Theoretical morphological analysis of differential morphospace occupation patterns for terrestrial and aquatic gastropods

Abstract

Despite the morphological diversity of organisms, they only occupy a fraction of the theoretically possible spectrum (i.e., morphospace) and have been studied on several taxa. Such morphospace occupation patterns are formed through evolutionary processes under multiple constraints. In this study, we discovered a differential morphospace occupation pattern between terrestrial and aquatic gastropods and subsequently attempted to quantitatively understand these differences through morphospace analysis. These differential occupation patterns between terrestrial and aquatic species were observed in the morphospace of spire height and aperture inclination, including a bimodal distribution of shell height in terrestrial species alongside the absence of high-spired shells with high aperture inclination. Although terrestrial species were distributed along optimal lines of shell instability and shell hindrance to locomotion, aquatic species were distributed not only along this line but also within a suboptimal region of the low spire with low inclination. Based on numerical simulation and biometric analysis, here we propose the hypothesis that this difference was caused by the aquatic species being able to adopt a posture with the growth direction perpendicular to the substrate due to reduced functional demands. Our results provided an ultimate explanation for the differential occupation patterns between habitats alongside an overview of the morphospace.

Introduction

Organisms display morphological diversity, yet such organisms only occupy a small fraction of the theoretically possible spectrum, which is known as morphospace (McGhee, 1998; Raup, 1966). Such morphological diversity and occupation patterns have been formed through evolutionary processes under functional, environmental, developmental, structural, and phylogenetic constraints (Polly, 2008; Raup, 1972; Seilacher, 1970, 1991; Seilacher & Gishlick, 2015). One ultimate explanation for this is an adaptation: Organisms in a taxon are distributed on functional regions in the morphospace (McGhee, 1980; Niklas, 1994; Raup, 1966). Another ontogenic explanation for the observed patterns of morphological diversity is that a small fraction of the morphospace tends to be realized through specific developmental processes (Gilchrist & Nijhout, 2001; Rice, 2012; Salazar-Ciudad & Jernvall, 2010). However, in reality, these constraints interact with each other, restricting their occupation patterns in the morphospace and have therefore become a principal subject of theoretical morphology, morphometrics, and evolutionary developmental biology (Chartier et al., 2017; Klingenberg, 2010; Polly, 2008; Prusinkiewicz et al., 2007; Salazar-Ciudad & Marín-Riera, 2013; Shoval et al., 2012; Tendler et al., 2015). In particular, gastropod shells have been widely used for analyses of morphospace occupation patterns due to their suitable properties, such as geometrical regularity, diverse morphology, and well-preserved fossil records.

Gastropods, commonly known as snails and slugs, among other names, are the largest and most diverse taxa of the phylum Mollusca. Gastropods have expanded into remarkably diversified habitats over time, by developing a wide range of adaptations. As a result, they are distributed not only in woodlands, ponds, and seashores but also in deserts and the deep sea (Aktipis et al., 2008; Mordan & Wade, 2008). The primary function of the gastropod shell is to protect the soft body. This has been suggested as one of the reasons for the uneven distributions of organisms in the morphospace. Small relative aperture size can make it difficult for predators to access the interior; overlapping whorls can increase shell strength (Raup, 1966); tangential aperture, which is an aperture plane tangent to the body whorl, allows the organism to clamp itself to the substrate (Linsley, 1977); and low spire height and narrow aperture protect against predators (Vermeij, 1979). Mechanical and structural constraints of shells also play roles in the restriction of occupation patterns: calcium carbonate utilization for shell construction (Graus, 1974), available space for soft bodies (Heath, 1985; Stone, 1997), shell balance during resting and moving (Okajima & Chiba, 2009, 2011, 2013), and a lack of high spires with highly inclined apertures (Schindel, 1990; Vermeij, 1971). Differential occupation patterns among habitats have been observed in the gastropod shell morphospace, and some of these have been explained based on combinations of the factors mentioned above. For example, the bimodal shell height distribution in terrestrial species (Cain, 1977) has been attributed to the balancing of shells on vertical substrates (Okajima & Chiba, 2009). Terrestrial species also show a more narrowly distributed range of morphospace than marine species due to more severe functional demands (Noshita et al., 2012). These various functionalities and others such as defense against predators, desiccation tolerance, and buoyancy, contributing to shell morphological diversity, are expected to differ based on habitat and trophic level. In this study, we attempted to understand the differential morphospace occupation patterns among habitats by considering shell instability and hindrance to locomotion, which are unavoidable physical properties inherent to possessing shells.

