Finite element modeling of shell shape in the freshwater turtle Pseudemys concinna reveals a trade-off between mechanical strength and hydrodynamic efficiency

Finite Element Modeling of Shell Shape in theFreshwater Turtle Pseudemys concinna Reveals aTrade-Off between Mechanical Strength andHydrodynamic Efficiency

Gabriel Rivera1* and C. Tristan Stayton2

1Department of Ecology, Evolution, and Organismal Biology, Iowa State University, Ames, Iowa 500112Biology Department, Bucknell University, Lewisburg, Pennsylvania 17837

ABSTRACT Aquatic species can experience differentselective pressures on morphology in different flow regimes.Species inhabiting lotic regimes often adapt to these condi-tions by evolving low-drag (i.e., streamlined) morphologiesthat reduce the likelihood of dislodgment or displacement.However, hydrodynamic factors are not the only selectivepressures influencing organismal morphology and shapeswell suited to flow conditions may compromise performancein other roles. We investigated the possibility of morphologi-cal trade-offs in the turtle Pseudemys concinna. Individualsliving in lotic environments have flatter, more streamlinedshells than those living in lentic environments; however,this flatter shape may also make the shells less capable ofresisting predator-induced loads. We tested the idea that‘‘lotic’’ shell shapes are weaker than ‘‘lentic’’ shell shapes,concomitantly examining effects of sex. Geometric morpho-metric data were used to transform an existing finite ele-ment shell model into a series of models corresponding tothe shapes of individual turtles. Models were assigned iden-tical material properties and loaded under identical condi-tions, and the stresses produced by a series of eight loadswere extracted to describe the strength of the shells. ‘‘Lotic’’shell shapes produced significantly higher stresses than‘‘lentic’’ shell shapes, indicating that the former is weakerthan the latter. Females had significantly stronger shellshapes than males, although these differences were less con-sistent than differences between flow regimes. We concludethat, despite the potential for many-to-one mapping of shellshape onto strength, P. concinna experiences a trade-off inshell shape between hydrodynamic and mechanical per-formance. This trade-off may be evident in many other tur-tle species or any other aquatic species that also depend ona shell for defense. However, evolution of body size may pro-vide an avenue of escape from this trade-off in some cases,as changes in size can drastically affect mechanical perform-ance while having little effect on hydrodynamic performance.J. Morphol. 272:1192–1203, 2011. � 2011Wiley-Liss, Inc.

KEY WORDS: finite element; stress; flow regime; shellmorphology; trade-off

INTRODUCTION

The velocity of water flow is a critical feature ofthe environment that impacts numerous aspects ofthe biology of aquatic species, including reproduc-

tion (Denny et al., 2002; Riffell and Zimmer, 2007),feeding (Okamura, 1984, 1985; Marchinko, 2003;Pratt, 2008), and likelihood of dislodgement of ses-sile taxa (Carrington, 2002; Koehl et al., 2008;Stewart, 2008) or displacement of free-swimmingtaxa (Gibbins et al., 2007). Aquatic habitats differin terms of flow velocity, such that individuals liv-ing in different aquatic environments may experi-ence different flow regimes and be subjected to dif-ferent selective pressures. A relationship betweenflow velocity and morphology has been identifiedin a broad range of taxa, including plants andalgae (Puijalon and Bornette, 2004; Boller andCarrington, 2006; Stewart, 2008), invertebrates(Marchinko, 2003; Holomuzki and Biggs, 2006),and vertebrates (Pakkasmaa and Piironen, 2001;McGuigan et al., 2003; Peres-Neto and Magnan,2004; Rivera, 2008). In most cases, these morpho-logical differences appear to be adaptive: speciesliving in fast-flow regimes show morphological fea-tures that may reduce drag forces, thereby reduc-ing the risk of dislodgement or making it easierfor animals to move through the habitat. However,although these morphologies may be beneficialwith regard to water flow, organisms must alsocontend with other environmental factors for

Additional Supporting Information may be found in the onlineversion of this article.

Contract grant sponsors: SICB Grant-in-Aid-of-Research, AmericanMuseum of Natural History Theodore Roosevelt Memorial Award,American Society of Ichthyologists and Herpetologists Gaige FundAward (to G.R.).

*Correspondence to: Gabriel Rivera, Department of Ecology, Evo-lution, and Organismal Biology, Iowa State University, Ames, Iowa50011. E-mail: [email protected]

Received 21 December 2010; Revised 1 March 2011;Accepted 13 March 2011

Published online 31 May 2011 inWiley Online Library (wileyonlinelibrary.com)DOI: 10.1002/jmor.10974

JOURNAL OF MORPHOLOGY 272:1192–1203 (2011)

� 2011 WILEY-LISS, INC.

which morphology is important (e.g., predator–prey interactions, competition, and temperature).Characteristics that improve hydrodynamic per-formance may decrease performance in other func-tions, such as predator–prey interactions (Claudeet al., 2003; Holomuzki and Biggs, 2006; Blobet al., 2010). Therefore, it is important to under-stand how morphological differences associatedwith different flow regimes affect other aspects ofan organism’s biology.

