Journal of

Anatomy

J. Anat. (2014) 225, pp403--418

doi: 10.1111/joa.12220

Limb bone morphology, bone strength, and cursoriality in lagomorphs Jesse W. Young,1,2,3 Robert Danczak,4 Gabrielle A. Russo1 and Connie D. Fellmann5 1

Department of Anatomy and Neurobiology, Northeast Ohio Medical University (NEOMED), Rootstown, OH, USA Skeletal Biology Research Focus Area, NEOMED, Rootstown, OH, USA 3 School of Biomedical Sciences, Kent State University, Kent, OH, USA 4 Department of Microbiology, The Ohio State University, Columbus, OH, USA 5 Department of Anthropology, Colorado State University, Fort Collins, CO, USA 2

Abstract The primary aim of this study is to broadly evaluate the relationship between cursoriality (i.e. anatomical and physiological specialization for running) and limb bone morphology in lagomorphs. Relative to most previous studies of cursoriality, our focus on a size-restricted, taxonomically narrow group of mammals permits us to evaluate the degree to which ‘cursorial specialization’ affects locomotor anatomy independently of broader allometric and phylogenetic trends that might obscure such a relationship. We collected linear morphometrics and lCT data on 737 limb bones covering three lagomorph species that differ in degree of cursoriality: pikas (Ochotona princeps, non-cursorial), jackrabbits (Lepus californicus, highly cursorial), and rabbits (Sylvilagus bachmani, level of cursoriality intermediate between pikas and jackrabbits). We evaluated two hypotheses: cursoriality should be associated with (i) lower limb joint mechanical advantage (i.e. high ‘displacement advantage’, permitting more cursorial species to cycle their limbs more quickly) and (ii) longer, more gracile limb bones, particularly at the distal segments (as a means of decreasing rotational inertia). As predicted, highly cursorial jackrabbits are typically marked by the lowest mechanical advantage and the longest distal segments, non-cursorial pikas display the highest mechanical advantage and the shortest distal segments, and rabbits generally display intermediate values for these variables. Variation in long bone robusticity followed a proximodistal gradient. Whereas proximal limb bone robusticity declined with cursoriality, distal limb bone robusticity generally remained constant across the three species. The association between long, structurally gracile limb bones and decreased maximal bending strength suggests that the more cursorial lagomorphs compromise proximal limb bone integrity to improve locomotor economy. In contrast, the integrity of distal limb bones is maintained with increasing cursoriality, suggesting that the safety factor takes priority over locomotor economy in those regions of the postcranial skeleton that experience higher loading during locomotion. Overall, these findings support the hypothesis that cursoriality is associated with a common suite of morphological adaptations across a range of body sizes and radiations. Key words: mechanical advantage; mineralization; polar section modulus; robusticity; safety factor. Cursoriality, defined here as the anatomical and physiological specialization for running (Gregory, 1912; Camp & Borell, 1937; Bramble, 1989), is generally associated with a common suite of morphological features across several amniote groups. Such features include relatively long and

Correspondence Jesse W. Young, Department of Anatomy and Neurobiology, Northeast Ohio Medical University, 4209 State Route 44, PO Box 95, Rootstown, OH 44272, USA. E: [email protected] Present address: Gabrielle A. Russo, Department of Anthropology, Stony Brook University, Stony Brook, NY, USA. Accepted for publication 29 June 2014 Article published online 21 July 2014 © 2014 Anatomical Society

tapered limbs with mass concentrated at the proximal end, hinge-like joints that limit motion to parasagittal planes, fused distal limb bones, and loss of lateral digits (Smith & Savage, 1956; Gambaryan, 1974; Coombs, 1978; Hildebrand & Goslow, 2001). Though some researchers have questioned the degree to which an imprecise performance trait (i.e. ‘running’ ability, which could include both high endurance capacity and high speed) can be reliably associated with specific anatomies (Steudel & Beattie, 1993; Stein & Casinos, 1997), this general set of morphological features, alone or in combination, have been shown to correlate with running ability in mammals, lizards and birds (Howell, 1944; Gambaryan, 1974; Coombs, 1978; Carrano, 1999; Irschick & Jayne, 1999; Hildebrand & Goslow, 2001).

404 Lagomorph limb bone morphology, J. W. Young et al.

The primary aim of this study is to broadly evaluate the relationship between cursoriality and limb bone morphology in lagomorphs. Relative to most previous studies of cursoriality, our focus on a size-restricted, taxonomically narrow group of mammals permits us to evaluate the degree to which ‘cursorial specialization’ affects locomotor anatomy independently of broader allometric and phylogenetic trends that might obscure such a relationship (Steudel & Beattie, 1993). Our sample includes representatives of the two extant lagomorph families, the Ochotonidae (pikas) and the Leporidae (jackrabbits/hares and rabbits) (Table 1). Since splitting from a common ancestor at some time during the late Oligocene or early Miocene epoch (i.e. ca. 23– 32 million years ago; Matthee et al. 2004), pikas, rabbits, and jackrabbits have undergone substantial morphological divergence, much of it relating to variability in the degree of cursoriality. In general, pikas are the least cursorial and jackrabbits the most cursorial, with rabbits occupying an intermediate position (Camp & Borell, 1937; Gambaryan, 1974). A small number of previous studies have discussed the gradation in cursoriality among lagomorphs, and sought to identify morphological correlates of this behavioral cline (Camp & Borell, 1937; Gambaryan, 1974; Bramble, 1989). However, prior research has been based on measurements of only a few individuals per species or has focused on one specific trait or a small set of traits. In this study, we use a robust dataset of more than 100 individuals to address two specific hypotheses broadly relating limb morphology to cursorial specialization.