In this study, we discovered another differential morphospace occupation pattern between terrestrial and aquatic gastropod shells and subsequently attempted to quantitatively understand the differences between morphometric and theoretical morphological analyses. Differential occupation patterns between terrestrial and aquatic species were observed in the morphospace of shell height and aperture inclination, as has been previously reported, that is, a bimodal distribution of shell height in terrestrial species and the absence of high-spired shells with a high aperture inclination. Moreover, although terrestrial species were distributed in the morphospace along optimal lines of shell instability in relation to gravity and a degree of shell hindrance during locomotion, that is, for lines from the low-spired shell with a high inclination to the high-spired shell with low inclination, aquatic species were distributed not only along the peaks but also in a suboptimal region of the low spire with low inclination. We then conducted a numerical simulation for shell instability and hindrance using a theoretical morphological model that generated theoretically possible shell morphological diversities and qualitatively detected several regions that corresponded to different functional demands. Here, this analysis suggested that the differential occupation patterns were a consequence of the aquatic species being able to adopt a posture in which the growth direction aligned perpendicular to the substrate because of lower functional demands. Thus, our results provided both an ultimate explanation for the differential occupation patterns between terrestrial and aquatic species and an overview of morphospace in terms of morphological adaptation.

Materials and methods

Theoretical morphological model of gastropod shells

Theoretical morphological models have been used to quantitatively evaluate the morphology of diverse molluskan shells and subsequently to study the process of morphological changes during growth (Ackerly, 1989; Hammer and Bucher, 2005; Okamoto, 1988a; Raup, 1962; Raup & Michelson, 1965; Rice, 1998; Stone, 1995).

In this study, we used Raup’s logarithmic shell coiling model (Raup, 1962, 1966; Raup & Michelson, 1965) to mimic gastropod shell geometry. Raup’s model represents shells formed using the growth trajectory of a generating curve, which is a closed curve that approximates the aperture. During growth, the generating curve expands, rotates, and translates along the coiling axis. The basic Raup model uses four parameters to define the shell form: whorl expansion rate (W), rate of helicocone translation (T), relative position of the generating curve to the coiling axis (D), and aspect ratio of the generating curve (S). In this study, the orientation of the aperture was defined using two additional parameters: the angle between the generating curve and the coiling axis (Δ; vertical inclination) and the angle between the generating curve and the shell radius (Г; horizontal inclination; Figure 1A and B; Noshita et al., 2012). For simplicity, the generating curve was approximated as a circle (S = 1). Thus, the parametric surface representing a shell form was formulated as follows:

where θ and $ϕ$ represent the rotational angle around the coiling axis and a parameter that designates a point on the aperture, respectively. $Rw(α)$ is a three-dimensional rotation matrix around the w-axis. In total, five parameters were adopted (W, T, D, Δ, and Г), to describe the various shell forms (Figure 1C). The tangent vector of the generating spiral $ξ1$ (i.e., the growth direction) can be represented as follows:

where θ is the coiling angle.

Biometric analysis

To investigate morphospace occupation patterns, we collected and measured the model parameters (W, T, D, Δ, and Г) of 486 specimens, including 104 terrestrial, 122 freshwater, and 260 marine species. These were obtained from two data sets: a data set used in Noshita et al. (2012), which is publicly available at Dryad (Noshita et al., 2011), and another data set consisting of specimens selected from a collection at the Natural History Museum and Institute, Chiba (NHMIC; Supplementary Table S1). The measurements were acquired from two-dimensional images of specimens from lateral and umbilical views captured using a digital single-lens reflex camera (D5000; Nikon, Tokyo, Japan). For the lateral views, each shell was positioned, so that its coiling axis was horizontal and the aperture plane was vertical to the plane of projection (Figure 1A). Measurements obtained from the lateral view include the radii of successive whorls (d₁), the height of the helix (f₁), the height of aperture (h), and the coiling axis (Δ). The umbilical view was achieved by orienting the shell apex-down while preserving a vertical coiling axis (Figure 1B); measurements taken from this view include the distance between the coiling axis and the inner margin of the callus (c), the width of the aperture (b), the angle between the diameter of the aperture (in a plane normal to the radius), and angle between the diameter of the aperture (in a plane normal to the coiling axis) and the shell radius (Г). In most gastropod species, the values of the whorl expansion rate (W) and translation rate (T) exhibit variation during growth; thus, shells do not strictly follow the logarithmic model. As such, we estimated average value of W and T based on the measurements by

and

respectively (see Noshita et al., 2012 for the details). The value of D is given by $D=c/(b+c)$⁠.

