Earth-Science Reviews - Elsevier Publishing Company, A m s t e r d a m - Printed in The Netherlands
E V O L U T I O N A R Y P A L E O N T O L O G Y A N D T H E SCIENCE OF FORM
S T E P H E N JAY G O U L D
Mttseum o f Comparative Zoology, Harvard University, Cambridge, Mass. (U.S.A.)
SUMMARY
A science of form is now being forged within evolutionary theory. It studies
adaptation by quantitative methods, using the organism-machine analogy as a
guide; it seeks to reduce complex form to fewer generating factors and causal
influences. If a function 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 relationships) 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 predetermined 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 fossil shells, providing thereby a paleontological input to geophysics. Bivariate procedures, as the inevitable Gryphaea
story illustrates, have been plagued by errors of method. When properly applied,
they serve well in the separation of species and sexual dimorphs; they are the
standard tool of quantitative description. Multivariate methods are based on the
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s.J. GOULD
more satisfactory premise that an organism grows and evolves as a set of interacting 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 life's history. 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 radiations, but sets of competing
experiments 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 Phanerozoic has not been a time of endless ecological variation
on a static set of basic structures.
T H E S H A P E OF T H I N G S TO COME
Form and diversity are the two great subjects of natural history. Although
we now think of speciation and adaptation where we spoke once of plenitude and
design, it is only the terminology and not our concerns that have changed. Systematics, 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).
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EVOLUTIONARY PALEONTOLOGY AND THE SCIENCE OF FORM
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evolutionary problem of form, to the question of adaptation. Just as experimental
physiology 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. RUDWlCKunderstood 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 fossils,
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 fitness 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 morphology was the first triumph of biological
paleontology, but it "suffered a spectacular eclipse" with the acceptance of evolution (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 history of life (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
an d 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 production. 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 homology 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
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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
evolution 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 horses] 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 p r o b l e m . . , 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 organisms 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 adaptational science - - the criterion of mechanical fitness: "Consequently the range
of our functional inferences about fossils is limited not by the range of adaptations
that happen to be possessed by organisms at present 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 vertebrate 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 class lever). The physics of diductor
musculature in brachiopods 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 Ordovician strophomenids
were not sufficiently strong to open the valves. They were aided, he suggests, by a
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EVOLUTIONARY PALEONTOLOGY AND THE SCIENCE OF FORM
8l
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 Cretaceous 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 birds, fish and marine mammals). RUDWlCK (1961) noted that longitudinally
grooved spines of the Permian coralliform brachiopod 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 Mechanocythere (Fig.2). GRANT (1966b) compared spines of the Permian brachiopod
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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 sediment (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 combination of rigidity and lightness which recalls the geodetic construction familiar
to aeroplane designers. No one has seen it alive in its natural habitat. 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
ideal 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 nature 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
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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 approach 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 Jurassic 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 brachiopods 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 disappear 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 Silurian rhynchonellacean Sphaerirhynchia wilsoni and
the Upper Carboniferous 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
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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 s h o u l d equal 1. This is often observed (PauL, 1968, p.715). Other cystoids
d e v e l o p e d a sieve-like entrance pore - - a better solution to the p r o b l e m o f protection.
(b) M e c h a n i c a l analyses m a y prescribe m o d e s o f life a n d p r o v i d e ecological
i n f o r m a t i o n b a s e d p u r e l y on f o r m (MUIR-WOODa n d COOPER,1960;KAZMIERCZAK,
1967; GRANT,1966a a n d 1968 on b r a c h i o p o d spines). The p o s t e r i o r spines o f some
Silurian chonetids p r o v i d e stability by equalizing the f o r w a r d a n d b a c k w a r d
t u r n i n g m o m e n t s o f a b r a c h i o p o d living free on the substrate with its ventral valve
d o w n and nearly h o r i z o n t a l (B/JGER, 1968).
