Limb bone morphology, bone strength, and cursoriality in lagomorphs

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 μCT 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.

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 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).

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.

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 μCT sample are listed in parentheses below

	N	Humeri	Radii	Ulnae	Innominates	Femora	Tibiae	Calcanei	3rd Metatarsals
Ochotona princeps	53	51 (95/144/172)	48 (25/140/168)	48	53	51 (126/148/172)	47 (5/143/168)	13	12
Sylvilagus bachmani	35	35 (182/256/320)	31 (16/208/272)	31	32	35 (258/329/372)	30 (67/276/372)	26	22
Lepus californicus	27	26 (90/472/673)	24 (14/438/544)	23	26	25 (126/148/172)	25 (325/630/673)	21	2

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 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 half-bounds, and travel distances are relatively short (Chapman, 1971, 1974).

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 h⁻¹ (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).

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.

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.

Table 2.

Skeletal landmarks used to calculate length measurements

Measurement	Proximal landmark	Distal landmark
Scapula length	Junction of the spine and the vertebral border	Center of the glenoid fossa
Humerus length	Proximal-most point on the humeral head	Distal-most point on the trochlea
Radius length	Proximal-most point on the radial head	Tip of the styloid process
Olecrenon length	Proximal-most point on the olecranon process	Center of the trochlear notch
Innominate length	Cranial-most point on the iliac crest	Caudal-most point on the ischial tuberosity
Ischium length	Center of the acetabulum	Caudal-most point on the ischial tuberosity
Gluteal lever arm	Center of the fovea capitis	Proximal-most point on the greater trochanter
Iliopsoas lever arm	Center of the fovea capitis	Most medial point on the lesser trochanter
Femur length	Center of the fovea capitis	Distal-most point on the medial condyle
Quadriceps femoris lever arm	Anterior-most point on the medial condyle	Center of medial epicondyle
Tibia length	Superior-most point on the intercondylar eminence	Distal-most point on the lateral malleolus
Calcaneal tuber length	Insertion of gastrocnemius	Anterior-most point on fibular notch
3rd metatarsal length	Center of the proximal articular surface	Center of the phalangeal articular surface

μCT measurements

Limb bones were μCT-scanned at a resolution of 20.5 μm per pixel using a vivaCT 75 μCT scanner (Scanco USA, Inc., Southeastern, PA, USA) (Fig. 2). For each bone, a stack of 20.5-μm-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. mid-shaft) 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).

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.

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. Z_P, in mm³) and cross-sectional area (i.e. CSA, in mm²) across all slices in the stack. Z_P 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). Z_P is thus similar to the planar section modulus (Z) and is proportional to (twice) the bone's overall strength in bending. Z_P 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 cm⁻³).

Derived variables

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

Mechanical advantage

Mechanical advantage was calculated as the ratio of skeletal in-lever 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).

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	Olecrenon length	Radius length
Lesser gluteal mm.	Gluteal lever arm length	Femur length + tibia length
Hamstring mm. (at the hip)	Ischium length	Femur length + tibia length
Iliopsoas	Iliopsoas lever arm length	Femur length + tibia length
Quadriceps femoris	Quadriceps femoris lever arm length	Tibia length
Triceps surae	Calcaneal tuber length + 3rd metatarsal length	3rd metatarsal length

Measures of relative limb segment length

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 Z_P (our measure of long bone 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, 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 Z_P (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. σ_peak) are proportional to the product of the bending moment (M_max) and maximal perpendicular distance to form the neutral axis (c), divided by the second moment of area in the plane of bending (I ):

(1)

Because the inverse of the cI⁻¹ term (i.e. Ic⁻¹) is the equation for the section modulus in the plane of bending (Z), Eq. 1 could be algebraically rearranged as:

(2)

Thus, the maximal bending moment (M_max) that a long bone could resist should be proportional to the product of the bone's peak flexural strength (σ_peak) and the section modulus. In this study, we used BMD as a non-invasive morphometric proxy for σ_peak. 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 Z_P 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 Z_P 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 Z_P 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 μCT-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 min⁻¹ 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 experiment-wise 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 Z_P 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 joint-muscle 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.

