generalized the log spiral for ammonoid growth. SHIELLS' (1966) careful study of continually changing allometric parameters in the Vis6an productid Promarginifera trearnensis is a prototype for this kind of investiga- tion. l have tried to trace the ontogeny of Poecilozonites, a Pleistocene land snail,

Earth-Sci. Rev., 6 (1970) 77-119 102 s.J. GOULD in order to relate its complexity to separate influences upon growth (GOULD, 1968, 1969c). Non-monotonic trends are the composite result of two factors (proto- conch form and later growth rate), each monotonic in itself but opposite in direction.

Multivariate studies of ontogeny Although multivariate study is of very recent vintage in paleontology, the desirability of multivariate treatment was never at issue; it was simply impractical before the advent of high-speed computation. I am convinced that the computer can be to the science of form what the microscope, telescope and electron acceler- ator were to their respective fields. For we are now able to consider and manipulate simultaneously all the determinants of form that we can define and measure; we are no longer confined to the abstraction of form by pairs. Non-computerized multivariate treatments were, if they dealt with many variables, pictorial rather than quantitative -- e.g., PALMER'S use of Thompsonian transformed coordinates 1 to study the ontogeny of olenellid trilobites (1957); quantitative work was limited, by sheer labor of computation, to so few variables (usually three) that no adequate resolution of complexity was attained. Triangular diagrams were used by TASCH (1955) for the Permian brachiopod Crurithyris planoeonvexa, GRINNELL and ANDREWS (1964) to distinguish subspecies in the Late Paleozoic athyroid brachio- pod Composita and SHIELLS (1968); "Topological surfaces", drawn for Miocene astragali by MORRIS (1965), represent another three-dimensional technique. Some understanding of the appalling labor required to manipulate even small matrices by desk calculator can be seen in BURMA'S (1949) brave attempt. Multivariate methods in biology have been summarized by SOKAL and SNEATH (1963) and SEAL (1964); REYMENT (1960, 1963a, b, 1966b and others) has dealt specifically with their use in paleontology. This is the basic problem: given a set of points in n-dimensional space, what can we learn by defining their geometric position. Each point may be an individual measured by several variables (the Q mode), or a variable measured in many individuals (the R mode.) Two primary strategies are available: (a) Define a "distance" measure (SOKALand SNEATH, 1963, pp. 125-154)between all points or between points for the sample means of predetermined groups. The distance measures can be arrayed in a similarity matrix and submitted to "cluster analysis" to produce the dendrograms that now adorn so many papers. (b) Rotate the original axes to new positions and project all points upon the new axes. The appropriate rotation depends upon the aim of study. In principal components analysis, the first new axis maximizes the variance of points projected upon it. (If points are arrayed in an ellipsoid, it is the major axis; if the ellipsoid is

1 See SNEATH(1967) for a stimulating attempt to quantify the transformed coordinate method by trend surface analysis.

Earth-Sei. Rev., 6 (1970) 77-119 EVOLUTIONARY PALEONTOLOGY AND THE SCIENCE OF FORM 103 elongated by covariance due to growth, then the first principal component will represent the general growth trend.) In discriminant function and canonical analysis, the first new axis maximizes the separation of predetermined groups as projected upon it. In factor analysis, we resolve the points into a set of axes fewer than the original number of dimensions. REYMENT (1966b) applied distance measures to sexual dimorphs of Creta- ceous and West African ostracods. By comparing Mahalanobis distances in Bermudian land snails, I determined that, on the basis of shape alone, the juveniles of an ancestral are much more similar to paedomorphic adult descendants than to their own adult form (another approach to a problem treated by factor analysis in GouLo, 1968). Most multivariate studies of ontogeny are undertaken to study the inter- relationship among variables as an animal grows. OLSON and MILLER (1959) pioneered this work in paleontology with their technique of "morphological integration" for the clustering of correlation coefficients. Since then, principal component and factor analysis have been favored. The orthogonal axes of principal component or factor analysis are a set of new, uncorrelated variables, each a linear compound of the original measures; then can, moreover, often be given an interesting biological interpretation. REVMENT (1961) used four measures to study the Eocene foraminifer GIobigerina yeguaensis. The first three principal components explain 98.3 ~o of the original information and encompass the measured variability in only three dimensions. The first principal component reflects variation in size -- high positive contribution of all original measures. The second and third axes are composed almost entirely of one original measure and represent variation in shape that is not correlated with change in size. "It is clearly of importance to be able to cleave the biometric variation of a species into size and shape components, for size is generally more sensitive to environmental change than is shape" (REYMENT, 1961, p. 18). Move- over, the equation for the first principal component is a test for allometry. Yl = 0.51xj + 0.54x2 + 0.49x3 + 0.46x4 (where the x's are breadth and height oftest, aperture length and maximum test inflation). Since the coefficients do not differ significantly from each other, all variables make a proportionately equal contribu- tion to growth. CHEETHAM(1968) used principal components analysis to obtain uncorrelated variates in the Tertiary-Recent cheilostome bryozoan Metrarabdotos. Three axes explained 82~ of the information in six original variables; the new axes represent zooecial size, zooecial shape and avicularia shape. In addition to interpreting the new axes biologically, we may use them to assess the status of our original variables. This approach has often been applied to eliminate non-discriminating and redundant variables, but it is important primarily for the idea that we get closer to the causes of form by finding inter- related character clusters that are independent of each other. GOULD and GARWOOO (1969) studied and rodent dentitions by morphological integration and

Earth-Sci. Rev., 6 (1970) 77-119 104 S. J. GOULD factor analysis. widths form a separate group from lengths; the last molar exhibits a distinct pattern of variation. The first two canonical axes explained 99 % of REYMENT’S(1966~) information on the brine shrimp Artemia salina. Since prosoma length makes only a small contribution to both axes, it adds little to discrimination and could be removed. CHEETHAM (1968) eliminated three undiagnostic characters by noting their similar behavior on all principal components. REYMENT and NAIDIN (1962) computed a generalized distance for four variables among several samples of the upper Creta- ceous belemnite Actinocamax verus; three additional variables did not add to the distinction. We can also learn which characters are most influential in discrimina- tion. Selenizone width is an independent character in the ontogeny of some pleurotomarian gastropods (ELDREDGE, 1968); this affirms the traditional role of selenizonal features as the primary characters in pleurotomarian classification. I suspect that future paleontologists will look at these studies not for their specific insights but because they recast our thinking away from static description to the concept of covariance. The length of a bone is a simple datum; a correlation, or better yet an interrelated cluster of characters demands its explanation.

A note on absolute groltd Relative growth has been the paleontologist’s approach to ontogeny; absolute growth, increase related to time, had eluded us. Molt stages (ANDERSON, 1964, on ostracods; HUNT, 1967, on agnostid trilobites) or other indicators of development (FAGERSTROMand MARCUS, 1967, on septal number of rugose corals) might provide a better independent variable for bivariate plots than length, but time in the Newtonian sense can only be measured if astronomical periodicities are recorded in skeletal growth. The discovery of daily growth lines in corals by WELLS (1963) has been extended by SCRUTTON (1964) and applied to mollusks by BARKER ( 1964), HUDSON (1968), CLARKE (1968), PANNELLAand MACCLINTOCK (1968), and PANNELLA et al. (1968). Various periodicities, including diurnal, daily, synodic monthly and yearly, are now known. All studies agree that the number of days in a has been decreasing through time and that, consequently, the earth’s rotation has been slowing down. PANNELLA et al. (1968) now think they have evidence for Pennsylvanian and Cretaceous changes in the rate of deceleration; they relate these changes to the shifting positions of , , and shallow seas. Perhaps we are becoming the unwitting handmaiden of a different field, trading our indenture to for a geophysical master. But somehow, the thought that eminent physicists (RUNCORN, 1966a, b) arc studying humble corals does wonders for our self-respect.

