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Columellar muscle of neogastropods: muscle attachment and the function of columellar folds.

Introduction

Malacologists often assume that gastropod shell ornamentation is adaptive, but experiments that demonstrate the function of these presumed adaptations are rare (Morton, 1967; for notable tests of ornamentation function, see Palmer, 1977, 1979; Bertness and Cunningham, 1981; Appleton and Palmer, 1988; Marko and Palmer, 1991; West et al., 1991; Carefoot and Donovan, 1995; Donovan et al., 1999). Columellar folds, plications on the columella, or central column of a gastropod shell (see Fig. 1), are particularly intriguing ornaments because they evolved repeatedly in a number of clades, such as the Caenogatropoda, Opisthobranchia, and Pulmonata (Price, 2001). In the subclade Neogastropoda of the caenogastropods, the columellar folds may be an adaptation that is intimately related to the columellar muscle (Fig. 1). In fact, the muscle does attach the animal to the columella (Signor and Kat, 1984; Fretter and Graham, 1994) and has grooves that fit between each fold. In this paper, I test three hypotheses that purport to explain a functional relationship between the columellar folds and the columellar muscle.

[FIGURE 1 OMITTED]

Columellar folds are readily visible on the inner lip of many shells, and systematists have used the impressive diversity of fold shapes to distinguish species and higher taxa. I consider a fold to be any ridge on the inner lip of the aperture that extends along the columella for a number of whorls, usually extending all the way to the apex. Some folds occur at the bottom edge of the aperture, as in Nassarius vibex, whereas others, such as those in Terebra dislocata, are located in the center of the inner lip. Folds can be wide (Triplofusus giganteus) or narrow (Nassarius vibex), subtle (Busycon contrarium) or prominent (Vasum muricatum).

The columellar muscle conforms exactly to the shape of the folds where it lies over them, and this conformation has inspired the hypotheses that are most commonly cited to explain the function of folds. These hypotheses must be considered in light of the fact that the columellar muscle functions as a muscular hydrostat (Thompson et al., 1998), controlling protraction from, and retraction into, the shell. Like hydrostatic skeletons in general, the volume of a muscular hydrostat remains constant, so a contraction in one direction induces elongation in an opposing direction (Kier and Smith, 1985). The columellar muscle is composed of muscle fibers that are oriented longitudinally, transversely, and obliquely with respect to the long axis of the columellar muscle (Thompson et al., 1998). Thus, the columellar muscle controls its own twisting, shortening, and elongating in addition to protraction and retraction.

Dall (1894; restated by Fretter and Graham, 1994) published the only nonfunctional explanation of folds. His explanation does not pertain to the columellar muscle, relying instead on the nature of the mantle, the tissue that secretes the shell. Dall surmised that folds, and all other internal ornamentation including the parietal ridge, lirae, and teeth on the outer lip, were deposited in the wrinkles that would form when ah overly large mantle retracted into the shell. This idea predicts that ornamentation would be more pronounced at the aperture (Dall, 1894), but ornamentation around the aperture where the mantle is largest is exaggerated only in some species with determinate growth (Paul, 1991; Vermeij and Signor, 1992; Venneij, 2001a); furthermore, contrary to Dall's prediction, not all of these animals have columellar folds. Indeed, the internal morphology of gastropods is highly stereotyped, not random, and it is unlikely that the mantle would always wrinkle uniformly (Signor and Kat, 1984). There are also no obvious differences in mantle size between species with and without internal ornamentation in general, or columellar folds in particular (pers. obs.).

Three interrelated hypotheses have been presented to explain how the folds affect the function of the columellar muscle, thereby explaining both why folds have evolved and why so many neogastropod lineages maintain them:

1. Guidance. Columellar folds guide the columellar muscle as the animal moves in and out of its shell (Signor and Kat, 1984; Ponder, 1972). The analogy here is that the folds act like a railroad track guiding a train; that is, they prevent the animal from slipping in its shell. One manner in which the folds may guide the muscle is by protruding far into the columellar muscle, restricting the muscle movement along the folds. In this event, the area of contact should be greater in species with folds than in those without. I test this prediction.

Signor and Kat (1984) limited their guidance hypothesis to high-spired, narrow (turritelliform) species, implying that the columellar muscle would slip within the shell unless folds guided its movement. Any attempt to extend this hypothesis to low-spired shell shapes must account for the absence of folds in some large neogastropods, such as Syrinx aruanus, whose shell can reach almost a meter in length (Harasewych and Petit, 1989).

2. Maneuverability. Columellar folds enhance a snail's ability to maneuver its shell (Fretter and Graham, 1962; Vermeij, 1978). A number of authors have assumed that the shape of the muscle's physical attachment to the columella is small and circular, like the adductor muscle attachment in bivalves (e.g., Linsley, 1978; Signor and Kat, 1984; Morita, 1993; Thompson et al., 1998). Vermeij (1978) assumed that the attachment occurs immediately over the folds and predicted that animals with folds would consequently have a larger surface area of muscle attachment. An animal with greater attachment area might be better at maneuvering its shell, for example when it swings the shell back and forth to fend off a predator (Thompson et al., 1998), or when it pries open the shells of prey (Taylor et al., 1980). This hypothesis has remained untested because dissections usually begin by removing and discarding the shell, and because the muscle easily detaches from a cracked shell.

3. Predator avoidance. Snails with columellar folds can withdraw more deeply into their shells (Dall, 1894), increasing their ability to escape from predators. Dall (1894) commented that snails with columellar folds retract more deeply, but presented no data in support of this idea. Since then, others have documented that snails that retract more deeply are better at escaping predators: they are harder to reach, and they take so long to handle that the predator eventually abandons the task (Vermeij, 1978, 1987). Although it is not immediately obvious why these behaviors might be associated with columellar folds, the data required to confirm Dall's claim are easy to collect.

I have developed procedures for dissecting gastropods while keeping the columellar muscle intact; employed a novel mathematical algorithm that converts a photograph of a snail into a three-dimensional surface from which I can measure areas; and examined neogastropod species that represent a range of columellar fold morphologies, as well as species with smooth columellae. Contrary to what has been assumed, the muscle attachment to the columella is complex and leaves no scar. None of the three hypotheses outlined above adequately explain the functional relationship between the columellar folds and the columellar muscle.