Table 4.

Species differences in anatomical mechanical advantage

Test	Statistic*	P-value	Adj. P-value	Prediction
Triceps brachii AMA
Overall	χ2[2] = 61.7	< 0.001	–
O – S	U[48,31] = 1311	< 0.001	< 0.001	O > S > L
O – L	U[48,23] = 1088	< 0.001	< 0.001
S – L	U[31,23] = 576	< 0.001	< 0.001
Lesser gluteal AMA
Overall	χ2[2] = 15.4	< 0.001	–
O – S	U[47,29] = 968	0.001	0.002	O > S > L
O – L	U[47,22] = 778	0.001	0.001
S – L	U[29,22] = 345	0.314	0.314
Hamstring AMA at the hip
Overall	χ2[2] = 30.4	< 0.001	–
O – S	U[47,27] = 1020	< 0.001	< 0.001	O > S > L
O – L	U[47,22] = 879	< 0.001	< 0.001
S – L	U[27,22] = 333	0.334	0.238
Iliopsoas AMA
Overall	χ2[2] = 50.4	< 0.001	–
O – S	U[47,30] = 1333	< 0.001	< 0.001	O > S > L
O – L	U[47,22] = 858	< 0.001	< 0.001
S – L	U[30,22] = 186	0.996	0.996
Quadriceps femoris AMA
Overall	χ2[2] = 21.5	< 0.001	–
O – S	U[47,27] = 828	0.015	0.015
O – L	U[47,23] = 861	< 0.001	< 0.001	O > S > L
S – L	U[27,23] = 503	< 0.001	< 0.001
Triceps surae AMA
Overall	χ2[2] = 17.7	< 0.001	–
O – S	U[12,22] = 243	< 0.001	< 0.001
O – L	U[12,2] = 23	0.028	0.041	O > S > L
S – L	U[22,2] = 35	0.096	0.096

^*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.

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).

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).

Table 5.

Species differences in the relative distal limb segment lengths

Test*	Statistic*	P-value	Adj. P-value	Prediction
Brachial index
Overall	χ2[2] = 83.9	< 0.001	–
O – S	U[46,31] = 2	< 0.001	< 0.001	O < S < L
O – L	U[46,22] = 0	< 0.001	< 0.001
S – L	U[31,22] = 0	< 0.001	< 0.001
Crural index
Overall	χ2[2] = 54.2	< 0.001	–
O – S	U[47,29] = 300	< 0.001	< 0.001	O < S < L
O – L	U[47,23] = 40	< 0.001	< 0.001
S – L	U[29,23] = 70	< 0.001	< 0.001
Metatarsal/femur ratio
Overall	χ2[2] = 25.3	< 0.001	–
O – S	U[12,22] = 0	< 0.001	< 0.001	O < S < L
O – L	U[12,2] = 0	0.018	0.021
S – L	U[22,2] = 2	0.021	0.021

^*Post-hoc tests are one-tailed Mann–Whitney U-tests of the null hypothesis that the more cursorial taxon displays greater brachial and crural indices. Table formatting and abbreviations follow Table 4.

Fig. 4.

Box plots of variation in relative distal limb segment lengths 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. relative distal limb segment lengths should increase with increasing cursoriality).

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

Table 6.