THE QUANTIFUNCTIONAL STUDY OF PHYLOGENY

The quantifunctional analysis of changing form is indifferent to the cause of

Earth-&i. Rev., 6 (1970) 77-I 19 EVOLUTIONARY PALEONTOLOGY AND THE SC1ENCE OF FORM 105 change, to whether it be the unfolding of a genetic program in ontogeny or the alteration of that program in phylogeny. The ideas and methods ofquantifunctional study were introduced in previous chapters; I shall now attempt to show that the same themes provide insights to illuminate the study of specific phylogenies. The concluding chapter will then be devoted to the question: what, if any, implications do these themes have for our general view of the history of life? The presence of similar trends in ontogeny and phylogeny has usually been ascribed to such evolutionary "laws" as recapitulation, but a functional approach might illustrate the mechanical necessity of a given trend as a response to increasing size. It then matters little whether the increase occurs in ontogeny or phylogeny; the trend must proceed in either case. RUDWICK (1964a) noted the gradual ap- proach through ontogeny to a paradigmatic zigzag slit. WESTBROEK (1968) traced the lengthening of spines for increased crestal protection in the ontogeny and phylogeny of several uncinulid brachiopods. There are many reasons why a structure may not be maximally adapted when it first arises• If increase in mechanical fitness then occurs, the paradigmatic method can be applied to phylogenetic change• In strata younger than those con- taining P. uddeni, RUDWlCK (1961) found a prorichthofenid brachiopod with a better mesh of protective spines. In Permian strata of Pakistan, GRANT (1968) traced the improvement of a baffle and chamber system for protection against mud influx in the brachiopod Marginifera. HALLAM (1968, p.92) views the change from Liostrea to Gryphaea in the Lias as "relatively sudden and genetically simple"• He claims that it was adaptive for raising the mantle margins above the sediment, but that stability was sacrificed in the process: "The subsequent evolutionary history of Gryphaea largely can be interpreted as an attempt to rectify this and achieve, by the steady operation of selection pressure, a paradigmatic condition• •.. The end-product was a thin-shelled, saucer-shaped Gryphaea which expressed a good balance between stability and the need to keep the mantle margin above the muddy bottom" (HALLAM, 1968, p.126). The formal reduction of complexity allowed us to render molluscan ontogeny by very few factors• "Large" changes in phylogeny may also have a simple basis• HALLAM (1968, p. 125) states that the transition from Liostrea to Gryphaea required only a strong increase in the transverse component of growth as defined by OWEN (1953); the genetic change may have been small and rapidly fixed• In a different kind of reduction, I have shown that an iterative trend involving every measured character in the Pleistocene land snail Poecilozonites bermudensis is a result of paedomorphosis. Although the change in form seems complex, the genetic modifi- cation, involving the prolongation to adult sizes of all juvenile features, may be simple; its fourfold occurrence then ceases to be surprising (GouLD, 1968, 1969C). The inductive approach, as discussed in the last chapter, produces most of our quantitative information on phylogeny. Univariate analysis can document trends in single characters• The relation of form to environment is often seen in the

Earth-Sci. Rev., 6 (1970) 77-119 106 s.J. GOULD

temporal variation of such sensitive attributes as size. REYMENT (1966b) found the same size changes in seven ostracod species as a response to environmental shifts. Fluctuating, or zigzag evolution (HENN1NGSMOEN, 1964) is correlated, in many Pleistocene lineages, with climatic oscillations mediated by the advance and retreat of glaciers. Characters include size in mammals (KuRT~N, 1968b), coiling directions in planktonic Foraminifera (ERICSON et al., 1964) and shell thickness in land snails (GouLD, 1969 C). Univariate studies may have genetic implications. The difficulty of sorting genetic from phenotypic effects, for example, can be overcome in favorable cases of discontinuous variation in colonial organisms. TAVERNER-SMITH (1966) and OLIVER (1968) encountered less variation among individuals within colonies than between colonies for bryozoans and corals respectively. Oliver plotted bimodal frequency curves for septal number among full-grown corallites within a colony. Since he could cite neither sex nor environment as the cause ofbimodality, he assumed that two were present. This could result from the inter- growth of colonies, the fusion of larvae or an early somatic in one of the first-formed corallites. Too often, in phylogenetic studies, we neglect temporal changes in variance and study only the modifications of form expressed by mean values. Yet, as SIMPSON (1953) showed in reworking Brinkmann's data on Kosmoceras, changes in variance can be related to such evolutionary events as speciation. REVMENT(1966b) found that ostracod species vary chronologically with respect to the homogeneity of variance-covariance matrices. In bivariate studies, chi-square tests for association were used by SCHAEFFER (1956) to study in the polyphyletic subholostean fishes. The small number of significant associations among skull and fin features of 47 genera reveals the mosaic nature of character change: those that do occur are attributed to mechanical necessity, common morphogenetic mechanisms or the evolution, at similar rates, of characters not intimately related in function. Regression analysis is the major bivariate tool of phylogenetic study. Among hundreds of potential examples, I cite the imaginative work of KURT~N (1954, 1955, 1968a, and others) on and the study of FISHER et al. (1964)which, despite many peculiarities 1, is at least a stunning example of industriousness in the illustration of a Tertiary molluscan phylogeny. For phylogeny as well as for ontogeny, I believe that future progress in quantitative studies will occur primarily with multivariate methods and the more satisfactory biological premises under which they operate. In the previous chapter,

1 e.g., improper standardization (size-frequency histograms, using only 80~o of the observed range, to illustrate phylogenetic size increase and consideration of the "body whorl" as if it were a truly standardized adult feature rather than simply the last-formed whorl in any individual ontogeny) and uneconomical use of data (up to 868 points to fit a simple isometric width-height regression, plotting points and contours by computer and then fitting the regression line by eye with no statistics provided).

Earth-Sol. Rev., 6 (1970) 77-119 EVOLUTIONARY PALEONTOLOGY AND THE SCIENCE OF FORM 107

I outlined two multivariate strategies: distance measures and the placement of new axes. SCOTT (1966, 1967) used Mahalanobis distances to evaluate the famous Orbulina sequence (BLow, 1956). LERMAN (1965a, b) computed distances to deter- mine average rates of evolution for the bivalve Exogyra in Cretaceous of the Gulf and Atlantic coastal plains. CHEErHAM (1968) plotted time on a vertical axis and phenetic distance on a horizontal plane to study evolutionary rates and detect parallelism in the bryozoan Metrarabdotos. The Pennsylvanian gastropod Glabrocingulum welleri evolved from G. wannense. At three successive stratigraphic levels, the Mahalanobis distance between centroids for the two species is large, small and large again. Since the species were sympatric only at the lowest level. ELDREDGE (1968) attributes the first large difference to character displacement, the later reduction to allopatry and the final separation to evolution by G. welleri of a higher spire. HARPER (1969) computed a matching coefficient between all pairs of specimens for the branching pattern of ribs in sequential of the Devonian brachiopod Atrypa reticularis from Sweden. The mean value of this measure increased with time, indicating ever greater homogeneity within the population. BOYCE (1964) clustered distance measures on skulls of higher into hierarchical dendrograms. Distances were computed by several criteria. When shape, rather than size, was emphasized, skulls of juvenile pongids grouped with adult hominids rather than with full-grown of their own species; this result furnishes some evidence for the role of paedomorphosis in . REYMENT (1966b) calculated distances to demonstrate a northward geocline in the West African Paleocene ostracod Bairdia ilaroensis. The new axes of a canonical analysis then elucidated the 's structure. Equations for new axes are compounds of the original variables; the relative contribution of these variables to the northward trend is shown in the projection of samples upon the canonical axes. In OXNARD'S study of the primate shoulder girdle (1968, 1969), the first canonical axis separates species according to their ability to raise forelimbs in front and above the head during locomotion while the second distinguishes arboreal from terrestrial forms. BUZAS (1966) performed a canonical analysis on the foraminifer Elphidium. Since discriminant axes are fit to maximize the differences between centroids of pre-established groups, the projection of individual specimens can be used for phenetic classification. If the a priori groups have phenetic coherence, their individual members will lie near the group centroid and not be "misclassified" by a closer projection to the centroid of another group. Reyment (in BERGC~REN et al., 1967) performed such a test on three homeomorphic species of Maestrichtian and Eocene foraminifers. Only 55-69 ~ of the specimens were placed in their own groups. Since the discriminant axes reflect the interrelationships of variables in growth, the authors conclude (p.285) that "the homeomorphy lies not only in the phenotypic appearance of the tests but also in the mode of growth".

