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Ontogeny and the Explanation of Form: An Allometric Analysis Author(s): Stephen Jay Gould Source: Memoir (The Paleontological Society), Vol. 2, Supplement to Vol. 42, no. 5 of the Journalof Paleontology. Paleobiological Aspects of Growth and Development: A Symposium (Sep., 1968),

pp. 81-98Published by: Paleontological SocietyStable URL: http://www.jstor.org/stable/1315520Accessed: 01-04-2015 22:45 UTC

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ONTOGENY AND THE EXPLANATION OF FORM: AN ALLOMETRIC ANALYSIS

STEPHEN JAY GOULD Museum of Comparative Zoology, Harvard University, Cambridge, Massachusetts

ABSTRACr-Significant allometry occurs during the ontogeny of every variable in Poecilozo- nites bermudensis, a Pleistocene-Recent land snail from Bermuda. The adaptive significance of shell allometry may lie in the necessity for preserving a high value of the foot surface/ body volume ratio. In the absence of allometry, this ratio must decline as size increases. Three strategies could be used to keep this ratio sufficiently high: positive allometry of foot growth, structural strengthening of the foot, and the development of a foot initially large enough to withstand decline in the ratio during growth. As indicated by ontogenetic changes in apertural shape, a small amount of positive allometry occurs during ontogeny of the foot in P. bermudensis. This is not sufficient to prevent decline of the foot surface/body weight ratio, and I conclude that the strategy of possessing an initially large foot is also used. A simple model of doming, reflecting this latter strategy, is constructed (doming is a major allometric feature of P. bermudensis). In this model, the foot volume/body volume ratio is constant throughout ontogeny in each of two shells, but this value is higher in the more strongly domed shell.

Knowledge of ontogenetic allometry is a prerequisite for understanding the phylogeny of P. bermudensis, for paedomorphosis has been the primary evolutionary event in this taxon. Paedomorphic samples are scaled-up replicas of juvenile shells of the central stock, P. bermudensis zonatus. The degree of ontogenetic retardation in development is the same for all variables (color, thickness, and external shape). Paedomorphosis has occurred several times during the Pleistocene, providing an example of iterative evolution at the infraspecific level. Four paedomorphic taxa are known: P. b. fasolti, P. b. siegmundi, P. b. sieglindae, all new; and P. b. bermudensis (Pfeiffer). They have the geographic distribution (small, peripheral isolates) expected of diverging populations and seem to be genetically distinct entities, not mere phenotypic variants. The most paedomorphic subspecies originated in red soils; paedomorphs did not evolve in times of carbonate-dune deposition. The thin shells of paedomorphs might have been adaptive in the low-calcium environment of red soils. The general significance of iterative evolution at the infraspecific level does not provide an ade- quate model for corresponding events at higher levels.

EXPLANATION OF PLATE 10 All type and figured specimens have been deposited in the paleontological collection of

the Museum of Comparative Zoology, Harvard University.

FIGS. 1-6-Depiction of paedomorphosis in P. bermudensis. Adult nonpaedomorph, juvenile nonpaedomorph from the same sample, and adults of the four paedomorphic subspecies (same scale). 1, Adult nonpaedomorph, P. bermudensis zonatus Verrill, Southampton Formation, Sandys Parish; MCZ 28987. Note strong dome and well-developed parietal callus. 2, Juvenile nonpaedomorph, P. bermudensis zonatus, Southampton Formation, Sandys Parish; MCZ 28988. 3, Holotype of P. bermudensis fasolti, n. subsp., paedomorph from Shore Hills Formation; MCZ 28989. 4, Holotype of P. bermudensis siegmundi, n. subsp., paedomorph from Harrington Formation, Ireland Island; MCZ 28990. 5, Holotype of P. bermudensis sieglindae, n. subsp., paedomorph from Harrington Forma- tion, Rocky Bay; MCZ 28991. 6, P. bermudensis bermudensis (Pfeiffer) from St. George's Island, Southampton Formation; MCZ 28992. Actual widths. 1, 19.7 mm; 2, 11.5 mm; 3, 22.2 mm; 4, 21.5 mm; 5, 20.2 mm; 6, 23.0 mm.

7-9-Coloration in paedomorphs and nonpaedomorphs. 7, Paedomorphic retention of juvenile preband flame stage in a modern P. bermudensis bermudensis, x2; MCZ 28993. 8, Two-banded pattern of eastern nonpaedomorphs. P. bermudensis zonatus, Southampton Formation, x2; MCZ 28994. 9, One-banded pattern of western nonpaedomorphs. P. bermudensis zonatus, Pembroke Formation, x 2; MCZ 28995.

81



THE PALEONTOLOGICAL SOCIETY, MEMOIR 2, PLATE 10

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STEPHEN JAY GOULD

THE STUDY OF ONTOGENY IN FOSSILS

BEYOND the descriptive ordering that im- parts basic intelligibility to the diversity of

life, the central concern of evolutionary paleontology is the explanation of form. Among the many aspects of such explanation, the adaptive significance of morphology and the evolutionary processes responsible for its production are most often considered. The study of ontogeny can provide information crucial to both these facets of explanation and to their descriptive prerequisite. This threefold role for ontogenetic studies provides a framework for organizing the data of growth and development in fossils:

1. What is the complete sequence and range in variability of shapes assumed during the ontogeny of members of a population ? The resolution of this first question provides descriptions which are of most immediate use to taxonomists. Orders have been erected for the larvae of well-known species (most of the "phyllospon- dyl" amphibians, for example, are larval rhachi- tomes; Romer, 1939). Nyholm (1961) showed that, during the course of their complex ontogeny, individuals of the foraminifer Cibicides lobatulus assume shapes previously ascribed to several "genera." Species of snails with vir- tually identical postlarval shells can be distinguished by substantial differences in protoconch form (Powell, 1966, on the Turridae; Gould, 1966a, on the Siliquariidae). Separate phenetic analyses of larval and adult Aedes mosquitoes yielded marked discrepancies that negate the possibility of drawing a unique phylogenetic in- terpretation from the hierarchies formed by this clustering method (Rohlf, 1963).

2. What is the adaptive significance of this ontogenetic sequence of shapes?

It is in connection with adaptive explanations of the ontogenetic sequence that the concept of allometry1 assumes special importance. In- quiry is severely limited if no allometry occurs during ontogeny, for the question "why this change of shape?" (the standard approach to most successful adaptive explanations of form)

1In a recent paper (Gould, 1966b) I defined allometry very broadly to include size-correlated change of proportions arising in ontogeny, phylogeny, or the static comparison of related forms at one growth stage. Variates may be morphological, physiological, or chemical and the term is not confined to one form of mathematical expression-i.e., the power function. Cock (1966, p. 132-134) has discussed restrictions on the metrical study of growth and form, and his pro- viso that the criterion of homeomorphy-requiring that forms compared possess a common Bauplan-not be violated should be added as a limitation to my definition of allometry. One would not want to de- scribe tadpole metamorphosis as "allometric."

cannot be asked. Although it is true that varia- tions in the absolute rate of growth will occur in the absence of allometry, only rarely can paleontologists study growth in relation to time- as, for example, when a repeating organic structure corresponds to an astronomical periodicity (Wells, 1963; Scrutton, 1964; and Run- corn, 1966, on rugose corals; Barker, 1964, on clams; Moore, 1966, on sea-urchin spines).

