Muscle moment arms in Lesothosaurus
During locomotion, muscle activation patterns routinely coincide or overlap to produce the desired 3D control of the limb (e.g. Gatesy & Dial, 1993, 1996; Gatesy, 1997, 1999). Individual muscle function therefore varies during the step cycle, and examination of the moment arm of a single muscle, independent of other variables and the muscles with which it may interact, does not provide full details of its function. Muscle moment arm magnitude also interacts with other muscle properties in ways not accounted for in this study. While a relatively large moment arm allows a relatively small muscle to exert a relatively large joint moment, it also reduces the ability of the muscle to accelerate the joint (and hence to move the limbs quickly). Similarly, relatively smaller moment arms are not always a signature of reduced muscle size or functional importance, as there is good evidence for muscles with small moment arms playing important roles in limb movement, particularly those responsible for producing higher joint velocities (Sacks & Roy, 1982; Alexander & Ker, 1990; Payne et al. 2006a,b; Smith et al. 2006, 2007; Allen et al. 2010). The dramatically larger moment arm of ADD1 vs. that of CFL (the latter likely to be much more massive muscle; e.g. Gatesy, 1990, 1995; Bates et al. in press; Hutchinson et al. in press) for hip extension is a good example of this (see Fig. 5).
Thus, the 3D moment arm estimates produced herein should not be interpreted as a direct indicator of specific muscle function during locomotion. However, they can indicate whether a specific muscle had the ability to actuate a joint motion (e.g. to effect joint extension, adduction, etc.), and so can be used to directly test general hypotheses of muscle function (e.g. ‘muscle X acts to extend the hip’). Also, because our moment arm estimates can indicate the ease with which a muscle may apply moments about a particular joint by comparing relative moment arm magnitude, they also have a bearing on hypotheses of the relative function of different muscles in the same broad functional category (e.g. ‘muscle X is a more important extensor of the hip than muscle Y’), with the same caveats as above. As such, our estimates provide the first quantitative, repeatable dataset against which the hypotheses of muscle function suggested by workers such as Romer (1927) and Maidment & Barrett (2011) may be tested.
Previous authors (Romer, 1927; Galton, 1969; Coombs, 1979; Norman, 1986; Maidment & Barrett, 2011) have suggested that musculature originating on the elongate postacetabular iliac process (e.g. CFB, FTE) would have functioned to retract the femur, extending the hip. This assertion is strongly supported by our Lesothosaurus model, in which the muscles of the caudofemoralis (CFB, CFL), flexor cruris (FTE, FTI3), the iliofibularis (IFB) and the caudal part of the triceps femoris (ITBp) have the highest leverage for hip extension, particularly when the hip is extended. Similarly, these authors variously hypothesized that musculature originating cranial to the centre of rotation for flexion–extension, such as those on the elongate preacetabular process of the ilium (ITBa) and the prepubis (AMB) would have had large moment arms for hip flexion (femoral protraction), and our data support this, with ITBa and AMB having high moment arms for hip flexion, particularly when the hip is flexed in the case of the former, and extended in the case of the latter.
Confusion over the homology of various parts of PIFI (Walker, 1977; Rowe, 1986) and debate over their origins and insertions (e.g. Romer, 1927; Galton, 1969) has meant that there has been little agreement about the likely function of this muscle complex in ornithischians. Maidment & Barrett (2011) proposed that it was the predominant femoral protractor (in agreement with in vivo data on the function of PIFI and its homologues in extant archosaurs: Gatesy, 1997, 1999), and this is supported by our ‘ornithischian-biased’ reconstruction. However, uncertainty in both the origin and insertion of PIFI2 results in a degree of functional ambiguity about its relative moment arms (Fig. 5g). The ‘ornithischian-biased’ model predicts PIFI2 had highest leverage for femoral protraction (hip flexion) except when the hip was fully flexed (Fig. 5g). In the ‘theropod-biased’ model, an alternative origin located on the lateral surfaces of the dorsal vertebrae also results in the highest moment arm of PIFI2 being hip flexion. However, the use of an alternative insertion on the cranial femur suggests that PIFI2 had greater muscle leverage for medial rotation, except when the femur was held relatively vertically, at which point its flexion and medial rotation moment arms are both reduced but approximately equal. This iteration does not necessarily preclude a primary flexor function, but indicates that flexor moments exerted by the PIFI during locomotion may be accompanied by medial rotation moments, which would need to be incorporated into locomotion or resisted by the action of other muscles.
