JOURNAL OF MORPHOLOGY 275:391–397 (2014)
Morphological and Mechanical Changes in Juvenile Red-Eared Slider Turtle (Trachemys scripta elegans) Shells During Ontogeny Jennifer F. Fish and Charles T. Stayton* Department of Biology, Bucknell University, Lewisburg, Pennsylvania 17837 ABSTRACT Turtles experience numerous modifications in the morphological, physiological, and mechanical characteristics of their shells through ontogeny. Although a general picture is available of the nature of these modifications, few quantitative studies have been conducted on changes in turtle shell shape through ontogeny, and none on changes in strength or rigidity. This study investigates the morphological and mechanical changes that juvenile Trachemys scripta elegans undergo as they increase in size. Morphology and shell rigidity were quantified in a sample of 36 alcoholpreserved juvenile Trachemys scripta elegans. Morphometric information was used to create finite element models of all specimens. These models were used to assess the mechanical behavior of the shells under various loading conditions. Overall, we find that turtles experience complementary changes in size, shape, deformability, and relative strength as they grow. As turtles age their shells become larger, more elongate, relatively flatter, and more rigid. These changes are associated with decreases in relative (size independent) strength, even though the shells of larger turtles are stronger in an absolute sense. Decreased deformability is primarily due to changes in the size of the animals. Residual variation in deformability cannot be explained by changes in shell shape. This variation is more likely due to changes in the degree of connectedness of the skeletal elements in the turtle’s shells, along with changes in the thickness and degree of mineralization of shell bone. We suggest that the mechanical implications of shell size, shape, and deformability may have a large impact on survivorship and development in members of this species as they mature. J. Morphol. C 2013 Wiley Periodicals, Inc. 275:391–397, 2014. V
culminating in a fully ossified shell (Gilbert, 2001). These morphological and physiological changes have profound biomechanical implications: immediately after hatching, juvenile turtle shells are relatively weak and compliant, and provide little defense against the numerous predators that small turtles routinely encounter (Magwene and Socha, 2013). However, as the shell increases in size and degree of ossification, its resistance to stresses and strains imposed by outside forces (such as those from a predator’s jaws) increases, so that large adult turtles with fully ossified shells are, in contrast to juveniles, remarkably resistant to predation (Jackson and Janzen, 2000; Pritchard, 2008; Magwene and Socha, 2013). This resistance has been invoked to explain, in part, the remarkable survival rates of adult turtles when compared with other reptiles (Gibbons, 1987; Iverson, 1991b; Shine and Iverson, 1995). However, little is known about how those changes (in size, shape, and degree of ossification) quantitatively affect the defensive capabilities of the shell over ontogeny. It is clear that at some point during ontogeny the turtle shell changes from a relatively ineffective method of defense [juveniles use other methods of defense against predators instead (Britson and Gutzke, 1993)] to an immensely effective defensive structure. However, the exact timing and duration of this transition remains unknown. Moreover, the interaction
KEY WORDS: turtle; shell; biomechanics; ontogeny; ossification
Additional Supporting Information may be found in the online version of this article.
INTRODUCTION
Contract grant sponsor: DBI; Contract grant number: 0743460; Contract grant sponsor: IIS (T. Rowe); Contract grant number: 0208675.
Juvenile turtles experience numerous morphological, physiological, and biomechanical changes to their shells through ontogeny (Magwene, 2001; Gilbert et al., 2001; Angielczyk and Feldman, 2013; Magwene and Socha, 2013). Besides the obvious increase in size, their shells also change shape (Magwene, 2001; Angielczyk and Feldman, 2013) and degree of ossification as the initially separate bone growth centers of the carapace and plastron begin to interact and eventually merge, C 2013 WILEY PERIODICALS, INC. V
*Correspondence to: C. Tristan Stayton; Department of Biology, Bucknell University, 337 Biology Building, Lewisburg, PA 17837. E-mail: [email protected] Received 9 April 2013; Revised 6 September 2013; Accepted 3 October 2013. Published online 3 December 2013 in Wiley Online Library (wileyonlinelibrary.com). DOI 10.1002/jmor.20222
392
J.F. FISH AND C.T. STAYTON
of various aspects of the turtle shell, its size, shape, and degree of ossification, in determining its mechanical strength has never been studied. Such aspects, however, should have a great deal of influence over the ability of the turtle shell to resist predator attacks: as size and degree of ossification increase, presumably so does mechanical strength and stiffness, and previous studies (Rivera and Stayton, 2011; Stayton, 2009, 2011; Vega and Stayton, 2011) have revealed strong associations between shell shape and strength. Better studied are the general patterns of growth and ossification of the turtle shell. Juvenile turtles grow at a faster rate than adults (Gibbons and Greene, 1978). In general, the carapaces of juvenile turtles are more rounded and relatively taller than those of adults (Jolicoeur and Mosimann, 1960; Somers, 1986; Lestrel et al., 1989). Plastrons usually become more elongate, wider toward the read, and narrower at the bridge (Angielczyk and Feldman, 2013). Ossification begins, but does not complete, before hatching. In Trachemys scripta elegans, for example, the ribs begin to calcify 45 days after hatching. Only by 118 days posthatching has the ossifying dermis between the ribs coalesced. Similarly, the plastron starts to ossify before the time of hatching, but continues to grow and fuse posthatching until fully ossified (Gilbert et al., 2001; Magwene, 2001). Overall, turtle shell ossification and mineralization are still occurring posthatching, and size and shape continue to change until at least maturity, but to what degree these changes affect the mechanical behavior of turtle shells is still unknown. In this study, we examine the changes that occur in shell shape and shell mechanics during the growth of juvenile Trachemys scripta elegans. We address two main questions. First, how do the shape and deformability of the turtle shell change as size increases? Second, are changes in shape associated with changes in the mechanical behavior of turtle shells? We predict that the turtle shell will become less circular in dorsal view and more elongate as size increases, as has been noted (but infrequently quantified) in previous studies (Jolicoeur and Mosimann, 1960; Somers, 1986; Lestrel et al., 1989). Similarly, we predict that the turtle shell will become more rigid (less deformable) as size increases, and that this change in rigidity will be gradual, matching the aymptotic, matching the asymptotic rate of change in carapace length (CL). Finally, because changes in both shape and deformability were found among juvenile turtles of different sizes, we wanted to examine a potential relationship between those properties. Specifically, we were interested in the possibility that changes in deformability might be partially due to changes in shell shape, as opposed to changes in degree of ossification, shell bone thickness, or shell material Journal of Morphology
properties. Certain structural shapes are stronger than others, or less likely to deform significantly under loads. By isolating the effects of shell shape on shell strength, we can determine whether small juvenile turtles can partially mitigate the structural disadvantages of incompletely ossified, incompletely mineralized, or relatively thin shells with relatively strong shell shapes. We predict that the changes in shell shape over ontogeny will be associated with changes in relative shell strength and deformability, independent of other factors. Note that this prediction is not trivial, even with known changes in shape and a method of assessing function that only incorporates shape data – many-to-one mapping of form onto function in turtle shells [demonstrated in Stayton (2011)] means that changes in shape are not necessarily associated with changes in functional performance (Alfaro et al., 2005). It is also not clear whether the shapes of younger, smaller turtle shells are expected to be stronger or weaker than those of older, larger turtles. Small turtles could mitigate their other mechanical disadvantages with stronger shell shapes, as mentioned above, but smaller turtle shells might also provide inadequate protection against predators at any shape. In this case, smaller turtles might optimize their shell for other functions (e.g., crypsis or decreasing drag during swimming), and only attain strong shell shapes once the shell is sufficiently large and ossified that shell shape might make a difference in the animal’s ability to defend against predatory attacks. MATERIALS AND METHODS Specimens and Morphometrics Hatchling and juvenile Trachemys scripta elegans (WiedNeuwied, 1839) specimens (n 5 36) were obtained from the Carnegie Museum of Natural History (Supporting Information Table S1). All specimens were wild caught, fixed in formalin, and then preserved in 70% ethanol. Straight CL was measured on all specimens using digital calipers. Specimens ranged from 30.2 to 90.3 mm in length. Adults of these species average 265 mm in length, so the specimens range from 11 to 34% of their adult length (Ernst and Barbour, 1989). Adults were not used as we were only interested in changes up to the complete ossification of the shell. Each turtle was photographed against a black background in dorsal, lateral (right side), and ventral views with a Nikon Coolpix 60003 digital camera. For ventral and dorsal views the turtle was oriented with the plastron horizontal. For lateral views the midline was horizontal and the plastron was oriented perpendicular to the horizontal. Putty was used to ensure that turtles were oriented properly. The camera was mounted on a tripod and positioned approximately 40 cm above the specimen. Before photography, a grid was photographed to ensure that distortion was minimal. tpsDig (Rohlf, 2008) was used to digitize all images: a total of 59 landmarks were digitized on each shell (Fig. 1; Supporting Information Table S2). The coordinates of landmarks in all views were then assembled into a single, three-dimensional data set using a custom MATLAB routine written by one of the authors (Stayton, 2009). The coordinates were then aligned using a Procrustes fit