Earth-ScL Rev., 6 (1970) 77-119 108 s.J. GOULD

In a study of pelycosaurian reptiles, I used oblique factor axes to separate terrestrial from semi-aquatic species by postcranial characters and carnivorous from herbivorous forms by cranial measures (GOULD, 1967). A three axis solution for postcranial data yielded one group of primitive pelycosaurs in all suborders and two clusters focussed about terminal adaptations to terrestrial and semi- aquatic life. Two lineages of Dimetrodon, proposed by ROMER and PRICE (1940), were affirmed by the ever smaller projection of successive species upon the axis of primitive pelycosaurs. ELDRED~E (1968) illustrated the convergence of Penn- sylvanian gastropods Glabrocingulum welleri and Worthenia tabulata by plotting specimens on varimax axes. The convergent species formed a single cluster while Glabrocingulum wannense, the ancestor of G. welleri, clearly separated as a second group. A very different multivariate procedure has been proposed to reconstruct branching sequences in phylogeny from data on cladistic similarity. It is based on deductive models that must make assumptions about the course of phylogenetic transformation. EDWARDS and CAVALLI-SVORZA (1964, p.72), for example, modelled the process as a branching random walk and wrote: "It will be obvious that the knowledge necessary for the reconstruction of evolution is rarely available but, as in other problems of statistical estimation, deductions can always be made provided the assumptions on which they rest are remembered .... it is clear from this approach that there is no substantial logical difference about estimating the course of evolution with or without fossil evidence" (my emphasis). The last statement, while undeniably true, illustrates the prime difficulty of such simplified deductivism. Stochastic branching or notions of empirical parsimony that emphasize orthoselection and ignore convergence are not good assumptions. Fossils are needed precisely to show where simplified assumptions fail. They provide, for those rare cases of well-established phylogenies, points that must be connected; a set of living animals can almost always be hooked up according to a favored a priori scheme. The power of modelling should be used not to establish sequences for unknown lineages, but to test proposed assumptions about evolution by generating cladograms and testing their similarity with sub- stantiated phylogenies (see CAMIN and SOKAL, 1965, on horses).

MAJOR PATTERNS IN THE HISTORY OF LIFE: A REVISED PERSPECTIVE

As an informal test of its importance as a way of thought, we ask whether the quantifunctional approach provides a different and illuminating perspective on the history of life. Rarely do we realize how little our current perspective provides invertebrate life with a history of form -- defining history as directional change through time. A history of diversity it surely has, for the pulse of mass extinction established the larger divisions of history's time and still inspires paleontologists to intense debate

Earth-Sci. Rev., 6 (1970) 77--119 EVOLUTIONARY PALEONTOLOGY AND THE SCIENCE OF FORM 109

(ScHINDEWOLF, 1962; NEWELL, 1963; J. F. SIMPSON, 1966; G. G. SIMPSON, 1968). So too, in one sense, do we have change of form, but it is often placed in a strangely static framework that recalls the steady-state of Lyell's world -- change without history. Although we grant vertebrates a history, we often think that the major invertebrate groups were established early in the Paleozoic and have, in their subsequent development, merely produced endless ecological variations on the same basic designs. l will argue that our standard picture of evolution prevents us from seeing certain key phenomena in a light that would provide invertebrate life with a history. That picture is the , a model of diversity with ever diverging branches. The phenomena are parallelism and convergence on the one hand and an aspect of "adaptive " on the other. On the tree of life, convergence is at best a worthy of some awe and a few text-book pages and at worst the arch-confounder of phylogenetic speculation. But when the theme changes from branching diversity to mechanical optima and limited solutions defined in an engineer's language, then parallelism and convergence are among the normal results of adaptation and provide, more- over, a criterion for judging history: for short of being an all-knowing engineer, we must infer biological progress from the observation that, again and again, independent lineages develop the same design to perform a given function. And if parallelism and convergence are more common than we usually think, then the idea of biological improvement must be resurrected (from the works of such thinkers as LAMARCK (1809) and BERG (1926), but in a Darwinian framework that rejects their proposed mechanisms) and the notion of an invertebrate history reinstated. The mechanical necessity of many characters precludes their use as criteria of homology in tracing individual lineages. All quadrupeds use the same sequence of footfalls in walking, although theory allows for five alternatives. Only the sequence R(ight) H(ind)-RF-LH-LF provides an adequate series of dynamic tripods to support an animal's weight. "The walk developed in conformity with the demands of an almost Procrustean discipline" (BRowN, 1968, p.36). "A lenti- cular camera", wrote PANTIN (1951, p.148) of the eye, "is an inevitable class of sensory instrument both for animals and engineers." 'The physics of size and space exacts a class of mechanically required adapta- tions. In simple animals, they may even be mechanically produced (LIPPs, 1966 and GREINER, in press, a, on smaller Foraminifera and RAT, 1963, on convergence among large orbitolinids). If "foraminiferology" is to remove the shadow of its "twilight" (BOLTOVS~Y, 1965), it must stop defining taxa and lineages on criteria of gross morphology that environments can produce directly; the potential for phenotypic modification may be remarkably more extensive than we have wanted to admit (GREINER, in press, a, b, and personal communication, 1969). Direct genetic control increases in higher organisms, but the inevitability of an adaptation may

Earth-Sci. Rev., 6 (1970) 77-119 110 s.J. GOULD remain even though it must be produced by the indirect route of Darwinian processes. Organs, such as the brachiopod lophophore (GOULD, 1966b, p.59), that work through surfaces but serve the body volume must evolve in similar ways in independent lineages that increase in size. Rudwick showed that a spirolophe, to filter effectively, can be made in only two ways. "This intrinsic limitation points to the probability that each type was evolved independently several times... The occurrence of similarly oriented brachidia or lophophores ... cannot, by itself, be taken as evidence for evolutionary affinity between different taxonomic groups" (RuDwlCK, 1960, p.380). A more interesting class of parallelism and convergence involves the attain- ment of mechanical optima or Rudwickian paradigms, not for their structural necessity -- since the previous phyletic states are viable -- but because they provide a selective advantage that leads, over and over again, to their attainment in competition. Here we may speak of biological improvement; a size-imposed character, on the other hand, merely provides the same efficiency for a primary adaptation of altered size. Rudwick's "selected" list of taxa with zigzag commis- sures runs for five pages, includes a number of ontogenetic pathways to the same final result, and contains oysters as well as brachiopods. "The rigid specification of the paradigm points to the intrinsic probability that zigzag deflexions were evolved many times during the history of the Brachiopoda" (RUDWlCK, 1964a, p. 163). When taxa have traditionally been defined by criteria of gross morphology that are strongly subject to optimization, the frustration of those committed to disentangling individual lineages can be immense: "Over and over again, apparently unrelated stocks of brachiopods produce similar anatomical features at the same time and in the same place... In practice, when dealing with stocks of subordinal rank or below, it seems to be almost impossible to disentangle homeomorphy between independent stocks" (AGER, 1965, p. 144). The cases most relevant to my argument are not these multiple developments of optimal forms for specific environments but the evolution, in many independent lineages, of features that improve the basic design of a higher taxon. Fish evolution, for example, is replete with polyphyletic transitions to improved mechanics of swimming and eating (SCHAEFFERand ROSEN, 1961 and SCHAEFFER, 1965). Massive parallelism in basic design is also known in major groups of invertebrates (MOORE and LAUDON, 1943, on crinoids; BULMAN, 1963, on graptolites), but we have been embarrassed into silence by our inability to offer functional explanations for this evident history. That we may do so in the future is the greatest promise of the quantifunctional approach. PAUL (1968), for example, demonstrated that the independent transition from discrete to confluent dichopores in all lines of Ordo- vician glyptocystids produced an improvement in circulation that can be defined in quantitative and mechanical terms. Moving to the second phenomenon, we have long recognized that many invertebrate groups, near the time of their origin, show remarkable diversity at

