In vivo locomotor strain in the hindlimb bones of Alligator mississippiensis and Iguana iguana: implications for the evolution of limb bone safety factor and non-sprawling limb posture

Terrestrial tetrapods have evolved a diverse range of limb postures spanning a continuum from sprawling, in which the limbs are held lateral to the body, to fully upright, in which the limbs are held beneath the body (Jenkins, 1971a; Gatesy, 1991a). Differences in limb posture among species have been correlated with differences in many aspects of locomotor function, ranging from limb bone morphology (Bertram and Biewener, 1990; Gatesy, 1991b) to limb kinematics (Jenkins, 1971a; Gatesy, 1991a; Reilly and DeLancey, 1997a,b; Reilly and Elias, 1998). Yet studies of limb bone loading during locomotion have generally examined only mammalian or avian species in which limb motion is restricted to a parasagittal or nearly parasagittal plane: the consequences of non-parasagittal limb posture and kinematics for limb bone loading have not been investigated. Because upright, parasagittal posture is a derived condition among mammals (Jenkins, 1971a,b) and amniotes in general (Brinkman, 1980a,b, 1981; Gatesy, 1991a), broad extrapolations of skeletal loading patterns from mammals that use parasagittal limb motion to other species that use different limb postures and kinematics are suspect. Such extrapolations potentially oversimplify the functional diversity of loading patterns in tetrapod limbs and mask insights into the evolutionary history of tetrapod locomotor mechanics. To examine the evolution of locomotor mechanics across transitions from sprawling to non-sprawling posture, comparative biomechanical data from non-mammalian species with non-parasagittal kinematics are required.

One approach used to examine limb bone loading mechanics during terrestrial locomotion is in vivo measurement of limb bone strains (e.g. Lanyon and Smith, 1970; Rubin and Lanyon, 1982; Biewener et al., 1983, 1988; Biewener and Taylor, 1986). Results from studies of mammalian and avian bone strains have led to two general conclusions. First, tetrapod limb bones supporting the body during terrestrial locomotion are usually loaded in bending or axial compression (Biewener et al., 1983, 1988; Biewener, 1991); torsion is a less common loading regime (Keller and Spengler, 1989; Carrano, 1998). Second, tetrapod limb bones generally have safety factors between 2 and 4 (i.e. are able to withstand 2–4 times the strain they usually incur: Alexander, 1981; Biewener, 1993). However, because available strain data come from a restricted functional and phylogenetic range of animals (mammals and birds with parasagittal or nearly parasagittal limb kinematics), the generality of these conclusions among all amniotes is uncertain. The broader diversity of locomotor strain patterns and their implications for the evolution of skeletal design remain largely unexplored.

This study reports the results of in vivo locomotor strain recordings from the femur and tibia of the American alligator (Alligator mississippiensis) and the green iguana (Iguana iguana), species from the non-parasagittal end of the kinematic continuum and from previously unsampled phylogenetic lineages (Crocodylia and Lepidosauria respectively, sensuBrochu, 1997; Gauthier et al., 1988). These data are used to address two fundamental questions. (1) What are the consequences of non-parasagittal locomotion for the mechanics of limb bone loading? (2) What might the mechanics of non-parasagittal locomotion in modern species imply about possible factors in the evolution of non-sprawling posture? To approach these broad questions, we test three more specific hypotheses. First, we test the hypothesis that torsion is a more important mode of limb bone loading during terrestrial locomotion among non-avian saurians (taxonomy sensuGauthier et al., 1988) than among previously examined birds or mammals. Long-axis rotation of the femur and tibia during locomotion in lizards and crocodilians (Brinkman, 1980b, 1981; Gatesy, 1991a) suggests that torsion may predominate in the limb bones of these taxa, in contrast to the dominance of bending and axial compression typical in the limb bones of species with parasagittal limb kinematics (e.g. Biewener, 1983a; Biewener et al., 1983, 1988). Second, we test the hypothesis that the limb bone safety factors of crocodilians and lizards are similar to those observed in birds and mammals. Such similarity might suggest a potential optimal safety factor across all amniotes, regardless of differences in their locomotor function. Finally, we test the hypothesis that limb bone strains will decrease with the use of more upright limb posture by individual animals with the ability to use a range of limb postures. Evolutionary shifts from crouched to upright posture in mammals have been shown to mitigate expected increases in limb bone stress due to size-related increases in limb bone loading (Biewener, 1983a, 1989, 1990). Therefore, lower bone strains might be expected during more upright locomotion by an individual animal that is not incurring increased limb bone loads due to increases in body mass. Because of the wide range of femoral postures employed by Alligator (Gatesy, 1991a; Reilly and Elias, 1998), an examination of strain and kinematic data from this species provides an opportunity to test directly the relationship between load magnitude and limb posture within individual animals. By comparing strain data from Alligator and Iguana with data from previous studies of locomotor strains in birds and mammals, this study seeks to gain insight into mechanical factors potentially influencing the evolution of non-sprawling limb posture.

Three juvenile Alligator mississippiensis (body mass 1.73–2.27 kg, total length 0.98–1.04 m) were provided for strain experiments by the Rockefeller Wildlife Refuge (Grand Chenier, Louisiana, USA). Animals were housed together in a Plexiglas-walled enclosure (245 cm×100 cm×60 cm). Two large plastic cement mixing tubs filled with water were provided as a swimming area for the animals: the water was changed every second day. Temperature was maintained between 29 and 32 °C. Animals were fed a diet of chicken hearts, gizzards and livers mixed with a vitamin/mineral supplement. A 13 h:11 h light:dark cycle and full-spectrum light were provided. The diet supplement and full-spectrum light were supplied to help maintain natural limb bone mass in spite of captivity (Frye, 1995).

Four subadult Iguana iguana (body mass 320–516 g, snout–vent length 229–260 mm) were purchased from Glades Herps (Fort Myers, Florida, USA). The animals were housed in an enclosure similar to that used for the alligators, except that the large water tubs were removed and replaced with objects to climb on and hide in (promoting activity and exercise). The same light and temperature conditions were also maintained. Iguanas were supplied with shallow trays of water and fed a diet of assorted vegetables mixed with a vitamin/mineral supplement (Frye, 1995).

Definitions of anatomical orientations of limb element surfaces for both alligators and iguanas are those of Romer (1956). With the femur oriented such that both distal condyles are parallel to the ground, the ventral surface faces down (towards the ground), the dorsal surface faces up (away from the ground), and anterior and posterior are in the directions of protraction and retraction, respectively. In the crus, the tibia is medial to the fibula. The extensor surface of the tibia is defined as anterior, the flexor surface as posterior, the lateral surface as facing towards the fibula, and the medial surface as facing away from the fibula. During locomotion, the femur rotates during limb support such that the anatomical ‘dorsal’ surface shifts anteriorly in an absolute frame of reference and the anatomical ‘anterior’ surface shifts ventrally (Brinkman, 1980b, 1981; Rewcastle, 1980, 1983; Gatesy, 1991a).

Strain gauges were attached surgically to the left (alligator) or right (iguana) femur and tibia of each animal, using aseptic technique and following the protocol of Biewener (1992). All surgical procedures were approved by the Institutional Animal Care and Use Committee of the University of Chicago (protocols 61341 and 61371). Alligators were initially sedated with intramuscular injections of 50 mg kg⁻¹ ketamine and 0.5 mg kg⁻¹ xylazine, with volumes evenly divided among the three non-surgical limbs. After sedation, the animals were intubated, and surgical anesthesia was induced and maintained by administering Metofane (methoxyfluorane) through a closed-system anesthesia machine with relative control of inhalant concentration (Pitman-Moore, model 970). Anesthesia was induced in iguanas with initial injections of 100 mg kg⁻¹ ketamine and 1 mg kg⁻¹ xylazine into the muscles at the base of the tail; supplemental doses were administered as required. These doses were larger than typically recommended for lizards (Bennett, 1991; Boyer, 1992), but initially lower doses administered during the first surgery were insufficient to induce a surgical plane of anesthesia. The animals recovered uneventfully from the dosages used.