MORPHOFUNCTIONAL CHANGES IN JUVENILE TURTLE SHELLS
Fig. 1. Shell landmarks in A) dorsal view and B) ventral view. (Zelditch et al., 2004), and those values were used as the shape variables for subsequent analyses.
Shell Deformability The deformability of each turtle shell was measured by placing a series of loads (0.5, 1, and 1.5kg) on the dorsal-most point of the shell, and measuring the change in height of the shell, relative to its initial height. These measures thus correspond to whole-organism analogs of mechanical strain. For each specimen, the slope of the scaled deformation v. load relationship was computed using least-squares regression. While these slopes were computed from only four data points per specimen (three loads plus the origin), our data showed high repeatability (r2 5 0.81) such that slopes resulting from these data are probably robust. The slope, which we call deformability, is similar to elasticity, in a materials science context, in that it represents how readily the shells change shape in response to a load. However, it is not equivalent for two reasons. First, we were unable to calculate a cross-sectional area over which the load was applied, and thus did not scale load by area so as to calculate an analogue of mechanical stress. Moreover, we did not perform the more standard regression of load onto deformation as some large specimens did not measurably deform at all, which would have given an undefined slope for a standard load v. deformation curve. Thus, here, low values represent less easily deformed, or stiffer, turtle shells while higher slopes represent more easily deformed shells.
Modeled Shell Strength and Deformability Shell strength was modeled using finite element (FE) methods. FE methods are a suite of engineering techniques that can be used to model the mechanical behavior of complex structures
393
(Dumont et al., 2005). These methods operate by breaking up a complex shape (or more properly, a computer model of a complex shape) with an unknown response to mechanical stress into a large number of simpler shapes with known responses to mechanical stress. Here, a model of a turtle shell is built from 41.615 four-sided polyhedra, each defined by the x-, y-, and zcoordinates of four points known as nodes. Then a load or force is applied to a single node. The model is held in place at a set of other nodes known as “restraints”; these restraints ensure that the model deforms (instead of simply moving) in response to the load. The load produces stress and deformation on all elements that share that node. These stresses, in turn, affect neighboring elements, and so on, and the stress propagates throughout the entire model. FE methods model this propagation and calculate the stresses that develop in each element. Models with different shapes generate different stresses for a given load. Average or maximum stresses across all elements in each model can then be used to determine which model is stronger, that is, models that develop lower stresses for a given load are less likely to fail (fracture or break) for a given load or more deformable. Here, the landmark configurations of each specimen were used to generate a FE model of the shell using the method of Stayton (2009). Briefly, this method uses the thin-plate spline interpolation function to transform a preexisting FE model into one corresponding to the shape of a new set of landmarks. The base model used here captures all aspects of the morphology of the Emydid turtle shell, that is, vertebral column, ribs, and so on, so all models derived from this base have those features as well. This method has been validated on real turtle specimens (Stayton, 2009) and has been successfully used elsewhere to assess the mechanical behavior of shells both within (Rivera and Stayton, 2011; Vega and Stayton, 2011) and between (Stayton, 2011) species. Three restraints on the plastron were used: one on the midline close to the junction between the pectoral and humeral scutes, and one each on the posterior margins of the connection between bridge and plastron. Eight loads along the midline and margin of the carapace (Fig. 2) were assigned to the preexisting FE models before transformation. Thus, all restraints and loads were located on corresponding points on all models. We were interested in isolating the effect of shell shape on shell strength and deformability from all other factors. One important nonshape factor that can influence strength is size. Thus, all models were scaled to a common size before analysis. As strength is proportional to the cross-sectional area of structures, all models were scaled to the same volume to the twothirds power (Dumant et al., 2009). We also constructed a separate set of models which were scaled to the actual sizes of all specimens. Similarly, bone thickness and material properties were consistent among all models. All models were analyzed using Strand7 FE Analysis software (Strand 7 Pty. Ltd., Sydney, Australia). Transformed models were imported into the analysis program and cleaned to eliminate any extremely elongate elements (which can produce artifactually high stresses). All elements in all models were assigned an identical set of material properties: an elastic modulus of 20 GPa and a Poisson’s ratio of 0.3. These correspond to measured values of turtle shell bone (Rhee et al., 2009). Loads were set at 200 N, a value corresponding to the bite force of a medium-sized predator such as a coyote (Christiansen and Wroe, 2007). The shell was modeled as a linear elastic material (Dumont et al., 2005). This is probably an oversimplification of the actual mechanical behavior of adult turtle shells, but such approximations are appropriate for biological analyses (Straight et al., 2005), especially when relative rather than absolute performance is being assessed. Once models were run, von Mises stress values were extracted for all elements in all models. Von Mises stresses are composite measures of stress predict the behavior of biological structures quite well (Dumont et al., 2005). The average von Mises stress values for all elements and all loads in each model were used for all subsequent hypothesis testing. We also calculated deformabilities from these models using a similar
Journal of Morphology
394
J.F. FISH AND C.T. STAYTON factors (shell shape, shell thickness, shell bone mineralization, etc.) that could influence deformability, we had no a priori expectation of the nature of this relationship and used both a linear regression and Kendall’s rank correlation coefficient to assess significance. All else being equal, biomechanical first principals indicate that shell deformability should be proportional to shell cross-sectional area; assuming isometry, this means that deformability should scale as 1/CL2. We thus assessed the significance of this relationship as well using linear regression (log-log data were not used as some shells had deformability values of 0). We also inspected the deformability versus size plot for evidence of inflection points: sizes at which the relationships between size and stiffness changed. A strong relationship was found between shell size and deformability. To determine whether shell shape could account for some of the unexplained variation in deformability, we regressed the residuals from the deformability versus 1/CL2 relationship against deformability predicted from shape alone. To assess the relationship between shell size and strength, we ran a simple univariate regression of CL versus (size corrected) average shell strength (von Mises stresses averaged over all elements and all load cases for each specimen). Again, as a significant relationship was found, we used tpsRegr to separately analyze the relationships between strength and dorsal, lateral, and ventral aspects of shell shape. To more fully visualize the relationship between shell shape and strength, we conducted a two-block partial least-squares analysis (Rohlf and Corti, 2000) of all shape variables and the average shell strength (von Mises stresses averaged over all elements) for all eight load cases for each specimen. We also regressed CL against shell strength for shells scaled to actual size.