Materials and Methods

Sample

Quantitative data on the columellar muscle were collected from seven species with folds (from live genera and four families) and five species lacking them (from five genera and three families), affording phylogenetic breadth (Table 1). One of the species without folds, Strombus alatus, is not a neogastropod; it is a caenogastropod (a clade that contains the neogastropods) with shell shape similar to other species considered here. At least two and up to five specimens were studied for each species, for a total of 31 specimens for most measurements (36 specimens for attachment depth). These data were supplemented with qualitative observations from an additional nine species. All specimens were stored in 70% ethanol and deposited at the Field Museum of Natural History (FMNH), Chicago, Illinois. Except for Oliva sayana, all species have a functional operculum, eliminating any possible bias introduced by a relationship between folds and an operculum.

The sample includes species with a variety of columellar fold shapes and numbers (Table 2), but all have fairly modest folds. Prominent folds, such as those in the Mitridae, Volutidae, and Cancellariidae could not be included, because they were too difficult to collect or purchase alive. Oliva sayana has plications on the inner lip of the aperture that some authors describe as columellar folds (e.g., Abbott, 1974), but these do not continue inside the shell, and they therefore do not contact the columellar muscle, even when the animal is fully protracted. As such, these apertural plications cannot affect the function of the columellar muscle, so I consider Oliva sayana to be without folds.

Terminology describing orientation

A description of fold morphology requires terms that orient the reader to the snail shell (Fig. 1). In this paper, all terms refer to a snail shell in a standard orientation, with apex up and aperture visible (and on the right for dextral species). Top and bottom refer to positions along the coiling axis. The bottom of a whorl is farthest from the apex, whereas the top of the whorl is closest to the apex. The width of a feature is measured along a line parallel to the top-bottom axis, following the convention that the short axis of the columellar muscle represents width, whereas the long axis of the columellar muscle represents length (Fig. 1A, E, Fig. 2E). Apical and apertural refer to directions along the spiral of the shell towards the tip or opening respectively: the columellar muscle narrows apically, but is wide aperturally. A junction occurs where the bottom of one whorl meets the top of another. The depth of a feature indicates the number of revolutions between it and the aperture, where one revolution is 360[degrees]; for example, the columellar muscle attachment might begin at a depth of 300[degrees].

[FIGURE 2 OMITTED]

Dissections

Dissections were performed on live, untreated animals. Surprisingly, any treatment of animals, such as freezing, storing in ethanol, of relaxing in magnesium sulfate (Epsom salts), caused the muscle to detach from the shell, even when tugged only slightly. Fresh material is therefore essential to study columellar muscle attachment.

To expose the soft tissues while keeping them and the columella intact, 1 used a Dremel rotary tool with a 1.6-mm-diameter carborundum abrasive wheel to cut away the exterior. The size of the blade limited the specimens that could be dissected with precision to those with whorls larger than hall a centimeter. Thus, the attachment morphology could be quantified in the largest specimens of Nassarius vibex, but the available specimens of Columbella rusticoides were too small. The largest whorl of Terebra dislocata, a high-spired species, is only a few millimeters tall, so it could not be quantified with these methods. Although the most apertural point of the attachment was documented in Oliva sayana, the morphology of attachment throughout the test of its length was inaccessible, because the delicate columella cannot withstand even slight pressure.

To distinguish between muscle that was physically attached and muscle that was simply pressed against the columella, I used a blunt but flexible 34-gauge copper wire to probe between the tissue and columella. In all cases, only the top of the muscle (that closest to the junction between two whorls; see Figs. 1, 2) was physically attached. Since the bottom of the muscle was free, the attachment was not disturbed when probed.

Measurements

The measurements required to test the hypotheses (Table 3) were the standardized (see below) total area of muscle physically attached to the columella, the standardized total area of muscle in contact with the columella throughout the attachment, the depth of attachment, and the length of the attachment.

It was especially difficult to measure the total area of muscle physically attached to the columella (ATT in Figs. 1, 2). In these species, the columellar muscle attachment does not scar the shell, so the attachment area had to be observed directly. I tried removing strips of columellar muscle that were not attached to determine how much muscle was left on the columella, but this procedure inevitably destroyed the attachment. However, the attachment was so narrow relative to the total width of the columellar muscle that, when measured from digital photographs, it could be reasonably estimated as a thin but long box, only one pixel wide but many degrees long. The small bias introduced by this approximation should be the same in species with and without folds.

Another challenge was to measure the surface area of contact between the columellar muscle and the columella (CM in Figs. 1, 2G). The apertural end of the muscle grades into the foot (Voltzow, 1990; Thompson et al., 1998), so the only point that could be consistently identified at the apertural end of the columellar muscle was the point at which the muscle attachment began (ATT in Fig. 2E). I measured the total area of muscle in contact with the columella: beginning with the attachment, extending down the width of the muscle to the bottom of the whorl, and extending across the columella to include the most apical part of the muscle (CM in Figs. 1, 2G). Because the muscle always spanned the columella between the attachment and the bottom of the whorl, this measurement could be made in relaxed, contracted, and protracted animals. The position and length of the muscle attachment and the area under the attachment remain the same regardless of the animal's behavior. The exclusion of the area between the foot and the initial attachment was justifiable: it never included muscle that conformed to the morphology of the folds and was therefore not relevant to the present study; there was no reason to assume that it varied differently in species with and without folds.

Both the attachment area and the contact area were standardized to the columellar area (CA in Fig. 1; Table 3) to remove the effect of size. Columellar area is the area of the columella above, below, and including the length of attachment.

I used the depth of attachment as a proxy for depth of retraction, measured as the number of degrees behind the aperture. The two depths are intuitively related, because an animal cannot retract deeper than its attachment. Depth of attachment was much easier to measure, and it is not subject to behavioral variation. This proxy assumes that the amount of space between the columellar muscle attachment of the contracted animal and its operculum varies equally among species with folds and those without.

The length of attachment was defined as the number of degrees between the depth of attachment and the apical edge of the attachment, which occurred in the crease between the columella and the rest of the shell (Fig. 2F, G). Some muscle fibers and connective tissue extended even farther apically beyond this point, but they were small and thus likely to function differently from the rest of the muscle. My methods were too coarse to dissect this tiny strand of tissue accurately.

Because the length of attachment and the depth of attachment were both measured as the number of revolutions behind the aperture (in degrees), they were independent of size and did not need to be standardized.

Image processing

All measurements were taken from a series of digital photographs that documented each dissection. However, photographs distort three-dimensional data into two dimensions, so the surface areas in the photographs under-represent true areas. I therefore developed a procedure to process the series of photographs for each dissection, as well as a geometric algorithm that calculates the three-dimensional area projected into each photograph. The algorithm is presented in the Appendix.