H1) Muscle mechanical advantage should be inversely correlated with level of cursoriality among lagomorphs. The mechanical advantage of a lever is defined as the distance from the input force to the fulcrum (i.e. the in-lever) divided by the distance from the fulcrum to the output force (i.e. the out-lever; Smith & Savage, 1956). In general, due to the balance of moments about the fulcrum, levers with greater mechanical advantage are able to generate a greater output force for a given input force. Conversely, a short in-lever relative to the out-lever can achieve a high

output velocity for a given input velocity, i.e. such levers have a high gear ratio or ‘displacement advantage’ (McHenry, 2012). These relationships between limb joint mechanical advantage, force output, and velocity output generally hold true for the bony levers that make up limb joints as well, although it is also important to consider the force–velocity properties of the musculotendinous actuators powering the movements (Stern, 1974; Richards, 2011) and the nature of the resistance being countered (McHenry, 2012) when applying principles of force–velocity tradeoff to real world performance. Nonetheless, in accordance with these broad principles, previous surveys of mammals have generally documented an inverse relationship between mechanical advantage and cursoriality, reflecting preferential investment in limb output velocity over limb output force among more cursorial taxa (Gregory, 1912; Camp & Borell, 1937; Howell, 1944; Smith & Savage, 1956; Hildebrand & Goslow, 2001). We therefore predict that across all of the limb joints examined, limb muscle mechanical advantage should be lowest in jackrabbits, greatest in pikas, and intermediate in rabbits, emphasizing greater velocity output over force output in more cursorial species.

H2) Cursoriality should be associated with, elongated, gracile distal limb bones. Lightening distal limb elements reduces the moment of inertia about the shoulder and hip. Because the torque that must be generated to swing a limb forward is directly proportional to limb moment of inertia, lighter distal elements permit a quicker recovery phase with less muscular effort, which in turn increases stride frequency and locomotor speed (Gregory, 1912; Smith & Savage, 1956; Coombs, 1978; Hildebrand, 1985; Hildebrand & Hurley, 1985; Myers & Steudel, 1985; Hildebrand & Goslow, 2001; Raichlen, 2005). The hypothesis that cursorial species should lighten distal limb elements leads to several predictions. First, the relative length of distal limb segments should be greatest in jackrabbits, least in pikas, and intermediate in rabbits. Longer distal limb segments in the more cursorial species increase overall limb length (and thus stride length and speed) while still minimizing limb rotational inertia by not enlarging the

Table 1 Lagomorph skeletal sample used in this study, listed by species, number individuals and number of elements. The minimum, median, and maximum number of slices for the bones in the lCT sample are listed in parentheses below.

Ochotona princeps Sylvilagus bachmani Lepus californicus

N

Humeri

Radii

Ulnae

Innominates

Femora

Tibiae

Calcanei

3rd Metatarsals

53

51 (95/144/172) 35 (182/256/320) 26 (90/472/673)

48 (25/140/168) 31 (16/208/272) 24 (14/438/544)

48

53

12

32

26

22

23

26

47 (5/143/168) 30 (67/276/372) 25 (325/630/673)

13

31

51 (126/148/172) 35 (258/329/372) 25 (126/148/172)

21

2

35 27

© 2014 Anatomical Society

Lagomorph limb bone morphology, J. W. Young et al. 405

more muscular and massive proximal elements. Second, geometric correlates of long bone robusticity, particularly in the distal segments, should be least in jackrabbits, greatest in pikas, and intermediate in rabbits, reflecting a reduction in bone mass as means of decreasing rotational inertia in the more cursorial species. Third, in contrast to cross-sectional measures, long bone mineralization (a close correlate of tissue stiffness and strength: Currey, 2002), should either be similar across taxa or not vary predictably with levels of cursoriality. Currently, there is little evidence that variation in long bone material properties is well correlated with variation in locomotor loading across vertebrates (Erickson et al. 2002; but see Kemp et al. 2005). Finally, as a combined result of reduced cross-sectional robusticity and maintenance of bone mineral density, morphometric correlates of long bone bending strength should be reduced in more cursorial taxa, maximizing energetic efficiency at the expense of long bone safety factors.

Materials and methods Sample characteristics Taxonomic sample Available ecological and behavioral data indicate that pikas, rabbits and jackrabbits represent a gradation of increasing specialization for cursoriality, a trend that has also been suggested by previous morphological studies of lagomorphs (e.g. Camp & Borell, 1937; Gambaryan, 1974). Pikas (Ochotonidae) are the smallest lagomorphs. American pikas (Ochotona princeps, Richardson 1828), the species examined in this study, range in adult body mass from 121 to 184 g (Swihart, 1984; Smith & Weston, 1990). All pikas belong to one of two ecotypes, meadow-dwelling or talus dwelling, with O. princeps falling into the latter category (Garland & Janis, 1993; Reese et al. 2013). Ochotona princeps preferentially inhabits talus regions throughout mountain ranges across western North America, particularly favoring regions where rocky piles transition into meadowland. Compared with other lagomorphs, locomotion in pikas is typically slow and brief in duration, consisting of short bouts of travel between rocks (Smith & Weston, 1990; Fischer et al. 2002; Witte et al. 2002). They seldom range far from their home territory and will only move quickly to escape predation or to engage in intraspecific competition (DuBrul, 1950; Barash, 1973; Bramble, 1989). Cottontail rabbits (Sylvilagus) are abundant throughout North and South America (Chapman et al. 1980). Brush rabbits (Sylvilagus bachmani, Waterhouse 1838) are among the smallest cottontails, ranging in adult body mass from 511 to 960 g (Chapman, 1974; Swihart, 1984). Sylvilagus bachmani typically favor brushy habitats that offer dense undergrowth cover, a preference reflected in the common name of the species (Chapman, 1974). Sylvilagus bachmani inhabits small home ranges that are largely circumscribed by the availability of connected brush patches (Chapman, 1971). Individuals rarely enter open areas and when they do, they remain within a meter or two of a brush patch, as they largely depend upon these refugia to escape predation (Chapman, 1974). Locomotion consists of the typical lagomorph pattern of bounds and halfbounds, and travel distances are relatively short (Chapman, 1971, 1974). © 2014 Anatomical Society