The occurrence of allometry often gives insight into the relationship of form and habitat -e.g., the coincidence of the transition from regular coiling to loose uncoiling with the assumption of sessility in the gastropod Vermicu- laria and shell thickening of the foraminifer Globorotalia truncatulinoides in response to life at greater water depths in later ontogeny (Be & Lott, 1964). When ontogenetic change of shape is gradual, adaptive explanations are often to be sought, not in relation to any external condition, but rather in the consequences of absolute size itself, especially in the necessity for positive allometric increase of surfaces which serve the total body volume (Raup, 1966, p. 1186; Gould, 1966b, 1966c). Moreover, even when interest is confined to the adult form, the existence of an antecedent sequence of shapes exhibiting regu- larities of transformation provides a history that may suggest an explanation for its end result. In comparison, a fossilized adult lacking allometry in its ontogeny has a very impover- ished history indeed: no history of shape at all (if history be defined as change through time) and a history of size which generally cannot be linked to time.

3. What are the implications of ontogenetic studies for the understanding of phylogeny? The study of phylogeny offers to paleontologists their most direct source of insight into evolutionary processes. Ontogeny and phylogeny, although mechanically linked in the discredited doctrine of recapitulation, bear no necessary relationship to each other. Nonetheless, when it is recognized that phylogenies are sequences of ontogenies, not only of terminal adult points in ancestral-descendant series, two aspects of ontogeny appear to have phylogenetic consequences. If the fossil record contained no preadults, our understanding of phylogeny would be decreased in so far as the following conclusions have pro- vided information concerning evolutionary processes.

a) Evolutionary novelties can be introduced at any stage of ontogeny with varying effects on the subsequent course of individual development.

b) The time of appearance in ontogeny of a feature already present in the ancestor may be

82



ONTOGENY AND THE EXPLANATION OF FORM .7 .7

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TEXT-FIG. 1-A, Ontogenetic development of aperture form: plot of aperture height vs. aperture width for a single individual. Scale in micrometer units at 100 units = 7.3 mm. B, Ontogenetic allometry of apertural form ratio (width/height) for the individual of A (in mm).

altered during the course of phylogeny; this phenomenon is called heterochrony (de Beer, 1958). An overabundance of terminology, com- plicated by semantic arguments based on incon- sistent usage among authors, has obscured the fact that heterochrony occurs in only two forms. A feature may appear earlier in the descendant's ontogeny than in that of the ancestor, producing recapitulatory effects, or later, producing paedomorphic effects. Allometric analysis, which defines the proportions expected at each size in ontogeny, is essential to the study of heterochrony in fossils. Recapitulatory and paedomorphic effects can be spotted by the discovery that, relative to the ancestral ontogeny, given shapes appear at smaller or larger sizes in descendants. Obviously, there can be no morphological heterochrony when geometric similarity is preserved throughout ontogeny; heterochrony has allometry as a necessary condition of its occurrence.

The following study, which shall be presented in three sections according to the three ques- tions posed above, deals with the ontogeny of Poecilozonites bermudensis, a Pleistocene-Re- cent land snail from Bermuda. A major element of the endemic waif biota of Bermuda (Carl- quist, 1966), Poecilozonites is a remarkable genus of zonitoid pulmonates that has under- gone an adaptive radiation comparable in scope with the classic insular speciation and ecologic differentiation of Darwin's finches and the Ha- waiian honeycreepers (Gould, in press).

ONTOGENETIC ALLOMETRY IN

Poecilozonites bermudensis Were there no functional reason for its prev-

alence, the dominance of the logarithmic spiral among coiled accretionary structures would be mystifying. Yet the logarithmic spiral has the property, possessed by no other mathematical curve, of increasing in size by terminal addition without altering its shape (Thompson, 1942, p. 758). Allometry in the shell of a helically coiled gastropod is thus a function of its departure from the form of this ideal curve. When reasons for this departure are multiple, bivariate allometric plots may be quite complex. In Poeci- lozonites bermudensis, two primary factors de- termine the pronounced allometry evident in all measures made of ontogeny.

1. Doming of the spire. As is characteristic of many pulmonates, the spire of P. bermudensis is dome-shaped. The dome is produced, in part, by changes in shape of the generating curve or aperture. The smooth, concave-upward trend of the plot of aperture width vs. aperture height for a single individual (text-fig. 1A) indicates that increments to the aperture increase continually in relative height.

2. Nucleating influence of the protoconch. If the curve of text-figure 1A had its origin at (0,0), the value of the apertural form ratio (width/height) would decrease regularly as the shell grew. The postembryonic shell, however, is accreted onto the protoconch (embryonic shell), which is formed within the egg.

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STEPHEN JAY GOULD

The aperture of the protoconch, in keeping with the compact form of the embryonic shell, is rounded and relatively high. As the initial flat- tened whorls forming the apex of the dome are accreted onto the protoconch, the aperture becomes relatively wider even though the increments to it are increasing in relative height. (To a cube of 20 units edge length, accrete increments of continually decreasing relative width: 5 units of width for 1 of height, then 4 to 1, and finally 3 to 1. The rectangular dimen- sions are, successively, 25/21, 29/22, and 32/23, and the sequence of width/height ratios, 1.19, 1.32, and 1.39, exhibits continual increase of relative width..) As the increments of a spherical concretion with a rectangular nu- cleus become progressively more spherical, the influence of the protoconch is soon overcome, and the relative height of the aperture increases throughout subsequent ontogeny (text-fig. 1B).

That both protoconch and adult have similar apertural form ratios is entirely coincidental. Because it must fit into a squat, elliptical egg, the protoconch must be compact and rounded. The significance of doming and the rounded adult aperture will be discussed in the next section.

The nucleating influence of the protoconch is overcome by whorls 2-3 (when all allometric trends which are nonmonotonic as a result of this influence have passed the point of zero slope). Smooth unidirectional trends prevail beyond this point; these are described in the following paragraphs under three headings: color, shell thickness, and external form, the last in- cluding all those aspects of shape produced by rotation of the generating curve about the axis of coiling (Raup, 1966, p. 1181).

1. Color. Regularly spaced zigzag flames of color cover the juvenile whorls of P. bermudensis. As the shell grows, bands are produced by thickening of the flames and deposition of color between them. Of the three bands, the lowermost (just below the whorl periphery) coal- esces first, followed by the middle (just above the whorl periphery), and finally the upper (just below the suture with the preceding whorl). Relative width of the bands increases during ontogeny; upper and middle bands often fuse in large individuals. In summary, coloration intensifies throughout ontogeny as indicated by flame-band transitions and the increase in relative width of bands.

2. Thickness. Relative thickness of the shell increases during ontogeny. A parietal callus (pl. 10, fig. 1) may form during deposition of the 4th or 5th whorl and increase continually in relative thickness as the shell grows.

3. External Form. a) Spire. As in any domed object, relative height of the spire increases during growth. The intensity of doming can be described by the standard allometric power function that provides a good fit for height- width pairs from whorl 2 to the end of growth:

y = bxk

in which y is height and x width (see Gould, 1966c, for method of measurement). Since height increases faster than width, k is always greater than 1.