The morphospace occupation patterns in the common logarithm of the rate of whorl translation, log₁₀T, and apertural inclination Δ were compared among terrestrial, freshwater, and marine habitats (Figure 2). The Mann–Whitney U test with Bonferroni correction was subsequently performed to investigate habitat-specific differences in the apertural inclination Δ using SciPy v1.6.2 (Virtanen et al., 2020) and statsmodels v0.13.1 (Seabold & Perktold, 2010). The morphospace occupation patterns were then visualized as scatter plots with a contour plot of kernel density estimation.

Assumptions on postures of gastropods in functional evaluations

To evaluate functional properties of gastropod shells, we considered two possible postures based on the theoretical morphological model: the posture with the aperture parallel to the substrate (P_aperture, Figure 3A) and the posture with the growth direction perpendicular to the substrate (P_growth, Figure 3B). To align the generated shell shapes in each posture, the following procedure was used: (a) the center of the aperture (O_a; for the definition, see the Evaluating shell functionalities: instability in relation to gravity and hindrance to locomotion subsection) was translated to the origin; (b) the shell was then rotated to be the unit vector perpendicular to the aperture (η) corresponding to the unit vector directing the negative z-axis $(−ez)$ for P_aperture, and to be the growth vector $(ξ1)$ corresponding to $(−ez)$ for P_growth; (c) the shell was rotated about the z-axis to locate the center of gravity (G) on the y-z plane; and finally (d) the shell was translated along the z-axis to place the point with the minimum z-value (K) on the x–y plane.

Evaluating shell functionalities: instability in relation to gravity and hindrance to locomotion

In order to evaluate shell balance during both rest and locomotion, several methods have been proposed for specific coiling patterns (Okamoto, 1988b; Peterman & Ritterbush, 2022; Raup & Chamberlain, 1967) as well as for general cases (Noshita, 2010; Raup & Graus, 1972; Stone, 1997). Okajima & Chiba (2009) calculated the moment-of-force of shells on vertical and horizontal substrates to evaluate the shell balance. However, gastropods inhabit a wide range of topographies, not just vertical and horizontal substrates. Following Noshita et al. (2012), the average moment-of-force on inclined surfaces (Λ) was defined as follows:

where $OG→(μ,ν)$⁠, g, and p (µ, v) are a positional vector of the center of gravity of the shell (G) from the fulcrum point (O) on an inclined surface defined by the pitch (µ) and roll (v) angles, the gravitational vector, and the probability of inclined surface of (µ, v), respectively. For simplicity, we used the norm of $OG→$$(N=|OG→|=const.)$ as a measure of shell instability in relation to gravity (called the “shell instability”) because Λ is proportional to N if p (µ, v) follows a spherical uniform distribution. In this study, we calculated N for both postures, P_aperture and P_growth (Figure 4A), through a voxel-based approach, in which each voxel is segmented into shell/soft-body regions if it is inside the growing curve. The center of gravity of the entire shell was estimated as the center of gravity of the set of voxels corresponding to the shell/soft body based on the theoretical model. The shell shapes generated using Raup’s model with a coiling angle of 8 π were then discretized into 170 voxels for their shell width. To ensure sufficient spatial resolution, the data were rediscretized to at least 722,500 voxels if the shell length was less than 25 voxels. When the aperture overlapped with the previous whorl in the generated shell shapes, the part overlapped was removed from the ideal generating curve. Here, the part removed from the aperture was estimated based on the overlapping of the last $π2$ to $5π2$ successive generating curves. The center of aperture O_a is defined as the center of the voxels on the aperture plane that was cut off. The shell became unstable when the norm of the vector was large. This model was standardized by volume in order to focus on the shell shape.

Additionally, the projected area of shells on the x–z plane is considered to be an important factor in hindering the movement of snails. Linsley (1978) noted that a large projected area makes it difficult for snails to move forward. In fact, the projected area is often used as a reference area for the evaluation of fluid drag (Denny, 1988; Hebdon et al., 2022; Verhaegen et al., 2019). Gastropods with a smaller projected area can more easily move through narrow spaces. It has been reported that burrowing turritelliform gastropods have shells with a small projected area relative to their body size (Signor, 1982). In this study, we therefore used the projected area of shells standardized by whole volume onto the x–z plane to evaluate the degree of shell hindrance during locomotion (called the “shell hindrance”). The projected area A was calculated by projecting the center points of the shell/soft-body voxels onto the x–z plane at both postures, P_aperture and P_growth (Figure 4B).