Romer (1927) and Maidment & Barrett (2011) suggested that ADD1&2 were primarily femoral adductors and retractors, as has also been suggested for theropod dinosaurs (Hutchinson & Gatesy, 2000; Hutchinson et al. 2005; Bates & Schachner, in press; Bates et al. in press). Our results suggest that ADD1&2 only had large moment arms for adduction at extended joint angles. The largest moment arms of ADD1&2 were for hip extension (femoral retraction) in Lesothosaurus at all joint angles studied, except high angles of hip extension when extension moment arms became relatively small and were exceeded by those for adduction and lateral rotation (Fig. 5a,b).
Maidment & Barrett (2011) reconstructed the iliofemoral musculature as a ‘complex’ referred to as IFM because they could not identify osteological correlates to distinguish between the origin of the two distinct heads present in extant birds (ITC and IFE). These authors suggested that IFM would function primarily as an abductor in bipedal ornithischians. Romer (1927) and Galton (1969), who reconstructed both avian muscles, suggested IFE ‘stabilized’ the femoral head, preventing disarticulation of the hip, while Norman (1986) suggested that IFE was a femoral protractor in Mantellisaurus. We modelled a cranial head of IFM, (IFMa) and a caudal head (IFMp) to encompass the full extent of this muscle complex on the ilium, and these roughly correspond with ITC and IFE, respectively, in the theropod reconstructions. Both IFMa and IFMp have their highest moment arm magnitudes for femoral abduction, although IFMp also had relatively high hip flexion leverage at flexed hip joint angles (Fig. 4g,h).
Maidment & Barrett (2011) suggested that PIFE would have primarily had leverage for lateral femoral rotation, while Romer (1927) and Galton (1969) both suggested that PIFE may have been a femoral retractor. Our results highlighted ambiguity in the relative moment arm magnitudes of PIFE (Fig. 5f). The ‘ornithischian-biased’ model suggested that PIFE was a protractor at extended hip angles and a retractor at flexed hip angles (having a relatively high flexion–extension moment arms, but high degree of angular dependency; Fig. 5f), but maintained relatively high adduction and lateral rotation moment arms across this range of postures. However, the ‘theropod-biased’ model suggested that PIFE would have had a very small moment arm for flexion–extension regardless of hip joint angle (hence reduced angular dependency), and instead would have predominantly functioned to adduct and laterally rotate the femur.
Maidment & Barrett (2011) proposed that ISTR adducted and laterally rotated the femur. Our data suggest that ISTR primarily had leverage for lateral femoral rotation in Lesothosaurus, although at highly flexed joint angles it also had a relatively high moment arm for hip extension (Fig. 5c).
Moment arm polarities and magnitudes in Lesothosaurus and the other taxa modelled are very similar in many respects. This is perhaps to be expected because they also share many homologous myological and osteological features related to their shared ancestry, as well as functional constraints as obligate bipeds. Taxa compared in this study, and indeed bipedal archosaurs in general, are characterized by at least moderate post- and preacetabular expansion of their pelvic elements relative to the plesiomorphic archosaurian condition, as broadly represented by extant Alligator (Hutchinson & Gatesy, 2000). Thus, many pelvic muscle origins are shifted craniad and caudad relative to the hip joint centre, and their highest moment arms are for hip flexion and extension, as they are in Lesothosaurus (Figs 4 and 5; Fig. S1 in Supporting Information). In all of the taxa modelled, the ilium is dorsoventrally deep dorsal to the acetabulum, and musculature originating here (such as the muscles of the IFM complex) originates medial to the hip joint centre and extends over the hip to insert ventrolateral to it, abducting the femur. Likewise, in all taxa, the ischium extends caudoventrally from the acetabulum, so that musculature originating on it (e.g. ADD1&2; ISTR) extends cranially to insertions on the femur, and therefore acts to extend the hip.