Species differences in the long bone robusticity indices

Test*	Statistic	P-value	Adj. P-value	Prediction
Humeral robusticity index
Overall	χ2[2] = 41.3	< 0.001	–
O – S	U[34,19] = 523	< 0.001	< 0.001	O > S > L
O – L	U[34,14] = 476	< 0.001	< 0.001
S – L	U[19,14] = 265	< 0.001	< 0.001
Radial robusticity index
Overall	χ2[2] = 24.1	< 0.001	–
O – S	U[34,18] = 518	< 0.001	< 0.001	O > S > L
O – L	U[34,14] = 408	< 0.001	< 0.001
S – L	U[18,14] = 139	0.317	0.317
Femoral robusticity index
Overall	χ2[2] = 18.1	< 0.001	–
O – S	U[34,19] = 461	0.005	0.005	O > S > L
O – L	U[34,14] = 402	< 0.001	< 0.001
S – L	U[19,14] = 204	0.005	0.005
Tibial robusticity index**
Overall	χ2[2] = 0.9	0.637	–
O – S	–	–	–	O > S > L
O – L	–	–	–
S – L	–	–	–

^*Post-hoc tests are one-tailed Mann–Whitney U-tests of the null hypothesis that the more cursorial taxon displays greater robusticity. Table formatting and abbreviations follow Table 4.

^**Because the overall Krukal–Wallis test comparing tibial robusticity index among species was not significant, post hoc comparisons were not carried out.

Fig. 5.

Box plots of variation in the limb robusticity index 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 robusticity should decrease with increasing cursoriality).

Limb bone mineral density

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.

Table 7.

Species differences in limb bone mineral density

Test*	Statistic	P-value	Adj. P-value
Humeral mineral density
Overall	χ2[2] = 21.7	< 0.001	–
O – S	U[50,25] = 583	0.641	0.641
O – L	U[34,25] = 1005	< 0.001	< 0.001
S – L	U[25,25] = 515	< 0.001	< 0.001
Radial mineral density
Overall	χ2[2] = 15.5	< 0.001	–
O – S	U[44,24] = 606	0.320	0.320
O – L	U[44,21] = 734	< 0.001	< 0.001
S – L	U[24,21] = 375	0.005	0.008
Femoral mineral density
Overall	χ2[2] = 17.7	< 0.001	–
O – S	U[49,24] = 219	< 0.001	0.001
O – L	U[49,23] = 449	0.049	0.073
S – L	U[24,23] = 354	0.264	0.264
Tibial mineral density**
Overall	χ2[2] = 2.6	0.275	–
O – S	–	–	–
O – L	–	–	–
S – L	–	–	–

^*Because we had no a priori expectation for how limb bone mineral density should vary with levels of cursoriality, all post hoc tests are two-tailed Mann–Whitney U-tests of the null hypothesis there bone mineral densities are equal among species. Table formatting and abbreviations follow Table 4.

^**Because the overall Krukal–Wallis test comparing tibial bone mineral density among species was not significant, post hoc comparisons were not carried out.

Fig. 6.

Box plots of variation in bone mineral density (BMD) 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.

Limb bone bending strength index

Validation of bone strength index

The product of Z_P 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 ρ = 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 Z_P 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 Z_P, 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.

Fig. 7.

Association between the maximal bending moments (M_max) and product of polar section modulus (Z_P) and bone mineral density (BMD) in the laboratory rabbit (Orytolagus cuniculus) 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.

Table 8.

Species differences in limb bone bending strength indices

Test*	Statistic	P-value	Adj. P-value	Prediction
Humeral bending strength index
Overall	χ2[2] = 37.4	< 0.001	–
O – S	U[34,15] = 410	< 0.001	< 0.001	O > S > L
O – L	U[34,13] = 442	< 0.001	< 0.001
S – L	U[15,13] = 195	< 0.001	< 0.001
Radial bending strength index
Overall	χ2[2] = 29.7	< 0.001	–
O – S	U[34,15] = 449	< 0.001	< 0.001	O > S > L
O – L	U[34,13] = 409	< 0.001	< 0.001
S – L	U[15,13] = 122	0.134	0.134
Femoral bending strength index
Overall	χ2[2] = 29.7	< 0.001	–
O – S	U[34,14] = 329	0.020	0.020	O > S > L
O – L	U[34,13] = 366	< 0.001	0.001
S – L	U[14,13] = 141	0.008	0.012
Tibial bending strength index**
Overall	χ2[2] = 0.5	0.783	–
O – S	–	–	–	O > S > L
O – L	–	–	–
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.