To expose gauge attachment sites, medial incisions were made through the skin of the leg and thigh at midshaft. The muscles surrounding the bones were separated along fascial planes and retracted to gain access to the bone surfaces. For femoral sites, it was necessary to penetrate a portion of the extensive attachment of the femorotibialis muscle to expose the bone surface and to attach the gauges slightly distal to midshaft to avoid excessive interference with the origin of this muscle. At each site, a ‘window’ of periosteum was removed to expose the bone cortex. Bone surfaces were lightly scraped with a periosteal elevator, cleaned with ether, and allowed to dry. Gauges were then attached using a self-catalyzing cyanoacrylate adhesive. In the alligators, single-element gauges (type FLG-1-11; Tokyo Sokki Kenkyujo) were attached to the anterior femur and the medial and posterior tibia; rosette gauges (type FRA-1-11) were attached to the dorsal and ventral femur and the anterior tibia (Fig. 1A). In the iguanas, single-element gauges were attached to the anterior, medial and posterior aspects of the tibia and to the dorsal surface of the femur; a rosette gauge was attached to the anterior aspect of the femur (Fig. 1B). Single-element gauges and the central elements of rosette gauges were aligned with the long axis of the bone to which they were attached. Angular deviations from the long axis were measured during post-experimental dissections and accounted for in calculations where required (mean deviation <5 °). Once all gauges were in place, lead wires from the gauges (336 FTE, etched Teflon; Measurements Group) were passed subcutaneously through a small incision posterodorsal to the acetabulum. All incisions were sutured closed, and the lead wires were soldered into a microconnector and secured to the animals by a self-adhesive bandage wrap. These solder connections then were reinforced with epoxy adhesive.

After 2–4 days of recovery, strain recordings were made over the following 2–3 days. A shielded cable was plugged into the microconnector to carry strain signals to Vishay conditioning bridge amplifiers (model 2120; Measurements Group). Raw strain signals were sampled through an A/D converter at 100 Hz (alligators) or 250 Hz (iguanas), calibrated, and stored on a computer for analysis. Owing to the length of the lead wires, strain signals were also corrected for lead wire desensitization (+5 % increase in strain magnitude) as recommended by Biewener (1992). For the alligators, strain data were collected predominantly during treadmill exercise, although some locomotion on a 5 m walled trackway was also recorded. Training consisted of six 90 s periods of exercise (with periods of rest between), 5 days per week for 3 months. Multiple treadmill trials approximately 40 s in duration were conducted at 0.17 m s⁻¹ and 0.37 m s⁻¹ for each alligator. The lower speed represented a slow walk for animals of this size (Brinkman, 1980b; Gatesy, 1991a), whereas the faster speed required considerable exertion and was close to the top speed that the animals could sustain. Because the number of data channels from which recordings could be made at the same time was limited, femoral and tibial data were collected during separate trials. For the iguanas, strain data were generated by placing the animals at one end of the 5 m trackway, then startling them by thumping the floor or track walls behind them, causing them to run or walk towards the other end of the track. Multiple trials (with periods of rest between), each recording strains for multiple steps, were conducted for each iguana. Data were collected simultaneously from the femur and tibia. S-VHS (60 Hz) video recordings (Panasonic AG-450) were made of all trials for both species to document locomotor behavior. In the treadmill trials for the alligators, video recordings were obtained from a standard lateral perspective so that kinematic variables and duty factors (the portion of the stride during which the foot contacts the ground) could be calculated. For the iguanas running in the trackway, duty factors were calculated from the strain recordings as the length of time over which a strain peak was present, divided by the length of time from the start of one peak to the start of the following peak. Upon completion of the recordings, the animals were killed (Nembutal sodium pentobarbital, 200 mg kg⁻¹ intraperitoneal injection) and stored for later dissection.

Conventions for analysis and interpretation of strain data were as follows. Tensile strains are recorded as positive and compressive strains are negative. The magnitudes of peak longitudinal strain (strain aligned with the axis of the bone) were digitized from each gauge location for each step. The distribution of tensile and compressive strains on the cortex of a bone provides information about the loading regime to which the bone is subjected. For instance, compressive strains at all sites would suggest loading in axial compression, whereas equal magnitudes of tensile and compressive strains on opposite cortices would indicate pure bending; unequal magnitudes of tension and compression on opposite cortices would suggest a combination of axial and bending loads. Magnitudes and orientations of principal strains (maximum and minimum strains at a site, potentially not aligned with the long axis of the bone) were calculated from the rosette gauge data (Dally and Riley, 1978). Shear strains also were calculated following the methods of Carter (1978) and Biewener and Dial (1995). In conjunction with calculations of principal strain orientations, calculations of shear strains allowed evaluation of the importance of torsional loading. Defining the long axis of the bone as 0 °, pure torsional loads would show principal strain orientations (deviations from the bone long axis) of +45 ° or −45 °, depending on whether the bone was twisted in a clockwise or counterclockwise direction. Orientations of principal tensile strain (ϕ_t) differing by 180 ° are equivalent, and orientations of principal tensile and compressive strains are orthogonal.

Following muscular dissections of the hindlimbs of the animals, the instrumented leg bones were excised and embedded in epoxy resin. The bones then were sectioned transversely at the gauge sites using a diamond annular saw (Microslice II; Cambridge Instruments Ltd), and the sections were mounted on glass slides. Using a digitizing tablet, coordinate data were generated from outlines traced from the cross sections, and the locations of the gauges on the bone perimeter were digitized. Following the methods of Carter et al. (1981) and Biewener and Dial (1995), the digitized coordinates of the bone outline and gauge locations, together with strain data from the three separate recording sites for the alligator femur, alligator tibia and iguana tibia were used to calculate the location of the neutral axis of bending (where strain is zero) and the planar distribution of longitudinal strains through cross sections of those elements.

Upon removal of the instrumented leg bones, the intact remains of the iguana and alligator specimens were frozen. Specimens were later thawed, and the femora and tibiae contralateral to the instrumented limbs were excised for measurements of yield and failure strain in bending tests. Care was taken to avoid scratching or damaging bone surfaces during extraction. Soft tissue was cleared from the bone diaphyses by firmly rubbing the surface using a saline-soaked cotton-tipped applicator, although residual ligamentous tissue was allowed to remain on the articular surfaces. Hydration of the bones was maintained with saline solution after the removal of soft tissue. Upon cleaning the bones, exposed surfaces were lightly sanded with 600 grit paper to ensure removal of any surface flaws. Three single-element strain gauges (type FLK-2-11) were then bonded to the bone cortex around the midshaft circumference of each element. For tibiae, anterior, medial and posterior sites were selected; for femora, a dorsal site was selected, as well as two ventral sites, one anterior and one posterior to the ventral muscle scar of the femorotibialis. Attachment sites were cleaned with methyl-ethyl-ketone only, using no additional scraping, and gauges again were bonded with cyanoacrylate adhesive. No gauge orientation deviated by more than 5 ° from the long axis of a bone.