Morphospace analysis of spire height and apertural inclination

Based on Raup’s model, we generated 400 virtual shell shapes and calculated their shell instability and hindrance. We visualized these properties in terms of spire height log₁₀T and aperture inclination Δ along an adaptive landscape, which allowed us to explore the morphospace.

Theoretical morphological models were created using parameters in the ranges of $−π2≤Δ≤π2$ and $−1.0≤log10T≤1.0$ by assuming two possible postures (i.e., P_aperture, P_growth). For simplicity, it was assumed that the generating curve came into contact with the coiling axis, and the plane including the generating curve was parallel to the coiling axis (D = 0 and Г = 0). The results focused on the case of W = 10^0.2; however, the same results were also qualitatively obtained for the other cases: W = 10^0.2, 10^0.3, and 10^0.4, with D = 0 and Г = 0 (Supplementary Figures S1–S4 and S9), and D = 0.2 and 0.4 with W = 10^0.2 and Г = 0 (Supplementary Figures S5 and S6); morphospace of T and Δ (Supplementary Figure S7).

Results

Difference in morphological diversity between terrestrial and aquatic gastropod shells

Here, biometric analysis revealed differential, yet not mutually exclusive, occupation patterns in shell height and aperture inclination in the morphospace (Figure 2). The Mann–Whitney U test with Bonferroni correction was subsequently conducted on the aperture inclination, which found significant differences between the terrestrial and freshwater species (p < .001), as well as between terrestrial and marine species (p < .001; Table 1). Aquatic species were shown to have smaller aperture inclinations than terrestrial species (Figure 2A). This trend was a consequence of two different occupation patterns in the morphospace of spire height and aperture inclination (Figure 2B): One of two peaks of terrestrial species’ distribution in the morphospace corresponded to the low spire and high aperture inclination (Figure 2B, region i; Figure 2C), while some aquatic species had shells with low spires and a low aperture inclination (Figure 2B, region ii; Figure 2D and E). In contrast, the absence of shells with both a high spire and a high aperture inclination was observed across all habitats (Figure 2B, region iii).

Gastropod shells with high spires and a high aperture inclination were unstable and hindering

Here, the functional properties of shells were summarized by adopting the functional posture (i.e., having smaller values of N and A) from the P_aperture and P_growth (Figure 5). Contour plots for each posture with the other W values are shown in Supplementary Figures S1–S4 and S9.

Shell instability with respect to gravity tended to be higher with a high-spired shell (Figure 5A). As the spire height (log₁₀T) increased, the norm between the fulcrum and center of gravity (N) also increased. This trend became stronger in the region where log₁₀T was higher. The optimal (low instability) region where −0.7 < log₁₀T < 0.5 and 0.8 < Δ < 1.5 was also found here (i.e., stable shells were achieved with a spire aspect ratio ≈1 and an aperture inclination that did not interfere with the previous whorl).

Shell hindrance showed a similar trend, in which the projected area (S) was increased with a high spire (Figure 5B). This trend intensified when $|Δ|$ increased.

Terrestrial gastropods tended to have functional shell shapes

Most specimens across all three habitats were distributed in regions where shells were relatively neither unstable (Figure 5A) nor hindering (Figure 5B). The absent region of the specimens, in which shells exhibited high spires and a high aperture inclination (Figure 2B, region iii), showed low functionalities (high instability/high hindrance).

It was found that specimens of terrestrial species were distributed close to the optimum lines of Δ against log₁₀T in which the instability and hindrance reached a minimum. Some aquatic species distributed in region ii of Figure 2B also showed stable and less-hindered shapes to some level, although they were farther from both optimal lines.

P_growth was a functional posture when shells had a noninclined aperture

In this study, shell instability and hindrance were evaluated based on two postures (P_aperture and P_growth). For each shell shape, one of two postures was adopted as the functional posture with the lowest instability/hindrance. For both shell instability and hindrance, P_growth was a functional posture when shells had noninclined apertures (Δ ≈ 0), excluding when T became large (log₁₀T > 0.7; Figure 6A and B). This was because when Δ ≈ 0 and log₁₀T < 0.7, gastropods made their center of gravity closer to the substrate by extending their soft body in the direction of growth to avoid the previous whorl (Figure 6C). When Δ ≈ 0 and T were high, P_growth pointed downwards compared with P_aperture, resulting in the coiling axis becoming erect against the substrate (as shown in Figure 6D). One of the two peaks for terrestrial species and the majority of aquatic species were distributed within this region.