Relative height of the adult dome depends not only upon k (for a shell like Turritella is ex- tremely high yet completely lacks a dome; i.e., k = 1), but also upon the relative height of the shell when growth begins to conform to the power function. Since the power function applies from whorl 2 to the end of growth, this "initial form ratio" is defined as the height/width ratio at whorl 2. Two adult shells of the same size may attain the same large height/width ratio in two ways: by having a high initial form ratio or by growing with high k. These modes can be distinguished because the shell with the high k value will be more strongly domed; k is a measure of the intensity of doming.

b) Aperture. i) Form Ratio. After overcom- ing the protoconch's nucleating influence, relative height of the aperture increases as the shell grows.

ii) Rounding of the Aperture. The two trends of shape alteration most evident during growth of the aperture both lead to increased rounding of the apertural profile. First, the upper surface of the outer lip becomes arched and rounded (C-B of text-fig. 2). Secondly, the lowermost point of the outer lip (point D of text-fig. 2, the distal point of a line of maximal length drawn perpendicular to A-B and ex- tending from A-B to the lower edge of the aperture) moves during ontogeny from the umbil-

TEXT-FIG. 2-Definition of apertural measures. Aper- ture width, A-B; aperture height, C-D.

84



ONTOGENY AND THE EXPLANATION OF FORM

ical border to the middle of the aperture or slightly beyond (measured as the ratio A-D'/A-B where D-D' is perpendicular to A-B-here termed the "lower eccentricity"). The lower eccentricity increases slowly at first, but undergoes a rapid increase late in ontogeny (text-fig. 3). It is the only measure of shape that consistently undergoes its most rapid modification toward the end of growth.

c) Umbilicus. Absolute width of the umbilicus is a redundant measure in P. bermudensis. Umbilical width reaches a maximum early in growth, after which it remains constant (text- fig. 4). Analysis of correlations among variables shows that this value is mechanically related to the form ratio of the shell at the size at which umbilical width attains its maximum. The umbilicus will be wide if the shell is relatively wide at this point (Gould, in press). Since both umbilical width and form ratio are among the "standard" measures used in pulmonate studies, the generality of this redundancy should be tested, for when it occurs, the same dimension of variation is being measured twice. (As an- other plea for a discriminating choice of variables in quantitative studies, it is noted that pulmonate workers often use relative width of the umbilicus in the belief that, in this manner, the effects of size are removed. If absolute umbilical width is constant during ontogeny, then the value of its ratio with size will decrease during growth and this decrease will be entirely a function of the variable whose effects were sup- posedly removed in forming the ratio.)

ADAPTIVE SIGNIFICANCE OF ONTOGENETIC

ALLOMETRY

Speaking of the logarithmic spiral, Thompson remarked: "In the growth of a shell, we can conceive no simpler law than this, namely, that it shall widen and lengthen in the same unvar-

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ying proportions: and this simplest of laws is that which Nature tends to follow. The shell, like the creature within it, grows in size but does not change its shape" (1942, p. 757). This statement suggests an approach to the functional significance of shell allometry. Since a shell's departure from the form of a logarithmic spiral usually implies corresponding allometry in the soft anatomy, we may focus on the or- gans of the body and ask whether the primary datum of ontogeny, increase in size, requires any functional modification of body shape. Such modifications are often required to maintain constancy in surface/volume ratios, which must decline progressively when geometric similarity is preserved with growth. Indeed, Haldane (1965, p. 476) has written that "comparative anatomy is largely the story of the struggle to increase surface in proportion to volume."

A terrestrial snail uses the surface of its foot for support as well as for locomotion. Living specimens of P. bermudensis frequently climb vertical surfaces and hang upside down from rock crevices or vegetation. As Morton (1964, p. 385) has noted for terrestrial snails in general: "The foot acts as a holdfast as well as a locomotor surface, relying generally upon the adhesive properties of its mucus rather than suction." If geometric similarity were maintained with growth, the foot-surface area would increase as the square of length; the weight which it must support, as the cube. To prevent a situation in which, upon reaching a certain size, the foot could no longer support the body, three strategies are available.

1. The foot can grow with positive allometry, thus maintaining a favorable ratio of foot surface to weight.

2. Structural strengthening can occur without allometry of external shape. Smith & Saville (1966), for example, showed that the increased breaking strength of leg bones in bipedal rats is due not only to increased thickness, but also to "a change in the quality of the bone material itself" (1966, p. 164). Since it is mucus and not

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85



STEPHEN JAY GOULD

TEXT-FIG. 5-Camera-lucida drawings of successive apertures of a single individual. Note change in orientation of width axis and increase in relative height.

musculature that provides the holdfast function, this solution seems unlikely for land snails, un- less, of course, the adhesive quality of mucus increases with age.

3. In the absence of allometry or structural strengthening, the foot may start out a good deal larger than it need be to support the body weight. Subsequent decrease of the surface/volume ratio during ontogeny will re- duce the margin of safety but never, at the largest sizes reached by the animal, attain a value sufficiently low to impede the holdfast function. This situation is quite common and explains many of the puzzling size sequences in which predicted allometry does not occur. To choose an interspecific analogy: Davis (1962) found no allometry of musculature in a series of adult felines (domestic cats to lions). Al- though locomotory flexibility is reduced in large felines, lions and tigers are hardly near the point of gravitational collapse.

In the following section, I shall try to demon- strate that the major features of shell allometry in P. bermudensis can be explained under the hypothesis that foot growth follows strategies one and three. Since the foot, when retracted, occupies the most recently formed portions of the shell, we can compare the latest whorls of the shell with earlier ones for clues to the course of foot growth.

1. Functional significance of doming: Cam- era-lucida drawings of successive apertures (protoconch to adult) from a single individual (text-fig. 5) show that the dome of P. bermudensis is produced in two ways:

a) by rotation of the long axis of the generating curve from an orientation strongly oblique to the axis of coiling to a position perpendicular to it (low-er chart, text-fig. 6).

b) by increase in relative height of the generating curve (after the nucleating influence of an initially high protoconch is overcome; upper chart, text-fig. 6).

We may compare a snail whose dome is produced (at least in part) by increase in relative height of its generating curve with one exhibiting no allometry at all. Since the shell may be treated "as being essentially a cone rolled up" (Thompson, 1942, p. 798), the simplest representation of these two snails would depict the latter as a regular cone with a circular generating curve and the former as a cone whose generating curve, initially circular, becomes in- creasingly elliptical as the shell grows. If the minor axis of this ellipse (here termed width) increases in constant proportion to cone length while the major axis (here termed height) ex- pands with positive allometry, then a cross section of the cone through the apex and minor axis has the form of an isosceles triangle while one through apex and major axis yields a flar- ing, trumpet-shaped figure. (This model of "relative height increase" must be distinguished from one of "relative width decrease" in which

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the generating curve likewise becomes elliptical, but it is the major (height) axis which increases in constant proportion to cone length while the ratio of minor (width) axis to cone length continually decreases. These two modes of producing a progressively more elliptical generating curve must be separated because the hypothesis to be proposed for the significance of relative height increase is contradicted in the case of relative width decrease. As demonstrated by comparing aperture widths and heights with coil lengths as measured by wrap- ping a piece of thread about the whorl sutures, change of shape in the aperture of P. bermudensis occurs by relative height increase.)

With the following stipulations, let us compare the regular cone with a constantly circular generating curve with that illustrating relative height increase:

a) For each n-fold increase in cone length, there is a .corresponding n-fold increase in the diameter of the generating circle of cone one and of the minor axis of the generating ellipse of cone two, but an n-times-m (m>l) fold increase of the major axis of the generating ellipse of cone two.

b) Throughout ontogeny of the two cones, the snail's foot, when retracted, occupies the same constant fraction of the cone's length.