Although the majority of comparisons between the taxa modelled revealed few qualitative differences in moment arms (and therefore provide no indications of differential muscle function), several key differences were observed, which can be related to previously observed trends in osteology and hypotheses of archosaur locomotor evolution. Pelvic osteology in Lesothosaurus and birds is convergent, with independent acquisition of the retroverted pubis and elongate preacetabular process (Fig. 1). It has been suggested, based on observations of gross morphological similarity, that the muscles associated with retroverted pelvic elements in basal ornithischians may have functioned more similarly to those of non-avian maniraptoran theropods and extant birds than those of other archosaurs (Romer, 1927; Hutchinson et al. 2008). If this is the case, moment arms estimated by the Lesothosaurus model would be expected to be more similar to the Velociraptor and ostrich models than to those of other non-avian archosaurs with cranially orientated pubis. Alternatively, the hypothesis that the pelvic elements of basal ornithischians and extant birds functioned similarly can be rejected if our quantitative approach suggests that the musculature of Lesothosaurus had mechanical leverages that differed from Velociraptor and ostrich.
Our results suggest that locomotor muscle leverage in Lesothosaurus (and by inference basal ornithischians in general; Maidment & Barrett, 2011) has a number of important distinctions from the ostrich, and generally shows greater similarity to that of other non-avian dinosaurs in our analysis, contradicting hypotheses of ornithischian–maniraptoran functional convergence. Below, we discuss the reasons for differences in the leverage of specific muscles in the taxa examined, as well as gross differences in the architecture of the hip musculature.
CFB is an abductor in Lesothosaurus, but an adductor in theropods
CFB originates on the caudoventral margin of the ilium in all taxa examined, and a robust osteological correlate for this muscle is present in dinosaurs (the brevis fossa: Hutchinson, 2001a). Although CFB has the greatest leverage for hip extension in all of the taxa examined (Fig. 7), it has a weak moment arm for abduction in Lesothosaurus, but a weak moment arm for adduction in non-avian theropods and the ostrich (Fig. 7). These differences arise from the location of the brevis shelf relative to the acetabulum: in Lesothosaurus the brevis shelf is dorsal to and level with the acetabulum (Fig. 7b), so that CFB passes dorsal to the hip joint. In contrast, in theropods (Fig. 7d), the brevis shelf and its equivalent surface on the ostrich ilium (Fig. 7e) is located more ventrally and more medially, so that CFB extends ventral to the centre of rotation. Thus, although the brevis shelf is present in basal ornithischians and theropods, the musculature extending from it appears to function differently in the two groups.
IFMa (ITC) has a considerably larger moment for medial rotation in the ostrich than non-avian dinosaurs
The posterior head of the IF group musculature (IFMp in Lesothosaurus, IFE in other taxa) has a similar moment arm (Fig. 8d–f), consistent with its conservative path relative to the hip joint (Fig. 8g–i). However, in the ostrich, the anterior head of the IF group (IFMa in Lesothosaurus, ITC in other taxa) has much higher leverage for medial femoral rotation relative to non-avian dinosaurs (Fig. 8c). In non-avian taxa the abduction moment arm of IFMa (ITC) is higher than its medial rotation moment arm, the converse of the situation in the ostrich (Fig. 8b,c). The origin of the avian homologue of IFMa (ITC) on the ilium is much more cranial in birds than in non-avian dinosaurs because of the development of the elongate preacetabular process, on which it originates (Hutchinson, 2001a). Although basal ornithischians convergently developed an elongate preacetabular process, there is no indication of muscle scarring on the lateral surface and no suggestion that IFM migrated onto this area, and it appears that this muscle retained its primitive position on the lateral surface of the ilium directly above the acetabulum (Maidment & Barrett, 2011; Figs 2 and 8).