When Δ > 0.2 and log₁₀T < 0.7, the P_aperture was more functional than P_growth since the previous whorl did not interfere and was able to attach more closely to the substrate. Another peak for terrestrial species, as well as a portion of aquatic species, was also distributed in this region.

Contour maps of shell instability and hindrance were generated with W = 10^0.2, and the same patterns were observed for other values of W (see Supplementary Figures S1, S3, and S4 for the results of W = 10^0.1, 10^0.3, and 10^0.4) and D (see Supplementary Figures S5 and S6 for the results of D = 0.2 and 0.4).

Discussion

Morphospace occupation patterns formed through evolutionary processes are closely associated with habitat. In the analysis presented here, different morphospace occupation patterns for spire height and aperture inclination were identified between terrestrial and aquatic species, which was found to be a result of (a) the bimodal spire height distribution of terrestrial species (Cain, 1977), (b) the concentration of aquatic species in the region of 0.1 < log₁₀T < 0.5 and 0 < Δ < 0.4, and (c) the different aperture inclinations of low-spired shells (i.e., if shells were low-spired, a highly inclined aperture was common in terrestrial species whilst a less-inclined aperture was more common in aquatic species; Figure 2).

Several subregions in which shells exhibited different functional properties and distributions of specimens were identified in the morphospace of spire height and aperture inclination (Figure 7A and B). There were no high-spired shells with highly inclined apertures (Schindel, 1990; Vermeij, 1971) corresponding to region II, in which shell hindrance became larger (Figures 6D and 7B, region II). Furthermore, no specimens were observed in region VI, in which shells showed a small soft-body ratio against their volume (Figure 7C and Supplementary Figure S8). It has been previously reported that gastropod shells were efficiently constructed (but did not attain the theoretical optimal construction because of functional trade-offs) based on the evaluation of the soft-body ratio (Heath, 1985; Noshita et al., 2012; Stone, 1999). Low shell instability in region VI-a may reinforce the pattern (Figure 5A). On the other hand, region VII was possible in theory, yet physically impossible. The general absence of regions II, VI, and VII could be attributed to adaptations for shell instability, hindrance, and soft-body ratio, although the limiting factors differ. The arrangement of these subregions within the morphospace indicates that aperture inclination (Δ) has a crucial role, particularly in high-spired shells, in achieving functional shapes. Consequently, high-spired shells typically showed low-inclined apertures (region IV); besides, there was a tendency to exhibit lower D values to mitigate shell instability and hindrance (Supplementary Figures S5 and S6; Noshita et al., 2012; Signor, 1982). The bimodal spire height distribution in terrestrial species (Cain, 1977) could be attributed to the balancing of shells on vertical substrates (Okajima & Chiba, 2009). These two peaks corresponded to regions I and III-b, respectively, in which the optimal lines of aperture inclination against the spire height were located. Deflection of the last whorl was also observed in these regions (Figure 7D), which was also previously attributed to be an adaptation for balance (Okajima & Chiba, 2013). Although terrestrial species were equally distributed throughout regions I and III-b, aquatic species were more concentrated within region III-b. These results implied the different postural constraints of these two regions (Figure 7B, regions I and III-b). In addition, only marine and freshwater species were distributed in region III-a, in which the P_growth was better for both functions (Figure 7B, region III-a; Figure 7E). In region V in which the P_growth was better for shell hindrance (Figure 7B, region V), three freshwater species of Plabininae with planispiral shells and upward inclined apertures were observed (Anisus vortex, Gyraulus acronucus, and Planorbarius corneus, Figure 7F).