In both cones, the ratio of volume occupied by the foot to volume of the rest of the cone remains constant. That ratio, however, will be greater in cone two, and the greater the rate of increase in relative height (i.e., the stronger the dome of the coiled shell), the larger the foot in proportion to the rest of the animal. Because the ratio of foot volume to rest-of-body volume is constant throughout growth in this model of doming, the foot surface/body weight ratio must decline during ontogeny. The foot of a young individual must therefore be large enough to insure that the surface/weight ratio never becomes debilitatingly low at adult sizes. Thus doming may reflect strategy three.

Doming is, of course, not the only way to produce a shell with a high concentration of internal volume in the most recently formed increments. Our undomed shell of constantly circular generating curve can attain the same condition if the ratio of its diameter to cone length is high (large value of Raup's (1966) parame- ter W, the whorl expansion rate). This alternate solution commonly applies to large pulmonates (in several species of Mesomphix, for example). Doming, by providing for greater com- pactness and reinforcement by contiguity, may yield a stronger shell.

Any satisfactory answer to the doming problem must consider, as a fundamental datum, the rarity of this shape among marine snails as con- trasted with its near ubiquity in terrestrial faunas. I am suggesting that this is no accident of phylogeny, but rather an adaptive solution to the problem of housing a foot which, due to gravitational problems of terrestrial life, must be large in relation to that of most marine snails. Because solutions to this problem are limited, repeated independent acquisition of doming is to be expected in the evolution of large pulmonates. Doming, of itself, should not be used as an indicator of phyletic relationship.

2. Functional significance of apertural allometry: Actual shells of P. bermudensis depart from the previous model in their ontogenetic sequence of apertural shapes. Apertural allometry is complex and does not closely approximate the gradual deformation of an ellipse. After over- coming the influence of a rounded protoconch, the juvenile aperture is angulate and narrow. As growth proceeds, it becomes rounded by increase in relative height (considered in the previous section), by arching of the upper surface of the outer lip, and by rounding of the lower margin with increase in lower eccentricity (previous section and text-fig. 2). A general measure of rounding may be obtained by comparing the area enclosed by the apertural outline with that of a rectangle circumscribed about that outline. (In his study of chelonian allometry, Mosimann, 1958, compared turtle volume to volume of a circumscribed rectangular prism.) Apertural outlines were drawn for 27 shells of P. bermudensis (Government quarry, Shore Hills soil) spread evenly over the total sample range of size. In addition, 10 apertures of a single individual were traced (as the incremental growth lines indicate previous apertural posi- tions, it is not difficult to break off the most recently formed portion of the shell and reconsti- tute any earlier aperture). I measured apertural areas with a polar planimeter and compared them with the area of the circumscribed rectangle to form an aperture/rectangle ratio which, multiplied by 100, is the percentage of the rectangle area enclosed by the aperture. The same three-stage pattern of ontogenetic change in this ratio is apparent in both the individual and mass plots (text-fig. 7):

a) an initial decrease as the rounded protoconch aperture is transformed to the narrow, angular form of the juvenile shell.

b) a steady increase during the middle stage of growth.

c) a fairly sharp decrease between 20-25

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mm (shell width plus shell height) followed by a steady increase, culminating in a sharp rise near the end of growth. This sharp rise corresponds to the rapid increase of lower eccentricity at large sizes.

To assess the functional significance of this pattern, we construct the following model, which, with a few simplifying assumptions, closely approximates the actual situation:

a) Consider a cone of circular generating curve, the radius of which is one-fifth the length of the cone (relative height increase is ignored).

b) Assume that the foot occupies the volume corresponding to the most recently formed 25 percent of cone length.

c) To simulate the observed ontogenetic pattern of change in aperture/rectangle ratio, generate the following scheme for percentage of ideal cone volume occupied by snail (here termed actual/potential ratio).

i) 0-10 units cone length (protoconch)-multiply cone volume by 0.7.

ii) 10-20 units (first doubling)-multiply volume of this cone frustrum by 0.6 (transition from rounded protoconch aperture to narrow angular aperture of juvenile shell).

iii) 20-40 units (second doubling)-multiply

frustrum volume by 0.5 (protoconch influence is fully overcome at 40 units when the actual/potential ratio reaches its minimum).

iv) 40-80 units (third doubling)-multiply first half (40-60 units) by 0.52 and second half by 0.54 (increase of actual/potential ratio in middle period of growth; the 20-25 mm drop in ratio, to be discussed later, is not included. In P. bermudensis, the aperture/rectangle ratio begins to increase, as in this model, when the aperture length is about 40 percent maximum).

v) 80-100 units (final growth, corresponding to maximal sizes in P. bermudensis)-multiply by 0.60 (sharp rise in actual/potential ratio at large sizes).

Table 1 gives the foot volume/rest-of-body volume (last quarter/first three-fourths of cone length neglecting shell thickness) at first, second, and third doublings of length and at the end of growth. This ratio is a constant 1.37 for the ideal cone of circular generating curve (case 1); it begins somewhat lower and ap- proaches this value by the end of growth when the protoconch-juvenile decrease of actual/potential ratio is not followed by any increase (case 2). When change in the actual/potential ratio follows the pattern defined above (corresponding most closely to that of P. bermudensis), the foot volume/rest-of-body volume ratio declines at first, but rises quite sharply to 1.53 at the end of growth (case 3). This suggests a functional explanation for the increase in aperture/rectangle ratio that occurs during the last 60 percent of growth in shell length (last 93.6% of internal volume): it provides the requisite internal volume for a foot growing with positive allometry in order to preserve a sufficiently high value of the foot surface/body weight ratio (strategy 1). Moreover, the sharp rise in aperture/rectangle ratio at the end of growth reflects the fact that effects of a declin- ing surface/volume ratio become progressively more acute as size increases.

What of the 20-25 mm drop in P. bermudensis? If the rise of apzrture/rectangle ratio occurs to accommodate a foot growing with positive allometry, then a rapid drop in body weight, which would allow the foot to be retracted farther into the shell, would decrease the need for subsequent apertural rounding (increase in relative length of cone occupied by foot is an alternate means of accommodating a differentially expanding foot). This suggests either estivation or egg laying as a cause of weight decrease, and its presumed occurrence at a fairly definite size indicates the latter. I have often observed modern P. bermudensis in the

88

.600

.575

t5

Ul

s1 <

.600

C .575 z Z

i .550

o: <,

SIZE 15 30




TABLE --FOOT VOLUME/REST-OF-BODY VOLUME (LAST QUARTER/FIRST THREE-QUARTERS OF CONE LENGTH) FOR THREE CASES DESCRIBED IN TEXT

Volume Ratio Ratio Ratio of of Actual/ of of

C - Radius Cone Volume Poten- Column Volume Actual Column Volume Lngth at Frus- last tial 3 last Pt 3 last

Iengr End trum to Ratio X to RatiX to Inl of In- in first for Column first a Column first val for va terval this 3 Case 5 3 Ce 8

Inter- for 2 for for val* Case 1 Case 2 Case 3

0-10 2 40 .7 28 .7 28

10-15 3 95 .6 57 .6 57

15-20 4 185 1.37 .6 111 1.31 .6 111 1.31

20-30 6 760 .5 380 .5 380

30-40 8 1480 1.37 .5 740 1.28 .5 740 1.28

40-60 12 6080 .5 3040 .52 3161.6

60-75 15 8235 .5 4117.5 .54 4446.9

75-80 16 3605 1.37 .5 1802.5 1.356 .54 1946.7 1.43

80-100 20 19520 1.37 .5 9760 1.365 .60 11712 1.53

* 1r/3 extracted as common factor.

act of egg laying and have marveled at how so small a creature could produce a clutch of 6-8 eggs. (The smallest egg layer I have seen measured 19.7 mm in width plus height.) I am not suggesting that P. bermudensis produces only one clutch of eggs during its life. This may be so for the snail in the individual plot (upper chart, text-fig. 7), but relatively low aperture/rectangle ratios of some large specimens in the mass plot may indicate a subsequent egg-laying episode. Central to this entire argument is the notion that large changes in apertural shape and internal volume can occur as a response to feedback from the soft anatomy which the shell must enclose (Warburton, 1955). Much in the spirit of Thompson, I suggest that the genetic determinants of shell form allow a great range of plasticity for mechanical molding of the shell by the body which it sur- rounds.