Eartk-Sci. Rev., 6 (1970) 77-119 EVOLUTIONARY PALEONTOLOGY AND THE SCIENCE OF FORM 1 11 high taxonomic levels. This has been attributed to the tilling of a range of environ- ments with variations on a newly-evolved and successful design -- a classic . I prefer to regard the lineages not as a set of equally well-constructed mechanisms that exploit a range of non-overlapping environments, but as a group of competitive experiments that test the possibilities of a new construction. Then, by the normal process of selection, a small subset of best solutions survives. The unsuccessful experiments are the bugbear of traditional : classes and phyla of small membership and minor diversity. There has been much resistence to the proliferation of new classes among early echinoderms (DURHAM and CASTER, 1963; ROBISON and SPRINKLE, in press) and molluscs (YoCHELSON, 1969). Yet if the theme of early experimentation-later standardization replaces the misplaced analogy to adaptive radiation, then we must welcome the idea that classes of small membership should exist at the outset of a 's history. We now have the outline of a history: the weeding out of unsuccessful designs and multiple evolution of mechanical optima ~. The evolution of most major groups is not the story of ecological variation on successful designs that originated in Cambrian or Ordovician times, but a history of mechanical improvement. This history is recognized only when we can specify biological tasks, define the structures that fit them best and monitor the evolutionary changes that lead, usually in in- dependent lineages, to new "grades" (HUXLEY, 1958) or "functional (as opposed to adaptive) zones" (RuDWICK, 1968b). The temporal distribution of foraging patterns in worm tracks was studied by SEILACHER (1967). A series of structural grades -- scribbling, spiralling, and meandering -- define increasing efficiency of areal coverage and this is, indeed, the temporal sequence of dominant patterns. Both eocrinoids and crinoids, at the time of their first appearance in the Cambrian, were attached to the substrate by holdfasts. Stems are more flexible and can be made longer since they are stronger and contain no major extension of the soft anatomy (J. Sprinkle, personal communication, 1969); it is not surprising that both groups developed them independently. Such specific examples can be multiplied indefinitely, but a more important conclusion is that major groups often have a history that can be described on the basis of a few functional themes. Fish, as we have said, progress to more efficient levels of feeding and locomotion. SPASSKIY (1967) has elucidated the history of rugose corals as a series of improvements in feeding mechanisms. The main outlines of gastropod evolution involve advantages of torsion and the development of more efficient current systems (ROLLINS and BATTEN, 1968). Mantle fusion, siphon formation, and the subsequent invasion of more protected infaunal niches is, according to Stanley, the dominant theme of bivalve evolution. The story occupies

1 I speak, of course, only of the broadest outlines of basic design. I am completely bypassing one of the great themes of life -- the enormous diversity of adaptation, within each basic design, to a great range of environments.

Earth-Sci. Rev., 6 (1970) 77-119 112 s.J. GOULD the entire span of Phanerozoic time: "Just as pre-Permian terrestrial environments had not been extensively invaded by higher vertebrates, Paleozoic bottoms had apparently not been invaded by an infauna comparable to the one we see today... The post-Paleozoic radiation was a consequence of mantle fusion and siphon formation" (STANLEY, 1968, p.224). contain a lower percentage of infaunal bivalves than their counterparts (NicoL, 1968). Trends in Paleozoic echinoids were analyzed by KIER (1965, p.446), who wrote: "All the changes do not seem to require a change in habitat to explain their origin but resulted from the gradual improvement of the animal as a living mechanism." The branching tree of life, our traditional model, has no claim to necessary superiority over its rivals -- to the gradal scheme of HUXLEY (1958) for example. It has been preferred chiefly because we can define, document and catalog the diversity on which it is based. When we employ form only to delineate taxa, it reinforces our traditional emphases on diversity. If, on the other hand, we use it to judge the functional efficiency of structural designs, then the science of form may reinstate paleontology as a source of new themes for evolutionary theory.

REFERENCES

AGASStZ, L., 1860. Prof. Agassiz . Am. J. Sci., 30: 142-154. AGER, D. V., 1965. The adaptations of Mesozoic brachiopods to different environments. Palaeo- geography, Palaeoclimatol., Palaeoecol., 1: 143-172. ALEXANDER, R. MEN., 1967. Functional Design in Fishes. Hutchinson University Library, London, 160 pp. ALLmON, R. C., 1965. Apical development in turritellid classification with a description of Cristispira pugetensis Gen. et sp. nov. Palaeontology, 8: 666-680. ANDERSON, F. W., 1964. The law of ostracod growth. Palaeontology, 7: 85-104. ARMSTRONG, J., 1968. Analysis of the function of the diductor muscles in articulate brachiopods. Neues Jahrb. Geol. Palaeontol., Monatsh., 11 : 641-654. BARKER, R. M., 1964. Microtextural variation in pelecypod shells. Malacologia, 2: 69-86. BECKMANN, H., 1951. Zur Ontogenie der Sehfl~che gross~.ugiger Phacopiden. Paliiontol. Z., 24: 126-141. BERG, L. S., 1926. Nomogenesis or Evolution Determined by Law (reprinted ed. 1969). M.I.T. Press, Cambridge, Mass., 477 pp. BERGGREN, W. A., OLSSON, R. K. and REYMENT, R. A., 1967. Origin and development of the foraminiferal Pseudohastigerina BANNER and BLOW, 1959. , 13: 265-288. BLOW, W. H., 1956. Origin and evolution of the foraminiferal genus Orbulina D'OR~ICNV. Micropaleontology, 2: 57-70. B6GER, H., 1968. Pal/i.o6kologie silurischer Chonetoidea auf Gotland. Lethaia, 1: 122-136. BOLTOVSKY, E., 1965. Twilight of foraminiferology. J. Paleontol., 39: 383-390. BONNER, J. T., 1968. Size change in development and evolution. In: D. B. MAeURDA (Editor), Paleobiologieal Aspects of Growth and Development, A Symposium -- J. Paleontol., 42(5): 1-15 (suppl.); Paleontol. Soc., Mere., 2. BOYCE, A. J., 1964. The value of some methods of numerical taxonomy with reference to hominoid classification. In: V. H. HEYWOOD and J. MCNEILL (Editors), Phenetic and Phylogenetic Classification -- Systematies Assoc., Publ., 6: 47-65. BRAVERMAN, M. H. and SCrtRANDT, R. G., 1966. Colony development of a polymorphic hydroid as a problem in pattern formation. In: W. J. REES (Editor), The and Their Evolution -- Symp. Zool. Soc. London, 16. Academic Press, New York, N.Y., pp.169-198.