Whole bone specimens were tested in three-point bending using a Type K (Monsanto) tensometer fitted with a 600 N steel force beam to which a strain gauge had been bonded. The gauge length of the three-point bending jig was 30 mm, yielding a 15 mm bending moment arm (bone lengths ranged from 40 to 57 mm). Bones were positioned in the jig so that the strain gauges bonded to them were at the level of the central point of load. In addition, bones were oriented so that during testing tensile strains would develop on the surfaces on which they developed during the locomotor trials, on the basis of the in vivo strain recordings. Thus, femora were positioned to place the ventral surface in tension, whereas tibiae were positioned to place the anterior surface in tension. These positions placed at least one gauge on each bone (ventroposterior for femora, anterior for tibiae) on a surface where maximum tensile strains would be expected to develop during the tests. Bones were loaded at a constant displacement rate (0.08 mm s⁻¹ ) until failure. The voltage outputs from the force beam and the gauges bonded to the test bones were collected through bridge amplifiers and an A/D converter and stored on a computer for analysis. For each trial, applied bending moment (applied force multiplied by the bending moment arm) was plotted versus maximum tensile strain. Yield strains were then calculated following the protocol of Currey (1990): the slope of the initial, linear portion of the curve was calculated, and the point at which strain magnitude deviated by 200 microstrain (hereafter abbreviated με=strain×10⁻⁶ ) from the magnitude expected on the basis of this slope was considered to be the point of yield.

‘Mean’ safety factors were calculated from the mean values of peak strains and mechanical properties. In addition, when error ranges were available for yield strains or peak functional strains, ‘worst-case’ (i.e. lowest possible) safety factors were calculated, on the basis of (mean yield strain minus 2 S.D.) and (mean peak functional strain plus 2 S.D.).

True femur lengths were measured directly from the animals, and higher values of γ reflect greater femoral adduction (i.e. a more upright posture). Reduced major axis (RMA) regressions of strain magnitude on γ were calculated for each recording location to evaluate correlations between these variables (for similar treatment of angular kinematic data, see Reilly and DeLancey, 1997b). RMA is the most appropriate method of regression for the evaluation of structural relationships between variables when both are subject to error (LaBarbera, 1989; Sokal and Rohlf, 1995).

Representative principal, shear and longitudinal strain traces from the alligator and iguana limb bones are illustrated in Figs 2–5; mean peak strain magnitudes at the different recording locations are summarized in Tables 1–4. Except for traces from the tibia and anterior femur of Iguana (Fig. 4), all graphs are drawn to the same scale to facilitate direct comparisons. Detailed results for the femur and tibia of each species are described below. Generalizations about limb bone strains during fast and slow locomotion for each species are made on the basis of the most common strain patterns observed for each recording site, interpreting these patterns as standard behavior. Some repeated, but non-standard, patterns are described in a separate section after these general characterizations.

Representative strain traces from an alligator femur during fast locomotion are illustrated in Fig. 2; mean peak strain magnitudes for each femoral recording site during fast steps are reported in Table 1. Peak strain magnitudes are quite variable (coefficients of variation between 0.39 and 0.80), but loading patterns (i.e. patterns of tensile and compressive strain at each recording site) are consistent among steps. Peak strains at all locations are approximately synchronous and typically occur slightly before midstep. Longitudinal strain traces often exhibit two peaks per step, reflecting the initial deceleration of the animal upon contact of the foot with the ground, followed by the reacceleration of the animal when the foot pushes off from the ground (Alexander, 1977a). However, ventral and dorsal principal strain traces often show only single peaks, consistent with the pattern seen during faster locomotion in previous studies of mammalian limb bone strains (e.g. Lanyon and Bourn, 1979; Rubin and Lanyon, 1982; Biewener and Taylor, 1986; Biewener et al., 1988).

The distributions and relative magnitudes of tensile and compressive strains indicate that the alligator femur is subject to a combination of bending, axial compression and torsion. Anterior and ventral aspects of the alligator femur experience tension: longitudinal strains are positive on both surfaces, and ventral principal tensile strains are larger than ventral principal compressive strains (Table 1; Fig. 2A,C). Mean peak strains recorded from these sites were +708 με (ventral, principal) and +377 με (anterior, longitudinal). In contrast, the dorsal surface of the femur experiences compression: longitudinal strains are compressive, and compressive principal strains are greater than tensile principal strains (mean peak principal strain −468 με; Fig. 2B; Table 1). The presence of tensile and compressive strains on opposite bone surfaces suggests that the alligator femur is loaded in bending. In addition, because dorsal compressive longitudinal strains are greater in absolute magnitude than ventral tensile longitudinal strains during single steps in which recordings were taken from both locations (Fig. 2A,B), bending loads appear to be superimposed on axial compression induced by supporting the weight of the body. However, mean peak principal tensile strain orientations (ϕ_t) on the dorsal (+47 °, proximoanterior) and ventral (+29 °, proximoposterior) femoral surfaces deviate strongly from the long axis of the bone, suggesting that the alligator femur also experiences torsion (Table 1; Fig. 2). The direction of torsion (clockwise for the left femur viewed from its proximal or distal end) is consistent with the direction of stance phase femoral rotation observed in cineradiographic studies of crocodilian locomotion (Brinkman, 1980b; Gatesy, 1991a): anterior femoral rotation is produced by the caudofemoralis muscle, which inserts proximally on the femur (Gatesy, 1997), but femoral rotation is resisted distally by the ligaments of the knee joint. Shear strain magnitudes further suggest that the alligator femur experiences substantial torsion: mean peak dorsal (619 με) and ventral (1027 με) femoral shear strains exceed mean peak femoral principal strain measurements from these sites by 32 % and 45 % respectively (Table 1; Fig. 2A,B).

Representative strain traces from an alligator tibia during fast locomotion are illustrated for four sequential steps in Fig. 3A, and mean peak strain magnitudes for each tibial recording site during fast steps are reported in Table 1. Loading patterns are consistent among steps, although load magnitudes are variable (coefficients of variation between 0.39 and 0.57). All longitudinal traces and most principal strain traces exhibit two peaks, one before and one after midstep.

The alligator tibia, like the alligator femur, is loaded in a combination of bending, axial compression and torsion. Longitudinal recordings show that, through the first half of stance, the anterior and medial aspects of the tibia are loaded in tension, whereas the posterior surface is loaded in compression (Fig. 3A). After midstep, loading patterns are unchanged for the anterior and posterior surfaces, but medial longitudinal strains shift from tensile to compressive. Nonetheless, the presence of both tensile and compressive surface strains and the greater magnitude of posterior compression (mean −880 με) compared with anterior (mean +231 με) or medial (mean +415 με) tension suggest that bending is superimposed on axial compression in the tibia. The deviation of peak principal tensile strains from the long axis of the tibia on its anterior surface (mean ϕ_t −35 °, proximolateral; Table 1) suggests that the alligator tibia is also loaded in torsion. This torsion is counterclockwise for the left tibia (viewed from its proximal or distal end), consistent with cineradiographic observations of outward crural rotation during locomotion in Caiman sclerops (Brinkman, 1980b) resisted by the foot (planted on the ground) and the ligaments of the ankle. Shear strain calculations reflect the likely importance of torsion in the tibia: mean peak anterior shear strain (677 με) exceeds mean peak anterior principal tensile strain (+391 με) by 73 % (Table 1; Fig. 3A).

Except for ventral longitudinal strains, all longitudinal, principal and shear strains in the femur decrease significantly in magnitude during slow locomotion compared with fast locomotion (Tables 1, 2; compare dorsal, ventral and anterior recording locations: Mann–Whitney U-tests, P<0.01 for all comparisons). However, at some locations, these differences are fairly minor (e.g. <50 με for dorsal principal tensile strains). Mean peak strain magnitudes for the femur are still variable during slower locomotion (coefficients of variation between 0.26 and 0.60), but the distribution of tensile and compressive strains is essentially the same during fast and slow steps.