RESULTS Shell Size and Shape
Fig. 2. Trachemys scripta elegans, sample shell model. A) Dorsal view with all loads indicated by filled circles. B) Ventral view with restraints indicated by Xs. procedure as was used for real specimens. Shell height was calculated as the vertical distance between the dorsal-most point on the carapace and the ventral-most point on the plastron. Heights were calculated before and after loading, and the difference was divided by the original height. Since there was no measurement error for these calculations and we assumed linear elastic behavior for all models, all slopes were calculated from a single load.
Data Analysis A series of linear multivariate or univariate regressions was run to test all of the hypotheses. Unless otherwise indicated, all statistical analyses were conducted using PAST (Hammer et al. 2001). To assess how shape changes with size, we ran a multivariate regression of all shape variables on CL. A significant relationship between size and shape was found, so to further dissect the nature of the shape changes we used tpsRegr (Rohlf, 2010) to separately analyze size-related shape changes of the shell in dorsal, lateral, and ventral view. To assess how shell stiffness changed with growth, we regressed shell deformability versus CL. Given the numerous
Journal of Morphology
The multivariate regression revealed a significant relationship between size and shape (P < 0.001; see also Fig. 3). Significant correlations were also observed in dorsal, lateral, and ventral views (all P < 0.001). In general, smaller turtles have a more highly domed and more circular (in dorsal view) carapace with relatively larger marginal scutes, while larger turtles have a more elongated shell with more compact anterior and posterior regions. Smaller turtles have a slightly more circular plastron, with a more rounded bridge region, compared to larger turtles. These shape changes are most noticeable in lateral view; the changes in plastron shape are most subtle (Supporting Information Fig. S1). Shell Deformability A significant correlation between shell size and deformability was found using both linear regression (r2 5 0.637, P 5 1.52 3 1028) and Kendall’s rank correlation coefficient (s 5 20.719, P 5 2.27 3 1029). The relationship between deformability and 1/CL2 was even stronger (r2 5 0.718, P 5 2.69 3 10210). The plot of shell deformability versus size reveals an inflection around 30–50 mm CL (Fig. 4). At this point, the deformability of the shell, which had been decreasing rapidly with increasing size, begins to decrease at a much lower rate. At around 70 mm in length, the shell has become
MORPHOFUNCTIONAL CHANGES IN JUVENILE TURTLE SHELLS
395
Fig. 3. Trachemys scripta elegans, shell size versus average von Mises stress, calculated from all elements across all load cases. Diagrams of small and large turtle shells in dorsal and lateral view on x-axis; diagrams of weak and strong turtle shells on y-axis. These diagrams represent shapes associated with the extremes of the size and strength ranges. Diagrams in the lower left represent dorsal and lateral views of the average turtle shape.
approximately as stiff as it will be for the rest of the turtle’s ontogeny. Shape, that is, deformability predicted from shape independent of size, explained very little of the residual variation in deformability (r2 5 0.0289), and the relationship, although positive, was not significant (P 5 0.325). Modeled Shell Strength and Deformability There was a significant relationship between shell shape and modeled shell strength when all other factors were held constant. In general, shells that have taller and longer bridges developed lower stresses than those that have shorter and more compressed bridges. These differences are similar to those seen between small and large turtles. Indeed, if stresses are calculated from all models scaled to comparable sizes (see above), then there is a significant negative correlation between CL and shell strength (P 5 0.006; Fig. 3). In other words, smaller turtles have shell shapes which are stronger than those of larger turtles,
Fig. 4. Trachemys scripta elegans, shell deformability versus shell size. Inflection point in shell deformability lies between 30 and 50 mm CL.