Jackrabbits (hares) are the largest lagomorphs. The species examined in this study, the black-tailed jackrabbit (Lepus californicus, Gray 1837), ranges in adult body mass from 1510 to 3550 g, with some variation in size attributable to local climatic variation (Best, 1996). In contrast to pikas and rabbits, L. californicus prefers open habitats and deserts, and will actively avoid tall grasslands or forest where visibility may be compromised (Best, 1996). The species maintains large home ranges of 1.2 km2 and has been known to travel an average of more than 2.5 km in a single day (Best, 1996). As such, jackrabbits and hares have often been cited as exemplar cursors among small mammals, able to reach speeds of up to 70 km h1 (Gregory, 1912; Carrier, 1983; Williams et al. 2007a,b; Seckel & Janis, 2008).

Skeletal samples A total of 737 bones from 115 individuals were included in the dataset (Table 1). Postcranial skeletal samples of Lepus californicus, Sylvilagus bachmani and Ochotona princeps were obtained from the collections of several natural history museums across the USA (see Supporting Information Data S1 for a list of museums). Representative tracings of limb bones from each species are shown in Fig. 1. All specimens had been skeletonized from wild caught animals from several locations across the USA. Only adult individuals, as identified based upon epiphyseal fusion, were included in the sample. Because not every bone was present for each individual, sample sizes by element are variable within species (Table 1).

Raw measurements Length measurements We used a Microscribe 3D digitizer (Solution Technologies, Inc., Oella, MD, USA) to sample 3D coordinates corresponding to 35 skeletal landmarks located on the scapula, humerus, radius, ulna, innominate, femur, tibia, calcaneus and third metatarsal. Anatomical landmarks are defined in Table 2. We used a custom-written routine in MATLAB (Mathworks, Natick, MA, USA) to calculate segment lengths from 3D inter-landmark distances. Nearly all L. californicus skeletons in our sample were disarticulated, making the accurate identification of third metatarsal bones prohibitively difficult. As such, we were only able to measure two metatarsal bones in L. californicus.

lCT measurements Limb bones were lCT-scanned at a resolution of 20.5 lm per pixel using a vivaCT 75 lCT scanner (Scanco USA, Inc., Southeastern, PA, USA) (Fig. 2). For each bone, a stack of 20.5-lm-thick slices equal to 10% of overall bone length was scanned, centered at 40% of distal-proximal length for the humerus, to avoid the deltopectoral crest, and at 50% of distal-proximal length (i.e. midshaft) for the other bones. For the purposes of slice localization, femoral mid-shaft was defined at 50% of bicondylar length. We focused our measurements on midshaft as this is the location of peak bending strains in quadrupedal mammals (Biewener & Taylor, 1986) and measured a series of slices because it is unlikely that breaking forces would be limited to the slice localized precisely at midshaft (Doube et al. 2009). The median number of slices imaged per stack varied from five for O. princeps tibiae to 630 for L. californicus femora (the minimum, median, and maximum number of slices for each bone scanned for each species is recorded in Table 1).

406 Lagomorph limb bone morphology, J. W. Young et al.

Derived variables

Ochotona princeps

To make comparisons across species that vary considerably in body size, raw variables were first transformed into functionally important dimensionless indices.

Mechanical advantage

Sylvilagus bachmani

Lepus californicus

Mechanical advantage was calculated as the ratio of skeletal inlever length to skeletal out-lever length. Operational definitions of in-levers and out-levers for each joint examined are provided in Table 3. In all cases, higher values indicate greater mechanical advantage and lower values indicate lower mechanical advantage. It should be noted that our measure quantifies ‘anatomical’ mechanical advantage (AMA) (Carrier, 1983; Young, 2005, 2009; Fellmann, 2011) and only considers the bony contribution of effective muscle mechanical advantage (Biewener, 1989). Calculating effective mechanical advantage would require additional morphometric data on limb muscle force vectors in a variety of postures as well as in vivo kinematic and kinetic data on the spatial relationship between ground reaction force vectors and limb joint centers of rotation. Such data were, of course, unavailable for museum specimens. Nevertheless, multiple lines of evidence suggest that our anatomical estimates are valid proxies for actual mechanical advantage. First, Williams et al. (2007a,b) provide dissection-based measures of how in-lever arm lengths change with joint posture for all major limb muscles in the European hare (Lepus europeus), a leporine that is very close in body size and locomotor behavior to L. californicus. For every joint, our static bony measures fell within the distribution of their more accurate values. There is no a priori reason to think that this would not also be the case for the other lagomorph species in our dataset. Second, previous in vivo mechanical studies of other animals have suggested that bony out-lever arm lengths are well correlated with actual out-lever arm lengths (Young, 2009; Smith & Wilson, 2013), at least across the comparatively narrow range of body sizes sampled here (but see Biewener, 1991 for a discussion of the determinants of effective mechanical advantage with increasing size across mammals).

