Procoptodon goliah) had an estimated body mass of 240 kg, almost three times the size of the largest living kangaroos, and there is speculation whether a kangaroo of this size would be biomechanically capable of hopping locomotion. Previously described aspects of sthenurine anatomy  would limit their ability to perform the characteristic kangaroo pentapedal walking (using the tail as a fifth limb), an essential gait at slower speeds as slow hopping is energetically unfeasible. Analysis of limb bone measurements of sthenurines in comparison with extant macropodoids shows a number of anatomical differences, especially in the large species. The scaling of long bone robusticity indicates that sthenurines are following the “normal” allometric trend for macropodoids, while the large extant kangaroos are relatively gracile. Other morphological differences are indicative of adaptations for a novel type of locomotor behavior in sthenurines: they lacked many specialized features for rapid hopping, and they also had anatomy indicative of supporting their body with an upright trunk , and of supporting their weight on one leg at a time . We propose that sthenurines adopted a bipedal striding gait : in the smaller and earlier forms, this gait may have been employed as an alternative to pentapedal locomotion at slower speeds, while in the larger Pleistocene forms this gait may have enabled them to evolve to body sizes where hopping was no longer a feasible form of more rapid locomotion.Sthenurine kangaroos  were an extinct subfamily within the family Macropodidae (kangaroos and rat-kangaroos). These “short-faced browsers” first appeared in the middle Miocene, and radiated in the Plio-Pleistocene into a diversity of mostly large-bodied forms, more robust than extant forms in their build. The largest ( Macropus [Macropus] giganteus) or the red kangaroo (Macropus [Osphranter] rufus), members of the superfamily Macropodoidea (“kangaroos” in the broadest sense) contain animals of a diversity of sizes and habits, including the secondarily arboreal tree-kangaroos (Dendrolagus spp.). However, the recent past diversity of kangaroos, persisting to perhaps as recently as 30,000 years ago, included several kinds of kangaroos much larger than any known at present. The largest of the extant kangaroos  can weigh up to 90 kg, although the average weight for males of this species is only around 55 kg, with females averaging around 25 kg Kangaroos are famous for their style of locomotion – bipedal hopping , which is unique among relatively large mammals . While the popular notion of a kangaroo is of a fairly large animal, such as the grey kangaroo ; and the Macropodidae. The family Macropodidae is usually divided into four subfamilies: Potoroinae (rat-kangaroos), Lagostrophinae , Macropodinae , and Sthenurinae  Macropus (extinct species M. titan and M. ferragus), and the extinct genus Protemnodon .There are three families within the Macropodoidea  with an average body mass of around 4 kg Macropus titan (related to the extant grey kangaroo) had an estimated body mass of up to 150 kg M. ferragus (related to the extant red kangaroo) M. titan. Within the genus Protemnodon, all species were fairly large, although not all were larger than extant kangaroos. Protemnodon hopei had an estimated mass of 45 kg Protemnodon species, such as P. otibandus and P. snewini, were of a similar size (as estimated by measurements of foot bones). The largest species was P. roechus, with an estimated mass of around 166 kg P. anak) a relatively long neck. There has been speculation that at least some may have been secondarily quadrupedal in their locomotion The genus Protemnodon are similarly robust (see later discussion). Sthenurines, like Protemnodon spp., were all fairly large, but not all species were larger than extant kangaroos. Sthenurines are the kangaroos that are usually spoken of as being the “giant kangaroos”. They are distinguished not only by their size, but by many other features, such as their relatively short faces, the loss of the fifth digit in the foot in the Pleistocene forms, and their specialized arms and hands that have been interpreted as an adaptation for browsing Wanburoo hilarus , where it is considered to be primarily absent  habitually bound and only hop at high speed when alarmed Bettongia spp.) habitually hop like macropodines Setonix brachyurus) and tree-kangaroos (Dendrolagus spp.), and tree-kangaroos uniquely perform  a quadrupedal walk, with alternate movement of the limbs Hopping is the quintessential kangaroo gait, seen in all extant macropodoids with the exception of the musky rat-kangaroo (Pedetes capensis) with a body mass of around 4 kg . These rodents, like small macropodids, use quadrupedal gaits at slow speeds The adaptive reasons for adopting the hopping gait are not entirely clear. Hopping is clearly a very efficient form of locomotion in larger kangaroos (see discussion below), but it would have first evolved in relatively small forms, likely of a mass of less than 5 kg Macropus rufus), hopping is an extremely efficient gait: unlike the situation in placentals, where the energy costs of locomotion increase linearly with speed, in the larger kangaroos energy costs and speed become decoupled, and thus the daily expenditure of locomotor foraging is much less for the large kangaroos than for similarly-sized cursorial placentals.  Even in a medium-sized wallaby, the energy savings from elastic energy storage during hopping have been estimated at around 40% Potorous, Bettongia) show no such advantage, although hopping in Bettongia  is nevertheless less expensive than locomotion in a quadruped of similar size It is well known that, in larger kangaroos , weighing around 80–90 kg, would still be operating with a very low tendon safety factor of 1.1, and many extinct kangaroos have body mass estimates well in excess of 140 kg . Few extant kangaroo individuals can be found with a body mass of greater than around 50 kg, and most kangaroos weigh considerably less than this, see Procoptodon goliah, at a body mass of as much as 250 kg, would have had a tendon safety factor of around 0.89; they note that hopping would have been severely limited in this animal, especially during acceleration, if indeed possible at all. However, McGowan et al. Petrogale spp.) would have enabled them to exert higher forces at larger sizes. McGowan The mechanical tensile stress of tendons plays a limiting factor in body size and speed in all mammals. In placental mammals maximum locomotor performance peaks at a body mass of around 50 kg (cheetah or pronghorn size), and there is evidence that this is the size at which strain on the locomotor tendons becomes an issue. How does this relate to the condition in kangaroos? While larger species will be better able to use elastic energy recovery to assist in their locomotion, the larger the animal, the lower the tendon safety factor, and the greater the danger of tendon rupture: while smaller kangaroos have estimated tendon safety factors of around ten , the estimated safety factor of the Achilles tendon in large kangaroos approaches one. McGowan et al. Macropus), there are many anatomical differences that reflect the fact that these animals had a rather different functional biology. The classic work on sthenurine anatomy is that of Wells and Tedford Sthenurus  with the exant grey kangaroo, Macropus giganteus): they note that, while the overall postcranial proportions of Sthenurus resembles those of Macropus, there are some key differences.While sthenurine locomotor performance has rarely been considered as markedly different from that of modern large kangaroos  centra, but with shorter diapophyses and metapophyses, and vestigial anapophyses. This may indicate a reduced capacity for lateral extension of the tail The tail of Sthenurus are massive, with huge metapophyses, but the transverse processes have been reduced or lost, and the backbone appears to have been relatively rigid with limited flexion in the dorsoventral plane.The lumbar vertebrae of Sthenurus, especially in the hind limbs, are much more robust than those of Macropus: Wells and Tedford Sthenurus is almost double that of a Macropus of similar linear dimensions.And, finally, in general the limb elements of We present here a description of the hindimb locomotor anatomy of sthenurine kangaroos, which is essential for an understanding of the analyses performed. Much of this anatomical description is drawn from Wells and Tedford Sthenurus is more posterior , with no modification of the nature of the zygapophyses (as in Macropus). Large metapophyses appear on T11, and increase in size dramatically in the more posterior portion of the trunk. While metapophyses are also present in the posterior trunk of Macropus, they are smaller, and less deflected medially. The neural arches are shorter in Sthenurus, although broader in the anteroposterior direction, and are directed caudally . The lumbar vertebrae of Sthenurus are also markedly different in having greatly reduced transverse processes, and in the vestigial nature or absence of diapophyses and anapophyses , and the almost platycoelus centra indicate limited mobility.The number of precaudal vertebrae is similar in sthenurines and macropodines , but the overall appearance of the vertebral column is very different. The overall appearance in sthenurines is for massive vertebrae in comparison to macropodines, especially in the lumbar region, where large and laterally expanded metapophyses give the impression of rigidity. Wells and Tedford Sthenurus resistance would have been effected not only by the zygapophyses, but also by by the epaxial muscles (multifidi) and ligaments attached to the greatly enlarged metapophyses. They Wells and Tedford Sthenurus, as in Macropus , but the senior author has observed sthenurine sacra that are composed of three vertebrae, involving the incorporation of the first caudal vertebra . Wells and Tedford Sthenurus stirlingi than in Macropus . The sthenurine sacral anatomy is again indicative of a resistance to rotational torsion.The sacrum of sthenurines is broader and shorter than in macropodines, with more pronounced sacral wings  for the articulation with the ilium. Wells and Tedford Hypsiprymnodon moschatus, the only extant macropodoid considered to be primarily non-hopping), but to a slightly lesser extent than in other macropodoids, and it is also a feature of koalas and wombats. Elftman All macropoidoids exhibit the derived anatomy of a very distally-positioned attachment of the ilium to the sacrum, with the result that the ilia project dorsally above the sacrum. Personal observation by the senior author shows that this is also true for the musky rat-kangaroo  