Here, we propose a hypothesis stating that the differential morphospace occupation pattern is caused by the aquatic species being able to assume a posture in which the growth direction is aligned perpendicular to the substrate (P_growth) as a result of reduced functional demands. Terrestrial specimens were distributed along the optimal lines of both shell instability and hindrance (Figure 5), which was consistent with previous studies; the bimodal distribution of spire height on terrestrial species could be explained in terms of the shell balance adaptation for horizontal and vertical surfaces (Okajima and Chiba, 2009), whereby terrestrial species were under more severe functional constraints compared with marine species (Noshita et al., 2012). However, some aquatic species with low-inclined apertures were distributed within suboptimal regions (Figure 2B, region ii; Figure 5), that is, this difference could not be explained in terms of only shell instability and hindrance. The morphospace analysis conducted herein revealed that the majority of aquatic species, including those distributed in the suboptimal region, were distributed in regions where P_growth was more functional than P_aperture. This suggested that the constraints on posture were severe and/or the functional demands were mild for aquatic species. The former was not inconsistent with previous studies on aquatic species, which implied the importance of certain postures for maintaining lateral balance (Linsley, 1977) and internal water flow (Linsley, 1978). The latter was partially supported by previous studies, which showed that terrestrial species were under more severe functional constraints than marine species in terms of shell stability (Noshita et al., 2012). Considering that it would not be problematic that the direction in which the soft body was elongated corresponded with the growth direction, it was reasonable to assume that the functional demands were lower for aquatic species. Although the hypothesis proposed here still needs to be validated for whole across gastropods under field conditions, we conclude that it is promising as an explanation for the variations in morphospace occupation patterns among habitats. Nonetheless, it should be noted that this hypothesis did not sufficiently address high-spired shells (approximately W > 10). Despite the results of numerical simulations that the stability and hindrance of the shell improve as W increases, only a few specimens in our data sets displayed W values greater than 10^0.8 (Supplementary Figure S9). This sparse distribution of gastropods in the high W region may imply that dominant constraints diverge for high W shell morphologies (e.g., metabolic costs of secreting pedal mucus; Denny, 1980; Lauga & Hosoi, 2006).

In this study, we assumed isometric growth, even though gastropod shells often exhibit anisometric growth (Collins et al., 2021; Schindel, 1990; Urdy et al., 2010a, 2010b). Owing to its simplicity, our results provided both an ultimate explanation for the differential occupation patterns between terrestrial and aquatic species and an overview of morphospace in terms of morphological adaptation. However, several problems related to anisometric growth remain unresolved, such as the effect of changes in growth directions on optimal postures, appropriate methods for comparing different growth patterns, and quantitative analysis of more realistic shapes. Some recently proposed methods may pave the way by incorporating sufficient observations and measurement data for quantitative studies on molluskan shells exhibiting anisometric growth (e.g., Collins et al., 2021; Noshita, 2014; Urdy et al., 2010b). Changes in shell shape during growth, such as a “heteromorph” (Hoffmann et al., 2021; Liew & Schilthuizen, 2016; Liew et al., 2014; Okamoto, 1988a, 1988b; Seilacher & Gunji, 1993), deflection (Goodfriend, 1986; McNair et al., 1981; Okajima & Chiba, 2013), and other anisometric growth, would be good subjects for further research.

Conclusion

In this study, we attempted to explain the variations in the morphospace occupation patterns of terrestrial and aquatic gastropods based on adaptations. Through numerical simulation and biometric analysis, we hypothesized that the differential morphospace occupation pattern was caused by the aquatic species being able to adopt a posture with the growth direction perpendicular to the substrate (P_growth) due to reduced functional demands. Shells are formed through accretionary growth, and proximally, shell morphology is a consequence of integrating such incremental growth processes (Hammer & Bucher, 2005; Rice, 1998). Previous studies have implied that mechanical feedback, which is often dependent on posture, plays a crucial role in molluskan shell formation and resultant morphology (Checa et al., 1998; Morita, 1991). Our findings supported the importance of posture in shell formation and adaptation. To understand the morphological diversity and morphospace occupation patterns of gastropod shells formed through evolutionary processes under functional, environmental, developmental, structural, and phylogenetic constraints (Raup, 1972; Seilacher, 1970, 1991), the interplay among these factors must be investigated. Our morphospace analysis integrated information regarding various dominant factors within morphospace subregions, and it appears as a promising approach to exploring the morphological evolution of gastropods under such multifaceted constraints.

Data availability

The source code and examples are uploaded in Zenodo: https://doi.org/10.5281/zenodo.7878281.

Author contributions

K.N. supervised the study. A.A. and K.N. conceptualized the study and wrote the article. A.A. and K.N. worked out the mathematical details.

Conflict of interest: The authors declare no conflict of interest.

Acknowledgments

We thank T. Kurozumi and S. Isaji for their assistance in accessing specimens at the Natural History Museum and Institute, Chiba. This work was partially supported by the Japan Science and Technology Agency (JST) MIRAI Program Grant Number JPMJMI20G6 and Japan Society for the Promotion of Science (JSPS) KAKENHI Grant Numbers JP12J00760, JP18H01323, JP20H01381, and JP20KK0011 to K.N.

References