That the foot occupies a constant percentage of cone length is the most vulnerable simplifying assumption of both this and the last section. However, the suggested explanations hold in either of the alternate cases. If relative length occupied by the foot decreases (as it may, for example, when the gonads are ripen- ing), then the significance of doming and increase in aperture/rectangle ratio in accommo-

dating a relatively large foot is even greater. Positive allometric growth of the foot can occur simply by increase in relative cone length occupied; in this case, the rise in aperture/rectangle ratio can be seen as a supplementary mechanism for additional increase in relative foot volume.

Rounding of the aperture could be considered as a simple mechanical response to doming. This might lead to the argument that no special significance should be sought in apertural rounding if doming is considered as the primary effect. However, a mechanical correlate of a primary effect may have a separate adaptive significance and this would increase the pres- sure of selection for the primary feature.

In summary, doming and change in shape of the aperture, the major features of shell allometry in P. bermudensis, may both reflect the need for a high foot surface/body weight ratio in large terrestrial pulmonates. A relatively large foot can be accommodated within a dome produced by relative height increase while rounding of the aperture provides additional internal volume for a foot growing with positive allometry. Constancy of the foot surface/body weight ratio can be maintained only if foot length increases at the 1.5 power of the general linear dimension. This degree of foot allometry could not be accommodated by the observed increase

89



STEPHEN JAY GOULD

of aperture/rectangle ratio. Indeed, for 42 specimens of living P. bermudensis:

maximum foot length a (shell width))112

Since positive allometry (strategy 1) is not sufficient to prevent decrease of the foot surface/body weight ratio (although it slows the decrease considerably), the margin of safety must decline with growth.2 This further affirms the value of doming in providing for a foot large enough to withstand this decline without impairing the snail's ability to support itself (strategy 3).

THE EVOLUTION OF Poecilozonites bermudensis: INSIGHTS FROM ONTOGENY

Compared with the other species of its subgenus, P. bermudensis shows little morphological diversity during the late Pleistocene. Yet, in number of known phyletic branching points it equals or surpasses the others; P. bermudensis zonatus, central stock of the species, has split at least four times to produce independent branches of remarkably similar morphology.

A sequence of glacial red soils and interglacial carbonates (eolian dunes and shallow-water limestones) makes up the Pleistocene geologic column of Bermuda (table 2; see Bretz, 1960, and Land, Mackenzie, & Gould, 1967, on Ber- mudian geology). Snails are common in the red soils and in unindurated zones and pockets of the eolianites. P. bermudensis zonatus, central stock of the species (pl. 10, fig. 1), ranges from Shore Hills deposits to the youngest Southamp- ton dunes. From Harrington to latest South- ampton times (a span of some 120,000 years) eastern and western populations of P. b. zonatus can be distinguished by differences in coloration; eastern snails have two bands above the whorl periphery, whereas the upper band is very weak or absent in western specimens (pl. 10, figs. 8, 9). (I have found no other consistently significant difference either in single-variable comparisons or in multivariate distances.) This geographic distribution of color patterns sug-

2Reports of prodigious strength of some terrestrial pulmonates leads to a suspicion that the margin of safety in most adult land snails is still very great. If adult P. bermudensis compares in strength to some helicids that can tow ten times their weight, then the relatively minor degree of foot allometry cannot be very significant for the function of weight support. Nonetheless, foot allometry does occur (though my functional explanation in terms of weight support may be incorrect), and apertural rounding may still be seen as a device to accommodate the differentially growing foot.

gests a step dine (Clarke, 1966), two allopatric species, or a physical barrier separating poten- tially interbreeding populations. A single sample found in the narrow area separating eastern and western snails and combining the color characteristics of both can be viewed as an in- termediate local population in the first interpre- tation, a hybrid population in the second, and a rare example of contact in the third. Because the line dividing eastern and western snails did not shift more than a mile in 120,000 years and (with the single exception cited above) the dis- tinction does not become blurred near the area of closest contact, some persistent barrier, either partial or nearly total, to gene exchange is assumed.

Heterochrony in the phylogeny of P. bermudensis.-Samples that differ from the central stock in similar ways are found in four discontinuous zones of the spatiotemporal framework: in the Walsingham district during Shore Hills time (text-fig. 8, no. 1), on Ireland Island dur-

TABLE 2-STRATIGRAPHIC COLUMN OF BERMUDA

Forma- Description Interpre- tion tation

Recent poorly developed brownish soil or crust

interglacial South- complex of eolianities and

amptol discontinuous unindurated zones

St. George's red paleosol of island-wide glacial extent

Spencer's intertidal marine, beach, Point and dune facies

Pembroke extensive eolianites and discontinuous unindurated zones

interglacial Harrington fairly continuous unindu-

rated layer with shallow- water marine and beach facies

Devonshire intertidal-marine and poorly developed dune facies

Shore Hills well-developed red paleosol of island-wide extent glacial

Belmont complex shallow-water marine, beach, and dune facies interglacial

soil (?) a reddened surface rarely seen in the Walsingham dis- glacial? trict

Walsingham highly altered eolianites interglacial

90




0

TEXT-FIG. 8-Map of Bermuda showing distribution of paedomorphic samples. 1, P. b. fasolti. 2, P. b. siegmundi. 3, P. b. sieglindae. 4, P. b. bermudensis. All are at periphery of known ranges. This is evident for 2-4. Shore Hills nonpaedomorphs are known only to the south of 1. Parallel dotted lines indicate maximum eastern and western extent of boundary separating eastern and western color patterns during the Harrington-Southampton interval.

ing Harrington time (text-fig. 8, no. 2), at Rocky Bay during Harrington-Pembroke time (text-fig. 8, no. 3), and on St. George's Island during St. George's-Recent time (text-fig. 8, no. 4). An adult shell from any of these samples differs from an adult P. bermudensis zonatus of the same size in every measure of ontogenetic allometry:

1. Color: Coloration is much less intense. The lowermost band has formed, but flames are still present in presumptive areas of the upper bands; band (or flame) widths are relatively less than in P. b. zonatus of the same size. In short, the coloration resembles that of an onto- genetically younger P. b. zonatus (pl. 10, fig. 7).

2. Thickness: The parietal callus never forms (pl. 10, figs. 1, 4) or else is very weakly developed (pl. 10, figs. 2, 3); the shell in general is relatively thinner than in P. b. zonatus of the same size. The thickness characteristics are those of a juvenile P. b. zonatus.