Measures of relative limb segment length Fig. 1 Tracings of representative limb bones for each species in the comparative lagormoph sample. Within each species, the bones are, from left to right: left humerus, left radius/ulna, left femur and left tibia/fibula. Forelimb bones are shown in medial view and hind limb bones in anterior view. Scale bars: 1 cm.

Cross-sectional images were imported into NIH IMAGEJ (Rasband, 1997–2007) where we used the plug-in program BONEJ (Doube et al. 2010) to measure polar section modulus (i.e. ZP, in mm3) and cross-sectional area (i.e. CSA, in mm2) across all slices in the stack. ZP is calculated as the quotient of the polar moment of area (i.e. J: a measure of the average distribution of bone away from the central axis of the cross section, equal to the sum of any two orthogonal second moments of area), and the maximum radius of the cross-section (Turner & Burr, 1993). ZP is thus similar to the planar section modulus (Z) and is proportional to (twice) the bone’s overall strength in bending. ZP therefore served as our primary measure of bone strength in the sample (Ruff, 2003). Additionally, to measure taxonomic differences in bone density, a pre-set hydroxyapatite calibration phantom was used to convert the linear attenuation of each scanned voxel to bone mineral density (BMD: mg HA cm3).

We used brachial indices, crural indices and metatarsal/femur ratios to quantify the relative degree of distal limb elongation within each species (Gregory, 1912; Howell, 1944). The brachial index quantifies distal forelimb elongation by expressing radius length as a percentage of humeral length. Similarly, the crural index quantifies distal hind limb length by expressing tibia length as a percentage of femur length. Finally, the metatarsal/femur ratio quantifies 3rd metatarsal length as a percentage of femur length, and has proven a reliable predictor of cursorial ability across mammals, with more cursorial mammals exhibiting higher ratios than less cursorial mammals (Gregory, 1912; Gambaryan, 1974; Garland & Janis, 1993; Steudel & Beattie, 1993; Christiansen, 2002). For all three measures, increasing values indicate increasing distal limb elongation relative to proximal limb length.

Measures of relative limb bone robusticity and strength The average magnitude of the bending moments that long bones must resist is expected to vary as a function of bone length (proportional to the load arm of the bending moment) and body mass (proportional to the bending load) (Polk et al. 2000; Ruff, 2003; Young et al. 2010). Therefore, it is important to consider both bone length and body mass when scaling ZP (our measure of long bone © 2014 Anatomical Society

Lagomorph limb bone morphology, J. W. Young et al. 407

Table 2 Skeletal landmarks used to calculate length measurements. Measurement

Proximal landmark

Distal landmark

Scapula length Humerus length Radius length Olecrenon length Innominate length Ischium length Gluteal lever arm Iliopsoas lever arm Femur length Quadriceps femoris lever arm Tibia length Calcaneal tuber length 3rd metatarsal length

Junction of the spine and the vertebral border Proximal-most point on the humeral head Proximal-most point on the radial head Proximal-most point on the olecranon process Cranial-most point on the iliac crest Center of the acetabulum Center of the fovea capitis Center of the fovea capitis Center of the fovea capitis Anterior-most point on the medial condyle Superior-most point on the intercondylar eminence Insertion of gastrocnemius Center of the proximal articular surface

Center of the glenoid fossa Distal-most point on the trochlea Tip of the styloid process Center of the trochlear notch Caudal-most point on the ischial tuberosity Caudal-most point on the ischial tuberosity Proximal-most point on the greater trochanter Most medial point on the lesser trochanter Distal-most point on the medial condyle Center of medial epicondyle Distal-most point on the lateral malleolus Anterior-most point on fibular notch Center of the phalangeal articular surface

Table 3 Operational definitions of anatomical mechanical advantage for focal limb musculoskeletal joints (landmarks used to define length measurements are listed in Table 2). Joint

In-lever

Out-lever

Triceps brachii Lesser gluteal mm. Hamstring mm. (at the hip) Iliopsoas Quadriceps femoris Triceps surae

Olecrenon length Gluteal lever arm length Ischium length Iliopsoas lever arm length Quadriceps femoris lever arm length Calcaneal tuber length + 3rd metatarsal length

Radius length Femur length + tibia length Femur length + tibia length Femur length + tibia length Tibia length 3rd metatarsal length

1 cm

strength in bending) to body size. Unfortunately, body masses were only available for a few of the museum specimens in our skeletal sample of lagomorphs. We therefore created a ‘skeletal size proxy’ (SSP) of body mass as the geometric mean of six linear variables (scapula length, humerus length, radius length, innominate length,

A M

femur length and tibia length) and four scaled areal variables (the square root of average mid-shaft CSA for the humerus, radius, femur and tibia). Several studies have shown that SSPs based on the geometric mean of metric variables from disparate anatomical regions are robust estimates of overall body size when body mass data are unavailable (Mosimann, 1970; Jungers et al. 1995; Gordon et al. 2008; Gordon, 2013). Dimensionless limb bone robusticity (i.e. strength scaled to an appropriate measure of body size: Ruff et al. 1993; Kemp et al. 2005) was quantified as the quotient of ZP (taken to the two-thirds power, to ensure lack of dimensionality), and the product of bone length and SSP. A size-adjusted ‘bending strength index’ (BSI) was calculated as the product of dimensionless limb bone robusticity and BMD. Beam theory dictates that the maximal bending stresses long bones can resist (i.e. rpeak) are proportional to the product of the bending moment (Mmax) and maximal perpendicular distance to form the neutral axis (c), divided by the second moment of area in the plane of bending (I ): rpeak ¼ Mmax cI1