Photographs were taken with a Nikon CoolPix 950 digital camera. The image plane of each photograph was parallel to the coiling axis, to which the optic axis was perpendicular. Each photograph also included a scale bar, was centered on a landmark, and showed the muscle attachment and the edge of the columella.

The outside of each shell was marked with radial lines running perpendicular to the junctions between whorls (LM in Fig. 1) every quarter of a whorl for small specimens and every eighth of a whorl for larger specimens (generally, those with shells longer than 2 cm). These landmark lines were used to locate the image within the series.

Each series consisted of between 4 and 12 photographs, with at least one photograph per quarter whorl. To create each series, all images were scaled and oriented identically. Only the middle 90[degrees] sector within each photograph was measured (45[degrees] on either side of the landmark line), thus eliminating overlap among the images (Fig. 2C).

The algorithm employed to estimate surface area converted tracings of photographs into three-dimensional surfaces (Fig. 2A-C). I used a mouse of mouse tablet (Wacom Graphire2) to trace the surface areas of the muscle attachment, the muscle in contact with the shell, and the columella within each image. Tracings were transformed according to the procedure described in the Appendix (implemented in MATLAB ver. 6.0; Fig. 2D), and then areas were summed from each image in the series. The procedure used to calculate the number of degrees from the aperture to the apertural and apical ends of the attachment is also described in the Appendix.

The 20 largest specimens were used to determine the precision of each measurement. I had two quarter-whorl series for these specimens, because they were photographed every eighth of a whorl; one series, for example, depicted the attachment centered on landmarks at 135[degrees], 225[degrees], 315[degrees], and 405[degrees], and the other centered on landmarks at 180[degrees], 270[degrees], 360[degrees], and 450[degrees]. I averaged the final measurements from the two series.

Fold modifier

The three-dimensional reconstruction technique employed here did not take into account the presence of folds. To account for folds, I employed a scale factor ("modifier") defined as the length of the projected outline of the folds divided by the minimum distance between the two endpoints of the folds (Fig. 1B; Eq. 1):

(1) modifier = [Length.sub.outline]/[Length.sub.minimum]

When there are no folds, the minimum length equals the length of the outline, so the lower limit of the modifier is 1.

I measured the fold modifier in each of the photographs of a series that clearly showed the folds' silhouette. This measurement is highly sensitive to shell orientation and to the endpoints of the fold outline, for which I used inflection points. To compensate for this sensitivity, I always used the maximum fold modifier; this approach favored finding a statistical difference between groups with and without folds. Although there was considerable variability in fold modifier values within a species, the variance for the entire sample of species with folds was low (fold modifier variance, 0.003; range, 1.0 to 1.2; 114 measurements over 17 specimens).

After measuring the surface area of the columellar folds, and transforming it according to the algorithm in the Appendix, I applied Equation 2:

(2) [Area.sub.final] = [A.sub.T] - [A.sub.fT] + ([A.sub.fT] x modifier)

where [A.sub.T] is the area transformed by the algorithm into an estimate of the area of a three-dimensional surface (cither attachment area or contact mea), and [A.sub.fT] is the similarly transformed area of the folds. In other words, I subtracted the transformed fold area from the attachment area, multiplied it by the fold modifier, added the product back to the attachment area, and then repeated the adjustment for the contact area.

The total surface area of the columella was not adjusted, because that measurement is used to standardize the other metrics. If fold surface area were added to columellar area, the difference between species with and without folds would be erased.

Statistics

Statistical comparisons between species with folds and those lacking them were performed with a Mann-Whitney U test using StatView 5.0 for Windows.

Results

Morphology of columellar muscle attachment

These dissections demonstrated that the columellar muscle attachment in neogastropods is far more complex than previously assumed (by authors such as Linsley, 1978; Signor and Kat, 1984; Morita, 1993; Thompson et al., 1998). The muscle did not leave a scar, so there was no macroscopic feature on the columella that approximated attachment shape. The shape of the attachment was similar in all species, regardless of the presence of folds (Fig. 2E-G). In most of the species examined, the attachment began about three-quarters of a whorl (~275[degrees]) back from the aperture (Fig. 3C, raw data for the histogram is in Table 4). The depth of attachment might be much deeper in high-spired shells. In Terebra dislocata, attachments began about two whorls back from the aperture (pers. obs.). T. maculata and T. subulata, muscles were previously reported to attach more deeply at about 2.5 and 4.5 whorls back from the aperture, respectively (Signor and Kat, 1984). In general, the attachment was long and sometimes extended for more than one revolution; it was restricted to the upper edge of the muscle (blue line is ATT in Fig. 2E-G).

[FIGURE 3 OMITTED]

The relative position of the attachment changed as it moved from the apertural edge of the muscle across to the apical edge. At its most apertural end, the attachment lay immediately under the junction of the two whorls. Tracing it apically along the rising junction, the attachment shifted in position progressively downward and across the columella toward the bottom of the whorl, with the rate of descent gradually increasing. Shortly before reaching the bottom of the whorl, the angle of the attachment changed dramatically, becoming more oblique to the junction and curving sharply down to the base of the whorl; this is where the attachment crossed the folds when they were present. Here the muscle was remarkably less robust than elsewhere along its length. Farther apically, the muscle was only a thin extension situated in the crease between the columella and the base of the whorl. Within the area where the muscle was attached, the muscle width was maximal at its apertural end and minimal towards the apex.

Functional hypotheses

Contrary to the prediction drawn from the functional hypotheses outlined in the Introduction, no significant differences were found between species with and without folds with respect to the surface area of muscle attachment (P = 0.71), the amount of contact between muscle and columella (P = 0.16), or the length of muscle attachment (P = 0.21) (Fig. 3; Table 4). The depth of attachment in species with folds was significantly closer to the aperture than in species without folds (P = 0.020), which is opposite to what was predicted.

Three specimens (Busycon contrarium FMNH299449, B. contrarium FMNH299459, and Cantharus cancellarius FMNH299487) had fold modifier values close to unity (1.02, 1.00, and 1.04, respectively), meaning that the folds were almost flush with the columella and thus did not protrude enough to increase the topographic relief above that of specimens lacking folds. The data were consequently re-analyzed categorizing these three specimens as lacking folds. Results were identical for the contact area, attachment area, and length of attachment. However, the depth of attachment was no longer significantly different between species with folds and those lacking them (P = 0.19).