3. External form: a) Spire: Relative height of the spire is less

than that of an adult P. b. zonatus but equal to that of a juvenile. The value of k is less than that for P. b. zonatus, k being an ontogenetic constant of a power function that applies from

the end of whorl two onward. During formation of the first two postprotoconch whorls, however, its value varies; it begins low and steadily increases to the constant value of later ontogeny. Thus, a lower constant value in these samples may represent an arrest of change at a charac- teristically juvenile value with consequent fail- ure to develop the strong dome of a normal adult P. b. zonatus.

b) Aperture: Relative height of the aperture is equal to that of a juvenile P. b. zonatus. Rounding of the aperture has progressed not nearly so far as in adult P. b. zonatus; in weak arching of the outer lip and persistent small value of the lower eccentricity, the .shape of the aperture differs from that of an adult, but ap- proaches that of a juvenile P. b. zonatus.

c) Umbilicus: As umbilical width is a function of relative shell width at the size at whiclh umbilical width reaches its maximum, and as the relative width of shells in these samples i- greater than that of P. b. zonatus at any corresponding postprotoconch size, the umbilicus i- and must be absolutely wider than that of P. b. zonatus. Its relative width is therefore equal to that of a younger P. b. zonatus.

In summary, an adult shell of these samples i.

91



STEPHEN JAY GOULD

TABLE 3-PREDICTED VALUES FOR SHAPE FACTORS IN SHORE HILLS PAEDOMORPHS AT 30 MM COMPARED WITH SIZE AT WHICH THE SAME VALUE IS ATTAINED IN SHORE HILLS NONPAEDOMORPHS

Direction of Value at Predicted size at which Variable change in later 30 mm in same value is

ontogeny paedomorphs nonpaed mo nonpaedomorphs

Total Width/Total Height decrease 2.00 22.0 Lower Eccentricity increase .182 20.9 Relative Spire Height (CD/Total

Height. See text-fig. 2) decrease .748 21.7 Relative Umbilical Width decrease .150 23.9 AC/CB (See text-fig. 2) decrease 1.64 21.0

a scaled-up replica of a juvenile P. b. zonatus (pl. 10, fig. 2). Although the number of nonredundant measures yielding significant differences between adults of these samples and simi- larly sized shells of P. b. zonatus is large, the genetic differences are probably small. These samples are paedomorphic branches of the P. b. zonatus stock and may have arisen by selection for retention of over-all juvenile growth patterns. General developmental rates may be regu- lated by a simple genetic mechanism (de Beer, 1958, ch. 3).

Moreover, the rate of ontogenetic retardation is similar for all measures, indicating that paedomorphosis involves the entire developmental pattern of the shell, not just a few of its features. This is illustrated in table 3, which cDm- pares the paedomorphic Shore Hills sample with a normal P. b. zonatus sample of the same age and adjacent locality. Reduced major-ax's fits for the relationship of several variables with shell size (total width plus total height) were computed for both samples (see Waller, 1968, for a description of the program). Using these equations, I determined the value of five ratios in average paedomorphic shells of 30 mm height-plus-width and the size at which the same values are reached in the P. b. zonatus sample. These latter range from 20.9 mm to 23.9 mm with an average of 21.9 mm. Thus, as a best estimate, the shape of a paedomorph at 30 mm is most similar to that of a nonpaedomorph at 21.9 mm. The average whorl number for paedomorphs at 30 mm is 5.45; nonpaedomorphs at 21.9 mm average 4.43 whorls. The total developmental retardation of these Shore Hills paedomorphs is about one whorl.

Taking 21.9 mm as a median value, I selected 10 juvenile specimens of P. b. zonatus and compared them with the 10 largest adults of the same sample and the 10 largest adult paedomorphs. Using seven ratio measures of shape (see caption, text-fig. 9), I performed a factor analysis on these 30 shells. When plotted

against the first and second Varimax axes (text-fig. 9), the 30 shells separate into two dis- crete clusters, one containing all adult paedomorphs and juvenile nonpaedomorphs, the other

composed of all adult nonpaedomorphs (see

Y P

P

.79

.42

.04

y yy p

p y y

p y p

y Y

P?

A

A

A A

A

A

A A

A --a.

TEXT-FIG. 9-Multivariate comparison of adult Shore Hills paedomorphs with juvenile and adult shells of Shore Hills nonpaedomorphs. Each point is an individual shell characterized by 7 ratio measures of shape; hence, relative similarity of shape is de- picted and size is not considered. Plotted against first (ordinate) and second (abscissa) Varimax axes accounting for 91.8 percent of the total information. Y = young nonpaedomorph; A = adult nonpaedomorph; P = adult paedomorph. Axis scales are projection magnitudes of shells on the axes. The seven measures are (see text-fig. 2): aperture-form ratio (AB/CD); relative height of spire (CD/total height) ; upper eccentricity (C'B/AB); lower eccentricity (AD'/AB); total shell width/total shell height; AC/CB; and relative umbilical width.

92

Y

-.4, -.45




Manson & Imbrie, 1964, for description of factor-analysis program; Imbrie & van Andel, 1964, and Gould, 1967, illustrate its use).

Mechanism of paedomorphosis.-When just one or very few features of adult descendants resemble earlier stages of ancestral ontogeny, the mechanism of phyletic change cannot be directly inferred. When, as in P. bermudensis, equal paedomorphic effects are seen in the entire set of allometric variables, there can be little doubt that developmental retardation has occurred. In previous discussions of paedomorphosis, such retardation has often been considered relative to the time of gonad maturation (de Beer, 1958). Boettger (1952) demonstrated that the absolute growth rate of pulmonates tends to decline abruptly when the gonads mature. With this rapid decline from juvenile growth rates, morphologic features of late ontogeny begin to appear. However, parasitically castrated individuals of Helix pomatia, Arianta arbustorum, and Bradybaena fruticum never develop the following normal adult features- thickening and increase in coloration of the aperture and change in the direction of growth- even though these castrated forms grow faster and become larger than normal adults (Roths- child & Rothschild, 1939).

There are two ways of interpreting the weaker coloration of P. bermudensis paedomorphs: either less pigment is deposited per unit time in paedomorphs and the absolute growth rate is similar in paedomorphs and nonpaedomorphs, or the rate of pigmentation per unit time is constant in both forms and the faster growth rate of paedomorphs spreads the color more thinly. That the second explanation often applies is indicated in Comfort's (1951, p. 286) statement: "The intensity of pigmentation varies with the growth rate, periods of diapause giving rise very often to darker varices and periods of rapid growth to paler zones." Thick- ness of the parietal callus also increases during diapauses; maintenance of a sufficiently high growth rate might prevent its formation alto- gether and lead to the thin shell characteristic of paedomorphs.

I suggest therefore that paedomorphosis in P. bermudensis occurs by a slowdown in retardation of rapid juvenile growth rates. If the gonads of paedomorphs and nonpaedomorphs mature at approximately the same time after hatching, the paedomorph will be larger at this time due to its maintenance of the high juvenile growth rate. Since both paedomorphs and nonpaedomorphs reach the same adult size and whorl number, features which appear late in the ontogeny of nonpaedomorphs will be so delayed

in size of appearance in paedomorphs that they never develop at all.

Iterative evolution of paedomorphs.-The usual inference from the distribution of paedomorphic samples would be that two lineages of P. bermudensis, the normal P. b. zonatus and the paedomorphic P. b. bermudensis, inhabited Bermuda from Shore Hills to latest Southamp- ton time. For once, however, the literal in- terpretation seems to be correct; each of the four sample groups represents an independent episode of paedomorphosis. The phylogeny of P. bermudensis is a story of recurrent splitting of paedomorphic offshoots from a central stock (text-fig. 10), an example of iterative evolution at the infraspecific level.