PIFE is a lateral rotator and extensor in birds and Lesothosaurus, but a medial rotator and flexor in non-avian theropods
PIFE1&2 originate on the pubis in theropods (Hutchinson, 2001a); in birds retroversion of the pubis, and close approximation of the pubes and ischia has resulted in their homologues, the obturators, originating on the puboischiadic membrane (Hutchinson, 2001a; Gangl et al. 2004). In Lesothosaurus and other ornithischians, the postpubis, the homologue of the pubis, is extremely thin and delicate and it is unlikely that it could have supported musculature of practical size. Maidment & Barrett (2011) suggested that, if present and an active role in locomotion maintained, PIFE would probably have migrated onto the much more robust ischium following pubic rotation. The sensitivity analysis performed here suggests that ambiguity in the precise reconstruction of the anatomy of PIFE affects the degree to which this muscle is estimated to have been able to flex and extend the hip in Lesothosaurus, (Fig. 5f). However, the differences in magnitude of the ‘ornithischian-biased’ model vs. the ‘theropod-biased’ model are extremely small when compared with the range of magnitudes observed in the other taxa (Fig. 9a): PIFE had a very weak moment arm for flexion/extension in Lesothosaurus when compared with all other taxa, regardless of the myological reconstruction used.
Hutchinson et al. (2008) modelled the flexion/extension moment arm in the dromaeosaurid theropod Velociraptor (Fig. 9), and demonstrated that PIFE maintained a moment arm for hip flexion despite retroversion of the pubis. PIFE inserts on the greater trochanter in theropods, which projects slightly higher than the femoral head in Velociraptor (Hutchinson et al. 2008, fig. 3.2D), meaning that it inserts dorsal to the hip centre of rotation resulting in a weak flexor moment about the hip. In our ostrich and Lesothosaurus models, we also reconstruct PIFE inserting on the greater trochanter and its avian homologue, the trochanteric crest (Hutchinson, 2001b), but our insertions are located level with or slightly ventral to the joint centre (Fig. 9), and as a result PIFE extends the hip. This demonstrates how very slight repositioning of musculature that inserts close to the joint centre can result in changes in moment arm polarity, and highlights an area where caution is required when making functional interpretations.
Our comparisons with other taxa indicate that PIFE has a much weaker moment arm for flexion/extension in all three taxa with retroverted pubes, and the primary function of the muscle likely switched to adduction and lateral rotation (Fig. 9). Hutchinson & Gatesy (2000) hypothesized that the medial inflection of the femoral head in tetanuran theropods would have increased the lateral rotation moment arms of PIFE1&2 by shifting their insertion on the greater trochanter laterally. The implication of this hypothesis is that PIFE1&2 had functionally attained their derived neornithine condition in basal tetanuran theropods, although Hutchinson & Gatesy (2000) noted that with cranial origins maintained (i.e. non-retroverted pubes), some femoral protraction would have remained. Our results contradict this hypothesis and suggest that PIFE1&2 maintained a medial rotation moment arm in tetanuran theropods, despite medial inflection of the femoral head (Fig. 9). The hip joint centre in our models is assumed to be at the centre of a spheroid fitted around the most ‘ball-shaped’ (medial most) part of the femoral head. This places the hip medially offset from the femoral shaft and greater trochanter, resulting in PIFE1&2 passing lateral to the hip joint, and thereby producing medial, rather than lateral, rotation. Given this geometry, our models indicate that it would have been impossible for PIFE1&2 to induce lateral rotation while their pubic origin remained cranial to the hip joint centre. We therefore suggest that the derived neornithine lateral rotation function of PIFE1&2 did not evolve until pubic retroversion had occurred in maniraptoran theropods, rather than being present in basal tetanurans as postulated by Hutchinson & Gatesy (2000).
However, this hypothesis rests upon the assumption of a geometrically discrete ball-and-socket joint at the hip. The more open acetabulum of basal tetanurans and the presence of accessory articulations, such as the iliac antitrochanter (Gauthier, 1986; Sereno, 1991; Novas, 1996; Carrano, 2000; Hutchinson, 2001a,b), which are not accounted for in our models, may have allowed the long axis of the femur to rotate about an axis placed lateral to the geometric centre of the more spherical area of the femoral head. This in turn could reduce or remove hip long axis rotation moment arms from a cranially positioned PIFE1&2, leaving a moment arm for protraction. It is also possible that accessory articulations may have limited rotation, thereby negating any long axis rotation moments provided by this muscle group, but this remains speculative and untested. However, with a lack of comparative data from which to build robust, quantitative reconstructions of more complex hip joints, our hypothesis that PIFE1&2 caused medial, rather than lateral, femoral long axis rotation seems less speculative.