In the tibia, anterior principal tensile and compressive strains are both significantly lower in slow steps, as are anterior and posterior longitudinal strains (compare Table 1 with Table 2; Mann–Whitney U-tests, P<0.05 for anterior principal compressive strain, P<0.002 for other comparisons). However, mean peak strains at the medial recording site increase significantly during slower locomotion (Mann–Whitney U-test, P<0.001; Table 1); in addition, medial strains remain tensile throughout the stance phase at slow speed and no longer exhibit the compressive peak seen at the end of the support phase in fast steps (Fig. 3B). Torsion remains important during slow steps. Deviations of principal tensile strains from the long axis of the tibia are virtually identical in slow and fast steps (mean ϕ_t −36 ° and −35 ° for slow and fast steps, respectively; Tables 1, 2), and mean peak anterior shear strain (617 με) still exceeds mean peak anterior principal tensile strain (+342 με) by 80 % during slow locomotion (Table 2; Fig. 3B).

Running steps (mean velocity 2.0 m s⁻¹ ) were elicited from two of the four experimental iguanas (iguanas B and D). Representative principal and axial strain traces for iguana B are illustrated in Fig. 4A, and representative principal and shear traces for iguana D are illustrated in Fig. 5A; mean peak strain magnitudes for both animals are listed in Table 3. The iguana femur, like the alligator femur, appears to be loaded in bending with the anterior cortex in tension and the dorsal cortex in compression (Fig. 4A; Table 3). However, patterns of femoral torsion differed among the individual iguanas. In iguana B (N=45 steps), anterior principal tensile strains were aligned very closely with the long axis of the femur (mean ϕ_t −3 °, proximoventral), and femoral shear strains were negligible (Fig. 4A; Table 3). In contrast, in iguana D (N=7 steps), ϕ_t deviated considerably from the long axis of the femur at peak strain (mean −49 °, proximoventral; Fig. 5A), resulting in anterior shear strains 78 % greater than anterior principal tensile strains (mean peak shear 1121 με, mean peak anterior principal strain +629 με; Table 3). Thus, torsion appears to be unimportant for the femur of iguana B, but large shear and off-axis principal strains suggest considerable torsion in the femur of iguana D. The counterclockwise torsion measured on the right femur of iguana D is consistent with the clockwise torsion measured on the left femur of alligators, as patterns of torsion in contralateral limbs would be expected to mirror each other. Furthermore, the direction of torsion in iguana D is consistent with the direction of stance phase femoral rotation observed in previous cineradiography of iguana locomotion (Brinkman, 1981): anterior femoral rotation is produced by the caudofemoralis, which inserts proximally on the femur (Snyder, 1962), but rotation is resisted distally by the ligaments of the knee.

Strain patterns for the tibia were similar among the individual iguanas (Fig. 4B). Longitudinal strain traces show single peaks with synchronous maxima at approximately midstep. Like the alligator tibia, the iguana tibia is subject to bending: the anterior and medial tibial surfaces experience tensile strains (mean peaks +1650 με and +982 με, respectively), whereas the posterior surface experiences compressive strains (mean peak −840 με). The greater magnitude of anterior tensile strains relative to posterior compressive strains suggests that the iguana tibia is loaded in net tension. This result is unexpected for a limb element supporting the weight of the body and is explored further through cross-sectional analyses of planar strain distributions (see below). Torsion could not be assessed for the iguana tibia because the cortical surfaces were too narrow to attach rosette gauges.

Loading patterns for the iguana femur during slow locomotion show some differences from those during fast locomotion. Anterior principal strain traces typically showed double peaks during stance in walking steps, contrasting with the single anterior principal peaks typical of running steps (compare Fig. 5A and 5B). Steps were nearly evenly divided between those in which the first peak (N=118) or the second peak (N=119) was greater in magnitude (Table 4), as might be expected for normal variation in relative components of deceleration versus reacceleration produced by the limb during stance. Principal tensile strain orientations also showed different patterns between walking and running steps. For running steps by iguana D, ϕ_t ranged almost exclusively between 0 ° and −90 °; however, for walking steps, ϕ_t shifted through nearly 180 ° during each step (Fig. 5B). As a result, mean ϕ_t orientations at peak strain were −41 ° for walking steps in which the first strain peak was greater in magnitude, but +18 ° for walking steps in which the second strain peak was greater in magnitude (Table 4). This is consistent with a shift from counterclockwise to clockwise femoral torsion at midstep (viewing the right femur from its proximal or distal end).

Walking steps show the same distributions of tensile and compressive strains as running steps in the iguana tibia: the anterior surface experiences the highest tensile magnitudes, the medial surface experiences relatively lower tensile magnitudes, and the posterior surface remains in compression (Table 4). Mean strain magnitudes at all tibial locations are significantly lower during walking steps than during running steps (compare pooled data for tibia in Tables 3 and 4; Mann–Whitney U-tests, P 0.005).

In addition to the interindividual variation in femoral strains observed for running by iguanas, other less common, but repeatable, patterns and behaviors were also observed. Although principal strain traces from the alligator femur usually showed a single peak per step, and principal strain traces from the alligator tibia usually had first peaks much greater in magnitude than second peaks, femoral or tibial traces with large second peaks were occasionally evident. In these steps, the sign of ϕ_t was reversed, suggesting that, as in the iguana femur, the direction of bone torsion was reversed during the second half of stance. These steps generally showed the same patterns of axial and principal strains as standard steps and did not consistently exhibit significantly higher or lower mean peak principal or axial strain magnitudes.

During a femoral recording session in the trackway, one alligator darted to the end of the trackway and attempted to climb out, quickly pushing its snout up the wall and raising its trunk off the ground until it was standing on its hindlimbs. It then jumped alternately off each hindlimb several times, so that the body (except for much of the tail) was supported on a single leg during landings. Peak dorsal principal strains recorded from the alligator during jumps (N=5) averaged +566±151 με (tensile) and −821±225 με (compressive), as much as twice the mean peak strains recorded from this location during fast treadmill locomotion (+232±122 με and −468±254 με, respectively; Fig. 6; means ± S.D.).

Shifts in neutral axis orientation during limb support obtained from cross-sectional analyses of the planar distribution of longitudinal strains are summarized in Fig. 7 for the alligator femur and tibia, as well as the iguana tibia (a similar analysis of the iguana femur was precluded because strain data were available for only two sites). Graphs of cross-sectional strain distributions are compared for the alligator femur and tibia in Fig. 8 and for the iguana tibia in Fig. 9.

In the alligator femur, at the beginning of the step, the neutral axis of bending (NA) is closely aligned with the anteroposterior axis of the bone but displaced ventrally from the cross-sectional centroid (Figs 7, 8A; time 1), causing the dorsal cortex to be loaded in compression and the ventral cortex in tension. As strain levels increase through the step, the neutral axis shifts towards the centroid and rotates to an anterodorsal/posteroventral direction (−30 ° to −40 °) for most of the remainder of stance. In the context of our principal strain orientation data and the kinematic observations of Brinkman (1980b) and Gatesy (1991a), these changes in NA orientation are consistent with the maintenance of dorsoventral bending (in an absolute frame of reference) through the course of anterior femoral rotation. The displacement of the neutral axis from the centroid and the extent of compressive strains across the femoral cortex confirm axial compression in addition to bending and torsion of the alligator femur. Because peak tensile strains occur at the anteroventral cortex and peak compressive strains at the posterodorsal cortex, rather than at the locations from which strains were recorded on the femur (dorsal, ventral and anterior), peak strains in the alligator femur are probably 35–45 % greater than those measured.