and the greater deformability of smaller turtle shells occurs despite, not because of, their shapes. Of course, if the FE models are scaled to actual size, the shells of larger turtles are stronger (P < 0.001). Journal of Morphology
396
J.F. FISH AND C.T. STAYTON
DISCUSSION We found a significant relationship between size and shape. As predicted, smaller turtles were more domed in lateral view and more circular in dorsal view. This is consistent with previous studies (Jolicoeur and Mosimann, 1960; Lestrel et al., 1989; Somers, 1986). There are many possible explanations for this pattern, both adaptive (see below) and nonadaptive. Among the latter are the possibilities that the shapes of juvenile turtle shells are primarily determined by the ossification patterns of the shells, or with the necessity of prehatching turtle shells fitting efficiently into eggs. Turtle shells showed a significant tendency to become less deformable as they grew, as predicted. Biomechanical first principals concerning shell thickness (assuming isometry) explain approximately 70% of the variation in deformability. However, some of the unexplained variation in this relationship is manifested in the fact that the plot of deformability versus CL does not show a smooth curve. Instead, and in contrast to our expectations, an inflection point for increased stiffness was observed at 30–50 mm CL. This inflection point shows a drastic change in the slope of the relationship between shell size and deformability, and helps to discriminate between possible explanations for residual variation in deformability. One possible explanation for this pattern can be rejected; modeled differences in deformability based on shape alone could only account for a small (3%) and nonsignificant amount of variation in residual observed deformability. Instead, the decreased deformability in the shells of larger turtles could result from increases in the elastic modulus of their shell bone (higher elastic moduli being associated with stiffer materials), possibly due to greater mineralization of the skeletal tissues. Or it could result from increases in relative shell thickness, which would lead to disproportionate increases in the cross-sectional area of the turtles’ shells, leading in turn to lower stress and strain in the bone and less deformation overall. Changes in material properties or relative thickness may well be responsible for some of the changes in turtle shell deformability. However, neither of these causes would necessarily produce an abrupt change in slope, although rapid increases in mineralization, shell thickness, or both at 30–50 mm CL could produce the observed inflection point. Alternately, the inflection point could represent the time at which the formerly separate ossification centers in the turtle’s shell unite into a single element (Gilbert et al., 2000). At this point, loads that formerly were resisted only by small individual bones and the connective tissues between them would now be resisted by a single unified structure which will still continue to ossify and stiffen after the separate ossification centers have united. Such a change would necesJournal of Morphology
sarily produce an inflection point in a plot of shell deformability versus age or size. If such inflection points prove to be common features of the ontogeny of turtle shell mechanics, this will provide greater evidence for the role of shell developmental patterns as proposed here. Finally, a significant relationship was also found between shell shape and shell strength. Smaller turtles were modeled as having stronger-shaped shells than larger turtles, in proportion to their size, although larger turtle shells were stronger in absolute terms. This finding suggests a possible adaptive interpretation for the changes in shell shape as turtles grow. When resisting predator attacks, juvenile turtles are at a disadvantage in terms of size and shell stiffness (Iverson, 1991a). It is highly unlikely that juvenile turtles can completely compensate for their thin, poorly ossified, and incomplete shells with relatively strong shell shapes. However, such shapes might make a difference in a small but evolutionary significant proportion of predator encounters. With older turtles, shell size itself may provide sufficient strength to withstand predator attacks so that changes in shape can optimize other shell functional properties such as reducing drag during swimming. These adaptive explanations are not necessarily incompatible with previously mentioned nonadaptive explanations; shells that fit well inside eggs may also fortuitously provide high strength for their size. Our results only apply to Trachemys scripta elegans and to turtles which show similar ontogenetic changes in shell ossification, shape, and deformability. The ossification patterns of turtle shells have only been studied in a few species (though these cover a fairly wide phylogenetic range; Gilbert et al., 2001), and while gross patterns of ossification are conserved there are differences which may have functional significance. Similarly, patterns of shape change have been well quantified for some groups but not others. Within Emydids, patterns of ontogenetic shape change in the plastron vary among species (Angielczyk and Feldman, 2013), and the same is likely true for carapace shape. This does not preclude similarity in change in shell strength among species, given the manyto-one nature of the morphology-function relationship (Alfaro et al., 2005) but further study is needed to determine whether the Trachemys scripta elegans pattern is typical for turtles. In conclusion, this study confirmed and quantified expected ontogenetic patterns in turtle shell shape and deformability. We demonstrate that turtle shells become stiffer and stronger during ontogeny, in spite of changes in shell shape. Although as turtles age their shells become stronger in an absolute sense, their shell shapes become relatively weaker. Overall, our results suggest that turtles experience complementary changes in size, shape, and relatively strength as they grow.
MORPHOFUNCTIONAL CHANGES IN JUVENILE TURTLE SHELLS
ACKNOWLEDGMENTS We thank S. Rogers at the Carnegie Museum of Natural History for access to the turtle specimens, and B. Dumont, I. Grosse, and S. Werle at the University of Massachusetts at Amherst for assistance in developing the original turtle shell FE model. J. Maisano and the staff of the University of Texas at Austin High-Resolution X-ray CT Facility provided access to the original CT scan of a bog turtle. LITERATURE CITED Alfaro ME, Bolnick DI, Wainwright PC. 2005. Evolutionary consequences of many-to-one mapping of jaw morphology to mechanics in labrid fishes. Am Nat 165:E140–E154. Angielczyk KC, Feldman CR. 2013. Are diminutive turtles miniaturized? The ontogeny of plastron shape in emydine turtles. Biol J Linn Soc 108:727–755. Britson C, Gutzke W. 1993. Antipredator mechanisms of hatchling freshwater turtles. Copeia 1993:435–440. Dumant ER, Grosse IR, Slater GL. 2009. Requirements for comparing the performance of finite element models of biological structures. J Theor Biol 256:96–103. Ernst CH, Barbour RW. 1989. Turtles of the World. Washington, DC: Smithsonian Institution Press. 313 p. Gibbons JW. 1987. Why do turtles live so long? BioScience 37: 262–269. Gilbert SF, Loredo GA, Brukman A, Burke AC. 2001. Morphogenesis of the turtle shell: The development of a novel structure in tetrapod evolution. Evol Dev 3:47–58. Hammer ï, Harper DAT, Ryan PD. 2001. PAST: Paleontological statistics software package for education and data analysis. Palaeontologia Electronica 4:1–9. Iverson J. 1991a. Life history and demography of the yellow mud turtle, Kinosternon flavescens. Herpetologica 47:373– 395.
397
Iverson J. 1991b. Patterns of survivorship in turtles (order Testudines). Can J Zool 69:385–391. Jolicoeur P, Mosimann JE. 1960. Size and shape variation in the painted turtle. A principal component analysis. Growth 24:339–354. Lestrel PE, Bernard SG, McNabb EG. 1989. Carapace growth of the turtle Chrysemys scripta: A longitudinal study of shape using fourier analysis. Anat Anz 168:135–143. Lindeman PV. 1999. Growth curves for Graptemys, with a comparison to other Emydid turtles. Am Midl Nat 142:141–151. Magwene PM. 2001. Comparing ontogenetic trajectories using growth process data. Syst Biol 50:640–656. Magwene PM, Socha J. 2013. Biomechanics of turtle shell: How whole shells fail in compression. J Exp Biol 319:86–98. Pritchard PCH. 2008. Evolution and structure of the turtle shell. In: Wyneken J, Godfrey MH, Bels V, editors. Biology of Turtles. Boca Raton, FL: Taylor & Francis Group. pp 45–84. Rivera G, Stayton CT. 2011. Finite element modeling of shell shape in the freshwater turtle Pseudemys concinna reveals a trade-off between mechanical strength and hydrodynamic efficiency. J Morphol 272:1192–1203. Rohlf FJ, Corti M. 2000. Use of two-block partial least-squares to study covariation in shape. Syst Biol 49:740–753. Shine R, Iverson JB. 1995. Patterns of survival, growth and maturation in turtles. Oikos 72:343–348. Somers K. 1986. Multivariable allometry and removal of size with principal components analysis. Syst Zool 35:359–368. Stayton CT. 2009. Application of thin-plate spline transformations to finite elements models, or, how to turn a bog turtle into a spotted turtle to analyze both. Evolution 63: 1348–1355. Stayton, CT. 2011. Biomechanics on the half shell: Functional performance influences patterns of morphological variation in the emydid turtle carapace. Zoology 114:213–223. Vega C, Stayton CT. 2011. Dimorphism in shell shape and strength in two species of emydid turtle. Herpetologica 67: 397–405. Zelditch ML, Swiderski DL, Sheets HD, Fink WL. 2004. Geometric Morphometrics for Biologists: A Primer. San Diego: Elsevier Academic Press. 416 p.