P. bermudensis fasolti, new subspecies (pl. 10, fig. 3), the Shore Hills paedomorph, shares with all nonpaedomorphs of its time those unique morphological attributes which distinguish Shore Hills P. bermudensis samples from all geologically younger shells. These attributes, extreme flatness of the apical region and small size at any postprotoconch whorl, are related neither to the allometric variables nor to each other (Gould, in press). Moreover, in all allometric variables, P. b. fasolti displays its relationship to Shore Hills nonpaedomorphs. Shore Hills P. b. zonatus has the widest umbilicu; among nonpaedomorphs; P. b. fasolti exceeds all other paedomorphs in umbilical width. At the fifth whorl, Shore Hills shells are relatively widest among nonpaedomorphs; relative width of P. b. fasolti surpasses that of all other paedomorphs. Values of the lower eccentricity at comparable sizes are smaller in Shore Hills samples than in more recent nonpaedomorphs; the value of this measure in P. b. fasolti is min- imal among paedomorphs. This list could be ex- tended to cover the entire set of such variables. The extent of the morphological gap separating Shore Hills and more recent samples is evidenL in the Varimax plot of all P. bermudensis samples (text-fig. 11). The first axis (ordinate) distinguishes paedomorphs from nonpaedomorphs, while the second (abscissa) separates all Shore Hills shells from all more recent samples. Mean values for each of 35 variables char- acterize each sample in this plot (N = 20 in most cases). Each variable is measured at the same size or whorl number in each sample.

Combining the evidence of morphology and geographic distribution (only one known locality), I conclude that P. b. fasolti is a paedomorphic side branch, derived from typical Shore Hills P. b. zonatus and disappearing without issue after brief existence as a diver- gent local population.

93



STEPHEN JAY GOULD

west zonatus

R _I

I II

' 4%

^ ----l^~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

east zonatus

TEXT-FIG. 10-Schematic representation of the phylogeny of P. bermudensis, showing iterative development of paedomorphs.

As measured by 35 variables, paedomorphs of the Harrington Formation (12, 13, and 17 of text-fig. 11) are closer to nonpaedomorphs of the same age than they are to P. b. fasolti. The derivation of these paedomorphs from P. b. fasolti would require that Harrington paedomorphs and nonpaedomorphs both develop a large suite of similar features that show no significant interrelation within samples. Parallel acquisition of many features is not improbable in itself and must occur if paedomorphosis is recurrent in P. bermudensis; it is the independent development of large numbers of unrelated features, each requiring a separate genetic modification, that is deemed unlikely. The many features that distinguish paedomorphs from nonpaedomorphs may be modified together by a sin-

gle factor that affects the developmental rate uniformly. I assume, therefore, that Harrington paedomorphs were derived from contemporary populations of P. b. zonatus.

Harrington paedomorphs are found in two areas. P. b. siegmundi, new subspecies (pl. 10, fig. 4), from Ireland Island is typically western in coloration, while P. b. sieglindae, new subspecies (pl. 10, fig. 5), from Rocky Bay retains the uppermost band area of eastern forms (flame- band transitions are, of course, delayed in both subspecies). Both eastern and western paedomorphs lived at the peripheries of the known ranges of contemporary P. b. zonatus. Because gene flow between western and eastern populations was limited or curtailed and because each Harrington paedomorph has the geographic dis-

SG

H

!

94

I1




tribution of a peripheral local population, P. b. siegmundi and P. b. sieglindae are regarded as distinct branches of the P. b. zonatus stock.

The case for a separate origin of the St. George's-Recent paedomorph, P. b. bermudensis (Pfeiffer) (pl. 10, fig. 6), is weakened by the citation of P. b. sieglindae as a possible ancestor. However, I prefer the hypothesis of a fourth independent origin from P. b. zonatus for the following reasons:

1. P. b. bermudensis evolved on St. George's Island at the range periphery of P. b. zonatus, opposite the point of origin of P. b. sieglindae.

2. P. b. sieglindae seems to have been a small, isolated, and short-lived population. It extends from upper Harrington to lowest Pembroke and was probably annihilated by the rapid and vig- orous deposition of Pembroke dunes. In lowest Pembroke times, its range is narrowly limited by P. b. zonatus samples to the east and north- west; the entire east-west extent of its Pem- broke range did not exceed 200 meters.

1W

10 1121 7 15 9 8 /

26 6 1625 2724

1

18 14 20 ,

22 ,/ ,"' 17

/ '

13 33

,,/' 12 31 36 28

32 / 34

35 30

23 29

+.64

+.22

.00

-20 5

-.73 -.41 -09

TEXT-FIG. 11-Multivariate comparison of all P. bermudensis samples. Each point represents a sample and is characterized by the means of 35 variables (N= 20 in most cases) measured at a standard size or whorl number in each sample. Plotted against first and second Varimax axes, the scale of which represents projection magnitudes of samples on the axes. Shore Hills samples (1-5) are widely separated from all others. Dashed line separates all nonpaedomorphs (above) from all paedomorphs (below). Four clusters are evident: Shore Hills nonpaedomorphs (1-4), Shore Hills paedomorphs (5), post-Shore Hills nonpaedomorphs (above dashed line) and post-Shore Hills paedomorphs (below dashed line).

2

3 4 1

31'

loll

"I .

The argument must be taken one step farther before much biological significance can be read into the multiple origin of paedomorphic populations. Is paedomorphosis genetically significant? If the paedomorphic snails are, as the axolotl of Ambystoma, merely phenotypic variants induced by certain environmental conditions, then the recurrence of paedomorphosis should provoke no surprise. In fact, this phenotypic recurrence is part of the Pleistocene history of Ambystoma tigrinum. Tihen (1955, p. 243) stated that "in all Pleistocene deposits of this Kansas-Okla- homa area the populations represented in the interglacial stages are of the normally metamor- phosing types, whereas those from the glacial stages are of the giant neotenic type." The case is different for P. bermudensis. Paedomorphosis has a genetic base in these snails for the following reasons:

1. Paedomorphs and nonpaedomorphs lived contemporaneously for 120,000 years in similar red soil and dune environments. P. b. bermudensis on St. George's Island and P. b. zonatus on the main island were never separated by more than a kilometer.

2. Geographic distributions imply that each episode of paedomorphosis occurred in a population isolated at the periphery of the known range of its parental form. That deviations from the "typical" form of a species occur most often in peripheral isolates is a central concept in our understanding of natural populations and the basis of the principle of allopatric speciation. "Taxonomists have long been aware of the importance of these peripheral isolates and have pointed out, again and again, that major deviations from the 'type' of a species will most likely occur in such populations. . . . They are usually comparatively small in area, with a low absolute population size. . . . Some are sufficiently different to be regarded as distinct subspecies" (Mayr, 1963, p. 368).

Hecht (1965, p. 309) remarked: "If the basic principle of allopatric speciation is true, then the particular difficulties of paleontological re- search can make it nearly impossible to demon- strate the origin of species by known processes of speciation." In Bermuda, however, temporal and geographic resolution is sufficient to show that phyletic splitting occurred at the peripheries of a species range.

3. Modern populations of P. b. bermudensis have reacquired some typical nonpaedomorphic features, particularly the strong coloration. No modern shell, however, has redeveloped a color variation present in a good proportion (5-80%) of shells in all eastern samples of P. b. zonatus. In these "faded" variants, flames coalesce nor-

95



STEPHEN JAY GOULD

mally into bands, but the bands are replaced late in ontogeny by lines of color at the previous band peripheries. Throughout the St. George's- Southampton interval, shells of P. b. bermudensis did not develop beyond the flame stage (pl. 10, fig. 7). Since the "faded" phenotype could never be expressed, its genetic determinants were probably selected against and eliminated during this time.