among macropodines, while other more open-habitat, fast hopping kangaroos such as the nail-tail wallabies  and hare-wallabies (Lagorchestes spp.) parallel the Macropus species in having narrow tuber coxae , while this is broad in sthenurines, and narrower in species of oxae see . While tMacropus have elongated ischia , with a pronounced posteroventral projection to the bone. This long ischium provides an elongated moment arm for the muscles that retract the femur, both the hamstring complex and the adductor complex. Elftman Acinonyx jubatus) in comparison with less cursorial felids Macropus among the other macropodoids, which have a relatively shorter ischium (less than 60% the length of the ilium), although the nail-tail wallabies  have also elongated their ischia, to an even greater percentage of the ilium (>80%) than in Macropus   only among the tree-kangaroos. The ischia are only somewhat shorter than in the regular macropodid condition, but are tipped dorsally: Wells and Tedford pp.) see . This doSthenurus are almost as long as the ilium, but are no more than half the length of the ilium in MacropusMacropus are possibly somewhat reduced over the primitive macropodoid condition, but in Dendrolagus spp. the epipubics are of similar relative size to those of sthenurines (see A notable difference in the pelvic area is in the size of the epipubic bones see . The epiines see . The priDendrolagus spp.) also have relatively large femoral heads, as do Protemnodon spp. : tree-kangaroos  have a proportionally smaller greater trochanter Sthenurus. This echos the point made above, that a larger volume of gluteal musculature would enable sthenurines to balance their body weight over one leg: in humans, larger superficial gluteal muscles are important in preventing collapse of the body medially when the weight is borne on one leg The femoral shaft is curved in both Sthenurus, but it is placed more distally on the femoral shaft in sthenurines than in other macropodoids , increasing the moment arm for the iliopsoas , which originates from the ischium and is essentially the most proximal component of the adductor musculature complex. Hopwood and Butterworth Macropus, and suggest that it acts as a form of check ligament to prevent overflexion of the hip during jumping . Without knowing the more general condition for this muscle in all macropodids it is impossible to even guess whether or not this muscle was tendinous in sthenurines. The longer moment arm afforded by the more distal insertion on the femur might be indicative of more powerful limb retraction and abduction, or it might simply be the case that the different morphology of the sthenurine ischium (see above) changed the previous nature of the moment arm, and the more distal placement of the insertion is merely compensating for this. Tree-kangaroos (Dendrolagus spp.) also have a relatively distally placed adductor scar  locomotion, such as the New Guinea forest-wallabies (Dorcopsis and Dorcopsulus spp.). Sthenurines have tibiae of comparable lengths to generalized macropodids, but the extinct Protemnodon spp. have relatively short tibiae All macropodids have relatively long tibia, up to twice the length of the femur. Tibial length scales with positive allometry in macropodids in general Sthenurus and Macropus, but did not comment on the elongation of the tibial tuberosity in Macropus (which is derived relative to other macropodoids)  crest. Murray Procoptodon). By comparison with the potoroine condition, Murray On the proximal tibia, Wells and Tedford ids) see . The enlSthenurus than in Macropus, and an articular groove that is more of an “oblate cup” in shape than the “shallow, arcuate” form in Macropus. They comment that this morphology would mean a more constrained tibioarticular articulation in Sthenurus, but they do not specifically note a unique morphology of the sthenurine distal tibia: that is, of a plantar process that fits in a tongue-in-groove linkage into the astragalar trochlea .On the distal tibia, Murray hlea see . This moSthenurus lacks the distinctive posterior process of the head of the fibula seen in Macropus, which apparently allows for greater flexion of the knee. They conclude that this morphology may relate a longer groove in the proximal tibia for the insertion of the fibula, and interpret this as allowing for a greater internal rotation of the lower limb about the knee. They relate this to the notion of to sthenurines needing to achieve greater limb rotation to position their feet medial when landing while hopping, as their wider pelvis would otherwise result in more lateral placement of the feet. However, this could also relate to a rotation of the body around the knee when the foot was placed on the ground, as would be experienced with bipedal striding.With regards to the fibula, Wells and Tedford Sthenurus and Macropus: the astragalus is at a right angle to the longtitudinal axis of the pes in Sthenurus, but is rotated medially in Macropus by as much as ten degrees, and with a less robust connection of astragalus and calcaneum than in Sthenurus. A greater degree of rotation of the axis of the astragalus is seen in other macropodoids, in particular Dendrolagus spp. . This process is large in Macropus has a much longer calcaneal tuber than that of Sthenurus, and the orientation differs: the calcaneal tuber in Macropus is orientated straight up and slightly posteriorly, while in Sthenurus it is curved slightly forwards   see . In DendMacropus giganteusThe calcaneal tuber serves as the insertion of the gastrocnemius muscle, and also for a portion of the semitendinosus  have a suite of morphological adaptations related to the shifting of their weight to the medial side of the foot during locomotion The fibular facet on the calcaneum is more prominent in rsus see . The genMacropus and Sthenurus than in other macropodids, giving the calcaneum an asymmetric “hunched shoulders” appearance when viewed from the plantar side. A larger sustentaculum would indicate greater capacity for weight transmission, either from a larger body size and/or from greater forces encountered in rapid locomotion. However, the shape of the sustentaculum is notably different in sthenurines than in macropodines. Bishop o angle. Bishop The sustentaculum tali, on the medial side of the calcaneum, is where the weight of the animal's body is transmitted from the astragalus to the calcaneum, and from there to the foot. The sustentaculum is taller in the dorso-plantar direction in both Hypsiprymnodon moschatus), which is considered to be a primarily non-hopping form Dendrolagus spp. Macropus the “stepping” is more pronounced and the dorsolateral facet is wider in the mediolateral direction.On the distal calcaneum, all macropodoids have a “stepped” cubonavicular facet, with the dorsolateral facet being projected more ventrally than the dorsomedial or ventromedian facets. This morphology has been considered important as an adaptation for hopping, in limiting movement between the calcaneum and the cuboid Dorcopsulus and Setonix) is for equal-sized dorsolateral and dorsomedial facets, with a relatively narrow (in the dorsoplantar direction) ventromedian facet giving the distal surface a rectangular profile. In Dendrolagus the ventromedian facet is indistinct and merged with the dorsolateral facet, a morphology that Warburton and Prideaux Protemnodon did not broaden the ventromedian facet in this fashion , suggesting that large size alone is not the reason for this change in morphology.In distal view, the generalized macropodine condition of the calcaneum  that extends down the proximal third of the bone. The metatarsals are also curved in Sthenurus, but appear to be proportionally somewhat shorter, and Wells and Tedford Sthenurus is from 1.2 to 1.5 times larger than would be predicted for a Macropus of similar size. The plantar crest is deeper in sthenurines and extends further down the length of the bone. This crest serves as the insertion for the origin of interosseus muscles, and is reduced in placentals with an unguligrade stance where these muscles have been reduced to ligaments The fourth metatarsal is long and curved in Dorcopsulus and Setonix, is for relatively short metatarsals; the metatarsals of sthenurines are elongated over this general condition, but they tend to be shorter than those of Macropus and other more cursorial macropodines such as Petrogale, Onychogalea, and Lagorchestes (see Dendrolagus spp.) have been shortened, more so in the New Guinea species than in the Australian ones Protemnodon spp. also have fairly short metatarsals.The generalized macropodine condition, as seen for example in stes see , where tSthenurus than in MacropusMacropus. Sthenurines exhibit a derived condition for macropodids for all of these features  has a fairly flat anterior profile in most macropodoids, while in sthenurines this surface curves posteriorly both medially and laterally, resulting in a more plantar  positioning of the intra-articular groove ures see . All of MacropusThe distal articular surface of the fourth metapodial is fairly square-shaped in most macropodoids, but in sthenurines not only is the distal surface proportionally larger, but it is more mediolaterally elongated see . This isMacropus is relatively long, almost twice the length of the second phalanx, while in Sthenurus the second phalanx is around 80% of the length of the first. In comparison with other macropodids, this appears to represent a relative enlargement of the medial phalanx in Sthenurus, in addition to the lack of lengthening of the proximal one as seen in Macropus. The generalized macropodid condition is for a relatively short proximal phalanx, with elongation seen convergently in more cursorial kangaroos, such as Petrogale, Onychogalea, and Lagorchestes, while the proximal phalanx is shorter and broadened in Dendrolagus spp. A lengthened proximal phalanx is also seen in more cursorial ungulates , where it apparently relates to a lengthening of the plantar tendons, increasing the “springiness” of the foot The phalanges of sthenurines are distinctive: the proximal and middle phalanges appear “waisted”, with expanded proximal and distal ends, but a narrower median portion. The proximal phalanx of Dendrolagus. In contrast, the ungual phalanx in sthenurines is more blunt and rounded, described as “hoof-like” by Kear et al. Hadronomas and Rhizosthenurus, and convergently among Protemnodon spp. The ungual phalanx is curved and rather claw-shaped in most macropodoids, being narrow in the mediolateral direction. More distinctive claws are seen in the species of Sthenurus: Murray Hadronomas), represent more torque being placed on the first phalanx.Wells and Tedford Despite