Another aspect of functional performance thatcan be influenced by shape is defense against pred-ators. Prey species have evolved a variety of mor-phological strategies that reduce their risk of pred-atory encounters and/or increase their ability tosurvive predatory attacks. Structural adaptationsthat provide protection from predation includespines (Bollache et al., 2006), shells (Hoso andHori, 2008), cryptic (Vignieri et al., 2010), and mi-metic colorations and morphologies (Brodie, 1993;Huffard et al., 2010). Variation among such struc-tural adaptations (i.e., increased number of spinesand armor plates, thicker shells, etc.) has beenfound to correlate with different levels of predationand/or differences in predator regimes (Johanssonand Samuelsson, 1994; Riessen and Young, 2005;Benard, 2006; Lakowitz et al., 2008; Hovermanand Relyea, 2009; Marchinko, 2009). Furthermore,several experimental studies have demonstratedthat relatively small differences in morphology,including predator-induced intraspecific differen-ces, can impact survival during predation (Raw-lings, 1994; Mikolajewski, 2006; Grey et al., 2007;Hoso and Hori, 2008). Those morphological var-iants that display increased survival may in turnexperience trade-offs in other aspects of life history(e.g., growth and reproduction; Stemberger, 1988;LaFiandra and Babbitt, 2004). In particular, func-tional trade-offs between traits that protectagainst predation and those adapted for high flowshave been identified. Holomuzki and Biggs (2006)found that for the polymorphic mudsnail Potamo-pyrgus antipodarum, the predominant morphotypeinhabiting slow-flow habitats (i.e., lakes) possessedspines, whereas the predominant morphotype infast-flow habitats (i.e., streams) lacked spines.Additional experiments demonstrated that smooth-shelled snails were less prone to flow-induced dis-lodgement but were also more susceptible to pre-dation by fishes. Despite the insights provided byHolomuzki and Biggs (2006), little is knownregarding how flow-associated morphologies affectthe risk of predation or the ability to withstandpredatory attacks for the majority of aquaticorganisms.

The shells of freshwater turtles represent anexcellent model system in which to examine therelationship between flow-associated morphologiesand predation risk, and to test for possible trade-offs between morphology and function. The turtle

shell is a complex, rigid morphological structurewith a number of known functions; among these,the shell acts as a hydrodynamic element duringaquatic locomotion and resists loads applied bypredators. Because of its rigidity, physical andcomputational models are capable of closelyapproximating in vivo responses to forces, as per-formance can be evaluated without concern forbehaviorally-induced changes to morphology.Finally, considerable interspecific and intraspecificvariation in shell morphology exists within turtles,and although it seems reasonable that this varia-tion would affect hydrodynamic and mechanicalperformance, the actual effects of different mor-phologies on performance have only been studiedin a few cases (Rivera, 2008; Stayton, 2009).

Recent studies have suggested that aquatic flowregimes influence intraspecific variation in shellshape for multiple species of freshwater turtles(Aresco and Dobie, 2000; Lubcke and Wilson, 2007;Rivera, 2008). Animals inhabiting high flow (i.e.,lotic) environments experience increased hydrody-namic drag, which is a force that resists forwardmotion. Drag forces incurred by the shell increasein proportion to velocity squared, and, thus, areconsiderably higher in lotic habitats. Streamlinedmorphologies can help to reduce the effects ofthese forces (e.g., decreased locomotor efficiencyand increased energetic costs). In Pseudemysconcinna, the only species for which a hydrody-namic effect of this shape variation has beenexamined, shell flattening results in lower dragcoefficients, and thus, greater hydrodynamic effi-ciency (Rivera, 2008). Similarly, a correlationbetween flattened shells and lotic flow regimes hasbeen found for other turtle species (Lubcke andWilson, 2007). However, it is possible that theseflattened shells experience a trade-off betweenhydrodynamic efficiency and strength. More domedshells have been shown to withstand greater com-pressive forces than more dorsoventrally-flattenedones (Stayton, 2009). Still, Stayton (2009) demon-strated that turtle shells can show many-to-onemapping of overall shell strength onto morphology(Alfaro et al., 2004, 2005; Wainwright et al., 2005;Wainwright, 2007). Thus, it is possible that theshell shapes of lotic populations are both morestreamlined than, and equally as strong as, thosefrom lentic populations.

The general goal of this study is to assesswhether the flow-associated variation in shellshape observed in P. concinna (Rivera, 2008)affects the shell’s ability to withstand externalforces, as measured by the stresses modeled acrossthe shell under specific loads. Specifically, we usefinite element (FE) modeling in conjunction withthe original morphometric data used by Rivera(2008) to test two alternate hypotheses. 1) Theflatter, more hydrodynamic shells of turtles fromlotic habitats are weaker (that is, they experience

FINITE ELEMENT MODELING OF SHELL SHAPE IN P. concinna 1193

Journal of Morphology

higher stresses for a given load) than those of themore domed turtles inhabiting lentic waters, thusindicating a trade-off between hydrodynamic effi-ciency and mechanical strength in the shells ofP. concinna. 2) Shell stresses do not differ betweenhabitats, indicating that P. concinna demonstratesmany-to-one mapping of overall shell strengthonto morphology, so that the shell shapes of loticpopulations are both more streamlined than, andequally as strong as, those from lentic populations.The findings of this study have important implica-tions for understanding the evolution of complex,multifunction structures.