Discussion

Using novel methods to examine the columellar muscle in situ, I have described, for the first time, the surprisingly complex attachment of the columellar muscle in neogastropods. This attachment is remarkable for its delicate structure, lack of discernible muscle scars, and considerable length. The data presented here do not support any of the previously published hypotheses thought to explain the function of columellar folds, although the species included do not exhibit the most exuberantly developed folds. These data cast doubt on the hypothesis that folds act as struts, guiding the columellar muscle as the animal protracts from, and retracts into, its shell. Furthermore, the muscle probably does not need to be guided, because it is a muscular hydrostat. The muscle probably mirrors the morphology of the folds simply because it is physically adjacent to them. I reject the hypotheses that animals with folds maneuver better because their attachment area is larger, and that these animals avoid predators by retracting deeper. While I reject these hypotheses as general explanations for columellar fold function in neogastropods as a whole, future work may demonstrate that some of them adequately explain function within groups of species with similarly shaped folds.

Methodology

I developed two novel methods in this research: one is a practical dissection technique, and the other is ah analytical approach for measuring distances and areas from photographs of specimens. With the dissection technique, I described the columellar muscle attachment in 20 neogastropods and one caenogastropod (Table 1). The soft tissues of other gastropods can be dissected without damaging the columella, and future applications of this approach will provide a more general understanding of how soft tissues are situated within the shell. With the analytical approach, I determined the relative position of soft tissues and shell features. I quantitatively characterized the columellar muscle in 11 species of neogastropods and one caenogastropod (Tables 1, 3, 4). This algorithm will work for any organism arranged as a stack of circles--echinoderms, cnidarians, foraminifera, diatoms, and mushrooms, for example.

The measurements and their analysis test on three assumptions. First, to measure the area of contact between the columellar muscle and the columella, I assumed that the amount of muscle apertural to the attachment varies equally in species with and without folds. Second, I also assumed that the attachment area was only one pixel wide, which seems justified by the observation that the attachment was quite thin relative to the total width of the muscle. Third, areas were inflated by the algorithm that transformed the two-dimensional data, because the columella was assumed to be perfectly symmetrical (see Appendix). All of these assumptions were justified, especially in this first attempt to quantify differences in the columellar muscle. Furthermore, there is no a priori reason to believe that they would affect species with folds differently than species lacking them.

Note that the measurements are coarse (Table 4), and that subtle differences in contact area, attachment area, depth of attachment, and length of attachment cannot be resolved with these methods.

Columellar muscle attachment

The complexity and extent of the columellar muscle attachment has gone unrecognized because the attachment itself is remarkably delicate. A slight tug in the wrong direction (away from the aperture, toward the apex) tore the muscle from the columella, and the strength of the attachment deteriorated rapidly in preserved or relaxed animals. Its tenuous nature probably reflects the interplay between the physical mechanism of adhesion and the shape of the adhesive surface. Although the muscle was easily detached from the columella, the animal never naturally experiences a force pulling on the attachment from the angle or location I used during dissection; if the shell is opened as I have opened it, the animal is already too exposed to save itself from predators. An adhesive joint that can withstand large shear stresses will frequently fail when peeled (Portelli, 1986). The muscle attachment is analogous to a long piece of tape on a tabletop. When peeled backward, perpendicular to the table, the tape detaches easily, but when pulled along its length, it has great strength.

Surprisingly, none of the species studied here have muscle scars, even though scars are found in all major groups of shelled molluscs throughout their history (e.g., Abbott, 1974; Lindberg, 1985; Pojeta, 1985; Doguzhaeva and Mutvei, 1996; Isaji et al., 2002). In vertebrates, however, muscles frequently do not leave attachment scars (McGowan, 1982; Bryant and Seymour, 1990), especially when they insert directly into bone instead of attaching to a tendon which inserts into bone. In snails, the columellar muscle inserts into an epithelium that in turn inserts into the shell (Tompa and Watabe, 1976). Additional work is required to determine whether neogastropods and vertebrates lack muscle scars for similar reasons.

The fact that the muscle attachment is so much longer than previously thought (by authors such as Linsley, 1978; Morita, 1993; Thompson et al., 1998) has interesting implications for how the columellar muscle functions. Thompson et al. (1998) calculated, on theoretical considerations, the force required to buckle the columellar muscle and the amount of torsion the muscle could exert. The muscle, which has a crescentic cross section, buckled more easily and could not exert as much torsional force as a cylindrical muscle with a circular cross section. However, these authors assumed that the muscle was attached at only one end rather than throughout its length. The true, side-long attachment should help the muscle resist compressive forces (J. T. Thompson, St. Joseph's University, pers. comm.), so that the mechanical disadvantage due to buckling may not be so severe. Similarly, the net torsion exerted must be reconsidered in light of the new attachment data.

Guidance

I hypothesized that folds guide the columellar muscle during protraction and retraction by protruding far into the columellar muscle, compelling the muscle to move along the folds. I reasoned further that, if folds act as struts, then they should protrude far enough into the muscle to significantly increase the amount of contact between the muscle and columella. For the species analyzed here, however, there was no significant difference in the contact area or length of attachment between species with folds and those lacking them. Therefore, the folds-as-struts hypothesis, as explained here, was not supported.

From another perspective, the methods were relatively coarse, and the data were poorly resolved. If these methods are applied to species with a subtle fold topology, then no significant increase in the contact area may be detectable. In species with folds, I compared the unadjusted contact area to the contact area after it had been adjusted with the fold modifier. The two metrics differed by more than 2% in only one specimen, and the average difference was only 0.2% (n = 17). This difference is less than the precision of the measurement of contact area, which is only to one decimal place. Therefore, although the topography of folds does not increase the contact area in the specimens considered here, the contact area may be greater in species with more prominent folds, such as those in the Volutidae, Mitridae, and Cancellariidae. Thus, additional work with these species and with methods providing higher resolution may lend support to the guidance hypothesis and its corollary that folds act as struts.

A consideration of the association between the area of contact and the presence of folds suggests other functional relationships. For example, if the advantage offered by strut-like folds were offset by the benefit of a large contact area, species with folds should have a significantly smaller area of contact than those without. Similarly, species with folds could have the same area of contact as species without folds, provided that the increase in contact due to the protruding folds was offset by a shorter attachment length. However, no such significant differences were observed.

The guidance hypothesis assumes that, without the resistance offered by folds, the muscle would slip along the columella during both retraction and protraction, presumably causing the animal to expend more energy. However, the arrangement of fibers within the muscle, including some fibers that are wound obliquely around the robust, apertural end of the muscle, suggests that the fibers, and not the columellar folds, control the path of the muscle when it contracts (Thompson et al., 1998). Because the muscle is attached along its top edge (Fig. 2), it will shift across the columella when the oblique fibers contract. In light of this newer evidence about the columellar muscle in particular and the muscular hydrostats of molluscs in general (Kier and Smith, 1985, 1990; Hodgson and Trueman, 1987; Kier, 1988; Marshall et al., 1989), the muscle seems to function in the way that was previously thought inefficient (Signor and Kat, 1984).