In the alligator tibia, the anteromedial cortex is loaded in tension and the posterolateral surface in compression when the foot contacts the ground; the neutral axis is displaced far from the cross-sectional centroid (Fig. 8B; time 1). Through midstep (Figs 7, 8B; times 2–4), NA orientation shifts more steeply towards the anatomical anteroposterior axis of the bone cross section. In the context of the observed anterior principal strain orientations and Brinkman’s (1980b) kinematic data, this shift suggests that tibial bending remains aligned with the direction of travel (anteroposterior, in an absolute frame of reference), even as the bone rotates laterally through the step. During fast steps, NA orientation shifts back towards the mediolateral axis of the tibia soon after midstep and moves further from the centroid, crossing the medial gauge site to place this portion of the cortex in compression (Figs 7, 8B; times 5–7). A similar shift in NA orientation occurs during slow locomotion (Fig. 7), but the medial site does not experience compression because the NA remains closer to the tibial centroid. Because of its orientation and its displacement from the tibial centroid, at peak strain, the neutral axis is shifted quite near the recording sites for the tibial gauges; as a result, peak strain magnitudes during fast steps are probably 2–3 times greater than those recorded.

Planar strain analyses of the tibia were conducted for running steps obtained from each of the iguanas exhibiting the two patterns of femoral torsion. In the animal exhibiting pronounced torsion (iguana D), NA alignment is similar to that in the alligator tibia at the beginning of stance (anterolateral to posteromedial, 55 ° from the mediolateral axis), but the NA crosses the bone section much closer to the tibial centroid (Figs 7, 9A; time 1). Initially anterior to the centroid, the neutral axis shifts posteriorly through the step, placing the tibia in net axial tension for much of step duration (Fig. 9A; times 4–7). NA orientation also rotates during the step, but in the opposite direction to that observed in alligators. This is consistent with Brinkman’s (1980b, 1981) observations that initial rotation of the crus in Iguana iguana is opposite in direction to that in Caiman sclerops. These changes in NA orientation suggest that, despite differences in the initial direction of tibial rotation in lizards and crocodilians, the direction of tibial bending is correlated with the direction of travel in both species (anteroposterior in an absolute frame of reference). At peak strain, the anterior gauge is close to the site of maximum tensile strain predicted by planar strain analysis; however, planar strain calculations of maximum compressive strains are 50 % greater than those measured at the posterior recording site. The pattern exhibited during walking steps is similar (Fig. 7), except that the neutral axis shifts anteriorly by the end of the step, indicating a return of net axial compression.

Iguana B, which exhibited little torsion during running steps, shows a different pattern of NA orientations in the tibia (Figs 7, 9B). The neutral axis often begins the step posterior to the centroid, indicating net tension relatively earlier than in iguana D (Fig. 9B; time 1). Soon after the foot contacts the ground and throughout most of the remainder of the step, the NA is aligned close to the bone’s mediolateral axis (Fig. 9B; times 2–4). By the end of stance, the NA shifts anteriorly past the centroid and the tibia is again loaded in net compression (Fig. 9B; time 7). The anterior and posterior recording sites are both close to the locations of maximum strain predicted from planar strain calculations: predicted maxima exceed measured strains by less than 5 % at both locations. Differences in tibial NA orientation between iguanas B and D correlate with differences in the degree of femoral torsion they experience: iguana D, which experiences greater femoral torsion, also appears to experience greater tibial rotation relative to the direction of travel. However, despite these differences, in both iguanas, the tibia experiences net axial tension for a substantial portion of the step.

Catastrophic fracture occurred on the tensile surface in all limb bone specimens tested (Burstein et al., 1972; Currey and Brear, 1974). A representative plot of applied bending moment versus maximum recorded tensile strain is illustrated in Fig. 10; the results from all three-point bending tests are summarized in Table 5. Mean fracture strain from eight iguana limb bones (four tibiae, four femora) was +13 449 με (coefficient of variation 26 % of mean); mean yield strain from six specimens (excluding two that fell more than two standard deviations from the mean yield strain) was +9820 με (coefficient of variation 6 % of mean). Yield and fracture strains did not differ significantly between femora and tibiae (P>0.23 for both comparisons; Table 5). One alligator femur also was tested successfully: a fracture strain of +13 366 με and a yield strain of +6495 με were obtained (Table 5).

Prior to safety factor calculations, the mean peak tensile and shear strains measured during locomotion (i.e. peak functional strains; equation 1) were increased by 5 % for the iguana tibia, increased by 45 % for the iguana and alligator femora and multiplied by 3.0 for the alligator tibia to reflect the likely maximal strains indicated by the planar strain analyses (Table 6). Using values of +9820 με for yield strain in iguana bones and +6495 με for yield strain in alligator bones, ‘mean’ safety factors for bending range from 5.5 (alligator tibia) to 10.8 (iguana femur), and ‘worst-case’ safety factors range between 3.6 (iguana tibia) and 8.2 (iguana femur) (Table 6). Safety factors for shear are much lower. Assuming that bone will fail in shear at 8000 με (Currey, 1984), mean shear-based safety factors range from 3.9 (alligator tibia) to 5.4 (alligator femur), and ‘worst-case’ safety factors range between 2.7 (alligator tibia) and 4.3 (iguana femur) (Table 6).

Regressions for recording locations in two of the three alligators show significant (P<0.05) changes in strain magnitude as femoral posture varies, although correlations are generally weak (r2<0.35; Fig. 11; Table 7). Strains do not change uniformly across the cortex of the femur as an individual alligator shifts from a sprawling to an upright posture: anterior longitudinal strains decrease as a more upright posture is adopted, whereas dorsal and ventral principal and shear strains appear to increase (Table 7). However, comparisons of cross-sectional planar strain distributions for sprawling and upright steps at times of peak strain show that the femur consistently experiences relatively greater axial compression in more upright steps (Fig. 12; the neutral axis is displaced relatively further from the centroid).

Locomotor loading patterns of the hindlimb bones of alligators and iguanas are similar in many respects, but some key distinctions are also evident between these species, particularly in the tibia. Fig. 13 illustrates schematically the forces acting on an alligator femur and tibia during peak locomotor strain. In both alligators and iguanas, the femur experiences clockwise torsion (viewing the left femur from its proximal or distal end), dorsoventral bending (placing the dorsal cortex in compression and the ventral cortex in tension) and axial compression. In alligators, the tibia experiences counterclockwise torsion (viewing the left tibia from its proximal or distal end), anteroposterior bending (compression on the posterior surface, tension on the anterior surface) and axial compression. Although shear strains were not evaluated for the iguana tibia, the orientation of bending in the iguana tibia is similar to that in the alligator tibia (compression on the posterior surface, tension on the anterior surface). However, in contrast to results obtained for the alligator tibia, cross-sectional analyses of planar strain distributions for the iguana tibia consistently indicate net tension, rather than compression, at peak strain during walking and running. The prevalence of torsion of the femur and tibia of alligators and iguanas, as well as the presence of net tension of the iguana tibia, are unusual features that distinguish the limb bone loading patterns of these animals from those of most species in which limb bone strains during terrestrial locomotion have been examined.