the potential biomechanical problems of hopping locomotion in large kangaroos, the ability of sthenurines to use hopping as a mode of locomotion has rarely been questioned but see . SthenurOne possible reason for the lack of questioning about the mode of locomotion of sthenurines is the issue of monodactyly. This has been seen as analogous to the attainment of monodactyly in the equid lineage, and thus indicative of a highly cursorial lifestyle, rendering sthenurines even more specialized hoppers than the large macropodines see , p. 59, Diceros bicornis, a browser) and the white rhino : they are of a similar size , but there is no indication that there is any difference in the relative robusticity of their skeletal framework. Thus, on the basis of diet alone, one would expect the large grazing species of Macropus to be the more robust forms, which is clearly not the case. In addition modern kangaroos show little capacity for gut expansion The apparent “robusticity” of sthenurines has often been noted, but is not well understood. Wells and Tedford Protemnodon. Large species of Protemnodon showed similar robusticity to the sthenurines, despite a very different postcranial anatomy to either sthenurines or large species of Macropus . This raises the issue of what is the normal allometric scaling for kangaroos: we will discuss later the likelihood that the real issue is that it is the large species of Macropus that are relatively gracile, with sthenurines and Protemnodon spp. representing the “normal” condition.A clue to this issue of “robusticity” may be found in the proportions of a third lineage of kangaroos to reach “giant” proportions: species of the extinct macropodine Another hypothesis for the more massive hind limb structures in sthenurines is related to the supposed browsing posture, where the animal must raise its body up over the hips  and 78 extinct kangaroo individuals (belonging to 18 genera) see –4. All oProtemnodon spp., and representatives of the smaller fossil forms mentioned below). , and 14 from the pes see . We did Nambaroo gillespieae, the late Oligocene/early Miocene Ngamaroo archeri , and the late Miocene macropodine Dorcopsoides sp. Taxonomy was taken from Prideaux and Warburton Protemnodon. We also included information from two “giant”  Pleistocene species of the extant genus Macropus: M. titan and M. ferragus. The details of the specimens measured are presented in Every genus and almost every species of extant macropodoid was measured. Extinct taxa included not only sthenurines, but also a few other forms. For the purposes of seeing if the morphology of modern kangaroo species fell within the range of the smaller extinct taxa, we included information from the late Oligocene/early Miocene balbarid We performed both bivariate and multivariate analyses on the linear measurements using the statistical package SPSS v. 19. We created a number of bivariate plots of the different bony elements of the skeleton, primarily to confirm the visual observations discussed in the “Descriptive Anatomy” sections, and these are to be found in the supplementary information, along with some discussion of the distribution of taxa –S3. CertMacropus [M. titan and M. ferragus] were omitted, as their placement in the analyses was more like that of the sthenurines than that of the large extant species of Macropus): (i) all of the taxa; (ii) extant species only; (iii) all of the taxa except the extant species of the genus Macropus.Two of the bivariate plots , but areAs our interest here was in testing for differences in the regression slopes for pair of groups (see above), we performed a Student's t-test between the coefficients (b) of the three regression lines. The null hypothesis (of no difference between the slopes) will be rejected if the regression slopes of each adjusted model are not statistically significant different from each other. In addition, in order to explore if different scaling relationships follow an allometric trend or rather an isometric one, we performed a Student's t-test between the coefficients (b) of each regression line and the theoretical value of a slope equals to one . The null hypothesis  will be rejected if the slope of a given bivariate regression model significantly departs from unity, thus suggesting a significant allometric trend.(i) All hind limb bones combined: this did not allow for the inclusion of many extinct taxa, but three sthenurine species  could be included, two of which were composite specimens (see (ii) All hind limb bones except the pelvis: this allowed us to include many more extinct taxa, including species of Protemnodon, and the sthenurine genera Hadronomas and Procoptodon. (iii) On the calcaneum alone (using the separate dataset). The calcaneum is a highly informative bone in terms of locomotor behavior The multivariate analyses included both Principal Components Analysis (PCA) of log-transformed variables and Linear Discriminant Analysis. These were performed on the following sets of data. All the discriminant analyses were performed by the stepwise approach. This approach was preferred over the direct method because it only uses the best set of variables for discriminating among the groups compared e.g., . The selMacropus species M. titan and M. ferragus, as previously discussed) is 1.334 (slope 1); the slope for the extant species only is 1.179 (slope 2); the slope for all species excluding species of Macropus is 1.378 (slope 3). . To a first approximation, slope 2 is the regression line excluding the extinct “giant” kangaroos , and slope 3 is the regression line excluding the large extant, specialized fast-hopping kangaroos .The slope for all the taxa : that is the inclusion of the extinct kangaroos does not greatly affect the regression line that fits the extant taxa. However, slope 2 is different from both other slopes at the 99% level of significance ; that is, with the exclusion of the large extinct species, the slope is significantly less steep. We interpret this to mean that the femoral proportions of sthenurines and Protemnodon spp. are following the “normal” allometric relationships for kangaroos, and that the larger species of Macropus are acting to pull the slope down to a lower level.However, the differences between the slopes are interesting. There is no statistical difference between slopes 1 and 3  is 0.983 (slope 1); the slope for the extant species only is 0.842 (slope 2); the slope for all species excluding species of Macropus is 1.078 (slope 3). Slope 1 is not different from isometry at the 95% level of significance . Both slopes 2 and 3 are different from isometry at the 95% level of significance : that is, slope 2 represents negative isometry, and slope 3 positive isometry.Here the scatter around the regression line is considerably greater than for the femur proportions, and the 95% confidence limits of the slope are much broader. . The first PC  is interpreted as a size vector because all the variables had positive loadings and fairly high values , hop rarely , or which are unspecialized, forest-dwelling hoppers  The Oligo-Miocene balbarid Nambaroo gillespieae also falls within this clustering, supporting the hypothesis that these animals were not hoppers, or poor hoppers at best Dendrolagus bennettianus, is one of the more basal, Australian, members of this tribe , the rock-wallabies  the hare-wallabies (Lagorchestes spp. and Lagostrophus fasciatus), the nail-tail wallabies , and the species of the genus Macropus . The species of Macropus on M. parma, M. eugenii, and M. dorsalis), which cluster amongst the other terrestrial macropodines; medium-sized species , which have slightly more positive scores on the first component than any of the other macropodines; and large species with the highest scores on the first component . Note how the scores of Macropus species on the second component change with increasing size, with the smaller species having the least negative scores, and the larger ones the most negative scores. This is not merely an allometric issue as the species of nail-tail wallabies , which are of a similar size to the small species of Macropus, and which have evolved more cursorial anatomy convergently with Macropus (see previous discusson), have similarly negative scores on the second component as the large species of Macropus. The only specimen which appears to be “out of place” here is the brush-tailed bettong or woylie, Bettongia penicillata: this potoroine is not notably cursorial in its anatomy or behavior, but may be falling with low scores on the second component because of relatively small epipubic bones (see later discussion): note that, when the analysis is performed without the pubis Macropus. This serves as the area of origin of the pectineus, a short muscle that would act to rapidly move the leg forwards from a backwardly positioned femur, and may be important for rapid recycling of the limb during hopping. Three other variables  relate to an elongated posterior portion of the ischium, which provides for a longer moment arm for the hamstring and adductor muscle complexes, important in powerful limb retraction during hopping (see previous discussion). Another variable with negative loadings includes the size of the tibial crest, reflecting a large area for the origin of the tibialis anterior, possibly reflecting rapid foot flexion (see previous discussion).In contrast, length measurements figure prominently in the negative loadings on the second component: most important is the length of the fourth metatarsal and the first phalanx, with the length of the tibia and second phalanx being less important. The height of the iliopectineal process on the pelvis is an important element on this axis of the second component, and this can be seen especially in large species of The difference between the positive and negative loadings on the second component is that the variables loading positively largely reflect adaptations for stability and power ; while those loading negatively reflect adaptations for speed . Note that the position of the sthenurines on component two is despite their being unlike the other taxa in this position in many respects, in that they have variables with high negative loadings on this component, such as a long tibia, and a relatively long fourth metatarsal and first phalanx.As the pelvis is rarely completely preserved in fossil forms, we performed a second PCA, excluding those variables measured on the pelvis, in order to include more extinct taxa. Again, while the first PC  was interpreted as a size vector according to the loadings of the variables on this axis see , the secPotorous spp.), which are the least specialized hoppers among the potoroines. However, regarding the