Signor and Kat (1984) formulated the guidance hypothesis in part because Signor (1982) correlated burrowing behavior in high-spired gastropods with columellar folds: 55 of 59 burrowing species had folds, but only I in 46 non-burrowing species did. He concluded that columellar folds guide the columellar muscle in burrowing animals (Signor and Kat, 1984). However, 40 of his 59 burrowers were in the Terebridae, and only 4 of his 11 families included non-burrowing species. Thus, his results may be explained by phylogenetic bias and should be reanalyzed with comparative methods based on phylogenetic contrasts (as in Harvey and Pagel, 1991) once the appropriate estimates of relationship are available. The advantage of folds to burrowing animals is not obvious, especially if the guidance hypothesis is not true. Furthermore, many species with folds do not burrow (G. J. Vermeij, University of California, Davis, pers. comm.). The species considered here cannot be used to explore the relationship between folds and burrowing behavior, because species were not sampled randomly across burrowing and non-burrowing habitats.

In conclusion, since the inner surface of the columellar muscle is an exact impression of the columellar folds, it is only reasonable to assume that the muscle moves along the folds. This assumption does not require, however, that the folds dictate the muscle's motion. I suspect that the similarity in the shape of the muscle and folds is due simply to their proximity, and that the direction the muscle moves is governed instead by attachment morphology and muscle fiber orientation.

Maneuverability

As with contact area, the folds added insignificantly to the attachment area. The attachment was so long, and so much of it was distant from the folds, that the folds would need to protrude into the muscle six times more than they do (i.e., multiply the fold modifier by 6) to significantly increase attachment area in species with folds at the [alpha] < 0.05 level. If animals with folds are better able to maneuver their shells, it is not because they have a greater surface area of muscle attachment.

Signor and Kat (1984) suggested that the columellar muscle is divided by the folds into functionally discrete units joined only by connective tissue. However, judging by the observations presented here, the divisions they describe are probably part of a gradation between the robust, most apertural, part of the muscle and the weak, more apical pan (left and right sides of Fig. 2E-G). Since Signor and Kat (1984) did not mention the frequency or placement of their histological sections, nor illustrate their results, it is difficult to reevaluate their conclusions in the light of the newly recognized attachment morphology. The muscle histology of high-spired species with and without folds should be compared to determine whether the muscle is subdivided, and if so, whether those subdivisions are constrained by, of at least correspond to, columellar folds.

Maneuverability in a number of terrestrial pulmonates does appear to be enhanced by physically distinct subdivisions of the columellar muscle (Suvorov, 1993, 1999a, b, c). In these taxa, the columellar muscle originates from the most apical point (this is the only part of the muscle that is attached) and is divided into left and right pedal retractors, and left and right buccal mass retractors. These four branches continue to subdivide closer to the aperture. The four functional groups of the muscle are separated by a septum of connective tissue, but apertural teeth and columellar folds may playa secondary role in keeping subsets of branches separated. Thus, columellar ornamentation in pulmonates apparently evolved for a different reason than it did in neogastropods.

Predator avoidance

I was unable to substantiate Dall's (1894) claim that animals with folds retract deeper into their shells. Instead, animals lacking folds retract more deeply, because they have a significantly deeper attachment site. A larger sample of species is required to confirm this conclusion. Because all of the specimens from which quantitative data were obtained were collected in spring, seasonal variability in growth rate and attachment site were not considered. Variability in growth rate may be especially important to consider in genera such as Busycon, which exhibit highly episodic growth.

The depth of attachment was surprisingly constant among most species considered here (median depth = 295[degrees]; n = 36). Interestingly, the distribution of attachment depth was bimodal, with medians at 280[degrees] (n = 31) and 630[degrees] (n = 5) (Fig. 3), although, admittedly, there were few specimens in the higher mode. One species, Stramonita haemastoma, had specimens in both modes. This bimodality may reflect episodicity in growth.

Despite these overall similarities, the shallower attachment depth of species with folds implies that columellar folds do not help gastropods to escape from their predators by retracting into their shell. Moreover, my qualitative laboratory and field observations suggest that neogastropods are not subject to particularly intense predation. For example, a number of species (Leucozonia nassa, Stramonita haemastoma, S. rustica, Pisania tincta, and Melongena corona) neither retract quickly nor re-orient themselves quickly when their shells are overturned (pers. obs.). I have found wild specimens of Latirus mediamericanus (fasciolariid, with folds) lying on coral, each with the aperture pointed upward and the loot hanging outside the aperture.

Do folds have a single function?

Although the function of columellar folds remains unidentified, there are potentially fruitful paths for future research. As discussed above, the correlation between the presence of folds and burrowing habit in high-spired gastropods (Signor, 1982) must be studied in more detail. Also, columellar folds might strengthen the shell, thereby protecting the animal from predators. External features of the shell, such as thickness and the presence of spines, have been shown to increase resistance to predators, making it more difficult for a durophagous predator to break a snail's shell (reviewed in Vermeij, 1993; Kohn, 1999). In fact, some species have a corrugated shell, which presumably increases strength while minimizing the costs associated with building and moving a heavy shell (Vermeij, 1993). Perhaps, in a similar manner, columellar folds protect against predators by increasing the strength of the inner lip while minimizing the cost of thickening the entire columella. Supporting this idea, Hughes and Elner (1979) report that crabs open Nucella lapillus shells that have thin columellae by snapping the inner lip, breaking the shell in half. In contrast, N. lapillus individuals with thickened columellae are attacked at the apex of the shell. Both N. lapillus phenotypes lack folds, but these observations imply that strengthening the inner lip makes the columella harder to break more apically. However, predators of gastropods rarely break the inner lip. Most predators either crush the shell at its apex or peel back the shell al the outer lip (Vermeij, 1982; Johannesson, 1986); folds are simply ill-placed to affect either of these actions directly. There may be no evidence of damage on columella, as there are with failed attempts at predation in other parts of the shell, because when these attacks succeed, the shell fails catastrophically (G. J. Vermeij, pers. comm.).

Vermeij (1978) has observed that, within at least the families Vasidae and Mitridae, columellar folds are more common in tropical species, suggesting that the presence of folds might be correlated with latitude and increased predation intensity. This observation should certainly be tested quantitatively, although it is difficult to interpret the meaning of latitudinal diversity trends (Roy et al., 1998).