Summed (gross) extensor moment arms
Extant birds stand and move with ‘flexed’ postures (i.e. with a strongly cranially inclined femur; Gatesy, 1990, 1995, 1999; Rubenson et al. 2007). An increasingly well-supported hypothesis states that this flexed posture was acquired relatively gradually along the maniraptoran theropod lineage leading to modern birds (Gatesy, 1990, Hutchinson & Gatesy, 2000; Carrano, 1998, 2001). The available moment arm data for non-avian dinosaurs strongly suggest that hip extensor muscle moment arms are reduced as the hip becomes increasingly flexed (Figs 4–9; Fig. S1; Hutchinson et al. 2005, 2008; Bates et al. in press; Bates & Schachner, in press), thereby decreasing muscular capacity to support the hip in these postures. Various osteological and myological changes occurred during avian evolution that may have plausibly acted to alleviate this decrease in the magnitude of hip extensor moment arm (i.e. the angular dependency of the moment arm) in flexed postures.
Caudal elongation of the pelvis (Fig. S3 in Supporting Information), pubic retroversion and a reduction in femoral length relative to that of the ilium (Fig. S3 in Supporting Information) represent geometrical changes that potentially helped extant birds to reduce the strong angular dependency of hip extensor moment arms seen in more basal archosaurs (Fig. 6a). This geometric effect is demonstrated by our sensitivity analysis on the origins of muscles with pubic and/or ischial origins (i.e. ADD1&2, PIFE) in Lesothosaurus, which indicates that a more horizontal line of action reduces the angular dependency of hip extension moment arms through more horizontal muscle orientations; for example, a more proximal origin for PIFE, which produces a more horizontal line of action, reduced the angular dependency of its moment arm (Fig. 5f; note in this case by significantly reducing its flexion–extension moment arm due to the proximity of PIFE insertion to the hip joint). This effect may be important in ornithischian limb evolution; the presence of an elongate postacetabular process is a synapomorphy of Neornithischia (Butler et al. 2008), so it might be expected that the angular dependency of extensor muscles will be decreased in neornithischians relative to Lesothosaurus.
However, our data show that the peak in summed extensor moment arms is conservative along the theropod lineage leading to birds (Fig. 6a), although Lesothosaurus peaked at more extended postures. The models presented here also produce no evidence that the gross hip extensor moment of the ostrich is less angular dependant (i.e. no lesser decline with increasing hip flexion) than those of non-avian dinosaurs, with the relative average change in moment arm per degree of joint flexion–extension supporting conservatism (Lesothosaurus 0.011, Allosaurus 0.008, Struthiomimus 0.006, Tyrannosaurus 0.015, Velociraptor 0.015, ostrich 0.009). This suggests that overall gross pelvic geometry was not modified to reduce the overall angular dependency of hip extensor moment arms during avian evolution. This hypothesis should be tested further with additional models of theropod taxa, particularly those representing portions of the avian lineage not sampled by our analysis (e.g. basal Dinosauriformes, other non-avian coelurosaurs).
Summed (gross) flexion moment arms
The key hip flexors (AMB and ITBa; see Fig. S1 in Supporting Information) experience a large increase in their moment arm as the femur is held more vertically in all taxa in the sample, indicating strong angular dependency due to their almost vertical line of action from the pelvis to the knee. These muscles have by far the highest range in magnitudes (AMB 0.028 m and ITBa 0.022 m, vs. IFMa 0.005 m, IFMp 0.008 m, PIFE 0.004 m, PIFI1 0.013 m, PIFI2 0.008 m), confirming the relative postural trends visually apparent in the graphs (Fig. S1). Lesothosaurus has a consistently lower summed flexion moment arm than non-avian theropods, but is broadly similar to the ostrich at flexed hip joint angles (Fig. 6b). At more extended postures, the summed flexion moment arms in the ostrich increase significantly, reaching magnitudes similar to the non-avian theropods (Fig. 6b). Low summed flexion moment arms in Lesothosaurus relative to other dinosaurs are due to the loss of a hip flexor (PIFE) following pubic retroversion (see discussion of PIFE function above). This is further supported by a plot of the average summed flexor moment arms (Fig. S2 in Supporting Information), in which Lesothosaurus is much more similar to non-avian theropods, suggesting its lower total summed moment arms result from the non-avian theropods having a greater number of flexors, and not individual flexors with relatively greater leverage.