Earth-Sci. Rev., 6 (1970) 77-119 EVOLUTIONARY PALEONTOLOGY AND THE SCIENCE OF FORM l 13

BROWN, L. S., 1968. The right way to walk four-legged. Nat. Hist., 77(9): 32-39, 84-85. BULMAN, O. M. B., 1963. The evolution and classification of the Graptoloidea. Quart. J. GeoL Soc. London, 119: 401~-18. BURMA, B. H., 1949. Studies in quantitative paleontology, 2. Multivariate analysis -- a new analytical tool for paleontology and . J. PaleontoL, 23: 95-103. BURNABY, T. P., 1965. Reversed coiling trend in Gryphaea arcuata. GeoL J., 4: 257-278. BURNAB¥, T. P., 1966. Allometric growth of ammonoid shells: a generalization of the logarithmic spiral. Nature, 209: 904-906. BURNETT, A. L, 1966. A model of growth and cell differentiation in Hydra. Am. Naturalist, 100: 165-190. BUZAS, M. A., 1966. The discrimination of morphological groups of Elphidium (foraminifer) in Long Island Sound through canonical analysis and invariant characters. J. Paleontol., 40: 585-594. CAMIN, J. H. and SOKAL,R. R., 1965. A method for deducing branching sequences in phylogeny. Evolution, 19: 311-326. CARTER, R. M., 1967a. On Lison's model of bivalve shell form, and its biological interpretation. Proc. Malacol. Soc. London, 37: 265-278. CARTER, R. M., 1967b. On the nature and definition of the lunule, escutcheon, and corcelet in the . Proc. Malacol. Soc. London, 37: 243-263. CARTER, R. M., 1968. Functional studies on the Cretaceous oyster Arctostrea. Palaeontology, 11 : 458~J,85. CHEETHAM, A. H., 1968. Morphology and of the bryozoan genus Metrarabdotos -- Smithonian Inst. Misc. Collections, 153: 1-121. CLARKE, G. R., 1968. Mollusk shell: daily growth lines. Science, 161 : 800-802. CLARKSON, E. N. K., 1966a. Schizochroal eyes and vision of some Silurian acastid trilobites. Palaeontology, 9: 1-29. CLARKSON, E. N. K., 1966b. Schizochroal eyes and vision in some phacopid trilobites. Palaeon- tology, 9: 464487. CLARKSON, E. N. K., 1967. Fine structure of the eye in two species of Phacops (Trilobita). Palaeontology, 10:603-616. CocK, A. G., 1963. Genetical studies on growth and form in the fowl, 1. Phenotypic variation in the relative growth pattern of shank length and body weight. Genet. Res. Camb., 4: 167-192. CocK, A. G., 1966. Genetical aspects of metrical growth and form in animals. Quart. Rev. Biol., 41: 131-190. COLBERT, E. H., 1948. Evolution of the horned dinosaurs. Evolution, 2: 145-163. COLEMAN, W., 1967. Introduction. In: W. COLEMAN (Editor), The Interpretation of Animal Form. Johnson Reprint Co., New York, N.Y., pp.xi-xxx. COPE, E. D,, 1896. The Primary Factors of Organic Evolution. Open Court, Chicago, I11., 547 pp. CowE~, R., 1966. The distribution of punctae on the brachiopod shell. Geol. Mag., 103: 269-275. DURHAM, J. W. and CASTER, K. E., 1963. Helicoplacoidea: a new class of echinoderms. Science, 140: 820-822. EDE, D. A. and LAW, J. T., 1969. Computer simulation of vertebrate limb morphogenesis. Nature, 221: 244-248. EDWARDS, A. W. F. and CAVALLI-SFORZA, L. L., 1964. Reconstruction of evolutionary trees. In: V. H. HEYWOOD and J. McNEILL (Editors), Phenetic and Phylogenetic Classification -- Systematics Assoc., Publ., 6: 67-76. t~.LDREDGE, N., 1968. Convergence between two Pennsylvanian gastropod species: a multivariate mathematical approach. J. PaleontoL, 42:186-196. F~RICSON, D. B., EWING, M. and WOLLIN, G., 1964. The Pleistocene in deep-sea sediments. Science, 146: 723-732. VAGERSTROM,J. A. and MARCUS, L. F., 1967, Biometric study of ontogeny in the Pennsylvanian rugose coral Pseudozaphrentoides verticillatus from Nebraska. J. Paleontol., 4: 649-659. [~'ISHER, W. L., RODDA, P. V. and DIETRICH, J. W., 1964. Evolution of Athleta petrosa stock (Eocene, Gastropoda) of Texas. Bur. Econ. Geol. Univ. Texas, Publ., 6413: 1-117.

Earth-Sci. Rev,, 6 (1970) 77-119 114 s.J. GOULD

GOULD, S. J., 1966a. Allometry in Pleistocene land snails from Bermuda: the influence of size upon shape. J. Paleontol., 40:1131-1141. GOULD, S. J., 1966b. Allometry and size in ontogeny and phylogeny. Biol. Rev. Cambridge Phil. Sot., 41: 587-640. GOULD, S. J., 1966c. Notes on shell morphology and classification of the Siliquariidae (Gastro- poda). The protoconch and slit of Siliquaria squamata BLAINVILLE. Am. Museum Novitates, 2263:13 pp. GOULD, S. J., 1967. Evolutionary patterns in pelycosaurian reptiles: a factor-analytic study. Evolution, 21: 385-401. GOULD, S. J., 1968. Ontogeny and the explanation of form: an allometric analysis. In: D. B. MACURDA (Editor), Paleobiological Aspects of Growth and Development, A Symposium J. Paleontol., 42(5): 81-98 (suppl.); Paleontol. Soc., Mere., 2. GOULD, S. J., 1969a. and functional significance of uncoiling in Vermieularia spirata: an essay on gastropod form. Bull. Marine Sei. Gulf Caribbean, 19: 480-494. GOULD, S. J., 1969b. The byssus of trigonian clams: phylogenetic vestige or functional . J. Paleontol., 43: 1125-1129. GOULD, S. J., 1969c. An evolutionary microcosm: Pleistocene and Recent history of the land snail P. (Poecilozonites) in Bermuda. Bull. Museum Comp. Zool. HarvardUniv., 138 : 407-532. GOULD, S. J., 1970. Dollo on Dollo's law: irreversibility and the status of evolutionary laws. J. Hist. Biol., 3: in press. GOULD, S. J. and GARWOOD, R. A., 1969. Levels of integration in mammalian dentitions: an analysis of correlations in Nesophontes mierus (lnsectivora) and Oryzomys couesi (Roden- tia). Evolution, 23: 276-300. GRANT, R. E., 1966a. A Permian productoid brachiopod: life history. Science, 152: 660-662. GRANT, R. E., 1966b. Spine arrangement and life habits of the productoid brachiopod Waageno- coneha. J. Paleontol., 40: 1063-1069. GRANT, R. E., 1968. Structural adaptation in two Permian brachiopod genera, Salt Range, West Pakistan. J. Paleontol., 42: 1-32. GREINER, G. O. G., in press, a. Recent benthonic Foraminifera: environmental factors controlling their distribution. Nature. GREINER, G. O. G., in press, b. Environmental factors controlling the distribution of Recent benthonic Foraminifera. J. Paleontol. GRINNELL JR., R. S. and ANDREWS, G. W., 1964. Morphologic studies of the brachiopod genus Composita. J. Paleontol., 38: 227-248. HALDANE, J. B. S., 1965. On being the right size. In: H. SHAPLEY,S. RAPPORT and H. WRIGHT (Editors), The New Treasury of Science. Harper and Row, New York, N.Y., pp.474-478. HALLAM, A., 1959. On the supposed evolution of Gryphaea in the Lias. Geol. Mag., 96: 99-108. HALLAM, A., 1962. The evolution of Gryphaea. Geol. Mag., 99: 571-574. HALLAM, A., 1968. Morphology, palaeoecology, and evolution of the genus Gryphaea in the British Lias. Phil. Trans. Roy. Soc. London, Ser. B, 254: 91-128. HARPER JR., C. W., 1969. Rib branching patterns in the brachiopod Atrypa reticularis from the Silurian of Gotland, Sweden. J. Paleontol., 43:183 188. HARRIS, J. E., 1936. The role of the fins in the equilibrium of the swimming fish. 1. Wind tunne[ experiments on a model of Mustelus eanis (MITt'HELL). J. Exptl. Biol., 13: 476-493. HARRIS, J. E., 1938. The role of the fins in the equilibrium of the swimming fish. 2. The role of the pelvic fins. J. Exptl. Biol., 15: 32-47. HENNINGSMOEN, G., 1964. Zigzag evolution. Norsk Geol. Tidskr., 44: 341-352. HENNINGSMOEN, G., 1965. On certain features of palaeocope ostracodes. Geol. F6ren. F6rh., 86: 329-394. HIs, W., 1894.15ber meehanische Grundvorg~inge thierischer Eormenbildung. Arch. An. Physiol. Wiss. Med. An. Abhandl., pp.l-80. His, W., 1967. On the principles of animal morphology (originally published in 1888). In: W. COLEMAN (Editor), The Interpretation of Animal Form. Johnson Reprint, New York, N.Y., pp. 167-178. HOFFHAUS, C. E., 1963. A homogeneous theory of the origin of vertebrates. J. Paleontol., 37: 458-471.