Columellar folds may not have a function. Still, convergence is considered to be some of the best evidence for adaptation (Raup and Gould, 1974; Harvey and Pagel, 1991; Larson and Losos, 1996), and columellar folds have evolved at least six times within different families of neogastropods (Price, 2001). Direct observations on how fold shape has evolved over time may reveal patterns of evolution that are consistent with adaptation. This approach would require a phylogenetic context (Harvey and Pagel, 1991; Larson and Losos, 1996), although there are currently no well-resolved phylogenies that include a sufficiently large number of species with and without folds to give power to such ah analysis. With the phylogenetic comparative method, it would be possible to determine whether folds evolved by "hitchhiking" along with demonstrably adaptive characters (Maynard Smith and Haigh, 1974).

On the other hand, folds may have evolved as a common solution to a number of problems, especially because the function of folds in pulmonates obviously differs from that in neogastropods. Functional experiments on species from a number of smaller clades that contain closely related species with and without folds should be conducted to identify functions unique to those smaller clades. If columellar folds serve different functions in different clades, then they might be an easy-to-evolve, flexible solution to a number of problems.

Conclusions

Columellar folds probably do not guide the columellar muscle. Rather, the motion of the muscle is likely determined by muscle fiber orientation and by the attachment to the shell, which is along the upper edge of the muscle. The geometry of the attachment is probably responsible for its adhesive strength, and the weak physical connection between muscle and shell is not. The methods employed here show no association between the presence of folds and the length of columellar muscle attachment, surface area of attachment, or depth of attachment. The widely observed similarity in morphology between the folds and the columellar muscle may be due simply to their physical juxtaposition rather than to any functional relationship, with folds having some other and presently unknown functions. Because folds have evolved multiple times, the most plausible explanation for their existence might be that they are an easy-to-evolve solution to a number of functional demands.

Appendix

Measuring True Surface Area and Location on a Shell from a Series of Photographs

Measuring surface area

A photograph defines an XY-plane that contains an object (Appendix Fig. 1A), and the pixels within the object are "on," whereas those outside the object are "off." That object is a projection of a surface, Z, onto the XY-plane. The projected surface area, S[A.sub.z], is defined as

(A1) S[A.sub.z] = [[integral.sub.x] [[integral.sub.y] (1 + [([differential]z/[differential]x).sup.2] + [([differential]z/[differential]y).sup.2]) dxdy

(equation 6a in Thomas and Finney, 1984).

Because a digital photograph is pixelated, I approximated S[A.sub.z] by calculating the surface area of each pixel, i, then summing those values over all n pixels:

(A2) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII],

where [A.sub.i] is the area of the pixel. Since the area of a pixel is 1, Equation A2 reduces to

(A3) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII].

I found the partial derivative of Z with respect to x and the partial derivative of Z with respect to y by assuming that the object was a series of circles stacked on top of each other. Each row in the object corresponded to one circle, and all circles were centered about the Y-axis, which is also the coiling axis. Anyone familiar with the shape of neogastropods will recognize that the columella is somewhat asymmetrical. Imposing symmetry on the columella inflated true surface area, but this deviation was uniform across randomly sampled specimens with and without folds (28% inflation, st. dev. = 15%, n = 10).

Consider one row of pixels, i, of the photograph. The number of "on" pixels in that row equals the diameter of the circle, because the circle was projected straight onto that row. Thus, the circle's radius and origin were both known, the surface function, [z.sub.i], for a given row was

(A4) [x.sup.2.sub.i] + [z.sup.2.sub.i] = [r.sup.2.sub.i]

(Appendix Fig. 1B), and the partial derivative was

(A5) [differential][z.sub.p]/[differential][x.sub.p] = -[x.sub.p]/[square root of ([r.sup.2.sub.i] + [x.sup.2.sub.p)]

where p was any pixel in row i of the object.

The partial derivative of Z in the x-direction represented the distortion of the projection due to the curvature of the circle about the coiling axis. Therefore, a pixel located immediately on or above the coiling axis did not have any horizontal distortion, and the two pixels 90[degrees] from the coiling axis were the most severely distorted.

To calculate the partial derivative of Z with respect to y, I expressed the edge of the image as f(y) = r. Rewriting Equation A4 gives:

(A6) [x.sup.2.sub.i] + [y.sup.2.sub.i] = f[([y.sub.i]).sup.2]

where f(y) was found empirically by fitting a second-degree polynomial to the edge. The partial derivative [differentialz/[differential]y was evaluated from this polynomial.

The resulting area was measured in pixels.

Identifying a target region

A curved surface projects a 180[degrees] sector onto a row, so when a series contains photographs taken every 90[degrees] about a coiling axis, the photographs overlap. I eliminated overlap by using only the middle of each image (dashed lines in Appendix Fig. 1). This approach has the added benefit of using the region of the photograph with the best focus and least distortion.

One row of "on" pixels represented a circle projected onto its diameter. The coiling axis marked the midpoint of the diameter, and the end points of the row were 45[degrees] and -45[degrees] from the coiling axis. If we draw the circle, we can see that its radius is the hypotenuse of ah isosceles right triangle (Appendix Fig. 1B). The sides of this triangle equal the x-coordinate for the boundary of the target region.

Measuring degrees from aperture

I used the same circle to locate point [P.sub.i] relative to the aperture (Appendix Fig. 1), to calculate the edges of the attachment. In this case, I determined the X-coordinate of the point from the photograph, which is simply the distance between the coiling axis and [P.sub.i]. Here, the X-coordinate was known, but the triangle was not necessarily isosceles, so the angle, [theta] was not known. The angle that defined the are between the coiling axis and [P.sub.i] was calculated:

(A7) [theta] = asin(x/r)

If [P.sub.i] was apertural to the nearest landmark, I subtracted [theta] from the landmark's depth. Suppose, for example, that [P.sub.i] was depth of attachment, the curve f(y) in Appendix Figure I was coincident with the landmark at 270[degrees], and [theta] equals 20[degrees]. The value of attachment depth would be 290[degrees]. If [P.sub.i] were apical to the nearest landmark, then I would have added [theta] to the landmark's depth.
Table 1