Ochotona princeps

Sylvilagus bachmani

Lepus californicus

Fig. 2 Tracings of representative limb bone cross-sections for each species in our comparative lagomorph sample. Within each species, from top to bottom, the bones are humerus, radius, femur and tibia. Bones are oriented with the anterior cortex facing toward the top and the medial cortex facing toward the right. Scale bar: 1 cm. © 2014 Anatomical Society

ð1Þ

Because the inverse of the cI1 term (i.e. Ic1) is the equation for the section modulus in the plane of bending (Z), Eq. 1 could be algebraically rearranged as: Mmax ¼ rpeak Z

ð2Þ

Thus, the maximal bending moment (Mmax) that a long bone could resist should be proportional to the product of the bone’s peak flexural strength (rpeak) and the section modulus. In this study,

408 Lagomorph limb bone morphology, J. W. Young et al.

we used BMD as a non-invasive morphometric proxy for rpeak. Although factors other than mineralization also contribute to long bone material properties, such as water content and microstructural anisotropy, broad comparative studies by Currey (2002) have shown that across amniotes, varying levels of bone mineralization explain much of the variation in long bone material properties. More specifically, Currey (1999, 2002) has shown that the bending strength of compact bone varies as a function of elastic modulus and calcium content, both of which are dependent upon BMD. We therefore used the product of ZP and BMD, scaled to the product of bone length and SSP, as a dimensionless morphometric proxy of the maximum long bone strength in bending. Note that because not of all the elements required to calculate SSP were available for each individual, sample sizes for comparisons of long bone robusticity and long bone strength were necessarily reduced for each species.

Validation of relative bone strength estimate Previous studies have shown that measures of rodent long bone cross-sectional geometry and BMD can, in combination, explain more than 90% of the variation in whole limb bone material properties in bending (Ferretti, 1995; Martin et al. 2004). Nevertheless, to further validate our assumption that the BSI defined above was also a valid proxy for lagomorph long bone strength, we empirically tested how well the product of ZP and BMD predicted the maximum bending moment that lagomorph long bones could withstand. Because we were not permitted to destructively sample the museum specimens, we used a sample of 14 juvenile laboratory rabbits (Oryctolagus cuniculus) for these validation tests. The rabbits in our sample had been euthanized for an unrelated study at NEOMED. On average, they were 114 days old with a body mass of 2500 g at the time of euthanasia. Although BMD typically increases during mammalian growth (Currey & Butler, 1975; Torzilli et al. 1981; Carrier, 1983; Currey, 1984; Brear et al. 1990; Heinrich et al. 1999; Currey, 2001, 2002; Main & Biewener, 2004), maximal bending moments should still vary predictably with ZP and BMD in juveniles as well as adults, although juvenile bones will on average be less strong than those of adult conspecifics (Currey & Butler, 1975; Currey & Pond, 1989; Brear et al. 1990; Currey, 2001). Left and right humeri, radii, femora and tibiae were harvested from cadavers and stored in saline-soaked gauze in a freezer. Freezing bones for up to 12 months has been shown to have no detectable effects on bone shape or mechanical properties (Turner & Burr, 1993; Van Haaren et al. 2008). Each bone was lCT-scanned using the procedures described above. Bone lengths were measured to the nearest 0.01 mm using digital calipers. The ultimate bending load (N) each bone could sustain was empirically measured using an Instron ElectroPuls E3000 UTM material testing machine (Instron, Norwood, MA, USA). Following Carrier (1983), bones were secured in a flexure fixture and loaded in three-point bending in the anteroposterior plane at a displacement rate of 1.27 mm min1 until fracture occurred. Applied loads were registered using a 5-kN load cell and recorded using Instron BLUEHILL software. The maximal bending moment each bone could sustain (Nm) was calculated as the product of ultimate load and half the span between the supports of the flexure fixture.

Statistical methods All statistical analyses in this study rely on species as the fundamental unit of analysis, without employing phylogenetic corrective

methods. Previous studies have shown that datasets of fewer than 30 species lack sufficient power to detect a phylogenetic signal in comparative data (Freckleton et al. 2002). The use of phylogenetic corrective methods to analyze our dataset of three species would therefore not be appropriate. Statistical comparisons among lagomorph species were carried out using nonparametric tests. Although nonparametric tests generally have reduced power, they are more robust to the heteroscedasticity and deviations from normality inherent to our unbalanced statistical design. Overall differences among lagomorph species were quantified using Kruskal–Wallis tests. Post hoc comparisons were made using pairwise Mann–Whitney U-tests. Because for all variables except BMD we had directional predictions of how more cursorial species should differ from less cursorial species, most post hoc tests were one-tailed. The directionality of the null hypothesis in these cases is described in the text and in the figures and tables below. Post hoc tests for comparisons of limb BMD were two-tailed. To limit Type I error rates, P-values from these post hoc analyses were adjusted using the false discovery rate method (Benjamini & Hochberg, 1995), a method that simultaneously limits experimentwise error rates and minimizes the resulting loss of statistical power. Finally, a non-parametric Spearman’s rank correlation was used to quantify how well the product of ZP and BMD predicted empirical measures of bending strength in the laboratory rabbit sample. All statistical analyses were implemented using the R statistical platform (R Core Team, 2013), including the add-on libraries car (Fox & Weisberg, 2011), nlme (Pinheiro et al. 2013) and reshape2 (Wickham, 2007).