Earth-Sci. Rev., 6 (1970) 77-119 EVOI_.UTIONARY PALEONTOLOGY AND THE SCIENCE OF FORM 1 15

HOTTINGER, L., 1963. Les alv6olines pal6og~nes, example d'un genre polyphyl&ique. In: G. H. R. VON KOENIGSWALD, J. D. EMEIS, W. L. BUNlNG and C. W. WAGNER (Editors), Evolutionary Trends in Foraminifera. Elsevier, Amsterdam, pp.298-314. Hu, C. H., 1963. The dimorphism and ontogeny of Norwoodella halli RESSER. Trans. Proc. Palaeontol. Soc. Japan, 52: 129-132. Hu, C. H., 1964. The ontogeny and dimorphism of Welleraspis lata HOWELL (Trilobita). J. Paleontol., 38: 95-97. HUDSON, J. D., 1968. The microstructure and of the shell of a Jurassic mytilid (Bivalvia). Palaeontology, 11:163-182. HUNT, A. S., 1967. Growth, variation, and instar development of an agnostid trilobite. J. Paleontol., 41: 203-208. HUXLEY, J. S., 1958. Evolutionary processes and taxonomy with special reference to grades. Uppsala Univ./{rsskr., 1958: 21-38. JAANUSSON, V. and NEUHAUS, H., 1963. Mechanism of the diductor muscles in articulate brachio- pods. Stockholm Contrib. Geol., 13: 1-8. JACKSON, R. T., 1891. The mechanical origin of structure in pelecypods. Am. Naturalist, 25:11-21. JEVFRIES, R. P. S. and MINTON, P., 1965. The mode of life of two Jurassic species of "Posidonia" (Bivalvia). Palaeontology, 8: 156-185. JOVSEY, K. A., 1959. A study of variation and relative growth in the blastoid Orbitremites. Phil. Trans. Roy. Soc. London. Ser. B, 242: 99-125. KAZMIERCZAK, J., 1967. Morphology and palaeoecology of the productid Horridonia horrida (SOWERBY) from Zechstein of Poland. Acta Palaeontol. Polon., 12: 239-260. KEEN, A. M., 1961. A proposed reclassification of the gastropod Vermetidae. Bull. Brit. Museum, Zool., 7:183 213. KESLING, R. V., 1968. Note on ontogeny of the middle Devonian crinoid Proctothylacocrinus esseri KESLING. Contrib. Museum Paleontol. Univ. Mich., 23: 133-138. KIER, P. M., 1965. Evolutionary trends in Paleozoic echinoids. J. Paleontol., 39: 436-465. KOKSHAYSKIY, N. V., 1967. O diapazone chisel reynoldsa u biologicheskix obyektob. (On the range of the Reynolds number in biological objects.) Voprosi Bioniki. Akad. Nauk S.S.S.R., Moscow, pp.543-549. KOTAKA, T. and UozuMl, S., 1962. Variation and dimorphism of Pachymelania (Gastropoda) from the Eocene of Burma. Trans. Proc. Palaeontol. Soc. Japan, 47: 301-309. KUMMEL, B. and LLOYD, R. M., 1955. Experiments on relative streamlining of coiled shells. J. Paleontol., 29: 159-170. KtJRT~N, B., 1954. The type collection of lctitherium robustum (GERVAm ex NORDMANN) and the radiation of the ictitheres. Acta Zool. Fennica, 86: 1-26. KURT~N, B., 1955. Contribution to the history of a mutation during 1,000,000 years. Evolution, 9:107 118. KURT~N, B., 1968a. Geographic origin of the Scandinavian lynx (Fells lynx L.). Ark. Zool., 20:505-511. KURT~N, B., 1968b. Pleistocene Mammals of Europe. Aldine, Chicago, I11., 317 pp. LAMARCK, J. P. B., 1809. . Dentu, Paris, 428 pp. LEHMANN, U., 1966. Dimorphismus bei Ammoniten der Ahrensburger Lias-Geschiebe. Paliiontol. Z., 40: 26-55. LERMAN, A., 1965a. Evolution of Exogyra in the Late Cretaceous of the southeastern United States. J. Paleontol., 39: 414-435. LERMAN, A., 1965b. On rates of evolution of unit characters and character complexes. Evolution, 19: 16-25. L~pPS, J. H., 1966. Wall structure, systematics, and phylogeny studies of Cenozoic planktonic Foraminifera. J. Paleontol., 40: 1257-1274. LlSON, L., 1949. Recherches sur la forme et la m6canique de d6veloppement des coquilles des lamellibranches. Inst. Roy. Sci. Nat. Belg. Mdm., 34: 3-87. LUNDIN, R. F., 1964. Dimorphism in the thlipsurid ostracode Thlipsuroides striatopunctatus (ROTH). J. PaleontoL, 38: 1099-1102. MACURDA JR., D. B. (Editor), 1968. Paleobiological Aspects of Growth and Development, A Symposium -- J. Paleontol., 42(5): 119 pp.; Paleontol. Soc., Mere., 2.

Earth-Sci. Rev., 6 (1970) 77-119 116 s.J. GOULD

MAKOWSKI, H., 1962. Problem of sexual dimorphism in ammonites. Palaeontol. Polon., 12: 1-92. MAYR, E., 1963. Animal Species and Evolution. Belknap Press, Cambridge, Mass., 797 pp. MEISCHNER, D., 1968. Pernici6se Ep6kie von Placunopsis auf Ceratites. Lethaia, 1: 156-174. MERKT, J., 1966. I]ber Austern und Serpeln als Ep6ken auf Ammonitengeh/iusen. Neues Jahrb. Geol. Paliiontol., Abhandl., 125: 467479. MOORE, R. C. and LAUOON, L. R., 1943. Evolution and classification of Paleozoic crinoids. Geol. Soc. Am., Spec. Papers, 46:153 pp. MORRIS, W. J., 1965. Graphic analysis of some Miocene horse astragali from California. J. Paleontol., 39: 657-662. MORXON, J. E., 1965. Form and function in the evolution of Vermetidae. Bull. Brit. Museum Zool., I 1 : 585-630. Moss, M. L. and MEEHAN, M., 1968. Growth of the echinoid test. Acta Anat., 69: 409444. MUIR, B. S., 1969. Gill dimensions as a function of fish size. J. Fisheries Res. Board Can., 26: 165-170. Mum-WooD, H. and COOPER, G. A., 1960. Morphology, classification and life habits of the Productoidea (Brachiopoda). Geol. Sac. Am., Mem., 81 : 1447. NEVESSKAYA, L. A., 1967. Problems of species differentiation in light of paleontological data. Pah, ontol. J., 4: 1-17. NEWELL, N. D., 1963. Crises in the history of life. Sci. Am., 206: 77-92. NICOL, D., 1968. Are pelecypods primarily infaunal animals? Nautilus, 82: 3743. NYHOLM, K. G., 1961. Morphogenesis and biology of the foraminifer CibicMes lobatulus. Zool. Bidrag Uppsala, 33: 157-196. OLIVER JR., W. A., 1968. Some aspects of colony development in corals. In: D. B. MACURDA (Editor), Paleobiological Aspects of Growth and Development, A Symposium- J. Paleontol., 42(5): 16-34 (suppl.); PaleontoL Soc., Mere., 2. OLSON, E. C. and M1LLER, R. L., 1959. Morphological Integration. Univ. Chicago Press, Chicago, I11., 317 pp. OSTROM, J. H., 1964. A functional analysis of jaw mechanics in the . Postilla Peabody Museum Nat. Hist., Yale Univ., 88:35 pp. OWEN, G., 1953. The shell in the Lamellibranchia. Quart. J. Microscop. Sci., 94: 57-70. OXNARD, C. E., 1968. The architecture of the shoulder in some mammals. J. Morphol., 126: 249-290. OXNARD, C. E., 1969. , shape, and function. Am. ., 57: 75-96. PACKARD, A., 1969. Jet propulsion and the giant fibre response of Loligo. Nature, 221 : 875-877. PALFRAMAN, D. F. B., 1966. Variation and ontogeny of some Oxfordian ammonites: Taramel- liceras richei (DE LORIOL) and Creniceras renggeri (OPPEL), from Woodham, Buckingham- shire. Palaeontology, 9: 290-311. PALrRAMAN, D. F. B., 1967. Variation and ontogeny of some Oxford clay ammonites: Disti- choceras bicostatum (STAHL) and Horioceras baugieri (D'ORmGNY), from England. Palaeontology, 10: 60-94. PALMER, A. R., 1957. Ontogenetic development of two olenellid trilobites. J. Paleontol., 31: 105-128. PANNELLA, G. and MACCUNTOCK, C., 1968. Biological and environmental rhythms reflected in molluscan shell growth. In: D. B. MACURDA (Editor), Paleobiological Aspects of Growth and Development, A Symposium -- J. Paleontol., 42(5): 64-80 (suppl.); Paleontol. Soc., Mem., 2. PANNELLA, G., MACCLINTOCK, C. and THOMPSON, M. N., 1968. Paleontological evidence of variations in length of synodic month since Late Cambrian. Science, 162: 792-796. PANTIN, C. F. A., 1951. Organic design. Advan. Sci., 8: 138-150. PAUL, C. R. C., 1968. Morphology and function of dichoporite pore structure in cystoids. Palaeontology, 11 : 697-730. PHILIP, G. M., 1962. The evolution of Gryphaea. Geol. Mag., 99: 327-344. PHILIP, G. M., 1967. Additional observations on the evolution of Gryphaea. Geol. J., 5: 329-338. RAT, P., 1963. L'accroissement de taille et les modifications architecturales corr61atives chez les orbitolines. In: G. H. R. VON KOENIGSWALD, J. D. EMEIS, W. L. BUNING and C. W. WAGNER (Editors), Evolutionary Trends in Foraminifera. Elsevier, Amsterdam, pp.93-109.