Summed (gross) adduction moment arms
Summed moment arms for adduction indicate further differences between Lesothosaurus, non-avian theropods and the ostrich (Fig. 6c,d). Lesothosaurus has low moment arms for adduction across all joint angles relative to non-avian dinosaurs, while the adductors of the ostrich display stronger angular dependency (Fig. 6d; average change in moment arm per degree of hip flexion–extension; Lesothosaurus 0.0026, Allosaurus 0.0019, Struthiomimus 0.0019, ostrich 0.0031). Examination of adductor muscles in Lesothosaurus on a muscle-by-muscle basis suggests that the key difference between it and theropods relates to the total number of adductor muscles in each. CFB is an abductor in Lesothosaurus, but an adductor in theropods (see above), while the theropods in the study are reconstructed with three PIFE muscles (see Hutchinson, 2001a,b; Carrano & Hutchinson, 2002; Hutchinson et al. 2005; Bates et al. in press). Retroversion of the pubis in Lesothosaurus coincided with reduction of PIFE (Maidment & Barrett, 2011), and only one part of PIFE is reconstructed here. This means that Lesothosaurus has three fewer adductors than theropods, and consequently a lower total adduction moment arm.
The extremely low adductor moment arms observed in the ostrich at all but the most flexed joint angles are due to loss of the ischial symphysis and the caudolateral expansion of the pelvis relative to other taxa in the study, which moved muscle origins close to, and in some cases lateral to, the hip joint, switching their function to hip abduction as the hip is extended (e.g. IFB, ADD1&2, FTI3; see Fig. S1 in Supporting Information).
Summed (gross) abduction moment arms
Lesothosaurus has the lowest summed moment arms for abduction in any of the taxa sampled (Fig. 6c). Examination of abduction moment arms on a muscle-by-muscle basis in Lesothosaurus indicates that muscles of the IFM complex are responsible for low abductor moment arms: IFMa is a weaker abductor at extended joint angles than in other dinosaurs, while IFMp is a weaker abductor at flexed joint angles than in other dinosaurs (Fig. 8).
The dinosaur taxa modelled in this study share an enlarged, barrel-like femoral head and neck that laterally offsets the proximal femur and its associated muscle insertions from the mediolateral plane of the hip joint and pelvic muscle origins. The origin of IFMp on the lateral surface of the ilium is noticeably more caudally positioned in Lesothosaurus than in any of non-avian theropods modelled here or by Hutchinson et al. (2005, 2008). In Lesothosaurus the origin of IFMp is situated some distance caudal to the acetabulum, while in non-avian theropods it lies either directly in-line with (i.e. dorsal to) or only slightly caudal to the hip joint (Fig. 8; see also Hutchinson et al. 2005, 2008). From the more caudally positioned origin in Lesothosaurus, the reconstructed muscle path wraps laterally over the femur across the greater trochanter in a more craniocaudal orientation when the femur is held vertically (in contrast to a more dorsoventral orientation over the lesser trochanter in non-avian theropods). As a result, IFMp has a relatively lower moment arm for abduction but slightly greater leverage for lateral long axis rotation than the non-avian theropod models (Fig. 8).
While pelvic and femoral anatomy (e.g. iliac depth, femoral head size, height of the femoral trochanters) might have genuinely contributed to differences in IFMa moment arm magnitudes, it is equally likely that the subjectivity inherent in muscle reconstructions is also playing some role in generating these results. In non-avian theropods the cranial head of the IF group (ITC) inserted onto the lesser trochanter, which is homologous with the anterior portion of the trochanteric shelf (Hutchinson, 2001b). The centroid of ITC insertion in the non-avian theropod models was placed on the lateral surface, while in Lesothosaurus the centroid was located on the medial surface, which would have had a small impact on the abduction moment arm magnitude. Manipulation of these models also leads us to believe that greater uncertainty (i.e. subjectivity) exists in the path of IFE and ITC in non-avian theropods owing to the relatively dorsoventrally deeper ilia in these taxa than in Lesothosaurus (KTB, personal observation). Sensitivity analysis of ITC paths in the non-avian theropod models, combined with a shift of IFMa insertion to the lateral surface of the lesser trochanter in Lesothosaurus, would likely account for the relatively higher abduction moment arm magnitude for IFMa in non-avian theropods.