Journal of Morphology
Morphological and Mechanical Changes in Juvenile Red-Eared Slider Turtle (Trachemys scripta elegans) Shells During Ontogeny Jennifer F. Fish and Charles T. Stayton* Department of Biology, Bucknell University, Lewisburg, Pennsylvania 17837 ABSTRACT Turtles experience numerous modifications in the morphological, physiological, and mechanical characteristics of their shells through ontogeny. Although a general picture is available of the nature of these modifications, few quantitative studies have been conducted on changes in turtle shell shape through ontogeny, and none on changes in strength or rigidity. This study investigates the morphological and mechanical changes that juvenile Trachemys scripta elegans undergo as they increase in size. Morphology and shell rigidity were quantified in a sample of 36 alcoholpreserved juvenile Trachemys scripta elegans. Morphometric information was used to create finite element models of all specimens. These models were used to assess the mechanical behavior of the shells under various loading conditions. Overall, we find that turtles experience complementary changes in size, shape, deformability, and relative strength as they grow. As turtles age their shells become larger, more elongate, relatively flatter, and more rigid. These changes are associated with decreases in relative (size independent) strength, even though the shells of larger turtles are stronger in an absolute sense. Decreased deformability is primarily due to changes in the size of the animals. Residual variation in deformability cannot be explained by changes in shell shape. This variation is more likely due to changes in the degree of connectedness of the skeletal elements in the turtle’s shells, along with changes in the thickness and degree of mineralization of shell bone. We suggest that the mechanical implications of shell size, shape, and deformability may have a large impact on survivorship and development in members of this species as they mature. J. Morphol. C 2013 Wiley Periodicals, Inc. 275:391–397, 2014. V
culminating in a fully ossified shell (Gilbert, 2001). These morphological and physiological changes have profound biomechanical implications: immediately after hatching, juvenile turtle shells are relatively weak and compliant, and provide little defense against the numerous predators that small turtles routinely encounter (Magwene and Socha, 2013). However, as the shell increases in size and degree of ossification, its resistance to stresses and strains imposed by outside forces (such as those from a predator’s jaws) increases, so that large adult turtles with fully ossified shells are, in contrast to juveniles, remarkably resistant to predation (Jackson and Janzen, 2000; Pritchard, 2008; Magwene and Socha, 2013). This resistance has been invoked to explain, in part, the remarkable survival rates of adult turtles when compared with other reptiles (Gibbons, 1987; Iverson, 1991b; Shine and Iverson, 1995). However, little is known about how those changes (in size, shape, and degree of ossification) quantitatively affect the defensive capabilities of the shell over ontogeny. It is clear that at some point during ontogeny the turtle shell changes from a relatively ineffective method of defense [juveniles use other methods of defense against predators instead (Britson and Gutzke, 1993)] to an immensely effective defensive structure. However, the exact timing and duration of this transition remains unknown. Moreover, the interaction
KEY WORDS: turtle; shell; biomechanics; ontogeny; ossification
Additional Supporting Information may be found in the online version of this article.
INTRODUCTION
Contract grant sponsor: DBI; Contract grant number: 0743460; Contract grant sponsor: IIS (T. Rowe); Contract grant number: 0208675.
Juvenile turtles experience numerous morphological, physiological, and biomechanical changes to their shells through ontogeny (Magwene, 2001; Gilbert et al., 2001; Angielczyk and Feldman, 2013; Magwene and Socha, 2013). Besides the obvious increase in size, their shells also change shape (Magwene, 2001; Angielczyk and Feldman, 2013) and degree of ossification as the initially separate bone growth centers of the carapace and plastron begin to interact and eventually merge, C 2013 WILEY PERIODICALS, INC. V
*Correspondence to: C. Tristan Stayton; Department of Biology, Bucknell University, 337 Biology Building, Lewisburg, PA 17837. E-mail: [email protected] Received 9 April 2013; Revised 6 September 2013; Accepted 3 October 2013. Published online 3 December 2013 in Wiley Online Library (wileyonlinelibrary.com). DOI 10.1002/jmor.20222
392
J.F. FISH AND C.T. STAYTON
of various aspects of the turtle shell, its size, shape, and degree of ossification, in determining its mechanical strength has never been studied. Such aspects, however, should have a great deal of influence over the ability of the turtle shell to resist predator attacks: as size and degree of ossification increase, presumably so does mechanical strength and stiffness, and previous studies (Rivera and Stayton, 2011; Stayton, 2009, 2011; Vega and Stayton, 2011) have revealed strong associations between shell shape and strength. Better studied are the general patterns of growth and ossification of the turtle shell. Juvenile turtles grow at a faster rate than adults (Gibbons and Greene, 1978). In general, the carapaces of juvenile turtles are more rounded and relatively taller than those of adults (Jolicoeur and Mosimann, 1960; Somers, 1986; Lestrel et al., 1989). Plastrons usually become more elongate, wider toward the read, and narrower at the bridge (Angielczyk and Feldman, 2013). Ossification begins, but does not complete, before hatching. In Trachemys scripta elegans, for example, the ribs begin to calcify 45 days after hatching. Only by 118 days posthatching has the ossifying dermis between the ribs coalesced. Similarly, the plastron starts to ossify before the time of hatching, but continues to grow and fuse posthatching until fully ossified (Gilbert et al., 2001; Magwene, 2001). Overall, turtle shell ossification and mineralization are still occurring posthatching, and size and shape continue to change until at least maturity, but to what degree these changes affect the mechanical behavior of turtle shells is still unknown. In this study, we examine the changes that occur in shell shape and shell mechanics during the growth of juvenile Trachemys scripta elegans. We address two main questions. First, how do the shape and deformability of the turtle shell change as size increases? Second, are changes in shape associated with changes in the mechanical behavior of turtle shells? We predict that the turtle shell will become less circular in dorsal view and more elongate as size increases, as has been noted (but infrequently quantified) in previous studies (Jolicoeur and Mosimann, 1960; Somers, 1986; Lestrel et al., 1989). Similarly, we predict that the turtle shell will become more rigid (less deformable) as size increases, and that this change in rigidity will be gradual, matching the aymptotic, matching the asymptotic rate of change in carapace length (CL). Finally, because changes in both shape and deformability were found among juvenile turtles of different sizes, we wanted to examine a potential relationship between those properties. Specifically, we were interested in the possibility that changes in deformability might be partially due to changes in shell shape, as opposed to changes in degree of ossification, shell bone thickness, or shell material Journal of Morphology
properties. Certain structural shapes are stronger than others, or less likely to deform significantly under loads. By isolating the effects of shell shape on shell strength, we can determine whether small juvenile turtles can partially mitigate the structural disadvantages of incompletely ossified, incompletely mineralized, or relatively thin shells with relatively strong shell shapes. We predict that the changes in shell shape over ontogeny will be associated with changes in relative shell strength and deformability, independent of other factors. Note that this prediction is not trivial, even with known changes in shape and a method of assessing function that only incorporates shape data – many-to-one mapping of form onto function in turtle shells [demonstrated in Stayton (2011)] means that changes in shape are not necessarily associated with changes in functional performance (Alfaro et al., 2005). It is also not clear whether the shapes of younger, smaller turtle shells are expected to be stronger or weaker than those of older, larger turtles. Small turtles could mitigate their other mechanical disadvantages with stronger shell shapes, as mentioned above, but smaller turtle shells might also provide inadequate protection against predators at any shape. In this case, smaller turtles might optimize their shell for other functions (e.g., crypsis or decreasing drag during swimming), and only attain strong shell shapes once the shell is sufficiently large and ossified that shell shape might make a difference in the animal’s ability to defend against predatory attacks. MATERIALS AND METHODS Specimens and Morphometrics Hatchling and juvenile Trachemys scripta elegans (WiedNeuwied, 1839) specimens (n 5 36) were obtained from the Carnegie Museum of Natural History (Supporting Information Table S1). All specimens were wild caught, fixed in formalin, and then preserved in 70% ethanol. Straight CL was measured on all specimens using digital calipers. Specimens ranged from 30.2 to 90.3 mm in length. Adults of these species average 265 mm in length, so the specimens range from 11 to 34% of their adult length (Ernst and Barbour, 1989). Adults were not used as we were only interested in changes up to the complete ossification of the shell. Each turtle was photographed against a black background in dorsal, lateral (right side), and ventral views with a Nikon Coolpix 60003 digital camera. For ventral and dorsal views the turtle was oriented with the plastron horizontal. For lateral views the midline was horizontal and the plastron was oriented perpendicular to the horizontal. Putty was used to ensure that turtles were oriented properly. The camera was mounted on a tripod and positioned approximately 40 cm above the specimen. Before photography, a grid was photographed to ensure that distortion was minimal. tpsDig (Rohlf, 2008) was used to digitize all images: a total of 59 landmarks were digitized on each shell (Fig. 1; Supporting Information Table S2). The coordinates of landmarks in all views were then assembled into a single, three-dimensional data set using a custom MATLAB routine written by one of the authors (Stayton, 2009). The coordinates were then aligned using a Procrustes fit