Results Anatomical mechanical advantage Comparisons of limb muscle AMA are presented in Table 4 and Fig. 3. As predicted, S. bachmani and L. californicus have significantly lower AMA than O. princeps for all jointmuscle complexes examined, supporting the hypothesis that cursoriality should be associated with decreased AMA (i.e. increased displacement advantage). Comparisons among the leporids are more mixed. Lepus californicus has significantly lower AMA than S. bachmani for triceps brachii and quadriceps femoris, and lower AMA for triceps surae (although this last comparison did not reach statistical significance; adjusted P = 0.096). It is likely that the lack of significance for the triceps surae comparison is due to a small sample size for L. californicus metatarsal bones (n = 2). Anatomical mechanical advantage was statistically similar between the leporids for all other joints.

Relative limb segment lengths Species comparisons of relative distal limb segment lengths are presented in Table 5 and Fig. 4. As predicted, limb segment length ratios are lowest in O. princeps, greatest in L. californicus, and intermediate in S. bachmani (i.e. S. bachmani is characterized by significantly greater ratios than O. princeps and significantly lower ratios than L. californicus). © 2014 Anatomical Society

Lagomorph limb bone morphology, J. W. Young et al. 409

Table 4 Species differences in anatomical mechanical advantage. Test

Statistic*

Triceps brachii AMA Overall v2[2] = 61.7 O–S U[48,31] = 1311 O–L U[48,23] = 1088 S–L U[31,23] = 576 Lesser gluteal AMA Overall v2[2] = 15.4 O–S U[47,29] = 968 O–L U[47,22] = 778 S–L U[29,22] = 345 Hamstring AMA at the hip Overall v2[2] = 30.4 O–S U[47,27] = 1020 O–L U[47,22] = 879 S–L U[27,22] = 333 Iliopsoas AMA Overall v2[2] = 50.4 O–S U[47,30] = 1333 O–L U[47,22] = 858 S–L U[30,22] = 186 Quadriceps femoris AMA Overall v2[2] = 21.5 O–S U[47,27] = 828 O–L U[47,23] = 861 S–L U[27,23] = 503 Triceps surae AMA Overall v2[2] = 17.7 O–S U[12,22] = 243 O–L U[12,2] = 23 S–L U[22,2] = 35

P-value

Adj. P-value

< < <
S>L

O>S>L

O>S>L

Comparisons of limb BMD are presented in Table 7 and Fig. 6. Lepus californicus has significantly lower humeral and radial BMD than O. princeps and S. bachmani. BMD did not significantly differ between O. princeps and S. bachmani for either of the forelimb bones. Femoral BMD in O. princeps is significantly less than in S. bachmani and nearly significantly less than in L. californicus (adjusted P = 0.073). Tibial BMD is statistically similar across the three species.

Limb bone bending strength index O>S>L

O>S>L

O>S>L

*Post-hoc tests are one-tailed Mann–Whitney U-tests of the null hypothesis that the more cursorial taxon displays greater mechanical advantage. Subscript values indicate the available sample sizes for each species in the comparison, with the degrees of freedom for the test equal to the sum of the two values. Significant P-values, or adjusted P-value for post hoc multiple comparisons (adjusted using the False Discovery Rate method, Benjamini & Hochberg, 1995), are indicated by bold type. The prediction column indicates the directionality of the one-tailed tests. O = Ochotona princeps, S = Sylvilagus bachmani, L = Lepus californicus.

Limb bone robusticity Comparisons of limb bone robusticity (i.e. bending strength scaled to the product of bone length and SSP) are presented in Table 6 and Fig. 5. Interspecific differences in robusticity vary along a proximal to distal gradient. As predicted, humeral and femoral robusticity are greatest in O. princeps, least in L. californicus and intermediate in S. bachmani (i.e. significantly lower than in O. princeps but significantly greater than in L. californicus). Interspecific differences are more attenuated at the distal limb segments. Radial robusticity is significantly greater in O. princeps than in either L. californicus or © 2014 Anatomical Society

S. bachmani but is statistically similar between the leporid species, and tibial robusticity does not vary significantly across all three species.

Validation of bone strength index The product of ZP and BMD is significantly associated with maximal bending moments across all of the bones in the laboratory rabbit sample (Fig. 7; P < 0.001, Spearman’s q = 0.899), a finding consistent with the results of previous studies (Ferretti, 1995; Martin et al. 2004). For all bones except the radius, the product of ZP and BMD is significantly positively associated with maximal bending moments, despite limited within-bone variability in the laboratory rabbit dataset (Supporting Information Table S1). In all relevant measures (i.e. limb robusticity indices, BMD and BSI) the laboratory rabbit sample falls within the range of values for the wild lagomorph species in our museum sample (Supporting Information Fig. S1). Because there is therefore no a priori reason to expect that a similar predictive relationship among ZP, BMD and resistance to bending moments would not apply to wild pikas, rabbits and jackrabbits as well, this finding validates the use of the bone strength index in our comparative morphological sample. Interspecific comparisons Comparisons of long bone bending strength indices are presented in Table 8 and Fig. 8. As observed with relative robusticity indices, dimensionless proxies for long bone strength in bending vary along a proximal to distal gradient (Table 8; Fig. 8). As predicted, for the humerus and femur, bending strength indices are greatest in O. princeps, least in L. californicus, and intermediate in S. bachmani (i.e. significantly lower than in O. princeps and significantly greater than in L. californicus). In contrast, whereas O. princeps has significantly greater relative bending strength than S. bachmani and L. californicus, relative radial bending strength did not significantly different between the two leporid species, and relative tibial bending strength did not significantly vary across all three species.