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).

Discussion

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.

Limb muscle mechanical advantage and cursoriality

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 Ochotona alpina) Gambaryan (1974) found that hares had 1.5 times as much hind limb muscle mass as pikas (scaled to total limb muscle mass). This discrepancy was particularly striking for the knee and hip joint extensors, where pikas had only 54% the relative muscle mass of hares. Because the out-torque a limb can generate is equal to the product of the instantaneous muscle force and the muscle lever arm length, greater mechanical advantage in pikas could therefore partially compensate for reduced available muscle force. Conversely, increased muscle mass in combination with greater ‘displacement advantage’ may permit hares and jackrabbits to maintain high force output despite operating at low gear ratios, maximizing limb muscle work and power outputs.

Comparisons of mechanical advantage between L. californicus and S. bachmani were more mixed. As predicted, AMA at the elbow and knee was significantly greater in rabbits than in jackrabbits. However, contrary to our predictions, jackrabbits had greater AMA than rabbits for iliopsoas, a primary hip flexor muscle, and similar values to rabbits for the lesser gluteal and hamstring muscles, two primary hip extensor muscles. These data imply that the relationship between mechanical advantage and cursorial specialization within leporids may not be as straightforward as predicted. Specifically, our data suggest that unlike the distal limb joints, the jackrabbit hip joint is constructed for relatively high force output, a finding consistent with the relatively high hip muscle mass of Lepus (Williams et al. 2007a). Alternatively, these deviations from the predicted patterns could indicate that the skeletal metrics employed here are inadequate proxies for the mechanics of these joint–muscle complexes. Specifically, empirical measures of actual muscle moment arms (i.e. instantaneous perpendicular distance between the muscle line of action and the joint center of rotation: Williams et al. 2007a,b) and effective mechanical advantage (Biewener, 1989) may be required to discern more precisely the functional differences among the leporids.

Relative limb segment lengths and cursoriality

Previous studies have consistently shown that limb length is a strong predictor of both speed and locomotor economy across terrestrial vertebrates (Hildebrand, 1985; Garland & Janis, 1993; Irschick & Jayne, 1999; Hildebrand & Goslow, 2001; Christiansen, 2002; Pontzer, 2007). Relatively long-limbed animals can travel greater distances at faster speeds, and expend less metabolic energy doing so. Because limb muscle mass is primarily concentrated in the proximal segments (at least among species not specialized for manual and pedal grasping; Preuschoft & Günther, 1994; Raichlen, 2005), cursorial species typically augment limb length by specifically increasing the length of distal segments, which minimizes the tendency for longer limbs to increase rotational inertia (Hildebrand & Hurley, 1985). For this reason, intralimb indices of distal-to-proximal segment lengths are typically greater in more cursorial animals (Gregory, 1912; Howell, 1944; Garland & Janis, 1993; Carrano, 1999).

Gregory (1912) first noted that locomotor mode in mammals can be diagnosed by intralimb comparisons of forelimb and hind limb segment lengths. He found that the gradation of graviportal to cursorial mammals was paralleled by increases in brachial, crural and metatarsal–femur indices. In one of the few comparative studies of cursoriality to explicitly incorporate locomotor performance measures, Garland & Janis (1993) showed that the overall hind limb length and metatarsal–femur ratio significantly predicted running speed in a mixed sample of carnivores and ungulates, although much of the variance in running speed remained unexplained (hind limb length: R² = 0.181; metatarsal–femur ratio: R² = 0.119) (see also Christiansen, 2002).