Torsion is the dominant loading regime of the femur and tibia of alligators and the femur of iguanas (excepting the atypical strain patterns of iguana B). Deviations of principal strains from the long axes of these bones are substantial (ϕ_t=29–49 °), and peak shear strains exceed peak axial and bending strains by 45–78 %. Comparable magnitudes of shear strain due to torsion have been reported in the wing bones of bats and birds during flight (Swartz et al., 1992; Biewener and Dial, 1995), but few previous studies of in vivo limb bone strain during terrestrial locomotion have found torsion to be the most important mode of bone loading. Shear strains induced by torsion have been found to predominate in the femora of rats (Keller and Spengler, 1989) and chickens (Carrano, 1998), and moderate torsion (ϕ_t=25–30 °) has been reported for the tibia of sheep (Lanyon and Bourn, 1979) and the tibiotarsus of chickens (Biewener et al., 1986). However, most studies of terrestrial locomotion in mammals (e.g. Lanyon and Smith, 1970; Goodship et al., 1979; Rubin and Lanyon, 1982; Biewener et al., 1983, 1988; Biewener and Taylor, 1986) and birds (Rubin and Lanyon, 1984; Biewener et al., 1986; Biewener and Bertram, 1993) have found the limb bones to be loaded primarily in bending or occasionally in axial compression (e.g. horse metapodials; Biewener et al., 1983, 1988). The basic uniformity of these limb bone loading patterns is not entirely surprising, since most limb bone strain data have been collected from a phylogenetically limited set of species that move their limbs in parasagittal or nearly parasagittal planes (e.g. ungulate and carnivoran mammals, galliform birds). In contrast to the species examined in most previous studies, neither the lizard nor the crocodilian species examined in the present study employs strictly parasagittal hindlimb kinematics (Brinkman, 1980a, 1981; Gatesy, 1991a; Reilly and Elias, 1998). In addition, cineradiographic data show that, in both alligators and iguanas, the femur and tibia undergo considerable axial rotation (Brinkman, 1980a, 1981; Gatesy, 1991a). These kinematic observations suggested the potential for the limb bones of iguanas and alligators to experience substantial torsion, as well as bending and axial loads – predictions borne out by our measurements of bone strain. The basic kinematic similarities among many lizard and crocodilian species (Snyder, 1952; Sukhanov, 1974; Brinkman, 1980b, 1981; Gatesy, 1991a; Reilly and DeLancey, 1997a,b) further suggest that the limb bone torsion observed for iguanas and alligators could generally characterize their respective lineages, although in vivo strains must be measured from the limb bones of more species to evaluate this possibility. Strain data from a greater kinematic and phylogenetic diversity of animals, particularly from unsampled lineages such as salamanders, turtles and marsupials (especially non-saltatory species), would help to determine whether torsion is a more common mode of limb bone loading during terrestrial locomotion than had been recognized on the basis of the initial data from mammals and birds. Strain data from a broader phylogenetic sample of species could also help to establish the extent to which observed instances of limb bone torsion might be retentions of ancestral traits or derived features of particular lineages.

The axial tension observed in the iguana tibia not only differs from the axial compression observed in the alligator tibia, but is unusual among vertebrate limb bones in general. Net axial tension has been reported during non-terrestrial locomotion for the humerus and ulna of brachiating gibbons (Swartz et al., 1989), for the humerus of flying bats (Swartz et al., 1992) and for the initial portion of the downstroke in flying pigeons (Biewener and Dial, 1995). However, in contrast to suspensory locomotion and flight, axial tension is unexpected in limb bones during terrestrial locomotion because the limbs are positioned beneath the body to support it above the substratum, against gravity. As a result, external forces acting on the limb (the ground reaction force and body weight) tend to compress the limb skeleton, supplementing internally transmitted compressive forces exerted by contracting muscles (Swartz et al., 1989).

Two factors that could contribute to net tension in the iguana tibia are the distinctive kinematics and robust fibula of iguanas compared with those of most species for which in vivo limb bone strains have been measured. In contrast to previously studied mammals and birds, iguanas orient the crus with the long axis nearly parallel to the ground for much of the support phase, including periods of peak strain (Fig. 14A). Kinematic analyses (R. W. Blob and A. A. Biewener, unpublished results) show that iguanas orient the crus at an angle of more than 70 ° from vertical for a mean of 66±6 % (mean ± S.D., N=15) of step duration, consistent with the observations of Brinkman (1981; his Fig. 3). In such an orientation, the entire crus would be subject to dorsoventral bending (in an absolute frame of reference), probably placing the dorsal aspect of the iguana crus in compression and the ventral aspect in tension. Although the tibia is initially positioned medial to the fibula (in an absolute frame of reference), lateral rotation of the crus during the step causes the tibia to shift ventrally and the fibula to shift dorsally. Because the fibula is robust relative to the tibia in iguanas, the net centroid for the bones of the crus is located between them; thus, even if the crus as a whole experiences axial compression, the tibia can experience net tension because its cross section is positioned primarily on the tensile side of the crural neutral axis of bending (Fig. 14A,B). Other lizard species also appear to orient the tibia nearly horizontally for much of the support phase (e.g. Sceloporus clarkii; Reilly and DeLancey, 1997a,b) and, thus, might also experience tibial strain patterns similar to those observed for iguanas. In contrast to the iguana tibia, the alligator tibia exhibits the expected pattern of net axial compression. However, the tibia does not appear to be oriented horizontally for as substantial a portion of step duration in alligators (Gatesy, 1991a) as in iguanas. Furthermore, the tibia of Alligator is relatively more robust than that of Iguana (compare Figs 8B and 9), which would reduce the extent to which the crural centroid and neutral axis of bending are displaced from the tibia. Direct strain recordings from the fibula of both lizards and crocodilians would be useful to verify the loading regime of this element and its potential effects on the distribution of loads in the tibia of these species. Even though tension is an unusual loading regime for limb bones during terrestrial locomotion and bone is generally approximately 25 % weaker in tension than in compression (Currey, 1984), the iguana tibia would still be most likely to fail due to torsion if shear strains in the iguana tibia are as high (and torsional safety factors as low) as those observed in the alligator tibia.

Safety factors for the femur and tibia of alligators and iguanas are generally higher than those previously reported for mammals and birds. ‘Mean’ safety factors to yield in bending for these two bones range from 5.5 to 10.8, considerably higher than previous calculations for mammals and birds based on recorded bone strains, which have varied between 1.4 and 4.3 (Lanyon and Rubin, 1985; Biewener, 1990, 1993). However, the high shear strains observed in Alligator and Iguana indicate that the limb bones of these animals face a greater risk of failure by torsion: safety factors for shear failure range between 3.9 and 5.4 (Table 6). Although lower than safety factors calculated on the basis of bending strains, these values are substantially higher than those reported for other limb bones subjected to considerable shear (e.g. 1.9 for the pigeon humerus during flight; Biewener and Dial, 1995). Furthermore, safety factors for shear failure in alligator and iguana limb bones appear at least moderately high compared with safety factors for vertebrate limb bones in general. A non-parametric, one-sample sign test comparing a sample of safety factors to yield for the limb bones of terrestrial mammals and birds (2.9±0.8; N=14, mean ± S.D.) with the lowest ‘mean’ shear-based safety factor for alligators or iguanas (3.9) gives a significant difference (P=0.002; mammalian and avian safety factor data compiled from Lanyon and Rubin, 1985; Biewener, 1993). Only the ‘worst-case’ safety factor estimates for alligator and iguana limb bones show substantial overlap with mammalian and avian values.

Limb bone safety factors depend upon two proximate factors: the magnitudes of forces acting on the bones and the mechanical properties of the bones. Differences in both of these factors between alligators and iguanas, on the one hand, and mammals and birds, on the other, appear to contribute to the differences in limb bone safety factors observed between these groups. The magnitudes of peak ground reaction force acting on the limbs, relative to body weight (W_b), are lower in iguanas and alligators than in birds and mammals. Force-platform recordings indicate that peak ground reaction force magnitudes acting on a single limb range between 1.3 and 2.4W_b for quadrupedal mammals in fast trots or gallops and can exceed 3W_b in running bipedal birds (Cavagna et al., 1977; Biewener, 1983a), but average only 1.1W_b in iguanas and 0.5W_b in alligators (Blob, 1998; R. W. Blob and A. A. Biewener, in preparation). Low ground reaction force magnitudes for Alligator are correlated with high duty factors, which decrease peak forces by increasing the time over which force is exerted on the limb (Alexander, 1977b; Biewener, 1983a,b). During fast locomotion (0.37 m s⁻¹ ), hind foot duty factors for Alligator averaged 0.62±0.06 (N=173); in contrast, hind foot duty factors for Iguana averaged 0.44±0.03 (N=48) during running steps (Blob, 1998; R. W. Blob and A. A. Biewener, in preparation), similar to the values obtained for a broad size range of mammals at their trot–gallop transition (0.42±0.03; Biewener, 1983b).