MORPHOFUNCTIONAL CHANGES IN JUVENILE TURTLE SHELLS
Fig. 1. Shell landmarks in A) dorsal view and B) ventral view. (Zelditch et al., 2004), and those values were used as the shape variables for subsequent analyses.
Shell Deformability The deformability of each turtle shell was measured by placing a series of loads (0.5, 1, and 1.5kg) on the dorsal-most point of the shell, and measuring the change in height of the shell, relative to its initial height. These measures thus correspond to whole-organism analogs of mechanical strain. For each specimen, the slope of the scaled deformation v. load relationship was computed using least-squares regression. While these slopes were computed from only four data points per specimen (three loads plus the origin), our data showed high repeatability (r2 5 0.81) such that slopes resulting from these data are probably robust. The slope, which we call deformability, is similar to elasticity, in a materials science context, in that it represents how readily the shells change shape in response to a load. However, it is not equivalent for two reasons. First, we were unable to calculate a cross-sectional area over which the load was applied, and thus did not scale load by area so as to calculate an analogue of mechanical stress. Moreover, we did not perform the more standard regression of load onto deformation as some large specimens did not measurably deform at all, which would have given an undefined slope for a standard load v. deformation curve. Thus, here, low values represent less easily deformed, or stiffer, turtle shells while higher slopes represent more easily deformed shells.
Modeled Shell Strength and Deformability Shell strength was modeled using finite element (FE) methods. FE methods are a suite of engineering techniques that can be used to model the mechanical behavior of complex structures
393
(Dumont et al., 2005). These methods operate by breaking up a complex shape (or more properly, a computer model of a complex shape) with an unknown response to mechanical stress into a large number of simpler shapes with known responses to mechanical stress. Here, a model of a turtle shell is built from 41.615 four-sided polyhedra, each defined by the x-, y-, and zcoordinates of four points known as nodes. Then a load or force is applied to a single node. The model is held in place at a set of other nodes known as “restraints”; these restraints ensure that the model deforms (instead of simply moving) in response to the load. The load produces stress and deformation on all elements that share that node. These stresses, in turn, affect neighboring elements, and so on, and the stress propagates throughout the entire model. FE methods model this propagation and calculate the stresses that develop in each element. Models with different shapes generate different stresses for a given load. Average or maximum stresses across all elements in each model can then be used to determine which model is stronger, that is, models that develop lower stresses for a given load are less likely to fail (fracture or break) for a given load or more deformable. Here, the landmark configurations of each specimen were used to generate a FE model of the shell using the method of Stayton (2009). Briefly, this method uses the thin-plate spline interpolation function to transform a preexisting FE model into one corresponding to the shape of a new set of landmarks. The base model used here captures all aspects of the morphology of the Emydid turtle shell, that is, vertebral column, ribs, and so on, so all models derived from this base have those features as well. This method has been validated on real turtle specimens (Stayton, 2009) and has been successfully used elsewhere to assess the mechanical behavior of shells both within (Rivera and Stayton, 2011; Vega and Stayton, 2011) and between (Stayton, 2011) species. Three restraints on the plastron were used: one on the midline close to the junction between the pectoral and humeral scutes, and one each on the posterior margins of the connection between bridge and plastron. Eight loads along the midline and margin of the carapace (Fig. 2) were assigned to the preexisting FE models before transformation. Thus, all restraints and loads were located on corresponding points on all models. We were interested in isolating the effect of shell shape on shell strength and deformability from all other factors. One important nonshape factor that can influence strength is size. Thus, all models were scaled to a common size before analysis. As strength is proportional to the cross-sectional area of structures, all models were scaled to the same volume to the twothirds power (Dumant et al., 2009). We also constructed a separate set of models which were scaled to the actual sizes of all specimens. Similarly, bone thickness and material properties were consistent among all models. All models were analyzed using Strand7 FE Analysis software (Strand 7 Pty. Ltd., Sydney, Australia). Transformed models were imported into the analysis program and cleaned to eliminate any extremely elongate elements (which can produce artifactually high stresses). All elements in all models were assigned an identical set of material properties: an elastic modulus of 20 GPa and a Poisson’s ratio of 0.3. These correspond to measured values of turtle shell bone (Rhee et al., 2009). Loads were set at 200 N, a value corresponding to the bite force of a medium-sized predator such as a coyote (Christiansen and Wroe, 2007). The shell was modeled as a linear elastic material (Dumont et al., 2005). This is probably an oversimplification of the actual mechanical behavior of adult turtle shells, but such approximations are appropriate for biological analyses (Straight et al., 2005), especially when relative rather than absolute performance is being assessed. Once models were run, von Mises stress values were extracted for all elements in all models. Von Mises stresses are composite measures of stress predict the behavior of biological structures quite well (Dumont et al., 2005). The average von Mises stress values for all elements and all loads in each model were used for all subsequent hypothesis testing. We also calculated deformabilities from these models using a similar
Journal of Morphology
394
J.F. FISH AND C.T. STAYTON factors (shell shape, shell thickness, shell bone mineralization, etc.) that could influence deformability, we had no a priori expectation of the nature of this relationship and used both a linear regression and Kendall’s rank correlation coefficient to assess significance. All else being equal, biomechanical first principals indicate that shell deformability should be proportional to shell cross-sectional area; assuming isometry, this means that deformability should scale as 1/CL2. We thus assessed the significance of this relationship as well using linear regression (log-log data were not used as some shells had deformability values of 0). We also inspected the deformability versus size plot for evidence of inflection points: sizes at which the relationships between size and stiffness changed. A strong relationship was found between shell size and deformability. To determine whether shell shape could account for some of the unexplained variation in deformability, we regressed the residuals from the deformability versus 1/CL2 relationship against deformability predicted from shape alone. To assess the relationship between shell size and strength, we ran a simple univariate regression of CL versus (size corrected) average shell strength (von Mises stresses averaged over all elements and all load cases for each specimen). Again, as a significant relationship was found, we used tpsRegr to separately analyze the relationships between strength and dorsal, lateral, and ventral aspects of shell shape. To more fully visualize the relationship between shell shape and strength, we conducted a two-block partial least-squares analysis (Rohlf and Corti, 2000) of all shape variables and the average shell strength (von Mises stresses averaged over all elements) for all eight load cases for each specimen. We also regressed CL against shell strength for shells scaled to actual size.