MATERIALS AND METHODSMorphometric Data and Analyses

Coordinate data from a subset of P. concinna specimens previ-ously analyzed by Rivera (2008) were used (N 5 158; males,N 5 117; females, N 5 41). To facilitate accurate classificationof sex via secondary sexual characteristics (elongate foreclawsand greater precloacal tail length) and to avoid the confoundingeffects of ontogeny, all specimens originally used by Rivera(2008) were adults with carapace lengths of at least 16.0 cm(Fahey, 1987; Aresco and Dobie, 2000; Rivera, 2008). A detailedlist of specimens used in this study is provided as SupportingInformation.Coordinate data consist of x-, y-, and z-coordinates of 33 land-

marks located at the junctions of scutes on the right side of thecarapace (Fig. 1). The coordinates for all specimens werealigned using a Generalized Procrustes Analysis (Rohlf andSlice, 1990; Zelditch et al., 2004), which removes all nonshapeinformation (translation, scale, and rotation) from the data set.A principal components analysis (PCA) of these aligned coordi-nate data was then used to produce the shape variables (N 592) used in statistical tests. Note that to avoid data redundancyin this symmetrical structure, statistical analyses of shape wereconducted on data from the right half of the shell. However, asFE model generation (see below) required landmark coordinatesfrom the entire shell, a mirror left side was produced by reflect-ing the right side across the midline of the shell (defined bymidline landmarks; Fig. 1) for this portion of the study.

FE Models

A FE model was constructed for each of the 158 Pseudemysshells used in this study by transforming a base model of a bogturtle (Glyptemys muhlenbergii) by the method of Stayton(2009). Briefly, this method uses a thin-plate spline function fit-ted to geometric morphometric data to transform a preexistingFE model into a new model that matches a desired shape. BothG. muhlenbergii and P. concinna belong to the same family(Emydidae) of turtles and show the same pattern of shell con-struction and scute arrangement.The original bog turtle specimen (i.e., the base model) was

scanned at the University of Texas (Austin) Computer Tomogra-phy (CT) facility, and made available to the authors. The slicesfrom the original CT data were assembled in Mimics 12 (Mate-rialise Software; Leuven, Belgium), and the resulting three-dimensional data were assembled and cleaned in GeoMagic Stu-dio 10 (GeoMagic Software; Research Triangle Park, NC). Theoriginal model consists of 46,215 tetrahedral elements. Thesame 33 landmarks digitized on the Pseudemys specimens werealso digitized on the base model. The landmark coordinatesfrom each Pseudemys specimen were reflected across the mid-line (see above) and then used as input to transform the basemodel into a model matching that particular Pseudemys speci-men. Each model was then cleaned in Strand7 Finite Element

Analysis software (Strand7 Software; Sydney, Australia). Thecleaning procedure adjusts the shape of individual elements inthe model to eliminate particularly elongate, abnormally shapedelements (which can cause artifacts during analysis) withoutchanging the shape of the overall model. No elements wereeliminated during any of the cleaning procedures; thus, all mod-els in this study had the same number of elements. Beforetransformation of the FE model, all landmark configurationswere rescaled to mechanically comparable sizes (centroid sizesquared; Dumont et al., 2009), as a result, all mechanical differ-ences reflect differences in shape among the specimens, and notdifferences in size. Additionally, all models kept the same mate-rial properties as the original model (Stayton, 2009), and allload cases and restraints are located on identical elements inall models. Thus, our mechanical analyses only investigate dif-ferences in modeled stresses due to shell shape.

The transformation procedure changes the shape of the entiremodel, including areas not well-covered by the input land-marks. Thus, the plastra and bridges (i.e., the connectionsbetween the carapace and plastron) of each model were interpo-lated from the available landmark coordinates. As we did nothave detailed information regarding bridge shape in the origi-nal Pseudemys data, and because the most prominent differen-ces between turtles living in lentic and lotic environments per-tain to the carapace (Rivera, 2008), we restricted our analysesto loads on the carapace. Furthermore, while bridges experiencerelatively high stresses during carapacial loading, inspection ofour data demonstrates that these stresses are not highly de-pendent on bridge shape itself. As such, minor variations in

Fig. 1. Location of carapacial landmarks (circles) on the car-apace of P. concinna. Landmarks are located at the intersectionof three scutes or along the edge of the shell, on the sutureformed between two marginal scutes. Dashed lines indicate bor-ders between scutes. Closed circles (N 5 33) indicate landmarksof the right side used in GM analysis and are connected by solidlines. For FE models, the closed circles on the right side of theshell were reflected (with respect to the two posteriorly posi-tioned midline points) to generate a perfectly symmetrical shell.Anterior edge of shell oriented upward. Modified from Rivera G.Integr Comp Biol, 2008, 48, 769–787, �Oxford UniversityPress.