Earth-Sci. Rev., 6 (1970) 77-119 EVOLUTIONARY PALEONTOLOGY AND THE SCIENCE OF FORM 1 1 7

RAUP, D. M., 1956. Dendraster: a problem in echinoid taxonomy. J. Paleontol., 30: 685-694. RAUP, D. M., 1960. Ontogenetic variation in the of echinoid calcite. J. PaleontoL, 34: 1041-1050. RAUP, D. M., 1961. The geometry of coiling in gastropods. Proc. Nat. Acad. Sci., 47: 602-609. RAUP, D. M., 1966. Geometric analysis of shell coiling: general problems. J. PaleontoL, 40: 1178-1190. RAUP. D. M., 1967. Geometric analysis of shell coiling: coiling in ammonoids. J. Paleontol., 41 : 43-65. RAUP, D. M., 1968. Theoretical morphology of echinoid growth. In: D. B. MACURDA (Editor), Paleobiological Aspects of Growth and Development, A Symposium -- J. Paleontol., 42(5): 50-63 (suppl.); Paleontol. Soc., Mere., 2. RAUP, D. M. and MICrtELSON, A., 1965. Theoretical morphology of the coiled shell. Science, 147: 1294-1295. RAUP, D. M. and SEILACHER, A., 1969. Fossil foraging behavior: computer simulation. Science, 166: 994-995. REVMENT, R. A., 1960. Studies on Nigerian Upper Cretaceous and Lower Tertiary Ostracoda. 1. Senonian and Maestrichtian Ostracoda. Stockholm Contrib. Geol., 7: 1-238. REYMENT, R. A., 1961. Quadrivariate principal component analysis of GIobigerina yeguaensis. Stockhohn Contrib. Geol., 8: 17-26. REYMENT, R. A., 1963a. Paleontological applicability of certain recent advances in multivariate statistical analysis. Geol. Fdren. Fdrh., 85: 236-265. REYMENT, R. A., 1963b. Notes on the description of post-Paleozoic fossil ostracods. J. Paleontol., 37: 682-687. REVMENT, R. A., 1966a. Morphologische Variation bei zwei fossilen Arten der Gattung Cibicides MONTFORT (Foraminifera, Prot.). Paldontol. Z., 40: 65-69. REVMENT, R. A., 1966b. Studies on Nigerian Upper Cretaceous and Lower Tertiary Ostracoda. 3. Stratigraphical, paleoecological, and biometrical conclusions. Stockholm Contrib. Geol., 14:1 151. REVMENT, R. A., 1966c. Aspects of the multivariate morphologic variability of the brine shrimp Artemia salina (L.). Stockholm Contrib. Geol., 14: 143-151. REVMENT, R. A. and NAIDIN, D. P., 1962. Biometric study of Actinocamax verus s.1. from the Upper Cretaceous of the Russian Platform. Stockholm Contrib. Geol., 9: 147-206. RICHTER, R., 1929. Das Verh~iltnis yon Funktion und Form bei den Deckelkorallen. Seneken- bergiana Lethaea, 11 : 57. RomsoN, R. A. and SPRINKLE, J., in press. Ctenocystoidea: a new class of primitive echinoderms. Science. ROLLINS, H. B. and BATTEN, R. L., 1968. A sinus-bearing monoplacophoran and its role in the classification of primitive molluscs. Palaeontology, l 1 : 132-140. ROMER, A. S. and PRICE, L. I., 1940. Review of the Pelycosauria. Geol. Soc. Am., Spec. Papers, 28:538 pp. RUDwIcK, M. J. S., 1960. The feeding mechanisms of spire-bearing fossil brachiopods. Geol. Mag., 97: 369-383. RUDW~CK, M. J. S., 1961. The feeding mechanism of the Permian brachiopod Prorichthofenia. Palaeontology, 3: 450-471. R UDWICK, M. J. S., 1964a. The function of zigzag deflexions in the commissures of fossil brachio- pods. Palaeontology, 7:135-171. RUDWlCK, M. J. S., 1964b. The inference of function from structure in fossils. Brit. J. Phil. Sci., 15:27 40. RUDWlCK, M. J. S., 1965a. Adaptive homeomorphy in the brachiopods Tetractinella and Cheirothyris. Paliiontol. Z., 39: 134-146. RUDWlCK, M. J. S., 1965b. Sensory spines in the Jurassic brachiopod Acanthothiris. Palaeontology, 8: 604-617. RUDWlCK, M. J. S., 1968a. The feeding mechanisms and affinities of the brachiopods Thecospira ZUGMAVER and Bactrynium EMramCH. Palaeontology, 11: 329-360. RUDW~CK, M. J. S., 1968b. Some analytic methods in the study of ontogeny in fossils with accretionary skeletons. In: D. B. MACURDA (Editor), Paleobiological Aspects of Growth