RESULTS Shell Size and Shape
Fig. 2. Trachemys scripta elegans, sample shell model. A) Dorsal view with all loads indicated by filled circles. B) Ventral view with restraints indicated by Xs. procedure as was used for real specimens. Shell height was calculated as the vertical distance between the dorsal-most point on the carapace and the ventral-most point on the plastron. Heights were calculated before and after loading, and the difference was divided by the original height. Since there was no measurement error for these calculations and we assumed linear elastic behavior for all models, all slopes were calculated from a single load.
Data Analysis A series of linear multivariate or univariate regressions was run to test all of the hypotheses. Unless otherwise indicated, all statistical analyses were conducted using PAST (Hammer et al. 2001). To assess how shape changes with size, we ran a multivariate regression of all shape variables on CL. A significant relationship between size and shape was found, so to further dissect the nature of the shape changes we used tpsRegr (Rohlf, 2010) to separately analyze size-related shape changes of the shell in dorsal, lateral, and ventral view. To assess how shell stiffness changed with growth, we regressed shell deformability versus CL. Given the numerous
Journal of Morphology
The multivariate regression revealed a significant relationship between size and shape (P < 0.001; see also Fig. 3). Significant correlations were also observed in dorsal, lateral, and ventral views (all P < 0.001). In general, smaller turtles have a more highly domed and more circular (in dorsal view) carapace with relatively larger marginal scutes, while larger turtles have a more elongated shell with more compact anterior and posterior regions. Smaller turtles have a slightly more circular plastron, with a more rounded bridge region, compared to larger turtles. These shape changes are most noticeable in lateral view; the changes in plastron shape are most subtle (Supporting Information Fig. S1). Shell Deformability A significant correlation between shell size and deformability was found using both linear regression (r2 5 0.637, P 5 1.52 3 1028) and Kendall’s rank correlation coefficient (s 5 20.719, P 5 2.27 3 1029). The relationship between deformability and 1/CL2 was even stronger (r2 5 0.718, P 5 2.69 3 10210). The plot of shell deformability versus size reveals an inflection around 30–50 mm CL (Fig. 4). At this point, the deformability of the shell, which had been decreasing rapidly with increasing size, begins to decrease at a much lower rate. At around 70 mm in length, the shell has become
MORPHOFUNCTIONAL CHANGES IN JUVENILE TURTLE SHELLS
395
Fig. 3. Trachemys scripta elegans, shell size versus average von Mises stress, calculated from all elements across all load cases. Diagrams of small and large turtle shells in dorsal and lateral view on x-axis; diagrams of weak and strong turtle shells on y-axis. These diagrams represent shapes associated with the extremes of the size and strength ranges. Diagrams in the lower left represent dorsal and lateral views of the average turtle shape.
approximately as stiff as it will be for the rest of the turtle’s ontogeny. Shape, that is, deformability predicted from shape independent of size, explained very little of the residual variation in deformability (r2 5 0.0289), and the relationship, although positive, was not significant (P 5 0.325). Modeled Shell Strength and Deformability There was a significant relationship between shell shape and modeled shell strength when all other factors were held constant. In general, shells that have taller and longer bridges developed lower stresses than those that have shorter and more compressed bridges. These differences are similar to those seen between small and large turtles. Indeed, if stresses are calculated from all models scaled to comparable sizes (see above), then there is a significant negative correlation between CL and shell strength (P 5 0.006; Fig. 3). In other words, smaller turtles have shell shapes which are stronger than those of larger turtles,
Fig. 4. Trachemys scripta elegans, shell deformability versus shell size. Inflection point in shell deformability lies between 30 and 50 mm CL.