1194 G. RIVERA AND C.T. STAYTON


bridge shape not accounted for by the interpolations likely havelittle impact on the detection of mechanical differences betweengroups.

Mechanical Analyses

Finite element analysis requires a model with a specific ge-ometry, material properties for all elements, an input load on adesignated point or area in the model, and restraints on desig-nated points in the model. Without these restraints, a forcewould produce acceleration and motion of the model, ratherthan any stress or change in shape. The geometry was obtainedfrom the transformations described above. Elements of the orig-inal bog turtle model were assigned an elastic modulus of 22GPa and a Poisson’s ratio of 0.3. These are average values forturtle shell bone obtained from previous studies (Magwene andSocha, personal communication; Stayton, unpublished data).Eight load cases were used for all analyses (Fig. 2). Only a sin-gle load was run at a time (i.e., each model was used in eightFE analyses). Each load consisted of a 200-N force placed nor-mal to the carapace at a given point. A force of approximately200 N is produced in a strong bite from a medium-sized preda-tor such as a coyote (Christiansen and Wroe, 2007), and thusrepresents a reasonable load for the turtle shells in this study.However, note that, by conducting subsequent analyses usingrelative stresses, the specific input load (N) applied will notaffect our results, and thus can be extrapolated to much higherbite forces (e.g., from alligators). Three restraints were placedon points on the bottom of the plastron. All of these parameterswere carried over during the transformation process. As no ele-ments or nodes were eliminated from any of the models, allloads and restraints are located on the exact same places in allmodels, facilitating comparisons among shapes.All analyses treated the bone of turtle shells as a linear elas-

tic material. This is a typical condition for FE analyses (Rich-mond et al., 2005; Dumont et al., 2005, 2009) and is a reasona-ble approximation of the actual behavior of turtle shells (Krausset al., 2009). All models and load cases were inspected for arti-factually high stresses. After calculations were completed, vonMises stresses (a combined measure of stress commonly used inFE analyses; Dumont et al., 2005) were extracted for all ele-ments in all load cases.As all models were scaled to the same size (centroid size

squared), actual models were very small and generatedextremely high stresses that are only meaningful in comparisonwith other models. To standardize comparisons among models,modeled stresses for each element were divided by the modeledstresses in the corresponding element in the original basemodel. As an overall measure of the response of the shell to agiven load was desired, these standardized stresses for all ele-ments were then averaged to produce a single quantitative

measure of the relative response to each load. These averagestresses served as input for all subsequent statistical analyses.As stresses are what ultimately cause a material to fail (i.e.,break), models that produce relatively low stresses are referredto as strong and those that produced relatively high stressesare referred to as weak. Furthermore, in general, an associationbetween shape and modeled stress is also referred to as anassociation between shape and strength.

Statistical Analyses

Factorial multivariate analysis of variance (MANOVA) wasused to test the effects of flow regime and sex on shell shape. Forthis analysis, the model (flow 1 sex 1 flow 3 sex 1 site) includedsite as a covariate, as multiple sites were sampled per flow regime(Rivera, 2008). Because the sample size for our analysis of shape(N 5 158) is marginally low with respect to the number of shapevariables (N 5 92), results of MANOVA on shape were confirmedusing an additional, nonparametric test: permutational MAN-OVA using Euclidean distance matrix analysis [EDMA; con-ducted using the package ‘‘vegan’’ (Oksanen et al., 2010) in R2.11.1 (R Development Core Team, 2010)]. We then conducted amultivariate regression to determine the combined effects of thetwo principal shape variables (i.e., principal components (PCs) 1and 2), both of which are strongly associated with shell doming,on individual stress variables. Note that in this study, as allaspects of the models besides shape were kept constant, all differ-ences in shell strength are ultimately due to differences in shellshape, and, therefore, a regression of all shape variables wouldaccount for all of the variation in stress. However, many-to-onemapping (Alfaro et al., 2004, 2005; Wainwright et al., 2005; Wain-wright, 2007) of shape onto functional performance has been dem-onstrated for turtle shells (Stayton, 2009), meaning that differen-ces in shape do not necessarily lead to differences in strength.Next, a second factorial MANOVA was used to test the effects offlow regime and sex on shell strength. The model (flow 1 sex 1flow3 sex1 site) used was identical to that used in the MANOVAof shell shape. In essence, our MANOVA on shell stress deter-mined whether the combined effects of a) the differences in shapebetween the groups and b) the strength of the relationshipbetween shape and stress (as demonstrated by the multivariateregressions) were strong enough to produce significant differen-ces in stress between the groups. Finally, to determine the effectsof flow and sex on the stresses produced by individual load cases,separate analysis of variance (ANOVAs) were conducted on indi-vidual stress variables; these univariate analyses also used themodel: flow 1 sex 1 flow 3 sex 1 site. All ANOVAs and MANO-VAs were conducted using R 2.11.1 (R Development Core Team,2010); multivariate regressions were conducted using Systat 12(Systat Software; Chicago, IL).