I f the calyx is b u o y a n t , a p a r a d i g m for n o r m a l crinoids requires a stem that
is stiff near the r o o t a n d flexible at the calyx (SEILACHERet al., 1968). Since the
stem o f Seiocrinus subangularis is flexible at the r o o t a n d massive at the calyx,
Seilacher et al. c o n c l u d e that this crinoid a t t a c h e d to floating logs at the surface
and grew d o w n w a r d s .
(c) P a r a d i g m s establish a quantifiable criterion o f relative efficiency for the
comparison of adaptation.
C o m p a r i s o n s are m a d e between an o r g a n i s m a n d a theoretical ideal or
between two organisms. W h e n , in the f o r m e r case, a structure fails to a p p r o a c h
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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 tetrapods comes to mind - - or it may represent a compromise 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 history of paleontology, 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 Cambrian trilobite 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 trilobites (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 times 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 energy 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).
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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 animal 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 anatomy 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.
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EVOLUTIONARY PALEONTOLOGY AND THE SCIENCE OF FORM
87
Other physical laws also relate size and form. When growth conforms to the
power function, y = b x 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 Pleistocene 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
(ScHNEIRLAet al., 1968, p.542).
Close packing, an important law of space, determines the form of honeycombs and the hexagonal members of crowded coral colonies. It can also explain
the distribution of brachiopod punctae (CowzN, 1966), trilobite eye lenses (CLARKSON, 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 suture is surely a mixture of direct genetic
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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 experiment 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 cephalopods 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 aluminum 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 primate shoulder girdles on canonical 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 photoEarth-Sci. Rev., 6 (1970) 77-119
EVOLUTIONARYPALEONTOLOGYAND THE SCIENCE OF FORM
89
elastic plastic and determined stress gradients by observing the extinction 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 human wisdom intervened. SEILACHER(1968, p.285) penned these
remarks in showing, from the preferred direction of barnacle borings, that belemnites usually swam forward even though their rostra were streamlined for "emergency" backward escapes: "Paleontology as a whole too often has an 'oldfashioned' 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 years 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 performed 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 Devonian brachiopod. Another
class of natural experiments involves the regeneration and healing of damaged
structures. Regeneration, a major tool of modern experimental embryology, has
been studied by URBANEK (1963) in graptolites and HOTTINGER (1963) in Foraminifera. 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 c o l u m n . . . Although the Hydra
possesses 17 cell t y p e s . . , they all arise from two basic stem cells. The differentiation 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
EVOLUTIONARYPALEONTOLOGYAND THE SCIENCEOF 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 order
of many patterns in fossil feeding traces can be reduced to a few commands: "A
model program for the Scolithus animals 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
i s . . . 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 Paleozoic 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
93
EVOLUTIONARY PALEONTOLOGY AND THE SCIENCE OF FORM
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Earth-Sci. Rev., 6 (1970) 77-119
94
s . J . GOULD
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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 taxon 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 interpretation 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 interpenetrating umbones (STASEK, 1963): umbones are offset and coil past 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 gravity 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). Likewise, 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 vertebrate 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~ f
'front'F
7
lobe width W . /
A
10/
.............:~ii::ii:~ii] :i
~---"~-"
d
Icritical
~lobe length K
'
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 submedian 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 Eusthenopteron.[oordi, a rhipidistean fish, the paired fins
moved back and decreased in relative size while the caudal fin enlarged and developed pronounced upper and lower lobes (THOMSONand HAHN, 1968). Eusthenopteron 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
t i m e . . . 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 JEFFRIESand 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, RUDWICK (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 harmful 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, regardless 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
E V O L U T I O N A R Y P A L E O N T O L O G Y A N D 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 dinosaurs 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 R u o w l c ~ (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 histograms that showed a progressive increase in whorl number up the stratigraphic
sequence. Whorl number is a function of size; the Gryphaea sequence is characterized 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. Idealized 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 c o m m o n 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 c o m m o n sizes of R -- 20 and
30 m m from the equations given by Hallam and Philip. Hallam's data show increased 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 H A L L A M (1959) 1 AND P H I L I P (1962) 1