410 Lagomorph limb bone morphology, J. W. Young et al.

Cursorial prediction

0.10

0.30

0.25

0.20

0.15

Iliopsoas AMA

Cursorial prediction

Triceps brachii AMA

0.09 0.08 0.07 0.06 0.05 0.04

0.085 0.075 0.065 0.055

0.15

Cursorial prediction

0.095

Cursorial prediction

Lesser gluteal AMA

0.105

Quadriceps femoris AMA

0.10

0.13 0.11 0.09 0.07 0.05 0.03

0.045 1.55

0.19 0.18 0.17

Cursorial prediction

0.20

Triceps surae AMA

0.21

Cursorial prediction

Hamstring AMA (at the hip)

0.22

1.50 1.45 1.40 1.35

0.16 0.15

1.30

O. prin.

S. bach.

L. cali.

O. prin.

S. bach.

L. cali.

Fig. 3 Box plots of variation in anatomical mechanical advantage (AMA) in the comparative lagomorph sample. In each box plot, dark lines represent the median of the distribution, boxes extend across the interquartile range and whiskers extend to  150% of the interquartile range. Arrows indicate the directionality of our one-tailed post hoc test predictions (i.e. mechanical advantage should decrease with increasing cursoriality).

Discussion

Limb muscle mechanical advantage and cursoriality

The aim of this study was to broadly evaluate the relationship between locomotor mode and limb bone morphology in North American lagomorphs. Based on a large body of theory and empirical data (e.g. Gregory, 1912; Howell, 1944; Smith & Savage, 1956; Brown & Yalden, 1973; Gambaryan, 1974; Coombs, 1978; Garland & Janis, 1993; Carrano, 1999; Hildebrand & Goslow, 2001), we predicted that increasing cursoriality in lagomophs would be associated with decreased limb joint mechanical advantage (i.e. increased displacement advantage: McHenry, 2012) and longer, more gracile limb bones, particularly at the distal segments.

As predicted, observed anatomical mechanical advantage generally tracks reported levels of cursoriality in the lagomorphs sampled here. Across all joint muscle complexes examined, pikas consistently displayed greater anatomical mechanical advantage (i.e. lower displacement advantage) than either cottontail rabbits or jackrabbits. These data support the previous findings by Camp & Borell (1937), who demonstrated that hip muscles (e.g. tensor fascia latae and rectus femoris) have a ‘greater angle of pull’ (i.e. higher mechanical advantage) in O. princeps than in L. californicus. In a morphometric study of European hares and pikas (e.g. Lepus timidus, Lepus europaeus, Lepus tolai and Ocho© 2014 Anatomical Society

Lagomorph limb bone morphology, J. W. Young et al. 411

Table 5 Species differences in the relative distal limb segment lengths.

130%

– < 0.001 < 0.001 < 0.001

< < <
S>L

O>S>L

O>S>L

O>S>L

*Post-hoc tests are one-tailed Mann–Whitney U-tests of the null hypothesis that the more cursorial taxon displays greater long bone bending strength. Table formatting and abbreviations follow Table 4. **Because the overall Krukal–Wallis test comparing tibial bending strength index among species was not significant, post hoc comparisons were not carried out.

(size-scaled ZP and BMD), long bone robusticity (i.e. sizescaled ZP) follows the proximodistal gradient observed in the bending strength estimates, whereas BMD follows a forelimb/hind limb gradient, such that the more cursorial taxa have relatively high levels of femoral and tibial mineralization compared with their relatively low levels of humeral and radial mineralization. Nonetheless, absolute interspecific differences in BMD are more subtle than differences in size-scaled ZP (e.g. compare Figs 5 and 6), indicating that structural robusticity is a greater determinant of long bone bending strength than are material properties per se (see also Erickson et al. 2002; Kemp et al. 2005). Regional differences in levels of bone strength among the lagomorph species sampled here likely result from disparate levels of locomotor loading across the postcranial skeleton. Biewener (1983b) showed that in small mammals, radial and tibial stresses during locomotion are nearly twice as high as humeral and femoral stresses, suggesting that the need to maintain bone integrity by increasing robusticity may take priority over the need to lighten bone mass and improve locomotor economy at these distal segments. The regional differences that characterize the interspecific variation in bone robusticity and strength also argue against a purely size-related explanation for lagomorph long bone scaling, despite the pronounced differences in average pika, © 2014 Anatomical Society

Lagomorph limb bone morphology, J. W. Young et al. 415

7.5

Cursorial prediction

Humeral BSI

7.0 6.5 6.0 5.5 5.0 4.5 4.0

Cursorial prediction

3.3

Radial BSI

3.0 2.7 2.4 2.1 1.8

Cursorial prediction

10

Femoral BSI

9 8 7 6 5

rabbit and jackrabbit body mass. Broad comparative studies of mammals have generally found that long bone cross-sectional dimensions scale to body mass with slight positive allometry, particularly within ‘small’ mammals (i.e. those with body mass < 50 kg) (Alexander et al. 1979; Biewener, 1983a; Bertram & Biewener, 1990; Polk et al. 2000; Garcia & da Silva, 2004). These data indicate that larger mammals generally have more robust bones for the size, though morphological changes alone are insufficient to maintain bone safety across broad increases in body size, necessitating allometric adjustments in limb posture (Biewener, 1983a, 1989, 1990, 1991). If the lagomorphs sampled here followed general mammalian scaling patterns, the null expectation would be for rabbits to have slightly more robust limb bones than pikas and for jackrabbits to have more robust bones than either of the other two species. Instead, our data indicate that humeral and femoral robusticity decrease with size, whereas radial and tibial robusticity generally follow an isometric trend. Neither of these patterns matches the broad mammalian trend of slight positive allometry, suggesting that some factor other than body size accounts the observed differences in long bone robusticity and strength across the sample. We propose that interspecific variation in lagomorph limb bone robusticity reflects a tradeoff between the need for locomotor economy, which would select for longer, lighter bones in the more cursorial taxa, and the need to resist fracture, which would select for stronger, more robust bones in those regions of the postcranial skeleton that experience the greatest amounts of loading. In support of this hypothesis, Kemp et al. (2005) showed that dogs bred for running ability (i.e. greyhounds) had structurally more gracile and more brittle limb bones than dogs bred for fighting ability (i.e. pit bulls) at all limb segments except the metapodials, again suggesting a proximodistal gradient in the degree to which the postcranial skeleton responds to selection for cursorial specialization.