RESULTSMorphometric Analysis

PCA produced 92 shape variables (PCs) for eachspecimen. High scores for PC 1 and low scores forPC 2 were associated with more flattened shells,whereas low scores for PC 1 and high scores forPC 2 were associated with taller, more domedshells (Fig. 3). In general, lotic individuals scoredhigher than lentic individuals on PC1 and lowerthan lentic individuals on PC2 indicating that loticindividuals possess relatively flattened shells; incontrast, lentic individuals possess relativelydomed shells (Figs. 3 and 4A,B). Additionally,female turtles possess taller shells than males,especially toward the posterior of the animal, withmore blunted anterior regions (Figs. 3 and 4C,D).

Fig. 2. All load cases. Cases 1–5 are along the midline of thecarapace. Cases 6–8 are along the margin of the carapace. Ante-rior edge of shell oriented to right.



These results confirm to those found previously(Rivera, 2008).

Traditional MANOVA (Table 1) and permuta-tional MANOVA using EDMA (Table 2) indicatedthat these shape differences were significant. Bothflow regime and sex were significantly associatedwith the shape of turtle shells (P < 0.001). How-ever, there was no significant interaction betweenflow regime and sex (P > 0.05).

Relationship Between Shape and Stress

As shape provided the only variation betweenFE models, all variation in stresses is ultimatelyattributable to shape. The fact that we observedvariation in stresses across specimens (Table 3)indicates that many-to-one mapping of shell shapeonto stress is not so severe that shape is uninfor-mative about shell strength. More interesting isthe fact that shape variation along the first twoPC axes, which accounts for 39.1% of the variationin shape and is strongly associated with the levelof doming, was responsible for between 2 and 55%of the variation in stress for individual load casesand had significant effects on shell strength forseven of eight load cases (Table 4). Of the five loadcases with multivariate R2 values equal to orgreater than 0.29, shape variation associated withPC1 had a visibly larger impact than PC2 for loadcase 1 and a weaker influence for load cases 4 and5. For load cases 7 and 8, both shape axes (PC1

and PC2) explained similar amounts of variationin stress. These results also highlight that moredomed shells develop lower stresses than flattershells (Fig. 5). Particularly, shells characterized bylower scores on PC1, which are uniformly flatterthan those with higher PC1 scores, and those withhigher scores on PC2, which are flatter and nar-rower in the anterior of the carapace than thosewith lower PC2 scores, develop relatively highstresses. Stresses close to the point of load applica-tion do not greatly differ between models, thoughstresses remain high farther away from the loadin flatter shells relative to more domed shells.

Effects of Flow Regime and Sex on Stress

Results of a MANOVA testing the effects of flowand sex on modeled stresses found a significantrelationship for both factors (P < 0.001) but notfor their interaction (P > 0.05; Table 5). In gen-eral, lentic turtles displayed lower stresses thanlotic turtles, and female turtles displayed lowerstresses than male turtles (Table 3; Fig. 6). Lenticmales had lower stresses than lotic males forseven of eight load cases, and lentic females hadlower stresses than lotic females for all eight loadcases (Table 3). For the five load cases that dis-played significant effects of flow regime (Table 6),lentic groups always had lower stresses than theirlotic counterparts. In addition, females show a

Fig. 3. All specimens (N 5 158) and group averages (N 5 4) plotted on the two principal shapeaxes (PC1 and PC2). Shell models demonstrate the three-dimensional shapes (in lateral view)associated with extreme values of each axis. Anterior edge of shells oriented to right. Samplesizes for group means are given in Table 3.



stronger effect of flow regime than males, with theaverage difference of the eight load cases betweenthe two female groups being more than twice thatshown between the male groups (0.125 and 0.060,respectively; Table 3). Sex-associated differenceswithin a habitat are less consistent. Lentic maleshad lower stresses than lentic females for three ofeight load cases, and lotic males had lower stressesthan lotic females for four of eight load cases (Ta-ble 3); however, of the four load cases that dis-played significant effects of sex (Table 6), malesonly had lower stresses than their female counter-

parts for one. In addition, sex-associated differen-ces within habitats are much weaker than flow-associated differences within sexes, with the aver-age difference of the eight load cases between thetwo lentic groups being only slightly lower thanthat shown between the lotic groups (0.042 and0.050, respectively; Table 3).

DISCUSSION

This study found that the shells of P. concinnaliving in lotic environments develop significantly

Fig. 4. Average shell shapes of (A) lentic, (B) lotic, (C) female, and (D) male turtles in dorsal(top) and lateral (bottom) views. Differences exaggerated 31.33 for display. Anterior edge ofshells oriented to right.