scores of the different taxa, only Dendrolagus spp. have positive scores. Thus this analysis, more so than the first one, is distinguishing between tree-kangaroos and other forms. The position of the sthenurines on the second component, in a similar position to the less-specialized extant forms, largely reflects low values for the variables that have high negative loadings on this component. The sthenurines all have less negative scores on the second component than the large species of Macropus, including the extinct “giant” species M. titan. The Miocene sthenurine Hadronomas puckridgi falls relatively close to Macropus. Two sthenurines, unlike any extant form apart from Dendrolagus spp., have slightly positive scores on the second component: the largest, most specialized taxa, Procoptodon sp. (probably  =  P. goliath) and the somewhat smaller Simosthenurus occidentalis. Note that Procoptodon sp. and S. occidentalis tend to cluster together in all other analyses where both are included. A couple of Protemnodon species are included in this analysis, and they fall within the range of the less specialized sthenurines, likely indicating less specialized hopping abilities rather than any particularly sthenurine qualities.Despite the fact that the pelvis figured so prominently in the first analysis, with its exclusion the taxa fall in a similar position within the morphospace. One notable difference is the more negative position along component two of the potoroos  previously indicated by the large tuber coxae.New variables with negative loadings include a longer (in the anterior-posterior direction) proximal articular surface of the tibia , and several measurements of the length of the calcaneal tuber . The most important of the calcaneal tuber length measurements is the lateral length, which reflects a greater amount of “stepping” of the articulation of the calcaneus with the cubonavicular (see previous discussion). Thus the negative loadings on this axis represent modifications for rapid hopping, as with the previous analysis.Hypsiprymnodon moschatus, and the forest and woodland dwelling wallabies), and the loadings of the variables along the second component made sense in terms of the functional morphology. In the analysis with all hind limb bones the Pleistocene sthenurines clustered with the rare hoppers, although the smallest form, “Procoptodon” gilli, had the lowest scores. With the pelvis removed, the distinction was not so marked and the analysis appeared to be mainly separating the tree-kangaroos (Dendrolagus spp.) from the other forms. The position of the sthenurines was not so clearly separate from the more specialized macropodines in this analysis, but all sthenurine individuals had scores that were more towards the positive end of the component than did any of the large species of Macropus.The PCA of all the bones together proved excellent for distinguishing between extant macropodoids that are more specialized hoppers from those that are rare, or less specialized hoppers  were clearly separate from all other macropodoids (apart from Dendrolagus spp.), the second function appeared to be distinguishing potoroines from other macropodoids, with the extinct balbarid Nambaroo gillespeiae being an extreme outlier at the opposite end of this function from the potoroines. This analysis is presented in the Supplementary Information , excluding Dendrolagus spp.; Group 3 =  Dendrolagus spp. The extinct taxa were added as unknowns. The value of the Wilks' lambda statistic for the first function was close to zero and highly significant . Similarly, the value of the Wilks' lambda statistic for the second function was also highly significant . We obtained a 94.2% of correct reclassifications using the leave-one-out method of cross-validation, which suggests that both discriminant functions combined a set of skeletal traits that accurately distinguished the three groups compared.Three groups were defined: Group 1 =  species of Dendrolagus spp.  from other extant macropodines. The more specialized sthenurines , and the presumed male specimen of Sthenurus stirlingi  tend to have more negative scores than the Macropus individuals, possibly reflecting less specialization for hopping .The first function distinguishes ingi see  also havingi see  have somDendrolagus spp. based on their more mobile tarsal joint, and Procoptodon sp. may be falling into this area of the morphospace because of its large size . Two measures of the femur have high positive scores on this axis: the maximum width of the greater trochanteric ridge, and the length of the medial tibial condyle. The width of the trochanteric ridge reflects the insertion of the gluteals, perhaps indicating larger hind limb retractor musculature in the species of Macropus. The functional significance of the length of the medial tibial condyle is not clear: as all the macropodids have a medial condyle that is shorter than the lateral one, this variable may be reflecting a more symmetrical distal femur, possibly related to hopping behavior. The length of the fourth metatarsal also has slight positive loadings, probably reflecting the difference from the very short metatarsals of Dendrolagus spp.The only variable with negative loadings is the mediolateral width of the base of the astragalus. As notec previously, this feature may be distinguishing Procoptodon” gilli. Perhaps surprisingly, Hadronomous puckridgi has higher scores on both this function, and the first one, than “P.” gilli and the presumed female individuals of Sthenurus stirlingi. The only macropodine to cluster among the high-scoring sthenurines is the exinct “giant” Macropus titan, possibly reflecting the fact that this function is largely (but not entirely) a reflecting body size. Note that the smaller species of Macropus cluster with the other macropodines, but there is no simple size-sorting among the larger species of Macropus, and Hadronomas puckridgi is no larger than the large extant species of Macropus. And, of course, Dendrolagus spp., with higher scores than any of the non-Macropus species of macropodines, are not any larger than all of these taxa.The second function mostly separates the sthenurines from the macropodines, with the exception of “Dendrolagus spp. are explained by their more flexible ankle). The maximum width of the greater trochanteric ridge also has relatively high scores: all of the Macropus species have positive scores on this function, as they did with this variable on the first function. However, the sthenurines also have high scores: as previously discussed, sthenurines have large areas for gluteal origin and insertion, but here perhaps reflecting balance over an upright trunk rather than limb retraction. The length of the fourth metatarsal here has weakly negative scores, again possibly explained by the position in the morphospace of Dendrolagus spp. However, the length of the medial tibial condyle has the highest negative scores. This may reflect the relatively larger length of the lateral tibial condyle observed in sthenurines, as previously discussed.With regard to the variables with high loadings on the second function: here the mediolateral width of the astragalus has the highest positive loadings; this may be the variable that is acting to sort individuals by body size, in part (and the relatively high scores of Dendrolagus spp. (not illustrated): this resulted in just two predetermined groups (species of Macropus and other macropodines [plus Lagostrophus]), with the sthenurines classified as unknowns. The value of the Wilks' lambda statistic for the first function was highly significant  and the 89.8% of the taxa were correctly classified. The function incorporated only two variables, both loading positively. These were the height of the medial malleolus on the distal tibia (T14: highest loading) and the width of the greater trochanteric ridge (F12). On a univariate axis non-Macropus macropodines have the lowest scores, species of Macropus have intermediate scores, and the sthenurine species have the highest scores. These features relate to the relative stability of the ankle joint and to the relative size of the gluteals. Thus it seems that the Macropus species have a more stable ankle joint and larger gluteals than non-Macropus macropodines, perhaps due to greater hopping specializations, while the sthenurines are more extreme in these features, but perhaps for reasons unrelated to hopping. The larger gluteals in sthenurines could reflect the balancing of the trunk over the hips while foraging, and the more stable ankle joint could reflect balancing the body weight over one leg while striding. The fact that the width of the astragalus, which featured prominently in some earlier analyses, is not included here confirms the suspicion that the high loadings of this variable in other analyses largely distinguished Dendrolagus spp., with their more flexible ankles, from other macropodids.To investigate this further we performed a CVA with and without The analysis of the calcaneum yielded a first principal component , which represents body size, and a second component , which represents aspects of morphological differences among the specimens. Despite the fact that only the first PC had eigenvalues higher than one, which means that body size is responsible for a high amount of the total shape variation, we also extracted the second PC because it represents aspects of morphological differences among the specimens. The morphospace depicted from the scores of the specimens on these two PCs is shown in Dendrolagus spp.) Perhaps surprisingly, the basal species of Dendrolagus, D. bennettianus, is the one here with the highest negative loadings, falling away from the other kangaroos, whereas in the PCA for all hind limb bones it was the one Dendrolagus species that tended to cluster with the other kangaroos. The extant macropodoids that place with negative scores include mainly the non-specialized hoppers: Potorous spp. (potoroos), Setonix brachyurus (the quokka), Thylogale spp. (pademelons), and Dorcopsis spp. , but not Hypsiprymnodon moschatus. The Oligo-Miocene taxa  also have negative scores, but most of specimens of the late Miocene macropodine, Dorcopsoides sp., have positive scores. Perhaps surprisingly, the smallest species of Macropus, M. eugenii and M. irma, also have negative scores, as does the swamp wallaby, Wallabia bicolor.Taxa that have positive values on the second component (the first component representing body size) comprise most of the extant macropodoids, with the exception of the tree-kangaroos (Protemnodon spp.) have negative scores, with the largest forms  having the most negative ones. The smaller, and/or more gracile species of