Differences in the mechanical properties of the limb bones of alligators, iguanas, birds and mammals also appear to contribute to the differences in limb bone safety factor among these lineages, at least with respect to failure in bending. Tensile yield strains in bending for the limb bones of Alligator (+6495 με) and particularly Iguana (+9820 με) are higher than previously reported values for mammals and birds (+5250 με to +6000 με in tension, based on data from Currey, 1984; Biewener, 1993). These evaluations of yield strain for the limb bones of Alligator and Iguana appear conservative in the context of limited previous data on the mechanical properties of crocodilian and lizard limb bones. The high yield strain obtained for iguana limb bones is consistent with the relatively high tensile yield stresses (218–318 MPa) reported by Peterson and Zernicke (1987) for Dipsosaurus dorsalis, a closely related iguanian lizard (Norell and de Queiroz, 1991). Furthermore, Currey (1990) found a higher failure strain for the alligator femur (+21 000 με) than that measured in the present study (+13 366 με), although he did not report yield strain values. Because data for shear failure specific to alligator and iguana limb bones are not available, a general value for the failure strain of bone in shear (8000 με: Currey, 1984) was used in safety factor calculations. However, given the disparities in tensile yield strains observed among lizards, crocodilians, birds and mammals, it seems possible that differences in resistance to shear may also contribute to differences in the limb bone safety factors of these lineages.

Limb bone safety factor data are available for only a limited number of taxa, but the values calculated for Iguana and Alligator represent a starting point from which analyses of the evolution of limb bone safety factor throughout amniotes can eventually proceed. The higher safety factors found for the hindlimb bones of Iguana and Alligator indicate the potential for an unexplored lack of uniformity in amniote limb bone safety factors, suggesting that the evolutionary history of limb bone mechanical design might be more complex than recognized previously. For instance, if safety factors in the limb bones of Iguana and Alligator were representative of the broader diversity of taxa within their respective lineages, then birds and mammals might not have inherited their similar safety factors from a common ancestor, but rather have evolved lower limb bone safety factors independently. To test this hypothesis, additional species of lepidosaurs and crocodilians must be sampled before the general patterns of limb bone strains and safety factors in these clades can be evaluated. Only single species from these clades were examined in the present study, and individuals from both species were subadults; thus, bone strains must be measured from other species and ages of lizards and crocodilians to establish whether the patterns found for Iguana and Alligator are generally true of their respective lineages. In addition, to evaluate the ancestral limb bone safety factor of amniotes and permit the distribution of character states for this trait to be assessed throughout amniote phylogeny, safety factors must be determined for the limb bones of species belonging to clades that are outgroups to Sauria (e.g. turtles) and to Amniota (e.g. salamanders and frogs). Until such data are collected, evolutionary hypotheses suggested by strain data and safety factor calculations from Iguana and Alligator must be viewed as preliminary and interpreted with caution.

If the relatively high safety factors observed in Alligator and Iguana are characteristic of lizards and crocodilians in general, why might the limb bones of these taxa be ‘overdesigned’ to a greater degree than those of other amniotes? Natural selection is often viewed as a primary factor regulating the magnitudes of biological safety factors, tending to eliminate safety factors that are too low to prevent regular failure of structures, or that are too high in terms of the cost of energy or space necessary for their maintenance (Alexander, 1981; Lanyon, 1991; Diamond and Hammond, 1992; Diamond, 1998). However, the degree to which natural selection acts to maintain biological safety factors of ‘optimum’ magnitude has been disputed (Garland, 1998). According to this view, the higher limb bone safety factors of Alligator and Iguana might represent retentions of the ancestral amniote or tetrapod condition that have not proved sufficiently disadvantageous to be selected against over time. Whether excessive safety factors could be maintained through hundreds of millions of years of evolution is questionable. To test this possibility, bone strain measurements and safety factor calculations will be required for taxa from additional amniote outgroups and from additional lizards and crocodilians.

It is also possible that the high limb bone safety factors observed in Alligator and Iguana are a consequence of a correlated response to selection on other phenotypic traits, rather than direct selection on safety factor itself (Lande and Arnold, 1983). Developmental covariation between the limb bones and other traits subjected to selection could produce limb bones in these species that incidentally have high safety factors. Across the range of safety factors between those exhibited by alligators and iguanas and those exhibited by mammals and birds, differences in selective costs for lower safety factors, in terms of decreased resistance to bone failure, and for higher safety factors, in terms of increases in the energy required to transport and maintain the limb bones, might not be large enough to override patterns of developmental covariation. Data documenting changes in the distribution of limb bone safety factors and other potentially correlated traits through generations of iguanas and alligators would be required to evaluate this possibility.

Despite these caveats, several factors could favor higher limb bone safety factors among alligators and iguanas and potentially contribute to selection against lower safety factors. For instance, although temperature, diet and exercise can all affect rates of bone remodeling in ‘reptiles,’ crocodilians and lizards have generally been found to remodel their bones at lower rates than birds and mammals (e.g. Enlow, 1969; de Ricqlès, 1975; Currey, 1984; de Ricqlès et al., 1991; Owerkowicz and Crompton, 1997). One function ascribed to bone remodeling is repair of accumulated microdamage (Lanyon et al., 1982; Currey, 1984; Burr et al., 1985). Low rates of bone remodeling in crocodilians and lizards could reflect a low incidence of microdamage in these lineages, a low capacity for microdamage repair or perhaps both. If microdamage repair capacities were limited by low rates of bone remodeling in alligators and iguanas, but the incidence of microdamage in their limb bones were as high as in the limb bones of other tetrapods, then low limb bone safety factors could be disadvantageous because they might be correlated with a greater possibility of limb bone failure due to fatigue (Carter et al., 1981).

The high limb bone safety factors of alligators and iguanas might also be correlated with greater variability of their locomotor loads or the mechanical properties of their skeletons, relative to the variability found in birds or mammals. Alexander (1981) has argued that increased variability of either the loads imposed on a biological structure or the mechanical properties of that structure should lead to selection for higher safety factors. Lowell (1985) observed patterns consistent with these predictions in populations of intertidal Pacific limpets, finding higher safety factors among animals from populations with higher variance in shell strength. Similar data are unavailable for vertebrate skeletal structures; however, such selective pressures might also have contributed to the evolution of relatively high safety factors in the limb bones of alligators and iguanas. Peak strain magnitudes appear to vary much more in alligators and iguanas than in the mammal or bird species examined previously. Coefficients of variation for peak strain magnitudes for series of steps at the same speed are typically 8 % or less in mammals and birds (Biewener, 1991), but range between 14 % and 50 % during fast locomotion in iguanas (Table 3) and between 37 % and 80 % during fast locomotion in alligators (Table 1). In addition, the different strain patterns observed during fast locomotion in iguanas B and D (Figs 4, 5) suggest that marked interindividual differences in loading pattern, as well variation in load magnitudes, are possible in the locomotion of iguanas.

Bone strength also shows variability in crocodilians. Female alligators resorb endosteal structural bone from the femur during egg-laying, probably for use as a source of calcium for the formation of eggshells (Wink and Elsey, 1986). Such periodic bone resorption could lead to fluctuation in the mechanical strength of the femur, at least in females. Femoral bone resorption associated with egg-laying has also been identified in turtles (Edgren, 1960; Suzuki, 1963), suggesting that it may represent a plesiomorphic feature of amniotes and, therefore, might also occur in lizards. These observations suggest the potential for a combination of highly variable loading and bone material properties in crocodilians and lizards that may have favored the evolution of higher limb bone safety factors.