TABLE 1. Results of MANOVA performed on all shape variables (N 5 92)

Factor Df Pillai approx F num Df Den Df Pr (>F)

Flow 1 0.9253 7.6777 92 57 <0.001Sex 1 0.8993 5.5359 92 57 <0.001Flow 3 Sex 1 0.6810 1.3229 92 57 0.1278Site 6 4.6455 2.3112 552 372 <0.001Residuals 148

Site included as covariate. Bolded values represent significant relationships (P < 0.05).



higher stresses than the shells of conspecifics thatlive in lentic environments. This finding providessupport for an earlier hypothesis (Aresco andDobie, 2000; Rivera, 2008) that the more stream-lined shape of lotic turtle shells may reduce theload-bearing capabilities of those shells, relative tothe less streamlined shape of lentic turtle shells.The shells of turtles living in lentic environmentsare up to 48% stronger than those living in loticenvironments. As the same pattern of shell shapedivergence found by Rivera (2008) has also been dis-covered in other studies (Lubcke and Wilson, 2007),it may be reasonable to infer that the same patternof mechanical divergence would hold as well, thoughfuture studies on additional species would be usefulin confirming this as a general pattern.

More generally, studies of turtle shell morphol-ogy have often hypothesized or asserted a trade-offbetween hydrodynamic efficiency and mechanicalstrength (e.g., Claude et al., 2003). To our knowl-edge, this study provides the first quantitative testand confirmation of this perceived trade-off. Morespecifically, highly domed shells decrease hydrody-namic efficiency (by increasing drag coefficients asper Rivera, 2008) but increase shell strength. Incontrast, flatter shells increase hydrodynamic effi-ciency (via lower drag coefficients) but decreaseshell strength. Thus, this system is a perfectexample of a morphofunctional trade-off (Konumaand Chiba, 2007; de Schepper et al., 2008; Herrelet al., 2009).

Moreover, the shapes of turtles found in differ-ent environments seem to provide some indicationof the relative importance of these functionalattributes in influencing the evolution of shellshape. Domed shells are found in lentic habitats,where low flow velocities produce weak hydrody-namic pressures, but where predation pressure isstrong (Aresco and Dobie, 2000; Rivera, 2008). Inthis environment, decreased hydrodynamic effi-ciency may not produce a great decrease in fitness;in contrast, increased shell strength is likely veryimportant. As a result, it can be hypothesized thatpredation is the primary selective pressure influ-encing shell shape in lentic habitats. In contrast,flattened shells are found in lotic habitats, wherethe high flow velocities produce strong hydrody-namic pressures, but where predation pressure isweak (Aresco and Dobie, 2000; Rivera, 2008).Here, a flattened shell is likely a major advantage

in lotic habitats, whereas lower shell strength isnot of much consequence. Therefore, in lotic habi-tats, it can be hypothesized that flow velocity isthe primary selective pressure influencing shellshape. In other words, the habitats in which loticand lentic individuals live allow them to avoid thenegative consequences of their particular shellshapes. This perfect matching of morphology tothe selective pressures likely helps to drive themorphological distinction between habitats.

Because this study has provided evidence for acorrelation between carapace shape and carapacestrength, it has also rejected the hypothesis of astrong many-to-one relationship between form andfunction for the different shell shapes seen in len-tic and lotic morphotypes of P. concinna. Althoughmany-to-one mapping results in a less than perfectcorrelation between form and function, the magni-tude of this effect can vary from structure to struc-ture, in some cases permitting drastically differentmorphologies to exhibit the same level of predictedperformance (Alfaro et al., 2005; Wainwright,2007), but in other cases only slightly weakening atight form-function relationship (e.g., Cooper andWestneat, 2009). The latter seems to be the casefor our data with regards to shell strength. Such aweak relationship may be an intrinsic property ofthe turtle shell, or it may be due to the fact thatturtle shells are probably under multiple selectivepressures for determining shell shape. Strongmany-to-one mapping may theoretically be possiblefor either shell strength or hydrodynamic effi-ciency (or any number of other factors), but ifthese need to be considered together, then the lim-its on shell shape imposed by other pressures maynecessitate a stronger correlation between shellstrength and shape. Modeling experiments involv-ing both theoretical and actual shell shapes wouldbe required to determine whether a strong rela-tionship between shell shape and strength existsfor most possible turtle shell shapes or simply forthose that also show acceptable levels of perform-ance for other functions.

As a trade-off between hydrodynamic efficiencyand mechanical strength can become relevant formany aspects of turtle life history (sexual shapedifferences, terrestrial vs. aquatic habitats, differ-ent types of aquatic environment), this factorshould be considered in future studies which findconsistent differences in shell shape between turtle

TABLE 2. Results of permutational MANOVA using Euclidean distance matrices

Factor Df SS MS F model R2 Pr (>F)

Flow 1 0.025 0.025 18.1011 0.08904 <0.001Sex 1 0.012 0.012 8.7702 0.04314 <0.001Flow 3 Sex 1 0.002 0.002 1.3072 0.00643 0.186Site 6 0.037 0.006 4.5188 0.13337 <0.001Residuals 148 0.204 0.001 0.72802

Site included as covariate. Analysis based on 999 permutations. Bolded values represent significant relationships (P < 0.05).



groups. For example, this trade-off could be re-sponsible for many interspecific patterns in turtleshell shape, such as the differences in shell shapebetween aquatic and terrestrial turtles (Claudeet al., 2003).