Earth-Sci. Rev., 6 (1970) 77-119 118 s.J. GOULD

and Development, A Symposium -- J. Paleontol., 42(5): 35-49 (suppl.); Paleontol. Soc., Mem., 2. RUDWlCK, M. J. S. and COWEN, R., 1968. The functional morphology of some aberrant stropho- menide brachiopods from the Permian of Sicily. Boll. Soc. Paleontol. ltal., 6: 113-176. RUNCORN, S. K., 1966a. Corals as paleontological clocks. Sei. Am., 215(4): 26-33. RUNCORN, S. K., 1966b. Middle Devonian day and month. Science, 154: 292. SANDBERG, P., 1964. The ostracod genus Cyprideis in the Americas. Stockholm Contrib. Geol., 12: 1-178. SCHAEFEER, B., 1956. Evolution in the subholostean fishes. Evohttion, 10: 201-212. SCHAEFFER, B., 1965. The role of experimentation in the origin of higher levels of organization. Syst. Zool., 14: 318-336. SCHAEEEER, B. and ROSEN, D. E., 1961. Major adaptive levels in the evolution of the actinop- terygian feeding mechanism. Am. Zoologist, 1 : 187-204. SCHINDEWOLF, O. H., 1962. Neokatastrophismus? Deut. Geol. Ges. Z., 114: 430-455. SCHNEIRLA, T. C., GIANUTSOS, R. R. and PASTERNACK, B. S., 1968. Comparative allometry in tile larval broods of three army-ant genera, and differential growth as related to colony behavior. Am. Naturalist, 102: 533-554. SCHUMANN, D., 1967. Die Lebensweise yon Mucrospirifer GRABAU, 1931. , Palaeoclimat., Palaeoecol., 3: 381-392. SCOTT, G. H., 1966. Description of an experimental class within the Globigerinidae (Foraminifera), 1. New Zealand J. Geol. Geophys., 9: 513-540. SCOTT, G. H., 1967. Description of an experimental class within the G lobigerinidae (Foraminifera), 2. New Zealand J. Geol. Geophys., 10: 55-73. SCRUTTON, C. T., 1964. Periodicity in Devonian coral growth. Palaeontology, 7: 552-558. SEAL, H., 1964. Multivariate Statistical Analysis for . Wiley, New York, N.Y., 207 pp. SEED, R., 1968. Factors influencing shell shape in the mussel Mytilus edulis. J. Marine Biol. Assoc. U.K., 48: 561-584. SEILACHER, A., 1960. Epizoans as a key to ammonoid ecology. J. Paleontol., 34: 189-193. SEILACHER, A., 1967. Fossil behavior. Sci. Am., 217: 72-80. SEILACHER, A., 1968. Swimming habits of belemnites recorded by boring barnacles. Palaeo- geography, Palaeoclimatol., Palaeoecol., 4: 279-285. SEILACHER, A., DROZDZEWSKI, G. and HAUDE, R., 1968. Form and function of the stem in a pseudoplanktonic crinoid (Seiocrinus). Palaeontology, 11 : 275-282. SHAW, A. B., 1959. Quantitative trilobite studies. 3. Proliostracus strenuelliformis POULSON, 1932. J. Paleontol., 33: 474-487. SHIELLS K. A. G., 1965. Growth of a productid shell and its implication on a method of statistical correlation. Nature, 205: 878-880. SHIELLS K. A. G., 1966. A new productid brachiopod from the Upper Vis6an of Scotland. Palaeontology, 9: 426-447. SH1ELLS K. A. G., 1968. Kochiproductus coronus sp. nov. from the Scottish Vis6an and a possible mechanical advantage of its flange structure. Trans. Roy. Soc. Edinburgh, 67: 477-507. SIMPSON G. G., 1953. The Major Features of Evolution. Columbia Univ. Press, New York, N.Y., 434 pp. SIMPSON G. G., 1961. Principles of Animal Taxonomy. Columbia Univ. Press, New York, N.Y., 247 pp. SIMPSON G. G., 1968. Evolutionary effects of cosmic radiation. Science, 162: 140-142. SIMPSON, J. F., 1966. Evolutionary pulsations and geomagnetic polarity. Bull. Geol. Soe. Am., 77: 197-204. SNEATH, P. H. A., 1967. Trend-surface analysis of transformation grids. J. Zool. Lomhm, 151: 65 122. SOKAL, R. R. and SHEATH, P. H. A., 1963. Principles of Numerical Taxonomy. Freeman, San Francisco, Calif., 359 pp. SORNAY, J., 1968. Inoc6rames s6noniens du sud-ouest de Madagascar. Ann. PalOontol., 54: 25-47. SPASSKIY, N. YA., 1967. of tetracorals. Paleontol. J., 2: 1-6. SPJELDNAES, N., 1957. The Middle Ordovician of the Oslo Region, Norway. 8. Brachiopods of the suborder Strophomenida. Norsk Geol. Tidsskr., 37: 1-214.

Earth-Sci. Rev., 6 (1970) 77-119 EVOLUTIONARY PALEONTOLOGY AND THE SCIENCE OF FORM I 19

STAHL, W. R., 1962. Similarity and dimensional methods in biology. Science, 137: 205-212. STANLEY, S. M., 1968. Post-Paleozoic adaptive radiation of infaunal bivalve molluscs -- a consequence of mantle fusion and siphon formation. J. Paleontol., 42: 214-229. STANLEY, S. M., in press. Relation of shell form to life habits in the Bivalvia (). Geol. Soc. Am., Mem. S'rASEK, C. R., 1963. Geometrical form and gnomonic growth in bivalved Mollusca. J. Morpho/., 112:213 231. STEHL1, F. G., 1956. Notes on oldhaminid brachiopods. J. Paleontol., 30: 305-313. STRAUCH, F., 1968. Platzwahl, Siedlungsweise und Bautypen bei einigen k~inozoischen Balaniden. Paliiontol. Z., 42: 195-216. STRELNIKOV, I. and HECKER, R., 1968. Wladimir Kowalevsky's sources of ideas and their impor- tance for his work and for Russian evolutionary paleontology. Lethaia, 1: 219-229. SYLVESTER-BRADLEY, P. C., 1968. The science of diversity. Syst. Zool., 17: 176-181. TASCH, P., 1955. The triangular graph in population analysis -- use and limitations. J. PaleontoL, 29: 171-177. TAVERNER SMITH, R., 1966. The micrometric formula and the classification of fenestrate cryptos- tomes. Palaeontology, 9: 413-425. THOMPSON, D'ARCY W., 1942. On Growth and Form. Cambridge Univ. Press, Cambridge, Mass., 1116 pp. THOMSON, K. S. and HAHN, K. V., 1968. Growth and form in fossil rhipidistean fishes (Crossop- terygii). J. Zool. London, 156: 199-223. TRUEMAN, A. E., 1941. The ammonite body chamber with special reference to the buoyancy and mode of life of the living ammonite. Quart. J. Geol. Soc. London, 96: 339-383. URBANEK, A., 1960. An attempt at biological interpretation of evolutionary changes in graptolite colonies. Acta Palaeontol. Polon., 5: 127-210. URBANEK, A., 1963. On generation and regeneration of cladia in some Upper Silurian mono- graptids. Acta Palaeontol. Polon., 8: 135-254. URBANEK, A., 1966. On the morphology and evolution of the Cucullograptinae (Monograptidae, ). Acta Palaeontol. Polon., 11 : 291-544. VANDERCAMMEN, A., 1959. Essai d'6tude statistique des Cyrtospirifer du Frasnien de la Belgique. Inst. Roy. Sci. Nat. Belg., Mdm., 145: 1-175. VAN VALEN, L., 1962. Growth fields in the dentition of Peromyscus. Evolution, 16: 272-277. VAN VALEN, L., 1968. Gryphaea, evolution and . Evolution, 22:424 425. WALUSER, O. H., 1963. Dimorphismus bei Goniatiten. Paliiontol. Z., 37: 21. WELLNHOFER, P., 1968. Uber Pterodactylus kochi (WAGNER 1837). Neues Jahrb. Geol. PaliiontoL, Abhandl., 132:97 126. WELLS, J. W., 1963. Coral growth and geochronometry. Nature, 197: 948-950. WESTBROEK, P., 1968. Morphological observations with systematic implications on some Paleozoic Rhynchonellida from Europe, with special emphasis on the Uncinulidae. Leidse Geol. Mededel., 41 : 1-82. WESTERMANN, G. E. G., 1964a. Possible mechanical function of shell plication in a Triassic brachiopod. Can. J. Earth Sci., 1: 99-120. WESTERMANN, G. E. G., 1964b. Sexuell-Dimorphismus bei Ammonoideen und seine Bedeutung fi.ir die Taxionomie der Otoitidae (einschliesslich Sphaeroceratinae; Al~nmonitina, M. Jura). Palaeontographica, Abt. A, 124: 33-73. WES~ERMANN, G. E. G., 1965. Septal and sutural patterns in evolution and taxonomy of Thambo- ceratidae and Clydoniceratidae (M. Jurassic, ). J. Paleontol., 39: 864-874. WHITE, J. F. and GOULD, S. J., 1965. Interpretation of the coefficient in the allometric equation. Am. Naturalist, 99: 5-18. WOLt~ENBERG, M. J., 1969. Spatial order in fluvial systems: Horton's laws derived from mixed hexagonal hierarchies of drainage basin areas. Bull. Geol. Soc. Am., 80:97-112. YOCHELSON, E. L., 1961. The operculum and mode of life of Hyolithes. J.Paleontol., 35: 152-161. YOCHELSON, E. L., 1969. Stenothecoidea, a proposed new class of Cambrian Mollusca. Lethaia, 2: 49-62. ZEUNER, F., 1933. Die Lebensweise der Gryph~ien. Palaeobiologiea, 5:307 320. (Received June 17, 1969)

Earth-Sci. Rev., 6 (1970) 77-119