Femoral safety factors appear to be higher than those for the tibia among iguanas and alligators (Table 6). These results are consistent with the data of Currey (1984), who found the distal limb bones of horses to display fatigue fractures with greater frequency than the proximal limb bones, suggesting that the distal bones had lower safety factors. Currey (1984) argued that this pattern was related to the relatively greater contribution of distal mass to the moment of inertia of the leg and, therefore, to the energetic cost of moving the limb: selective pressure to reduce energetic costs would be expected to lead to decreased bone mass (and safety factors) distally. Alexander (1997, 1998) extended Currey’s (1984) argument, mathematically demonstrating that, if probabilities of failure for all components of a linked system such as the limb skeleton are not perfectly correlated, then for a given total energetic cost the system would have a lower overall probability of failure if safety factors were greater in less energetically costly components (e.g. proximal limb bones) and lower in more energetically costly components (e.g. distal limb bones), rather than if safety factors were equal throughout the system. Alternatively, it is also possible that the difference in safety factors between proximal and distal limb bones in alligators and iguanas is a mechanical consequence of the torsional loading of their limb bones, rather than the product of selection against high safety factors that are energetically expensive to maintain. Because greater freedom of rotation is possible at the hip compared with either the knee or the ankle in lizards and crocodilians (Brinkman, 1980a,b; Rewcastle, 1980, 1983), less deformation (i.e. lower strains) might be produced in bones articulating in joints with low resistance to rotational motion (such as the femur), even without natural selection for distal decreases in bone mass.

Correlations between strain magnitudes and limb posture observed in Alligator are counterintuitive. Biewener (1989, 1990) has shown that a size-related shift from a crouched to an upright posture among mammals helps to maintain nearly constant limb bone stresses as body size increases. This postural shift aligns the limbs more closely with the ground reaction force vector, reducing external bending and the compressive muscular forces required to counter joint moments and maintain equilibrium. Although patterns of change can differ among hierarchical levels of organization (e.g. individuals relative to species: Gould, 1971), this previous work might predict fairly uniform decreases in strain levels for the limb bones of individual animals during a shift from a sprawling to an upright posture and consequent closer alignment of the limbs with the ground reaction force. Instead, our data show that the femoral cortex does not exhibit uniform changes in strain as posture shifts from sprawling to upright in Alligator: whereas tensile strains on the anterior cortex decrease with the use of a more upright posture, principal tensile and compressive strains on the dorsal and ventral cortices, as well as shear strains, frequently show significant increases (Table 7). These patterns of posture-related changes in strain magnitudes in alligators are consistent with patterns of posture-related changes in limb bone stresses during locomotion in green iguanas (determined from force-platform/kinematic data: Blob, 1998; R. W. Blob and A. A. Biewener, in preparation).

The observed pattern of changes in strain with changes in posture in alligators could be related to two factors. First, comparisons of cross-sectional planar strain distributions for sprawling and upright steps at times of peak strain show that in more upright steps the femur experiences relatively greater axial compression (Fig. 12; the neutral axis is displaced relatively further from the centroid of the bone cross section). This could reflect greater compressive loads induced during body support in upright posture, which would tend to reduce tensile strains due to bending on the anterior and ventral cortices. Second, analyses of force platform data from iguanas suggest that increases in stress (or strain) on the dorsal and ventral cortices of the femur are correlated with increases in the force exerted by the knee extensor muscles as limb posture becomes more upright, with the increases in muscle force resulting from increased moments at the ankle and knee (Blob, 1998; R. W. Blob and A. A. Biewener, in preparation). Given the similarity in posture-related changes in loading observed between Alligator and Iguana (Blob, 1998), it seems likely that a similar mechanism of changes in muscle forces could account for the posture-related changes in limb bone loading observed in both species.

What are the implications of these observations for the interpretation of evolutionary shifts in limb posture? Limits to acceptable (i.e. safe) levels of limb bone strain have probably placed some boundaries on the diversity of locomotor morphology and terrestrial kinematics that have evolved in tetrapods. However, shifts from a sprawling to an upright posture within alligators appear insufficient to cause substantial reductions in limb bone strain. Therefore, it is possible that shifts in posture would have been similarly ineffectual as a means of reducing limb bone strain through evolutionary transitions from a sprawling to an upright stance. For example, shear strains appear to increase during upright locomotion in Alligator. Reduction of shear, which represents the most substantial strain experienced by the lizard and crocodilian species observed in this study, probably requires a shift to predominantly parasagittal limb kinematics and a reduction in axial rotation of the femur, not just an upright posture.

It is possible that limb bone strain might not have been maintained at similar magnitudes throughout the evolution of more upright posture in some lineages: for instance, the data from Alligator suggest that limb bone stresses and strains could increase through evolutionary transitions to an upright posture. However, in some lineages, an evolutionary decrease in size may have helped to mitigate posture-related increases in loads. Neglecting possible allometric effects, as body size in a lineage decreases, the loads limb bones must resist will decrease in proportion to the cube of mass, but the resistance of limb bones to loads (correlated with bone cross-sectional area) will decrease only in proportion to the square of mass, leading to relatively greater resistance to loads in the limb bones of smaller taxa. One postural transition that may have been subject to such effects is the evolution of non-sprawling posture in therapsids (derived ‘mammal-like reptiles’). In the locomotor evolution of therapsids, characters associated with upright posture (e.g. changes in pelvic and femoral morphology) are gradually acquired throughout the transition from gorgonopsians to basal mammals, but early mammals are considerably smaller than non-mammalian therapsids (Jenkins, 1971b; Jenkins and Parrington, 1976; Kemp, 1982, 1985; Hopson, 1991, 1994; Sidor and Hopson, 1998). This evolutionary decrease in size (and consequent relatively greater resistance to limb bone loads) might have helped to counter posture-related increases in limb bone strain and decreases in limb bone safety factor through the ‘reptile’-to-mammal transition.

The strain data collected in this study indicate that evolutionary transitions from sprawling to non-sprawling posture within a clade cannot be treated as directly analogous to size-correlated evolutionary transitions from a crouched to an upright posture, such as those seen in mammals that employ predominantly parasagittal limb kinematics. In species that use non-parasagittal kinematics, the use of a more upright posture could increase bone strains, rather than reduce them. Large increases in size within sprawling lineages might place restrictions on locomotor behavior similar to those seen among larger mammals (Biewener, 1990), a possibility that remains to be tested. However, without scale-dependent increases in loading associated with increases in size, posture-related increases in bone strain might not be a critical limitation, particularly for species with high limb bone safety factors. Selection pressure to limit bone loads probably contributed to the evolution of some shifts in limb posture, but may not have been a factor common to all such transitions.

We greatly appreciate the critical comments and thoughtful advice of M. Carrano, B. Chernoff, W. Corning, N. Espinoza, S. Gatesy, J. Hopson, F. Jenkins Jr, D. Konieczynski, M. LaBarbera, P. Magwene, E. Maillet, L. Panko, S. Reilly, C. Sidor, J. Socha, M. Temaner, M. Westneat, J. Wilson, the University of Chicago Biomechanics Discussion Group and two anonymous referees. We are also grateful to R. Elsey (Rockefeller Wildlife Refuge) for generously providing the alligators used in this research, to B. Brand, D. Croft, J. Furneaux-Noor, J. Kohler and H. Larsson for assistance with data collection, to M. LaBarbera for access to the tensometer, to J. Gilpin for building the animal enclosure and machining the tensometer grips, to C. Abraczinskas for advice on figures and to J. Alipaz, J. Schwartz and S. Seps for help with animal care. This research was supported by the University of Chicago Hinds Fund (R.W.B.), the Society of Vertebrate Paleontology Predoctoral Fellowship (R.W.B.) and by NSF grants IBN-9520719 (R.W.B.), IBN-9306793 and IBN-9723699 (A.A.B.).