Along those lines, Rivera (2008) also noted (butdid not test for significance of) consistent differen-ces in the shell shapes of male and female P. con-cinna. Previous studies have found significant dif-ferences in shell shape between male and femaleturtles (Tucker et al., 1998; Willemsen and Hailey,2003; Brophy, 2006). In general, such studiesfound that female turtles show taller, more domedshells, whereas males show shells that are flatterand generally more streamlined, with larger aper-tures for the limbs; Rivera (2008) also noted thatthe shells of females showed less divergenceamong environments and perhaps a greater degreeof constraint on shell shape. Some studies haveinterpreted the differences among males andfemales in terms of hydrodynamic efficiency andmechanical strength, hypothesizing that thegreater height of female turtle shells accommo-dates a greater volume of eggs while lending theshell additional load-bearing capabilities, whereasthe flatter, more streamlined shell and larger aper-tures of males increases swimming speed for pur-suit or mating with females (Tucker et al., 1998).

The results of this study suggest a morenuanced interpretation of shape differencesbetween males and females. Female P. concinnashells are indeed taller than those of males. How-ever, this does not seem to be associated with con-sistently stronger shells in these individuals.Female P. concinna shells do develop lowerstresses for a given load toward the posteriorregion of the shell, but the opposite pattern holdsfor the anterior of the shell, with males developingconsistently lower stresses than females. Thegreater strength of the posterior region of femaleturtle shells is perhaps explicable by the greaterheight of the shell in that area, where the oviductsand eggs would be located; the greater strength ofmale shells toward the anterior of the carapace is

TABLE

3.Averagemod

eled

shellstress

forea

chgroupandloadca

se

Group

N

Loa

dcase

12

34

56

78

Len

ticMale

78

1.139(0.121)

1.158(0.107)

1.105(0.092)

1.097(0.095)

1.064(0.073)

1.142(0.147)

0.991(0.076)

1.007(0.070)

Lotic

Male

39

1.276(0.178)

1.159(0.127)

1.102(0.105)

1.213(0.123)

1.165(0.0918)

1.154(0.148)

1.042(0.073)

1.068(0.075)

Len

ticFem

ale

29

1.123(0.140)

1.159(0.127)

1.122(0.104)

1.041(0.090)

0.957(0.068)

1.155(0.198)

0.934(0.075)

0.937(0.067)

Lotic

Fem

ale

12

1.321(0.183)

1.224(0.085)

1.169(0.080)

1.194(0.103)

1.128(0.083)

1.303(0.109)

1.039(0.086)

1.050(0.069)

Len

tic

107

1.134(0.126)

1.158(0.112)

1.109(0.095)

1.082(0.096)

1.035(0.086)

1.146(0.162)

0.975(0.080)

0.988(0.076)

Lotic

51

1.287(0.178)

1.174(0.121)

1.118(0.103)

1.209(0.118)

1.156(0.090)

1.189(0.153)

1.041(0.075)

1.064(0.073)

Male

117

1.184(0.156)

1.158(0.114)

1.104(0.096)

1.136(0.118)

1.098(0.093)

1.146(0.147)

1.008(0.078)

1.027(0.077)

Fem

ale

41

1.181(0.177)

1.178(0.119)

1.136(0.099)

1.086(0.116)

1.007(0.106)

1.199(0.188)

0.965(0.091)

0.970(0.085)

Allstresses

forea

chloadcase

are

scaledrelativeto

theaveragestresses

forcorrespon

dingloadcasesof

thebase

mod

el.Values

representthemea

nand(standard

dev

iation

).

TABLE 4. Results (R2 values) of univariate and multivariateregressions of shape variables (PC 1 and PC2) on stress

Load Case PC1 PC2 PC1 and PC2

1 0.252*** 0.038* 0.290***2 0.037* 0.007 0.044*3 0.015 0.007 0.0224 0.149*** 0.237*** 0.386***5 0.155*** 0.396*** 0.551***6 0.051** 0.005 0.056*7 0.239*** 0.234*** 0.473***8 0.216*** 0.234*** 0.450***

N 5 158; Significance levels*P < 0.05;**P < 0.01;***P < 0.001.



more puzzling. In any case, the notion that femaleturtles show shell shapes that are stronger thanthose of their male conspecifics should be evokedwith caution.