Protemnodon, P. snewini and P. anak, have positive scores, clustering with the larger species of Macropus, as do the several individuals of the Miocene sthenurine Hadronomas puckridgi. The smaller Miocene sthenurine Rhizosthenurus flanneryi has slightly negative scores, but still falls within the range of extant hopping macropodines. But basically, as with the PCA for all hind limb bones, the Pleistocene sthenurines and the larger species of Protemnodon fall with the rarely-hopping extant macropodines, in particular with the tree-kangaroos (Dendrolagus spp.).Most of the large extinct taxa  on this component. Almost all of the other variables loading positively on the second component reflect the length of the calcaneal tuber: a long calcaneal tuber indicates a longer moment arm for the gastrocnemius muscle, again indicative of powerful and/or rapid hopping. Also loading weakly with positive values is the dorso-ventral length of the CLAJ (continuous lower ankle joint), which may simply reflect a rather narrow calcaneal head.The highest positive loading variable on the second component is the width of the sulcus on the latero-plantar side of the calcaneal head for the tendon of the peroneus longus muscle. As discussed previously, this action of this muscle it to both flex the ankle and to counteract the action of the tibialis anterior in preventing the evulsion of the pes. Thus this reflects morphology specialized for rapid hopping, and accounts for the high scores of the larger species of The variables loading with high negative loadings on the second component largely reflect the width of both the calcaneal tuber and the calcaneal head, especially the CLAJ. A broader calcaneum reflects foot stability rather than rapid locomotion. Also loading with high negative values is the width of the sulcus for the tendon of the flexor digitorum longus, on the medio-plantar side of the calcaneal head. This loading largely reflects the width of this sulcus in the tree-kangaroos, and may be related to their climbing ability. Another variable with moderately negative high loadings on the second component is the size of the ectal facet, which is one of the places where the astragalus articulates with the calcaneum (the other being the sustentacular facet). Thus a large ectal facet represents morphology adapted for weight-bearing and foot stability.Dendrolagus plus Hypsiprymnodon moschatus); Group 2 =  regular hoppers (macropodines [including Lagostrophus] with the exception of the genera Dendrolagus and Macropus); Group 3 =  specialized hoppers (the species of Macropus). The extinct taxa were added as unknowns. The analysis yielded two functions that together allow a 93.2% of correct assignments using the leave-one-out method of cross-validation, which suggests that both discriminant functions combined a set of skeletal traits that accurately distinguishes among the three groups compared. The value of the Wilks' lambda statistic for the both functions is significant . The morphospace depicted from the scores of the specimens on both functions is visually displayed in Three groups were defined: Group 1  =  non-hopping or occasionally hopping taxa , one relating to the width of the calcaneal tuber, and one relating to the width of the cubonavicular facet at the base of the calcaneum, where the calcaneum contacts the cubonavicular bone.Macropus) have more positive scores, and most of the Pleistocene sthenurines also have highly positive scores. However, this function is one of the few that distinguishes between the tree-kangaroos and the sthenurines. Tree-kangaroos have strong negative scores on this function, probably as the result of their merging of the ventromedian facet with the dorsolateral facet, which may allow for greater intratarsal motion Dendrolagus spp. from the other macropodoids. The dorsoventral width of the CLAJ also has high negative values on function one, reflecting a relatively narrow articulation between astragalus and calcaneum, again a feature of the smaller macropodines and Dendrolagus spp.For the first function the positive values largely reflect the dorso-plantar width of the cubonavicular facets . This function appears to reflect body size, in part, as among the extant kangaroos the larger forms , while most of the other extant macropodoids have negative (or at least less positive) scores. A narrow CLAJ may reflect a tarsal morphology that is better adapted for a restricted range of motion of the leg about the foot in the parasaggital plane, at least in the smaller taxa. The widths of the calcaneal tuber and the cubonavicular facet have negative loadings on the second function, reflecting the low scores of the larger sthenurines. The smaller and/or more gracile Miocene sthenurines, Rhizosthenurus and Hadronomas, tend to cluster with the extant kangaroos on both functions.The variable with the highest positive loadings on the second function is the mediolateral width across the CLAJ: the tree-kangaroos have high positive scores on this function, and this may reflect an ankle joint that has some mediolateral mobility, as employed in climbing. The dorsoventral width of the CLAJ also has high positive values on this function: the larger species of Protemnodon, and especially the extinct Macropus ferragus, have relatively low values on function one, but high values on function two. This may represent independent evolution of large size and mode of weight bearing over the foot: while the sthenurines enlarge the ventromedian cubonavicular facet, other large kangaroos have a larger overall size of the CLAJ.An interesting observation is that, while function one seems to represent a size axis in part, with the large sthenurines having the highest scores, other “giant” kangaroos do not cluster in this morphospace: rather, the large species of Dendrolagus spp. and the less specialized terrestrial macropodines. The Miocene sthenurine Hadronomas puckridgi clustered with the larger species of Macropus, while the smaller Miocene sthenurine Rhizosthenurus flanneryi occupied a fairly middling position in the morphospace. The CVA was the only multivariate analysis to separate the sthenurines from the tree-kangaroos. Here the Pleistocene sthenurines occupied more or less their own area of the morphospace along the first function: the distribution of other large-bodied taxa showed that this was not simply an effect of their large size.The results of the PCA were similar to that of the other PCAs: the Pleistocene sthenurines were distributed along the second component in a similar fashion to Sthenurus stirlingi, Simosthenurus occidentalis, and Procoptodon sp.) invariably occupy a different portion of the morphospace to the macropodines ; and while the smaller “Procoptodon” gilli is usually distinct from the macropodines in the bivariate analyses . However, both Procoptodon and Simosthenurus are more specialized in their skull and dentition than SthenurusRhizosthenurus flanneryi, represented here only by the pes, is not distinguished from similar-sized macropodines. The larger, grey kangaroo-sized Miocene sthenurine Hadronomus puckridgi, represented here by all elements except the pelvis, sometimes clusters with the macropodines  in many of the analyses shows that they generally cluster with the extant macropodoids, supporting the hypothesis that it is the sthenurine anatomy that is distinctive from the general macropodoid bauplan (rather than representing the primtivie condition). The inclusion of the species of Protemnodon is interesting: the smaller (P. snewini) or more gracile (P. anak) forms often cluster with the similarly sized macropodines, especially on the bivariate plots. However, larger species tend to cluster with the sthenurines , these results may indicate that the larger species, at least, were not hopping , but did not have a similar type of locomotion to the sthenurines.The inclusion of other extinct taxa  also behave in an interesting fashion in the analyses. In terms of the tibia diameter, at least, they are as “robust” as the other large extinct kangaroos  anatomy of sthenurines that indicates they would have had difficulty with Macropus-like rapid hopping; (ii) anatomy indicative of a habitual more upright posture, with the femur at an angle more parallel to the iliac blade and with less flexed limbs; and (iii) anatomy indicative of bearing weight on one foot at a time, as would be the case with a locomotor gait of bipedal walking. While modifications listed under (ii) could be taken as indicative merely of bipedal browsing with an upright trunk, in combination with (i) and (iii) they also lend support to this posture being employed during locomotion. Important differences in anatomy are presented in We summarize the aspects of sthenurine anatomy that differ from those of large hopping macropodines as follows: The anatomy of the sthenurine lumbar spine is contraindicative to hopping. Hopping in extant kangaroos entails a considerable amount of flexion of the lumbar vertebral column, especially at the point of the anticlinal ( =  diaphragmatic) vertebra reduced the size of their tail. In addition, the tail is important in hopping locomotion: the tail is swung downwards as the hind limbs swing backwards, thus cancelling the inertia of the hind limbs Macropus-like fashion, then their heavier limbs would require an even more sturdy tail to balance out these inertial forces. However, if they were employing bipedal striding, then a large tail would no longer be necessary to cancel out inertial forces, and additionally a large tail could possibly impede such locomotion by dragging on the ground. The relatively shorter and less muscular tail of sthenurines may also reflect its lack of use in pentapedal locomotion.The reduction of the sthenurine tail is also a problematical issue. Macropodine kangaroos can use their tail as a support when standing on their hind legs, both when standing plantigrade in repose, or standing digitigrade to fight Macropus that are specialized for hopping : these features in Macropus include the elongated ilium, the long tibial tuberosity and prominent tibial crest, the elongation of the trochlea of the astragalus, the long calcaneal tuber, the enlarged sulcus on the calcaneum for the peroneus longus muscle, and the elongated proximal phalanx on the fourth medal digit. Note also the hoof-like ungual phalanges in sthenurines, which Kear et al. Sthenurines also lack many of the features of That is, with a fairly upright trunk, the femur in a more vertical position, and the limb joints with more obtuse angles .The morphology of the sthenurine ischium, tipped dorsally and forming a more acute angle to the ilium, repositions the moment arm for the hamstring muscles, important