Summed (gross) long axis rotation moment arms
The summed moment arms for lateral rotation in Lesothosaurus are similar to those of other dinosaurs (Fig. 6f), because they all share a barrel-like femoral head and neck that laterally offsets the proximal femur and its associated muscle insertions from the mediolateral plane of the hip joint and pelvic muscle origins, providing leverage for long axis rotation.
However, Lesothosaurus has lower summed moment arms for medial rotation than any other taxon (Fig. 6e). Examination of the moment arms of individual muscles for long axis rotation shows that PIFE, a medial rotator in non-avian theropods, functions as a lateral rotator in Lesothosaurus and the ostrich. PIFE originates on the cranioventrally directed pubis in theropods, inserting on the greater trochanter (Hutchinson, 2001b) lateral to the joint centre for long axis rotation, and therefore has a moment arm for medial long axis rotation. Retroversion of the pubis in ornithischians and birds (Fig. 1) results in a caudoventrally directed pubis, with PIFE originating on the ischium or puboischiadic membrane, respectively (Maidment & Barrett, 2011). PIFE therefore has a moment arm for lateral long axis rotation in these taxa, and is largely responsible for the reduction in the summed moment arms for medial rotation in Lesothosaurus.
PIFI1 is also a weaker medial rotator in Lesothosaurus than it is in other taxa (see Fig. S1 in Supporting Information). This difference appears to be due to the exact location of the insertion of this muscle on the femur: it inserts very close to the centre of rotation for long axis rotation, so very small changes in insertion can result in polarity differences in moment arms. This again emphasizes the sensitivity of our models to very small changes in soft tissue reconstruction for muscles that insert very close to centres of rotation.
The highest moment arms for medial rotation are observed in the ostrich (Fig. 6e). This is due to the development of the elongate preacetabular process of the ilium and the migration of the IFMa (ITC) and PIFI2 homologues onto it. These muscles, which have large abduction and flexion moment arms in non-avian dinosaurs (see Fig. S1 in Supporting Information) are therefore cranially offset in birds and orientated more perpendicular with respect to the long axis of the femur, resulting in large moments for medial rotation (Hutchinson & Gatesy, 2000).
Hutchinson & Gatesy (2000) conceptualized the functional evolution of the avian pelvis and hind limb from a quadrupedal archosaur common ancestor in a series of five incremental functional conditions. They stated that basal, bipedal dinosaurs, placing their standing foot medial to the hip joint, counteracted the adduction moment generated about the hip by the ground reaction force through an abduction moment generated by activation of the IF group musculature. During the subsequent evolution of theropods (including the origin of birds), abduction by IF was de-emphasized in favour of medial rotation, which also counteracts adduction in extant birds by outward rotation of the foot against the substrate when the femur is held sub-horizontally (Gatesy, 1999; Hutchinson & Gatesy, 2000). Medial rotation of the femora will only abduct the lower limb at flexed postures, suggesting that changes in medio-lateral control of the hip were synchronized with reduced habitual motion of the hip and evolution of the knee-based system of limb retraction (Gatesy, 1990, 1995; Hutchinson & Gatesy, 2000). The gradual adoption of flexed femoral postures and knee-based limb retraction are hypothesized to be reflected in the gradual changes in limb segment proportions (particularly reduced femoral length; Gatesy and Middleton, 1997; Carrano, 1998), and reduction in the size of tail-based hip extensors like the CFL (Gatesy, 1990, 1995) and overall tail length, the latter indicative of cranial migration of the centre of mass (Gatesy, 1995; Christiansen & Bonde, 2002). Although these changes occurred in an incremental or step-wise pattern in bird-line theropods, the most significant changes underpinning the evolution of this rotation-based system of medio-lateral support and knee-based system of limb retraction probably occurred in maniraptoran theropods (e.g. pubic retroversion, elongation of the preacetabular process; Hutchinson, 2001a,b; Hutchinson & Gatesy, 2000).