Stratigraphic level
Higher (Bucklandi-Gmuendense Zone)
Lower (Angulata Zone)
From Hallam's data
From Philip's data
at R
-- 20 m m
at R
30 m m
at R
20 m m
at R
30 m m
2.25
1.97
2.83
2.52
2.23
2.49
2.8 l
2.77
1 HALLAM (1959) gives one equation for each o f the stratigraphic levels. The figures for PHILIP
(1962) are mean values for four subsamples in the Angulata Zone and 3 in the Bucklandi-Gmuendense 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 extrapolation 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 proportion 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. orbiculatus. 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 developmental stage or else the allometric trends of ontogeny must be recognized and
removed. Eccentricity of the apical system is an important character in the classification of spatangoid echinoderms. 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 decreasing. 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 Eocene
gastropod Pachymelania by KOTAKA and UOZUMI (1962); and in the trilobites
Norwoodella halli and Welleraspis lata by H u (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 unrecognized 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 investigation. 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 (protoconch 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 accelerator 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 brachiopod Composita and SHIELLS (1968); "Topological surfaces", drawn for Miocene
horse 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 Cretaceous and Tertiary 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 population 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 interrelationship 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. " I t 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). Moveover, 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 contribution to growth. CHEETHAM(1968) used principal components analysis to obtain
uncorrelated variates in the Tertiary-Recent cheilostome bryozoan Metrarabdotos.
Three axes explained 8 2 ~ 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 interrelated character clusters that are independent of each other. GOULD and GARWOOO
(1969) studied insectivore and rodent dentitions by morphological integration and
Earth-Sci. Rev., 6 (1970) 77-119
S.
104
factor analysis.
exhibits
Tooth
a distinct
widths form a separate
pattern
group from lengths;
J. GOULD
the last molar
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 Cretaceous belemnite Actinocamax verus; three additional variables did not add to the
distinction.
We can also learn which characters are most influential in discrimination. 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
year 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 continents,
oceans, and shallow seas.
Perhaps
we are becoming
the unwitting
handmaiden
of a different
field,
trading our indenture to stratigraphy
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
The quantifunctional
STUDY
OF PHYLOGENY
analysis
of changing
form is indifferent
Earth-&i.
to the cause of
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 approach 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 containing 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 modification, 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 genotypes were present. This could result from the intergrowth of colonies, the fusion of larvae or an early somatic mutation 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 mosaic evolution 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 vertebrates 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 determine average rates of evolution for the bivalve Exogyra in Cretaceous sediments
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 populations 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 primates
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 crania of their own species; this result
furnishes some evidence for the role of paedomorphosis in human evolution.
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 cline'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 semiaquatic 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 Pennsylvanian 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 substantiated 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 PALEONTOLOGYAND 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 tree of life, a model of diversity with ever diverging
branches. The phenomena are parallelism and convergence on the one hand and
an aspect of "adaptive radiation" on the other.
On the tree of life, convergence is at best a curiosity 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, moreover, 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 ( i n d ) - R F - L H - L F 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 lenticular 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 adaptations. 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 t i m e s . . . 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 attainment 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 commissures 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 p l a c e . . . 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 Ordovician 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 environments with variations on a newly-evolved and successful design - - a classic adaptive
radiation. 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 taxonomy: 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 phylum'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 independent 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, o f course, only o f the broadest outlines of basic design. I a m completely bypassing one
of the great t h e m e s o f life - - the e n o r m o u s diversity of a d a p t a t i o n , within each basic design,
to a great r a n g e of e n v i r o n m e n t s .
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 ocean bottoms
had apparently not been invaded by an infauna comparable to the one we see
t o d a y . . . The post-Paleozoic radiation was a consequence of mantle fusion and
siphon formation" (STANLEY, 1968, p.224). Mesozoic faunas contain a lower
percentage of infaunal bivalves than their Cenozoic 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.
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