in limb retraction. This ischial anatomy is seen in placentals among primates that locomote with an upright trunk, as it maintains the moment arm of the hamstrings when the femur is rotated posteriorly in this posture The enlarged tuber coxae of the ilium, also echoed to a certain extent in tree-kangaroos see , reflectThe more distal placement on the femur of the adductor scar and the lesser tuberosity would increase the moment arms of the quadratus femoris and iliopsoas, respectively. This might relate to more powerful limb adduction and protraction, but might simply reflect compensation for the altered moment arms of these muscles occurred by a difference in the position of the femur relative to the pelvis with an upright trunk.Macropus reflects an increase in the moment arm for the limb extensors , to balance out the large ground reaction forces occasioned by a crouched posture, which become relatively larger with larger body size. The shorter tuber in sthenurines implies a lesser moment arm for the gastrocnemius, which given their large size would only be biomechanically possible if the moment arm for the ground reaction force was also reduced, as would be occasioned by a more upright posture at the ankle joint. The very broad area on the calcaneum for the attachment of the Achilles tendon in sthenurines may indicate an insertion that is fleshy rather than tendinious; if this were the case, this would definitely be in contradiction to a hopping mode of locomotion.The shorter calcaneal tuber in sthenurines might also reflect a change in posture at the ankle joint. In considering forces acting over any joint, the moment arm produced by the limb extensors must balance the ground reaction force. Crouched limb postures result in a long lever arm for the ground reaction force, and the postural changes in larger animals reduce this lever arm, increasing the limb's effective mechanical advantage Macropus are unusually gracile, so that sthenurines appear to be “robust” only in comparison with these highly specialized hoppers. Many morphological features of sthenurine hind limbs actually parallel those seen in humans that distinguish them from other apes. In the human condition this obviously relates to walking bipedally rather than quadrupedally, rather than a transition from hopping, but the same principles apply.Part of the greater “robustness” of the hind limbs of sthenurines could be explained by each limb having to bear the full weight of the animal at some point in the locomotor cycle, something not experienced by hoppers: as noted earlier, the real issue here may be that large species of The short and broad sacrum of sthenurines could be interpreted as resisting greater rotational forces, as occasioned by walking with alternate limbs . Humans have a broader sacrum than other apes, which is interpreted as relating to weight support and transmission during locomotion with a habitual bipedal posture The enlarged femoral head and distal condyles in sthenurines are reminiscent of the differences between the human and ape conditions Aspects of the sthenurine ankle joint have been interpreted as rotating the feet inwards for a more medial position, and/or for bearing more weight on the medial side of the foot: these include the rotation of the tibioastragalar joint in an anteriomedial direction; the longer groove in the proximal tibia for the insertion of the fibula, allowing for a greater internal rotation of the lower limb about the knee; the lateral displacement of the fibular facet as enabling greater ability to pronate the foot; a sustentaculum tali that is narrow in the mediolateral direction ; and the plantar crest of the calcaneum being more elongated on the medial side see . Humans Hadronomas). An analogous morphology is also seen in cursorial placental mammals such as canids and horses, and is also present in the thylacine . In conjunction with this, the trochlear groove on the astragalus is deeper in sthenurines, with a raised medial trochlear ridge. There is also evidence of an increase in the size in the ligaments that bind the astragalus to the calcaneum Another suite of features of the sthenurine ankle joint include ones relating to a greater stabilization of the tibia on the astragalus, and ones resisting movement of the astragalus on the calcaneum. Such features could indicate a need to resist greater rotational forces incurred by bearing weight on one leg at a time. Sthenurines are unique among macropodoids in having a plantar process on the distal tibia that fits in a tongue-in-groove linkage into the astragalar trochlea , thus rending the animal functionally monodactyl, this does not explain why the digit would become vestigial. An explanation is proposed here based on developmental trajectories. Pigs (Sus scrofa), like other artiodactyls, have digits three and four as the primary ones on both fore and hind feet, with the reduction of digits one, two and five. Developmental studies show that this has occurred through evolutionary modifications in the patterning of their limbs: developing limb buds of pigs are different from those of a mouse, with a reduction of the condensations of cartilages that form the lateral digits None of the scenarios of locomotor evolution in sthenurines account for the issue of the loss of the fifth pedal digit  prehallux in the foot. They Hadronomas was already functionally monodactyl, then there might have been no active selection pressure against such an anatomical change.The sthenurine hand shows an elongation of the second, third, and fourth digit, accompanied by the reduction of digits one and five, while the digits of the hands of other macropodoids are of more equal length The following is a scenario for the evolution of bipedal walking in sthenurines. The key to understanding sthenurine evolution is to realize that the forelimb and hind limb anatomy are linked in a way that channels their locomotor mode. Sthenurines inherited their “hopping anatomy”, with a long tibia and digitigrade foot posture while moving, from their macropodid ancestry; thus any change in locomotion from bipedal hopping would be within the constraints of this anatomy as a starting point. One of the characteristic features of at least the Pleistocene sthenurines is a forelimb that has been specialized for browsing, with the concomitant anatomy that would restrict them from putting the hand on the ground in a palmar stance, or from supporting their body weight on their forelimbs Rhizosthenurus flanneryi was fairly large for a macropodid by today's standards (probably around 12–15 kg). While it retained the fifth toe, it also had some modifications of the ankle joint indicative of shifting its body weight to the medial side of the foot, a morphology that can be interpreted as weight-bearing on one leg at a time. Rhizosthenurus had a few modifications of its forelimbs indicative of the type of specialized behavior proposed for later sthenurines, such as enlarged epicondylar areas on the humerus for digital flexors Hadronomas (estimated body mass of 30 kg) also retained the fifth digit, but had other hind limb features resembling those of later sthenurines Hadronomas sometimes clusters with the macropodines in our analyses, and sometimes with the Pleistocene sthenurines, perhaps indicating an intermediate functional morphology. Although the hand of this animal is unknown, it had features of the scapula resembling those of later sthenurines, including a reduced supraspinous fossa and an enlarged coracoid process, which have been functionally implicated in Pleistocene sthenurines for reaching with the forearms The middle to early late Miocene sthenurine Thus, the Miocene sthenurines, although still relatively small, showed postcranial modifications indicative of specialized browsing using their hands, and weight-bearing on one foot at a time. We propose that these animals, while likely still hopping for their faster locomotor gait, were starting to use some bipedal walking for locomoting at slow speeds: their capacity for slow pentapedal locomotion would be compromised by the more specialized forelimbs, and hopping at very slow speeds appears to be biomechanically impossible. Remember that bipedal walking has been observed in tree-kangaroos, so is certainly not an impossible gait for a macropodid. Additionally, sthenurines have been proposed to have been feeding with an upright trunk, and reaching up over their heads into tall vegetation. With this feeding posture, resorting to pentapedal motion to move to the next bush would mean frequent postural changes and energy expenditure. During their early evolutionary history sthenurines may have been performing some bipedal shuffling in order to move short distances, even if they retained hopping as their regular faster gait. Adaptations for bipedal posture for feeding would also preadapt them for maintaining this posture while moving and balancing their weight over a single limb .Rhizosthenurus and Hadronomas is unknown, but at some point sthenurines would have started to stabilize the lumbar region of their spine (as described by Wells and Tedford Sthenurus stirlingi), in order to support their trunk and stabilize their front end while foraging with an upright trunk. The lumbar vertebrae with greatly enlarged metapophyses and reduced transverse processes indicate an increase in size of the multifidous musculature and, concurrently, a decrease in size of the longissimus dorsi. However, this anatomy would pose a further conflict with locomotion, both pentapedal walking and bipedal hopping. With a stiff, shorter lumbar region they would no longer be able to arch the back to perform pentapedal locomotion (even if they could support their weight on their hands), and with the stiff lumbar spine and reduced longissimus musculature they would be unable to dorsiflex in the region of the anticlinal vertebra, as seen in modern kangaroo hopping locomotion.The spinal anatomy of Macropus species Procoptodon) abandoned hopping altogether is unknown, and would require more data to attempt to determine.The majority of the Pleistocene sthenurines were no larger than modern large Hadronomas was already functionally monodactyl, and we propose here a possible developmental reason for the reduction of this digit to vestigial remnant. One puzzling aspect of sthenurine anatomy, in the context of this hypothesis of bipedal walking, is that the knees that face outwards rather than inwards. Humans differ from apes in their more knock-kneed  stance, which relates to their placing of the foot in the midline during locomotion, which aids with balance over the hips in bipedal walking A likely reason that hopping locomotion has not been questioned for sthenurines is their generally kangaroo-like hind limb, with features such as a long tibia that are characteristic of hopping mammals. But, remember that this is the anatomy that they inherited from their macropodid ancestry. And, if sthenurines were indeed engaging in bipedal walking, then the long tibiae would give them a long length of stride, which would be energetically efficient. The loss of the fifth digit is perhaps counterintuitive for an animal that might require more foot support over a single leg, but Murray In conclusion, although a fossilized trackway would be the only means of completely verifying our hypothesis of sthenurines using a bipedal striding gait, their anatomy is clearly different from that of large macropodines. Sthenurines lack the specialized features for fast hopping seen in macropodines and the differences in anatomy from the extant forms can be functionally related to locomotion bearing weight on one leg at a time.Figure S1Ilium length versus other aspects of ilial morphology. (A) Ilium length versus width of the tuber coxa. (B) Ilium length versus the dorsal length of the ischium. (C) Ilium length versus the ventral length of the puboischiatic symphysis. (D) Ilium length versus the length of the epipubic bone.