Our results demonstrate that indices of relative limb segment lengths reflect variation in cursoriality among lagomorphs, paralleling the trends seen in more eclectic comparisons across broader mammalian groups. Coombs (1978) made the argument that since small animals – such as the lagomorphs studied here – are necessarily limited to taking absolutely shorter strides, adaptations to increase relative stride length and limit rotational inertia may be particularly pronounced in small-bodied cursors. Pikas, the least cursorial species in our sample, generally have the lowest brachial, crural and metatarsal–femur indices, whereas jackrabbits, the most cursorial species, consistently have the relatively longest distal elements. Metatarsal–femur ratios best fit predictions of how relative limb segments lengths should vary among the lagomorphs, supporting previous assertions that this ratio is a reliable metric of cursorial ability across mammals and other tetrapods (Gregory, 1912; Garland & Janis, 1993; Carrano, 1999; Christiansen, 2002). Our results also corroborate the more limited lagomorph studies of Camp & Borell (1937) and Gambaryan (1974), who also demonstrated that pikas have relatively shorter shank and foot lengths than hares and jackrabbits.

Limb bone strength and cursoriality

Several authors have posited that cursorial mammals may sacrifice bone mass and strength as a means of reducing costly rotational inertia (Hildebrand, 1985; Alexander, 1998), thereby compromising limb bone safety factors and increasing the risk of fracture. Lieberman et al. (2003) and Plochocki et al. (2008) provide experimental evidence that generally supports this hypothesis, showing that both immature sheep and immature mice respond to increased limb loading by accelerating periosteal modeling rates in proximal bones more so than in distal bones. Because periosteal modeling increases bone mass, these data suggest that there may be a tradeoff between the benefit accrued by improving bone strength in response to loading and the cost of increasing rotational inertia about the proximal limb pivot. Indeed, Myers & Steudel (1985) and Marsh et al. (2006) showed that experimentally increasing limb rotational inertia in running humans and guinea fowl can increase the metabolic cost of locomotion by as much as 20% above baseline values. By demonstrating a direct link between limb inertia and metabolic cost, these data support the hypothesis that decreasing limb inertia in fast-moving animals should be selectively advantageous. Nevertheless, decreasing bone mass to limit rotational inertia incurs a substantial cost – by reducing bone mass, bone strength and safety factor, the risk of fracture is increased. Horses, for instance, are 14 times more likely to fracture long and thin distal segments (e.g. metapodials) than shorter and more robust proximal ones (i.e. humerus and femur) (Alexander, 1998).

Our data provide only partial support for the hypothesis that safety factors decline with increasing cursoriality, at least in lagomorphs, suggesting instead that the tradeoff between locomotor efficiency and bone strength varies regionally across the postcranial skeleton. Specifically, long bone bending strength indices (i.e. the product of size-adjusted Z_P and BMD) reliably track levels of cursoriality at the proximal limb segments, such that jackrabbits have the weakest humeri and femora, pikas the strongest, and rabbits occupy an intermediate position. In contrast, interspecific differences in estimated distal segment bending strength are more attenuated, such that jackrabbits and rabbits have similar levels of predicted radial bending strength, and predicted tibial bending strength is similar across all three species. Empirical testing of domestic rabbit (Oryctolagus cuniculus) limb bone material properties showed that the product of Z_P and BMD is a valid predictor of maximal bending moments (Fig. 7), suggesting that relatively less force would therefore be required to damage the proximal, but not necessarily the distal, limb bones of the more cursorial lagomorphs in our sample. With regard to the variables that determine estimated bending strength (size-scaled Z_P and BMD), long bone robusticity (i.e. size-scaled Z_P) 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 Z_P (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, 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.

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 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).

Author contributions

J.W.Y. designed the study, helped collect and process morphometric, μCT, and material testing data, analyzed the combined dataset, and drafted the manuscript. R.D. collected and processed most of the morphometric and μCT data. G.A.R. helped collect and process the morphometric and μCT data and collected and processed most of the material testing data. C.D.F. helped collect and process the morphometric and μCT data. All authors contributed to the editing of the final manuscript.

Supporting Information

Additional Supporting Information may be found in the online version of this article:

Data S1. Morphometric data and identifying information for all lagomorph specimens.