This study has focused entirely on differences inshape among turtle shells. Variation in other fac-tors, such as the material properties of shell bone,can also influence the strength of turtle shells.The shells of turtles living in lotic environments,for example, could potentially withstand higherloads than lentic turtle shells if the former werecomposed of a stronger material. In particular, wehave neglected an aspect of shell morphologywhich can have consequences for both hydrody-namic efficiency and mechanical performance: size.Hydrodynamic properties can be affected by size,although for the range of sizes and Reynolds num-bers of turtle shells investigated here, the effect islikely negligible; thus, two shells with the sameshape but different sizes likely display equal

hydrodynamic efficiency. In contrast, strengthscales with the square of size; for a given shape, atwofold increase in size would lead to a fourfoldincrease in strength. Thus, size presents a mor-phological axis available for increasing shellstrength without too severely compromising thehydrodynamic properties of the shell. Neverthe-less, size does not appear to be compensating forthe weaker shell shapes of male and lotic P. con-cinna in this study. Sexual-size dimorphism in thisspecies is skewed to larger females (Aresco andDobie, 2000; Gosnell et al., 2009). Furthermore,our data, as well as that of Aresco and Dobie(2000) indicate that lotic P. concinna tend to besmaller than lentic P. concinna. Still, while sizedifferences here seem to be making stronger shellshapes stronger, size remains a potential mitigatorof relatively weak shell shapes in other species.

Turtle shells perform many functions besidesinteracting with fluids and resisting loads. Theyalso exchange heat with the environment, serve asan obstacle if the turtle is overturned (Domokosand Varkonyi, 2008), carry out multiple metabolicprocesses (Jackson et al., 2000a, 2000b), and ofcourse enclose the viscera and associated muscula-ture of turtles. As such, turtle shells probably en-counter many conflicting selective pressuresbesides those acting on hydrodynamic or mechani-cal properties. Shape differences among lotic andlentic populations of P. concinna seem well-explained by a consideration of just those two fac-tors, but future studies may need to consideradditional factors to explain other patterns of vari-

TABLE 5. Results of MANOVA performed on all stressvariables (N 5 8)

Factor Df Pillai approx FnumDf

DenDf Pr (>F)

Flow 1 0.55402 21.8944 8 141 <0.001Sex 1 0.46323 15.2101 8 141 <0.001Flow 3 Sex 1 0.08946 1.7317 8 141 0.096Site 6 0.91944 3.3027 48 876 <0.001Residuals 148

Site included as covariate. Bolded values represent significantrelationships (P < 0.05).

Fig. 5. Dorsal (top) and lateral (bottom) views of FE analysis (load case 8) results for (A) the most domed individual in the dataset (a lentic female), and (B) the least domed individual in the data set (a lotic male), showing visibly higher stresses in the lessdomed individual. ‘‘Hot’’ colors correspond to relatively high stresses, and ‘‘cool’’ colors correspond to low stresses. Anterior edge ofshells oriented to right. Stresses indicated by the legend are calculated for models scaled to the same, very small, size. Thus, theserepresent much higher stresses than would be experienced by actual-sized shells under similar loading conditions. However, pat-terns of stress distribution across each shell, and comparisons of relative stress levels between specimens, are unbiased.



Fig. 6. Dorsal (top) and lateral (bottom) views of FE analysis (load case 8) results for average (A) lentic, (B) lotic, (C) female,and (D) male shell shapes. ‘‘Hot’’ colors correspond to relatively high stresses, and ‘‘cool’’ colors correspond to low stresses. Anterioredge of shells oriented to right. Stresses indicated by the legend are calculated for models scaled to the same, very small, size.Thus, these represent much higher stresses than would be experienced by actual-sized shells under similar loading conditions.However, patterns of stress distribution across each shell, and comparisons of relative stress levels between specimens areunbiased.

TABLE 6. P-values of ANOVAs performed separately on each stress variable (N 5 8)

Factor

Load case

1 2 3 4 5 6 7 8

Flow <0.001 0.392 0.602 <0.001 <0.001 0.091 <0.001 <0.001Sex 0.903 0.303 0.053 0.006 <0.001 0.047 0.002 <0.001Flow 3 Sex 0.453 0.135 0.176 0.361 0.020 0.060 0.103 0.058Site <0.001 <0.001 0.002 <0.001 <0.001 0.001 <0.001 <0.001

Site included as covariate. Bolded values represent significant relationships (P<0.05).



ation (such as those between males and females inthis study) in turtle shell shape.

ACKNOWLEDGMENTS

We thank A. Rivera, K. Angielczyk, and ananonymous reviewer for helpful comments thathelped improve earlier drafts of this article andD. Adams for providing advice on statistical analyses.C.T.S. thanks B. Dumont, S. Wehrle, and I. Grossefor their assistance with Finite Element techniquesin general and Strand7 in particular. G.R. is gratefulto S. Rogers and B. Isaac (Carnegie Museum of Natu-ral History), C. Guyer (Auburn University NaturalHistory Museum), C. Franklin (Amphibian and Rep-tile Diversity Research Center, University of Texas,Arlington), R. Brown (University of Kansas NaturalHistory Museum), C. Austin (Louisiana State Univer-sity Museum of Natural Science), and H. Dundee(Tulane University Museum of Natural History) forproviding access to specimens. J. Maisano and thestaff of the University of Texas at Austin High-Reso-lution X-ray CT Facility provided access to theGlyptemys muhlenbergii scans. Funding for the scanwas provided by grant # IIS-0208675 to T. Rowe.

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Finite element modeling of shell shape in the freshwater turtle Pseudemys concinna reveals a trade-off between mechanical strength and hydrodynamic efficiency