and the greater deformability of smaller turtle shells occurs despite, not because of, their shapes. Of course, if the FE models are scaled to actual size, the shells of larger turtles are stronger (P < 0.001). Journal of Morphology
396
J.F. FISH AND C.T. STAYTON
DISCUSSION We found a significant relationship between size and shape. As predicted, smaller turtles were more domed in lateral view and more circular in dorsal view. This is consistent with previous studies (Jolicoeur and Mosimann, 1960; Lestrel et al., 1989; Somers, 1986). There are many possible explanations for this pattern, both adaptive (see below) and nonadaptive. Among the latter are the possibilities that the shapes of juvenile turtle shells are primarily determined by the ossification patterns of the shells, or with the necessity of prehatching turtle shells fitting efficiently into eggs. Turtle shells showed a significant tendency to become less deformable as they grew, as predicted. Biomechanical first principals concerning shell thickness (assuming isometry) explain approximately 70% of the variation in deformability. However, some of the unexplained variation in this relationship is manifested in the fact that the plot of deformability versus CL does not show a smooth curve. Instead, and in contrast to our expectations, an inflection point for increased stiffness was observed at 30–50 mm CL. This inflection point shows a drastic change in the slope of the relationship between shell size and deformability, and helps to discriminate between possible explanations for residual variation in deformability. One possible explanation for this pattern can be rejected; modeled differences in deformability based on shape alone could only account for a small (3%) and nonsignificant amount of variation in residual observed deformability. Instead, the decreased deformability in the shells of larger turtles could result from increases in the elastic modulus of their shell bone (higher elastic moduli being associated with stiffer materials), possibly due to greater mineralization of the skeletal tissues. Or it could result from increases in relative shell thickness, which would lead to disproportionate increases in the cross-sectional area of the turtles’ shells, leading in turn to lower stress and strain in the bone and less deformation overall. Changes in material properties or relative thickness may well be responsible for some of the changes in turtle shell deformability. However, neither of these causes would necessarily produce an abrupt change in slope, although rapid increases in mineralization, shell thickness, or both at 30–50 mm CL could produce the observed inflection point. Alternately, the inflection point could represent the time at which the formerly separate ossification centers in the turtle’s shell unite into a single element (Gilbert et al., 2000). At this point, loads that formerly were resisted only by small individual bones and the connective tissues between them would now be resisted by a single unified structure which will still continue to ossify and stiffen after the separate ossification centers have united. Such a change would necesJournal of Morphology
sarily produce an inflection point in a plot of shell deformability versus age or size. If such inflection points prove to be common features of the ontogeny of turtle shell mechanics, this will provide greater evidence for the role of shell developmental patterns as proposed here. Finally, a significant relationship was also found between shell shape and shell strength. Smaller turtles were modeled as having stronger-shaped shells than larger turtles, in proportion to their size, although larger turtle shells were stronger in absolute terms. This finding suggests a possible adaptive interpretation for the changes in shell shape as turtles grow. When resisting predator attacks, juvenile turtles are at a disadvantage in terms of size and shell stiffness (Iverson, 1991a). It is highly unlikely that juvenile turtles can completely compensate for their thin, poorly ossified, and incomplete shells with relatively strong shell shapes. However, such shapes might make a difference in a small but evolutionary significant proportion of predator encounters. With older turtles, shell size itself may provide sufficient strength to withstand predator attacks so that changes in shape can optimize other shell functional properties such as reducing drag during swimming. These adaptive explanations are not necessarily incompatible with previously mentioned nonadaptive explanations; shells that fit well inside eggs may also fortuitously provide high strength for their size. Our results only apply to Trachemys scripta elegans and to turtles which show similar ontogenetic changes in shell ossification, shape, and deformability. The ossification patterns of turtle shells have only been studied in a few species (though these cover a fairly wide phylogenetic range; Gilbert et al., 2001), and while gross patterns of ossification are conserved there are differences which may have functional significance. Similarly, patterns of shape change have been well quantified for some groups but not others. Within Emydids, patterns of ontogenetic shape change in the plastron vary among species (Angielczyk and Feldman, 2013), and the same is likely true for carapace shape. This does not preclude similarity in change in shell strength among species, given the manyto-one nature of the morphology-function relationship (Alfaro et al., 2005) but further study is needed to determine whether the Trachemys scripta elegans pattern is typical for turtles. In conclusion, this study confirmed and quantified expected ontogenetic patterns in turtle shell shape and deformability. We demonstrate that turtle shells become stiffer and stronger during ontogeny, in spite of changes in shell shape. Although as turtles age their shells become stronger in an absolute sense, their shell shapes become relatively weaker. Overall, our results suggest that turtles experience complementary changes in size, shape, and relatively strength as they grow.
MORPHOFUNCTIONAL CHANGES IN JUVENILE TURTLE SHELLS
ACKNOWLEDGMENTS We thank S. Rogers at the Carnegie Museum of Natural History for access to the turtle specimens, and B. Dumont, I. Grosse, and S. Werle at the University of Massachusetts at Amherst for assistance in developing the original turtle shell FE model. J. Maisano and the staff of the University of Texas at Austin High-Resolution X-ray CT Facility provided access to the original CT scan of a bog turtle. LITERATURE CITED Alfaro ME, Bolnick DI, Wainwright PC. 2005. Evolutionary consequences of many-to-one mapping of jaw morphology to mechanics in labrid fishes. Am Nat 165:E140–E154. Angielczyk KC, Feldman CR. 2013. Are diminutive turtles miniaturized? The ontogeny of plastron shape in emydine turtles. Biol J Linn Soc 108:727–755. Britson C, Gutzke W. 1993. Antipredator mechanisms of hatchling freshwater turtles. Copeia 1993:435–440. Dumant ER, Grosse IR, Slater GL. 2009. Requirements for comparing the performance of finite element models of biological structures. J Theor Biol 256:96–103. Ernst CH, Barbour RW. 1989. Turtles of the World. Washington, DC: Smithsonian Institution Press. 313 p. Gibbons JW. 1987. Why do turtles live so long? BioScience 37: 262–269. Gilbert SF, Loredo GA, Brukman A, Burke AC. 2001. Morphogenesis of the turtle shell: The development of a novel structure in tetrapod evolution. Evol Dev 3:47–58. Hammer ï, Harper DAT, Ryan PD. 2001. PAST: Paleontological statistics software package for education and data analysis. Palaeontologia Electronica 4:1–9. Iverson J. 1991a. Life history and demography of the yellow mud turtle, Kinosternon flavescens. Herpetologica 47:373– 395.
397
Iverson J. 1991b. Patterns of survivorship in turtles (order Testudines). Can J Zool 69:385–391. Jolicoeur P, Mosimann JE. 1960. Size and shape variation in the painted turtle. A principal component analysis. Growth 24:339–354. Lestrel PE, Bernard SG, McNabb EG. 1989. Carapace growth of the turtle Chrysemys scripta: A longitudinal study of shape using fourier analysis. Anat Anz 168:135–143. Lindeman PV. 1999. Growth curves for Graptemys, with a comparison to other Emydid turtles. Am Midl Nat 142:141–151. Magwene PM. 2001. Comparing ontogenetic trajectories using growth process data. Syst Biol 50:640–656. Magwene PM, Socha J. 2013. Biomechanics of turtle shell: How whole shells fail in compression. J Exp Biol 319:86–98. Pritchard PCH. 2008. Evolution and structure of the turtle shell. In: Wyneken J, Godfrey MH, Bels V, editors. Biology of Turtles. Boca Raton, FL: Taylor & Francis Group. pp 45–84. Rivera G, Stayton CT. 2011. Finite element modeling of shell shape in the freshwater turtle Pseudemys concinna reveals a trade-off between mechanical strength and hydrodynamic efficiency. J Morphol 272:1192–1203. Rohlf FJ, Corti M. 2000. Use of two-block partial least-squares to study covariation in shape. Syst Biol 49:740–753. Shine R, Iverson JB. 1995. Patterns of survival, growth and maturation in turtles. Oikos 72:343–348. Somers K. 1986. Multivariable allometry and removal of size with principal components analysis. Syst Zool 35:359–368. Stayton CT. 2009. Application of thin-plate spline transformations to finite elements models, or, how to turn a bog turtle into a spotted turtle to analyze both. Evolution 63: 1348–1355. Stayton, CT. 2011. Biomechanics on the half shell: Functional performance influences patterns of morphological variation in the emydid turtle carapace. Zoology 114:213–223. Vega C, Stayton CT. 2011. Dimorphism in shell shape and strength in two species of emydid turtle. Herpetologica 67: 397–405. Zelditch ML, Swiderski DL, Sheets HD, Fink WL. 2004. Geometric Morphometrics for Biologists: A Primer. San Diego: Elsevier Academic Press. 416 p.
Journal of Morphology