(TIF)Click here for additional data file.Figure S2Femur length versus other aspects of femoral morphology. (A) Femur length versus the anterior-posterior width of the femoral head. (B) Femur length versus the distance of femoral head to the base of the lesser trochanter. (C) Femur length versus the length of the femur from the proximal end to the base of the adductor scar. (D) Femur length versus the width of the femur across the distal condyles.(TIF)Click here for additional data file.Figure S3Other morphological variables from the tibia and pes. (A) Tibia average midshaft diameter versus the anterior-posterior length of the tibia tuberosity. (B) Width  of the base of the astragalus versus the width (dorso-plantar) of the fibular facet on the lateral trochlear ridge of the astragalus. (C) Width of the base of the astragalus versus the length of the calcaneal tuber. (D) Length of the femur versus the length of the fourth metatarsal.(TIF)Click here for additional data file.Figure S4Scaling of long bone length versus diameter (shown in ) with labeled taxa. (A) Femur length versus average femur cross-sectional diameter. (B) Tibia length versus average tibial midshaft cross sectional diameter.(TIF)Click here for additional data file.Figure S5Additional discriminant analyses. (A) Using all of the hind limb bones, for all of the taxa. (B) Without the pelvis, for all of the taxa.(TIF)Click here for additional data file.Table S1Taxonomy of the Superfamily Macropodoidea.(DOC)Click here for additional data file.Table S2Measurements taken.(DOC)Click here for additional data file.Table S3Specimens measured for analyses.(DOC)Click here for additional data file.Table S4Specimens measured for calcaneum only analyses.(DOC)Click here for additional data file.Table S5Data for all of the bones.(PDF)Click here for additional data file.Table S6Additional data on the calcaneum.(PDF)Click here for additional data file.Text S1Description of bivariate plots.(DOC)Click here for additional data file.Text S2Additional discriminant analyses, using all of the taxa. Table A, Coefficient loadings for additional Discriminant Analysis for all of the taxa: all hind limb bones. Table B, Coefficient loadings for additional Discriminant Analysis for all taxa: without the pelvis.(DOC)Click here for additional data file.


Pipeline inspection gauges (pigs) have been used for many years to perform various maintenance operations in oil and gas pipelines. Different pipeline parameters can be inspected during the pig journey. Although pigs use many sensors to detect the required pipeline parameters, matching these data with the corresponding pipeline location is considered a very important parameter. High-end, tactical-grade inertial measurement units (IMUs) are used in pigging applications to locate the detected problems of pipeline using other sensors, and to reconstruct the trajectories of the pig. These IMUs are accurate; however, their high cost and large sizes limit their use in small diameter pipelines (8″ or less). This paper describes a new methodology for the use of MEMS-based IMUs using an extended Kalman filter (EKF) and the pipeline junctions to increase the position parameters’ accuracy and to reduce the total RMS errors even during the unavailability of above ground markers (AGMs). The results of this new proposed method using a micro-electro-mechanical systems (MEMS)-based IMU revealed that the position RMS errors were reduced by approximately 85% compared to the standard EKF solution. Therefore, this approach will enable the mapping of small diameter pipelines, which was not possible before. Advances in micro-electromechanical-systems (MEMS) technology combined with the miniaturization of electronics, have made it possible to produce low cost and lightweight chip-based inertial sensors. These chips are small, lightweight, reliable and they consume very little power. They have therefore found a wide spectrum of applications in the automotive sector and other industrial applications. MEMS technology, therefore, can be used to develop navigation systems that are inexpensive, small, and consume low (microwatt) power. The attractive advantages of MEMS technology have led to remarkable research progress in the field of MEMS inertial sensors. However, on the negative side, the performance currently achieved by these low cost sensors is relatively poor due to their sensor errors. The goal of this paper is henceforth to introduce new constraints for pipeline navigation to increase the position parameters’ accuracy and reduce the total RMS.Pipelines are the lifelines of a dynamic country’s infrastructure; they provide fuel, water, and all kinds of other needs that touch millions of lives. In addition, they represent one of the safest transportation methods available for crude oil, natural gas, and chemical fluids; they provide a transport medium with speed, efficiency and reliability. Furthermore, they are considered an eco-friendly option. So-called smart pipeline inspection gauges pigs,  commonlyPigs are devices/tools that can be inserted into the pipeline and travel throughout the length of the pipeline, driven forward by the differential pressure across the tool ,2. Pigs i.e., bias, scale factor and non-orthogonality). Therefore, the errors in position, velocity and attitude of the motion pig grow rapidly in standalone mode. Therefore, aiding navigation systems become essential to solve the unpredictable problems of sensor errors and noises [This work addresses the issue of providing a MEMS-based aided inertial navigation system to replace the current high-end tactical grade IMUs. MEMS-based inertial sensors are characterized by large uncertainties and high noise . The process requires that extra navigation sensors be used to improve the performance of the pig’s location estimation methods. A wheel odometer, for instance, can measure traveled distances (by counting the number of wheel revolutions) that are translated later into velocity measurements. These measurements can be used as external updates for the navigation algorithms. An above ground marker (AGM) is another device that can be installed on the surface of the ground above the pipeline. This device detects and records the passage of the pig in the pipeline. AGMs provide the navigation coordinates of their position  along with the pig’s time passage. This information is used as a coordinate update  in the estimation algorithm. The cost of these devices often minimizes their use. Usually, these AGMs are installed every 1–3 km  when theA nonlinear sensor fusion algorithm has been applied in  to estimSimilarly, in , an IMU To allow proper maintenance operations and to reconstruct the pipeline trajectory in certain projects, a position referencing technique is required to find the exact coordinates of the defective parts detected by the pig’s sensors. The core of this work, therefore, is to improve the accuracy of the final reconstructed trajectories by introducing new sources of information and adding new constraints to the estimation technique.Generally, the pig carries inertial sensors (accelerometers and gyroscopes), along with other sensors, to assess its position coordinates. To minimize possible cumulative errors arising from the MEMS-IMU, the sensor fusion technique, which involves pairing inertial sensors with non-inertial sensors, is implemented. An odometer and AGM, employed as non-inertial sensors, are used to update the algorithm.Different estimation techniques can be used in such applications. The Extended Kalman Filter (EKF) ,9 is cometc.). The pipeline pieces are fabricated in straight-line shapes. Different methods can be used to connect these pipeline pieces with each other, such as push on, flanges, and welding techniques, as shown in Pipelines consist of multiple pieces of pipeline and fittings  and electromagnetic acoustic transducers for pipeline analysis purposes. However, due to sudden vibrations of the pig while passing through pipeline junctions, INS sensors are sensitive enough to capture these junctions. Sample accelerometer pipeline data outputs for a MEMS-based IMU (SiIMU02) and a high-end tactical grade IMU (LN200) are illustrated in To detect the spikes in the signal, different methods have been used in the signal processing literature. In this paper, a discrete wavelet transformation (DWT) has been used to detect these spikes due to its simple implementation. The definition of wavelet transform can be written as:Here The Mexican Hat mother wavelet has been applied to detect the signal patterns (pipeline junctions) as shown in Since these patterns represent the pipeline junctions, a constraint is introduced here and called Pipeline Junction Constraint (PJC). This constraint fixes both the heading and pitch angles during the movement inside the pipeline piece (not during the junctions) . New meai.e., bends), this assumption cannot be considered true all the time. Therefore, the PJC model will be supported by a bend detection algorithm (BDA) to detect the bends and disable the PJC model during the bend periods. BDA is introduced in the next section.Until now, we assumed that the period between two junctions represents a straight pipe. However, due to the fittings , the change in heading and/or pitch angles of the pig in motion should not exceed a certain threshold Here To cater for all three-dimensional dynamics of the pig motion, a total of six sensors are used in a full IMU, which comprises three