This suggests an answer to the question: Why do nonpaedomorphs give rise to paedomorphs so many times without the reverse transformation ever taking place? Although emphasis has properly been placed upon paedomorphosis as an escape from specialization, the extent to which it can serve as a genetic cul-de- sac for the prevention of oscillating trends at the infraspecific level should also be stressed. Nonpaedomorphs must possess the capacity for production of the paedomorphic phenotype, for it already exists as an early ontogenetic stage. Paedomorphic forms, on the other hand, will tend to lose genes for features of late ontogeny that can never be brought to phenotypic expression.

Adaptive significance of paedomorphosis.-In seeking an adaptive explanation for paedomorphosis, we note a correlation between morphology and environment of deposition:

1. The most paedomorphic subspecies originate in red soils. P. b. fasolti and P. b. bermudensis have very weak coloration and no callus.

2. Paedomorphosis is less pronounced in subspecies arising in unindurated carbonate zones ("accretionary soils" of previous authors). P. b. siegmundi and P. b. sieglindae have moderately weak coloration and a thin callus.

3. No paedomorphs originate in eolian dunes. (P. b. bermudensis survived in Southampton dunes of St. George's Island, but was isolated from competition with P. b. zonatus at that time. P. b. siegmundi became extinct at the onset of Pembroke dunes. P. b. sieglindae survived somewhat longer, but disappeared during Pembroke times.)

Most pulmonates obtain calcium for their shells by ingestion of the limestone upon which they live (Lozek, 1962). Deprived of calcium, shells of Murella murella globularis were paper thin and the animals died when half grown (Rensch, 1932). Oldham (1934) fed one group of Helix aspersa on cabbage, oatmeal, and chalk and a second on just cabbage and oatmeal. One year later, the shells were the same size, but those of animals supplied with chalk were 4.5 times as heavy. Ruhe et al. (1961) determined the calcium carbonate content of Bermudian

formations; it ranges from 92.6 to 99.3 percent in eolianites but reaches values as low as 1.9 percent in red soils. These facts suggest that paedomorphosis may have served as one path- way to the attainment of thin shells that were adaptive in the limited calcium environment of red soils.

The necessity for thin shells in red soils is further emphasized by zigzag trends in shell thickness in the phylogenies of both P. nelsoni and P. bermudensis zonatus. In these taxa, shells are invariably thin in red soils and thick in eolianites (Gould, in press).

A temporal picture of shifting selective pres- sures within P. bermudensis may be constructed from these data. During each period of conti- nental glaciation, sea level fell and red soils formed over most of Bermuda. Selective pres- sures for the development of thin shells arose in red-soil environments, and the snails responded in several ways. Less drastic pathways were uti- lized in the main populations (phenetic thinning within limits of the parental genotype or very minor genetic changes). The peripheral isolates with few individuals and limited gene exchange with the main population had better opportuni- ties to undergo a larger reorganization of genotype and phenotype (see Mayr, 1963, on the ge- netics of peripheral isolates). Furthermore, a study of intersample variability in nonpaedomorphic samples indicates that the latent potential for paedomorphosis was already present in the parental forms. When an R-mode factor analysis is performed on the correlation matrix obtained from the matrix of means of all P. b. zonatus samples (the means for each of 25 variables in each sample, considering each variable at a common size in all samples-thus the correlation matrix is composed of partial correlations with the influence of size removed), the following nonredundant features tend to cluster together: a weak callus, a low value of the lower eccentricity, and several measures of a relatively wide shell. These are all features of early ontogeny, but as the analysis is being carried out on shells standardized at the same size, this clustering indicates that general developmental accelerations and retardations occur within the P. b. zonatus stock itself. Paedomorphosis, a much greater developmental retardation, would result from an intensification of tendencies already present in the ancestral population.

CONCLUSION

Time is the unique element that paleontologists bring to the study of evolution. It is no accident of personality that a paleontologist wrote

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of evolution's "major features" and a neontolo- gist, of "animal species," for transspecific evolution can be studied directly only in the fossil record. Yet paleontologists, too, work mainly at the species level not only because it is here that detail sufficient for the study of evolutionary mechanisms is obtainable, but also because of the conviction that there is a continuum between infraspecific and transspecific evolution: "The origin of higher taxa or organizational levels represents an extension of the mechanisms that underlie intraspecific variation, species formation and species transformation" (Schaeffer & Hecht, 1965, p. 245).

Yet just as increase in size, of itself, subjects organisms to a different realm of forces and requires change in morphology, so also might extension in time bring emphasis to evolutionary events and processes that do not dominate at the species level. In particular, the great parallelism that occurs in independent lineages of most vertebrate classes and orders stands in contrast to the theme of splitting and diversification that predominates at lower levels. (It was not long ago that parallelism was treated as a taxonomic nuisance or an interesting oddity; its fundamental nature is becoming apparent only now; see Wood, 1965, on rodents for a specific example, and Schaeffer, 1965, and Huxley, 1958, for a general view).

It is particularly important to search for parallelisms of this sort at the species level both to test the continuum notion and, if affirmed, to apply the standard method of studying a process at the species level to learn about its operation at higher levels. To my mind, therefore, the major significance of multiple episodes of paedomorphosis in the phylogeny of P. bermudensis is that it provides, at the microlevel, an example of a common macrolevel event not often observed within species-iterative evolution or heterochronous parallelism.

The independent development of a large series of morphologic features in several lineages is the attribute of parallelism that most de- mands explanation. Three adaptive explanations will cover most instances:

1. The adaptation is only one among a number of possible solutions; independent development of a large number of features is possible because the genetic change is a small one even though its effects are large-e.g., paedomorphosis.

2. The adaptation arises many times because it is the only possible solution to a given problem: for example, differential thickening of weight-supporting bones and secondary quadru-

pedalism among dinosaurs to compensate for increasing size and streamlining in three orders of secondarily aquatic mammals in response to new environments.

3. The adaptation is a general biological improvement. This is a touchy subject because improvement is so difficult to define and has so often been discussed with anthropocentric bias. I would approach the problem by imposing a se- vere limitation and considering only mechanical improvements of the engineering type that occur in a constant physical environment. I would admit the increased efficiency of feeding in the phylogeny of actinopterygian fishes (Schaeffer & Rosen, 1961), but would exclude, on the basis of different function and environment, any comparison of the limb structures of rhipidistean fishes and early tetrapods. Parallel- ism in biological improvement is an aspect of the principle of limited solutions but is separated from the preceding category because the mechanical inevitability that necessitates adaptation is not involved here. The holostean feeding mechanism is viable, but a Brontosaurus with two spindly legs would collapse.

These three categories separate into two op- posing tendencies. In the first case, emphasis is on the ease of genetic change. In the second and third cases, it is on limited solutions. Multi- ple episodes of paedomorphosis in P. bermudensis are covered by the first category; there are many ways to make a very thin shell, but paedomorphosis may have required least disturbance of the genetic homeostasis of a well-integrated genotype to attain the requisite thinness. Such microlevel parallelisms will generally fall into the first category, whereas those that occur over millions of years in higher taxa refer more to the concept of limited solutions than to ease of genetic modification. I suspect that there is a fundamental difference in explanation for similar events at micro- and macrolevels and suggest that paleontologists not rest their hopes entirely upon species, but concentrate on the vast time spans that constitute their unique domain in order to understand the major features of evolution.

ACKNOWLEDGMENT

This study has been supported, in part, by grant GA901 from the National Science Foun- dation. Contribution number 431 from the Ber- muda Biological Station.

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