Species examined

                                          Collection
               Species                      site *           Family

Busycon contrarium (Conrad, 1840)         FS             Melongenidae
Busycon spiratum (Lamarck, 1816)          FS             Melongenidae
Fasciolaria hunteria (Perry, 1811)        FS, WFS, SM    Fasciolariidae
Fasciolaria tulipa (Linnaeus, 1758)       HT             Fasciolariidae
Nassarius vibex (Say, 1822)               FS, WFS        Nassariidae
Triplofusus giganteus (Kiener, 1840)      HT             Fasciolariidae
Cantharus cancellarius (Conrad, 1846)
  ([dagger])                              DIR            Muricidae
Chicoreus florifer distans (Adams,
  1855)                                   WFS            Muricidae
Melongena corona (Gmelin, 1791)           FS, WFS        Melongenidae
Stramonita haemastoma (Linnaeus, 1767)    WFS            Muricidae
Strombus alatus (Gmelin, 1791)            P              Strombidae
Urosalpinx perrugata (Conrad, 1846)       WFS, SM, ST    Muricidae

Columbella rusticoides (Heilprin,
  1886)                                   DIR            Columbellidae
Leucozonia nassa (Gmelin, 1791)           S              Fasciolariidae
Opeatostoma pseudodon (Burrow, 1815)      IV             Fasciolariidae
Pleuroploca salmo (Wood, 1928)            B              Fasciolariidae
Terebra dislocata (Say, 1822)             HT             Terebridae
Vasum muricatum (von Born, 1778)          G              Vasidae
Cypraea cervus (Linnaeus, 1771)           G              Cypraeidae
Oliva sayana (Ravenel, 1834)              SM, HT         Olividae
Polystira nobilis (Hinds, 1843)           GC             Turridae

               Species                    Folds         Museum ID

Busycon contrarium (Conrad, 1840)          Yes     299449, 299459
Busycon spiratum (Lamarck, 1816)           Yes     299444, 299463,
                                                     299468, 299472
Fasciolaria hunteria (Perry, 1811)         Yes     299450, 299492,
                                                     299493
Fasciolaria tulipa (Linnaeus, 1758)        Yes     299448, 299456
Nassarius vibex (Say, 1822)                Yes     299475, 299477
Triplofusus giganteus (Kiener, 1840)       Yes     299441, 299442
Cantharus cancellarius (Conrad, 1846)
  ([dagger])                               Yes     299486, 299487
Chicoreus florifer distans (Adams,
  1855)                                    No      299451, 299458
Melongena corona (Gmelin, 1791)            No      299453, 299457
Stramonita haemastoma (Linnaeus, 1767)     No      299452, 299454,
                                                     301941
Strombus alatus (Gmelin, 1791)             No      301942, 301943
Urosalpinx perrugata (Conrad, 1846)        No      299481, 299482,
                                                     299483, 299484,
                                                     299485
Columbella rusticoides (Heilprin,
  1886)                                    Yes     299473 299474
Leucozonia nassa (Gmelin, 1791)            Yes     299506, 299520,
                                                     299521, 299522,
                                                     299526, 299527,
                                                     299530, 299531
Opeatostoma pseudodon (Burrow, 1815)       Yes     299496
Pleuroploca salmo (Wood, 1928)             Yes     299494
Terebra dislocata (Say, 1822)              Yes     299488, 299489,
                                                     299490, 299491
Vasum muricatum (von Born, 1778)           Yes     299500
Cypraea cervus (Linnaeus, 1771)            No      299495
Oliva sayana (Ravenel, 1834)               No      299460, 299461,
                                                     299466, 299469
Polystira nobilis (Hinds, 1843)            No      299497, 299499

               Species                              Data type

Busycon contrarium (Conrad, 1840)         Quantitaive
Busycon spiratum (Lamarck, 1816)          Quantitaive
Fasciolaria hunteria (Perry, 1811)        Quantitaive
Fasciolaria tulipa (Linnaeus, 1758)       Quantitaive
Nassarius vibex (Say, 1822)               Quantitaive
Triplofusus giganteus (Kiener, 1840)      Quantitaive
Cantharus cancellarius (Conrad, 1846)
  ([dagger])                              Quantitaive
Chicoreus florifer distans (Adams,
  1855)                                   Quantitaive
Melongena corona (Gmelin, 1791)           Quantitaive
Stramonita haemastoma (Linnaeus, 1767)    Quantitaive
Strombus alatus (Gmelin, 1791)            Quantitaive
Urosalpinx perrugata (Conrad, 1846)       Quantitaive
Columbella rusticoides (Heilprin,
  1886)                                   Qualitative
Leucozonia nassa (Gmelin, 1791)           Qualitative
Opeatostoma pseudodon (Burrow, 1815)      Qualitative
Pleuroploca salmo (Wood, 1928)            Qualitative
Terebra dislocata (Say, 1822)             Qualitative
Vasum muricatum (von Born, 1778)          Qualitative
Cypraea cervus (Linnaeus, 1771)           Qualitative
Oliva sayana (Ravenel, 1834)              Qualitative ([double dagger])
Polystira nobilis (Hinds, 1843)           Qualitative

* Collection sites: B, Bique, Panama (Pacific Ocean); DIR, Dog Island
Reef, Florida (Gulf of Mexico); FS. Florida State University Marine
Lab, Turkey Bayou, Florida (Gulf of Mexico); G, Galeta, Panama
(Caribbean Sea); GC, Golfo de Chiriqui. Panama (Pacific Ocean); HT,
Hammock Trail, near St. Joseph Bay, Gulf County, Florida (Gulf of
Mexico); IV, Isla Venado near Playa Veracruz, Panama (Pacific Ocean);
P, Purchased from Gulf Specimen Aquarium and Marine Biological Supply,
Panacea, Florida; S, Sebastian, Florida (Indian River County); SM, St.
Mark's Wildlife Refuge, Florida (Gulf of Mexico); ST, Beach at St.
Teresa, Florida (Gulf of Mexico); WFS, West side of Florida State
University Marine Lab on oyster bar.

([dagger]) Tentatively placed in Soleneistra by Vermeij (2001b).

([double dagger]) Only the attachment depth was measured.

Table 2

Fold morphology in species examined

        Species                          Fold morphology

Busycon contrarium         1 subtle fold at the bottom of the whorl,
                             distinguished by a groove and angled
                             obliquely; difficult to observe at
                             aperture, but more prominent in older
                             whorls
Busycon spiratum           As in B. contrarium, but slightly more
                             defined
Cantharus cancellarius     1 fold at the bottom of the whorl, angled
                             obliquely; broader than in other species
Columbella rustticoides    1 fold immediately at the bottom of the
                             whorl
Fasciolaria hunteria       2 folds al the bottom of the whorl, angled
                             obliquely; the lower edge of the bottom
                             fold coincides with the edge of the
                             columella
Fasciolaria tulipa         As in F. hunteria, but with 3 folds
Leucozonia nassa           3 folds, angled obliquely and closely spaced
Nassarius vibex            1 well-defined fold at the bottom of the
                             whorl, angled obliquely; square, rather
                             than rounded, profile
Opeatostoma                As in L. nasssa
  pseudodon
Pleuroploca salmo
Terebra dislocata          2 large, broad folds spread throughout
                             whorl; the bottom fold is more prominent
                             than the top one
Triplofusus giganteus      As in F. tulipa, but top fold is more subtle
                             than the others
Vasum muricatum            5 folds in "1 prominent--1 weak--1
                             prominent--weak--1 prominent" pattern;
                             folds angled more perpendicular to coiling
                             axis than in any of the other species and
                             spread throughout the bottom two-thirds of
                             the whorl

Table 3

Summary of measurements required to test hypotheses

                                                         Use modifier
                                                         to adjust for
                                                             fold
           Measurement                  Hypothesis        topography?