Our analysis of pelvic muscle moment arms in Lesothosaurus indicates that it has many of the features characteristic of the basal dinosaur condition as described qualitatively by Hutchinson & Gatesy (2000). The IF group, including its anterior head (IFMa, corresponding functionally with ITC of birds: Hutchinson & Gatesy, 2000) has highest leverage for abduction (Fig. 4g), in contrast with medial rotation in the ostrich, which resulted from cranial migration of the origins of this muscle group on the ilia (Fig. 8). The non-avian theropod models discussed herein are similar to Lesothosaurus in this respect, supporting Hutchinson & Gatesy’s (2000) hypothesis of an abduction-based mode of lateral limb support in more basal taxa, as well as their suggestion that the medial rotation mechanism seen in extant birds may be related to cranial migration of the IF group during avian evolution (Bates & Schachner, in press).
All of these features suggest that Lesothosaurus is functionally more representative of a the condition qualitatively inferred for basal dinosaurs by Hutchinson & Gatesy (2000) in terms of pelvic muscle moment arms, despite the apparent convergence in basal ornithischian and avian pelvic osteology. Furthermore, although retroversion of the pubis in both birds and basal ornithischians would have resulted in similar reorganization of PIFE musculature, this appears to have had different effects on joint moments in basal ornithischians and birds. In Lesothosaurus, retroversion of the pubis led to lower overall flexor, adductor and medial rotator moment arms as PIFE leverage for these functions was reduced or lost. Instead, the PIFE of Lesothosaurus had leverage for adduction and lateral rotation but not for hip extension (Figs 4 and 9). In birds, PIFE also lost its leverage for flexion and medial rotation, and also offers considerable leverage for hip extension, in addition to adduction and lateral rotation (Fig. 9). The resulting reduction in summed moment arms for flexion, adduction and medial rotation seen in Lesothosaurus is not observed in the ostrich model because the cranial migration of ITC led to increased flexion and medial rotation leverage in this muscle (Hutchinson & Gatesy, 2000). Assessing PIFE function in basal ornithischians is therefore somewhat difficult. In Alligator, PIFE1&2 are active during swing to protract the femur, but also adduct the whole limb in late swing, returning the femur to a near-sagittal orientation for the next stance phase (Gatesy, 1997; Hutchinson & Gatesy, 2000). In birds, the homologues of PIFE1&2 (OL and OM, Table 1) are also active during swing, again adducting the lower limb but through lateral rotation of the femur (Gatesy, 1999; Hutchinson & Gatesy, 2000). With little or no moment arm for hip extension, it seems most parsimonious to infer that swing phase activation of the PIFE group was maintained in basal bipedal ornithischians and that this group continued to play a role in controlling swing phase abduction–adduction.
These new data therefore provide additional quantitative support to more qualitative anatomical traits that suggest the habitual gaits of basal, bipedal ornithischians were quite distinct from those of extant birds. Basal ornithischians retained long muscular tails seen in other basal dinosaur groups, housing large femoral retractor musculature (Maidment & Barrett, 2011). Femora also remained relatively long and gracile compared with the short, robustly proportioned avian femur, thought to be adapted for the high bending and torsional stresses incurred under a flexed ‘avian-like’ posture and a rotational-based system of muscular support (Carrano, 1998). Thus, basal, bipedal ornithischians likely employed a more upright posture and caudofemoralis-driven limb retraction quite unlike that of extant birds.
However, the pelvic muscle moment arms of Lesothosaurus clearly also differ from those of tetanuran theropods in several respects. CFB generates a weak abduction moment in Lesothosaurus because of the dorsal location of the brevis shelf relative to the acetabulum (Fig. 7). The peak in summed extensor moment arms occurs at more extended femoral postures in Lesothosaurus because modifications to the postacetabular ilium and pelvic proportions that occurred on the line to birds were not present (e.g. Fig. S3). Weaker summed abduction moment arms can be related to the primitive caudal origin of IFM. Basal dinosaurs have been the subject of fewer quantitative functional analyses than other clades, such as tetanuran theropods and extant birds, but it is possible that the features observed in Lesothosaurus are characteristic of basal dinosaur locomotor anatomy in general, and that Lesothosaurus represents the basal dinosaur condition.