gyroscopes and three accelerometers. In addition to the IMU, the odometer is used to measure the displaced travel distance of the pig. AGMs and their measurement model will be shown in this section, although the target is to use the fewest number of AGMs as possible.Position error Velocity error Attitude error Gyroscope bias error Accelerometer bias error A MEMS-based IMU was the main sensor used to collect the pig’s motion data. EKF was used as an estimation technique to overcome the poor performance and non-linearity of the dynamic system in this work. Both dynamic and measurement models developed in this section to estimate the states of the system. The state vector to be estimated was designed to include the errors associated with the position, velocity, attitude, and the stochastic bias errors associated with the gyroscopes and accelerometers. The state vector was defined as follows :(4)δx=[The dynamic model is non-linear and can be represented in discrete form as follows ,18:(5)xis the is the is the is the unit-variance white Gaussian noise.The linearized error state system model can be expressed as:Reciprocal of the correlation time of the processVariance of the white noise associated with the random processMeridian radius of curvature (North-South)Prime vertical radius of curvature of the Earth’s surface (East-West)Latitude, longitude and height, respectivelySpecific forces in east, north and up directions, respectively.Rotation matrix Rate change of time.By applying Taylor series expansion and ignoring the higher order terms, the linearized system model in the local level frame (LLF), represented as north, east, and down (NED), can be expressed as follows:The linearized measurement error model can be expressed as:Here refer to  for moreThe rotation matrix (direct cosine matrix—DCM) is updated at every epoch. The attitude angles  can be calculated using this matrix. Heading and pitch angles of the pig in the pipeline are computed from the elements of the following (DCM) :(19)R^vLet From Equation (19), the required From Equation (21), heading and pitch can be calculated as follows:Similarly, the estimated heading and pitch angles can be calculated from Equation (19) as follows:Ideally as per the algorithm assumption, the heading and pitch angles do not change in the pipeline piece; the change in these angles should be zero. Therefore, the approximated changes of heading and pitch angles model can be expressed as follows:The measurement design matrix can be expressed as follows:The design matrix elements are expanded in the This section introduces the equipment used and describes the pipeline inspection test performed to assess the efficacy of the PLJ algorithm. The results of the proposed method—Pipeline junctions integration—Will be discussed in detail and compared with the results of the traditional method of the EKF-based odometer/AGM integration for pipeline navigation. In figures and tables, EKF/PLJ will be referred to as the new developed method, while EKF will be referred to as the normal EKF method. Please note that odometer and AGM (if available) are used in both methods. The developed method was examined through real pipeline inspection trajectories, using as few AGMs as possible.The pig’s data and the reference trajectory have been provided by M/s ROSEN. A SiIMU02  MEMS-based inertial sensor was used for the experiment. SiIMU02 is a six degree of freedom inertial system that uses solid-state devices to measure the angular rate and linear acceleration. One point worth noting is that the pig operator did not provide the AGMs’ positions, however, they provided the full reference trajectory. As a result, an artificial AGMs were extracted from the true reference trajectory. The total pig journey distance is almost 3 km over a total travel time of 1 h.•Scenario #1: Processed IMU & odometer data using one AGM  to the navigation algorithm. Scenario #2 is similar to scenario #1, without adding any AGM. Directly from the output trajectory, the difference between both solutions is clear, as shown in The bar graphs in EKF/Odometer integration for pipeline navigation, using the developed method of EKF/PLJ, had a maximum position error of 11.59 m in the north direction, and EKF/odometer solution only had a maximum position error of 76.41 m in the same direction. This is an overall average improvement of 85%. Despite all the improvements in the horizontal plane (north and east directions), the above bar graphs reveal that height errors have slight increase using the new EKF/PLJ method. This increase does not affect the total solution for the pipeline trajectory, especially, if we consider that the pipeline is usually located 1–5 m below the Earth surface. Finally, the results can be summarized as shown in i.e., straight shapes), and how they connect to each other, pipeline junctions have been modeled and included as new measurements to update the navigation estimation algorithm. The new developed algorithm will also lead to a reduction in the total required number of AGMs. Two different testing scenarios were discussed based on real pipeline data that was collected using a MEMS-IMU-based system. These results show that the newly proposed method is capable of reducing the trajectory navigation RMS error by around 80% over one hour of operation and without using any AGM along the pig journey.The main objective of this work was to increase the accuracy of pipeline navigation. Based on the reality of constructing the pipelines (


Covariate adjustment methods are frequently used when baseline covariate information is available for randomized controlled trials. Using a simulation study, we compared the analysis of covariance (ANCOVA) with three nonparametric covariate adjustment methods with respect to point and interval estimation for the difference between means. The three alternative methods were based on important members of the generalized empirical likelihood (GEL) family, specifically on the empirical likelihood (EL) method, the exponential tilting (ET) method, and the continuous updated estimator (CUE) method. Two criteria were considered for the comparison of the four statistical methods: the root mean squared error and the empirical coverage of the nominal 95% confidence intervals for the difference between means. Based on the results of the simulation study, for sensitivity analysis purposes, we recommend the use of ANCOVA (with robust standard errors when heteroscedasticity is present) together with the CUE-based covariate adjustment method. When baseline covariate information is available for randomized controlled trials in the areas of environmental research and public health, statistical methods that perform covariate adjustment are usually employed. There are two main reasons to use covariate adjustment methods for the statistical analysis of randomized experiments: one is variance reduction for the estimators for the parameters of interest, which will lead to narrower confidence intervals and more powerful statistical tests; the other is to achieve the equivalence of the treatment groups that is expected as a consequence of randomization . We noteet al. (2000) 11]. Becaρ is set to 0.5 for all these five cases.For the second part of the simulation study, we consider scenarios involving unbalanced treatment groups, heteroscedasticity, and/or interactions between covariates and treatment group. For each distribution, we consider five different combinations of the parameters i.e., homoscedasticity, no covariate by treatment interaction) is affected.Specifically, Case 1 involves unequal group sizes, heteroscedasticity and interaction  and i.e., the intervention group or group 2), where For the third part of the simulation study, we have used descriptive statistics  from the real data, to consider scenarios where the mean difference is not null, to allow us to compare the statistical power of the four different methods. We have expressed the mean difference in standard deviation units. The setup of the simulations was as follows: i.e., either no covariate information is available, or the covariates are not used for adjustment although they are available). Overall, ANOVA and CUE perform equally well with respect to empirical coverage, and better than the EL and ET methods. The estimated RMSE for the EL method is smaller for the t-distribution and the lognormal distribution cases but that is associated with empirical coverage much below the nominal level.ρ.The results from i.e., the mean difference between the control group and the intervention group with respect to the natural log transformed blood lead concentration at the follow-up, adjusted for the natural log transformed blood lead concentration at the baseline. Given the very small estimates for Δ, we have provided all the results with five decimal places. Although, in the original study [i.e., the mean of the natural log transformed blood lead concentration at the follow-up for the intervention group, and for i.e., the common mean of the natural log transformed blood lead concentration at the baseline. The table also illustrates the difference between the types of results provided by ANCOVA versus the GEL-based methods: the GEL methods provide an estimate for the common covariate mean  performed equally well and better than the covariate adjustment methods based on EL and ET. In terms of computational complexity, however, ANCOVA is clearly the simpler method since it relies on the least squares estimation method. Among the GEL methods considered here, EL is the least computationally stable, especially when the distribution of the variables has heavy tails. For example, for our scenarios involving the t-distribution, 20 to 30 simulations out of the total of 10,000 simulations per scenario involved lack of convergence. We should note that the results for the EL method may be improved by using the Bartlett correction or bootstrap calibration . We haveBased on the results of our simulation study, for sensitivity analysis purposes, we recommend the use of ANCOVA (with robust standard errors when heteroscedasticity is present) together with the CUE-based covariate adjustment method. This recommendation is based on the similar overall good performance in our simulation study of these two different statistical methods. If the results of the ANCOVA and the CUE-based covariate adjustment method imply similar conclusions, then the robustness of these conclusions is supported. If the results of these two different methods imply qualitatively different conclusions, then the conclusion implied by the CUE-based covariate adjustment method may be preferred given that this method only assumes that the treatment has been randomly assigned.