Standardized total area of muscle    Maneuverability          Yes
  physically attached to the
  columella (ATT/CA in Fig. 1)
Standardized surface area of             Guidance             Yes
  contact between columella and
  columellar muscle throughout
  attachment when animal is
  relaxed (CM/CA in Fig. 1)
Depth of attachment, in degrees      Retraction depth         No
Length of attachment, in degrees     Maneuverability          No

Table 4

Measurements for all specimens

                                                         Standardized
                                                          attachment
                                                           area (x
Species                       Museum ID       Folds      [10.sup.-3])

Busycon contrarium              299449         Yes           3.0
Busycon contrarium              299459         Yes           2.7
Busycon spiratum                299444         Yes           2.2
Busycon spiratum                299463         Yes           1.8
Busycon spiratum                299468         Yes           2.3
Busycon spiratum                299472         Yes           2.4
Cantharus cancellarius          299486         Yes           3.6
Cantharus cancellarius          299487         Yes           3.4
Fasciolaria hunteria            299450         Yes           2.5
Fasciolaria hunteria            299492         Yes           2.4
Fasciolaria hunteria            299493         Yes           2.4
Fasciolaria tulipa              299448         Yes           2.5
Fasciolaria tulipa              299456         Yes           2.7
Nassarius vibex                 299475         Yes           1.9
Nassarius vibex                 299477         Yes           4.6
Triplofusus giganteus           299441         Yes           3.9
Triplofusus giganteus           299442         Yes           4.7
Chicoreus florifer distans      299451          No           3.1
Chicoreus florifer distans      299458          No           3.1
Melongena corona                299453          No           2.7
Melongena corona                299457          No           2.3
Oliva sayana                    299460          No            ND
Oliva sayana                    299461          No            ND
Oliva sayana                    299465          No            ND
Oliva sayana                    299466          No            ND
Oliva sayana                    299469          No            ND
Stramonita haemastoma           299452          No           2.3
Stramonita haemastoma           299454          No           2.2
Stramonita haemastoma           301941          No           3.0
Strombus alatus                 301942          No           2.4
Strombus alatus                 301943          No           2.6
Urosalpinx perrugata            299481          No           1.2
Urosalpinx perrugata            299482          No           4.7
Urosalpinx perrugata            299483          No           3.4
Urosalpinx perrugata            299484          No           3.5
Urosalpinx perrugata            299485          No           5.0

                                             Depth of     Length of
                             Standardized   attachment    attachment
Species                      contact area   (degrees)     (degrees)

Busycon contrarium               0.5           210           330
Busycon contrarium               0.5           240           330
Busycon spiratum                 0.4           280           230
Busycon spiratum                 0.3           270           290
Busycon spiratum                 0.4           270           450
Busycon spiratum                 0.4           250           270
Cantharus cancellarius           0.5           350           330
Cantharus cancellarius           0.3           360           230
Fasciolaria hunteria             0.5           310           290
Fasciolaria hunteria             0.5           280           370
Fasciolaria hunteria             0.5           260           390
Fasciolaria tulipa               0.6           260           390
Fasciolaria tulipa               0.5           230           420
Nassarius vibex                  0.5           630           250
Nassarius vibex                  0.4           570           240
Triplofusus giganteus            0.7           290           360
Triplofusus giganteus            0.8           280           370
Chicoreus florifer distans       0.4           270           190
Chicoreus florifer distans       0.4           330           260
Melongena corona                 0.6           270           460
Melongena corona                 0.5           320           400
Oliva sayana                      ND           280            ND
Oliva sayana                      ND           260            ND
Oliva sayana                      ND           370            ND
Oliva sayana                      ND           300            ND
Oliva sayana                      ND           290            ND
Stramonita haemastoma            0.4           320           370
Stramonita haemastoma            0.4           280           350
Stramonita haemastoma            0.4           660            90
Strombus alatus                  0.2           590           210
Strombus alatus                  0.2           650           170
Urosalpinx perrugata             0.4           310           300
Urosalpinx perrugata             0.5           330           330
Urosalpinx perrugata             0.3           360           320
Urosalpinx perrugata             0.6           420           170
Urosalpinx perrugata             0.5           360           310

ND--not determined. Measurements could not be taken because the
columella is too delicate to survive dissection.


Acknowledgments

I thank Dan Reuman, Moon Duchin, and Chris Degni for generously devoting their time to help develop the algorithm to reconstruct the 3-D surface of the shell. Jason Goodman and Gidon Eshel helped debug the programs that implemented the algorithm. Deirdre Gonsalves-Jackson, Greg Farley, Cheryl Swanson, Jessica Cande, the Smithsonian Marine Station, and the Florida State University Marine Lab helped with field collections. Jochen Gerber, Janeen Jones, and Martin Pryzdia at the Field Museum of Natural History helped deposit specimens. Additional thanks to Michael LaBarbera, David Jablonski, Rudiger Bieler, Susan Kidwell, Peter Wagner, and colleagues at the University of Chicago for support throughout this research and helpful comments on the manuscript. Geerat J. Vermeij, two anonymous reviewers, and especially Michael J. Green berg provided helpful suggestions that greatly improved this paper. This material is based upon work supported by the National Science Foundation under Grant No. 0073248. NSF grant 9903030 to David Jablonski, the Conchologists of America, the Link Foundation and Smithsonian Marine Station, and the University of Chicago Hinds and Gurley Funds provided additional support.

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REBECCA M. PRICE

Department of Geophysical Sciences, University of Chicago, 5734 S. Ellis Ave., Chicago, Illinois 60637

Received 22 October 2002; accepted 29 August 2003.

E-mail: rmprice@uchicago.edu
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Author:Price, Rebecca M.
Publication:The Biological Bulletin
Date:Dec 1, 2003
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