Cursorial prediction

Tibial BSI

5.0

4.5

4.0

3.5

O. prin.

S. bach.

L. cali.

Fig. 8 Box plots of variation in the long bone bending strength index (BSI) in the comparative lagomorph sample. In each box plot, dark lines represent the median of the distribution, boxes extend across the interquartile range and whiskers extend to  150% of the interquartile range. Arrows indicate the directionality of our one-tailed post hoc test predictions (i.e. limb bone BSI should decrease with increasing cursoriality).

© 2014 Anatomical Society

Conclusions The primary aim of this study was to investigate the degree to which variation in skeletal morphology tracked differences in cursoriality among North American lagomorphs. As we predicted, non-cursorial pikas (O. princeps) consistently display the greatest limb joint mechanical advantage, the shortest distal limb segments, and the most robust bones at all limb segments except the crus. Inversely, highly cursorial jackrabbits (L. californicus) are generally marked by the lowest limb joint mechanical advantage, the longest distal limb segments, and the most gracile proximal limb bones. Rabbits (S. bachmani) generally occupy an intermediate position, although several of the variables examined failed to distinguish significantly between rabbits and jackrabbits. Because rabbits and jackrabbits are phylogenetically more closely related to one another than either species is to pikas, structural similarity between the leporids could be due to

416 Lagomorph limb bone morphology, J. W. Young et al.

shared evolutionary history, independent of locomotor adaptation per se. Broader comparative studies, incorporating additional lagomorph species, would be required to test this hypothesis. Nevertheless, we argue that the frequent intermediate rank of rabbit limb bone morphology, suggesting a level of cursorial adaptation between that of pikas and jackrabbits, parallels reported variation in lagomorph locomotor behavior and therefore belies a purely phylogenetic explanation for the observed trends. Because long, structurally gracile limb bones are associated with a decrease in empirically validated estimates of bending strength, it is likely that the more cursorial leporid taxa compromise proximal limb bone integrity in favor of locomotor economy. In the future, these findings should be corroborated by direct testing of wild lagomorph limb bone material properties. Nevertheless, the current data suggest that cursorial adaptation may limit limb bone safety factors, at least at some regions, an idea previously suggested by other researchers (Alexander, 1998; Hildebrand & Goslow, 2001) but not empirically demonstrated prior to this study. Conversely, distal limb bone bending strength was generally maintained across the three species, indicating that safety factors take greater priority in those regions experiencing higher locomotor loading. Overall, our findings demonstrate that traditional skeletal proxies of cursorial ability are largely able to diagnose locomotor mode even in the size-restricted, taxonomically narrow lagomorph sample examined here. These data support previous assertions that cursoriality is associated with a common suite of morphological adaptations across a range of body sizes and radiations (Coombs, 1978; Steudel & Beattie, 1993; Carrano, 1999; Hildebrand & Goslow, 2001).

Acknowledgements We thank Laila Almassri, Elaine Kunzler, Derek Kruse and Kayla Reardon for help with data collection. Sharon Usip and Chris Vinyard provided advice as we were working with the Scanco lCT scanner and Instron MTS. Linda McCort graciously provided laboratory rabbit specimens from the NEOMED Comparative Medicine Unit. Individuals at several museums generously shared their lagomorph collections, including Chris Conroy at the University of California at Berkeley Museum of Vertebrate Zoology, Charles Dardia and Kimberly Bostwick at the Cornell University Museum of Vertebrates, Roberta Muehlheim at the Cleveland Museum of Natural History, Judith Chupasko at Harvard University Museum of Comparative Zoology, Suzanne McLaren and John Wible at the Carnegie Mellon Museum of Natural History, and Linda Gordon and Suzanne Peurach at the Smithsonian Institution. This research was supported by NSF IOS 1146916, NSF BCS 0959438, the NEOMED Skeletal Biology Research Focus Area, and the Department of Anatomy and Neurobiology at NEOMED.

Author contributions J.W.Y. designed the study, helped collect and process morphometric, lCT, and material testing data, analyzed

the combined dataset, and drafted the manuscript. R.D. collected and processed most of the morphometric and lCT data. G.A.R. helped collect and process the morphometric and lCT data and collected and processed most of the material testing data. C.D.F. helped collect and process the morphometric and lCT data. All authors contributed to the editing of the final manuscript.

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Supporting Information Additional Supporting Information may be found in the online version of this article: Table S1. Non-parametric rank correlations between maximal bending moments (Mb) and the product of ZP and BMD (our morphological proxy for long bone bending strength) within individual laboratory rabbit (Oryctolagus cuniculus) bones. Fig. S1. Morphometric correlates of long bone strength in the laboratory rabbit (Oryctolagus cuniculus) sample. Data S1. Morphometric data and identifying information for all lagomorph specimens.

© 2014 Anatomical Society

Limb bone morphology, bone strength, and cursoriality in lagomorphs.

The primary aim of this study is to broadly evaluate the relationship between cursoriality (i.e. anatomical and physiological specialization for runni...
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