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An ontogenetic perspective on locomotion in the Late Cretaceous dinosaur Maiasaura peeblesorum (Ornithischia: Hadrosauridae)

David W. Dilkes 0

Abstract: Ontogenetic growth in the forelimb and hindlimb of the dinosaur Maiasaura peeblesorum (Ornithischia: Hadrosauridae) from the Upper Cretaceous (Campanian–Maastrichtian) Two Medicine Formation of Montana is investigated by multivariate and bivariate morphometrics and the biomechanics of beam theory. Results support a hypothesis of an age-dependent selection of stance. Juveniles walked primarily as bipeds. As an individual matured, its predominant stance shifted to quadrupedality. Within the forelimb, morphometric results show a probable allometric enlargement of postural muscles, an allometric increase in the lever arms of protractor muscles, and an increased robustness of the humerus to enhance its resistance to bending stresses. In contrast, the hindlimb is characterized by a relative decrease in the resistance of the femur and tibia to bending stresses. In addition, there is an allometric enlargement of the femoral fourth trochanter and positive allometry of the lengths of metatarsals III and IV. The most likely explanation for the different growth patterns is that the hindlimb was sufficiently robust at a young age to accommodate increased postural and locomotory stresses through largely isometric growth, whereas a behavioral shift to quadrupedality in older individuals necessitated an allometric response in the forelimb. Osteological adaptations for weight-bearing in the manus include metacarpals that are united firmly with a resultant cross-sectional shape that is resistant to bending and hyperextendable joints between the metacarpals and first phalanges. It is probable that flexor muscles that attached to the caudal surface of the metacarpals reinforced the reduced carpus and lessened the likelihood of collapse during quadrupedality. Résumé : La croissance ontogénétique des membres antérieurs et des membres postérieurs du dinosaure Maiasaura peeblesorum (Ornithischia: Hadrosauridae) de la Formation de Two Medicine du Montana, du Crétacé supérieur (CampanienBMaastrichtien), est examinée en utilisant la morphométrie multivariée et à deux variables ainsi que la biomécanique de la théorie de la poutre. Les résultats appuient l’hypothèse d’un choix de posture reliée à l’âge. Les jeunes immatures avaient surtout avec une démarche bipède. À mesure que l’individu vieillissait, sa posture prédominante allait vers une démarche à quatre pattes. Pour le membre antérieur, les résultats morphométriques montrent un agrandissement allométrique probable des muscles de posture, une augmentation allométrique dans les bras de levier ou dans les muscles d’élongation et une augmentation de la robustesse de l’humérus pour accroître sa résistance aux contraintes de flexion. Par contre, le membre postérieur est caractérisé par une réduction de la résistance du fémur et du tibia aux contraintes de flexion. De plus, on voit un agrandissement allométrique du quatrième trochanter fémoral et une allométrie positive de la longueur des 3e et 4e métatarses. L’explication la plus plausible pour les patrons de croissance divergents est que le membre postérieur était assez robuste à un jeune âge pour permettre une augmentation des contraintes de posture et de locomotion par une croissance surtout isométrique, alors qu’un changement de comportement vers une démarche à quatre pattes chez les individus plus âgés exigeait une réponse allométrique du membre antérieur. Des adaptations ostéologiques pour la portance comprennent, dans la paume, des métacarpes qui sont fermement reliés pour donner une forme transversale résistant à la flexion et des articulations capables d’hyperextension entre les métacarpes et les premières phalanges. Il est probable que les muscles fléchisseurs qui se rattachaient à la surface caudale renforçaient le carpus réduit et amoindrissaient le risque d’affaissement lors de la démarche à quatre pattes. [Traduit par la Rédaction]

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Received July 7, 2000. Accepted January 22, 2001. Published on the NRC Research Press Web site at http://cjes.nrc.ca on August 20, 2001.

Paper handled by Associate Editor B. Chatterton. 25

D.W. Dilkes. Biology Department, Erindale College, The University of Toronto at Mississauga, 3359 Mississauga Road, Mississauga, ON L5L 1C6, Canada. (e-mail: ddilkes@credit.erin.utoronto.ca). Can. J. Earth Sci. 38: 1205–1227 (2001)

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DOI: 10.1139/cjes-38-8-1205

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Introduction 75

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Few published studies of the relative bipedality or quadrupedality of non-avian dinosaurs have incorporated juveniles. Although numerous fossils of juvenile dinosaurs are known (Carpenter and Alf 1994) and new discoveries are becoming increasingly frequent (e.g., Dal Sasso and Signore 1998), many of these juveniles are incomplete and make up only a very small portion of a growth sequence. As a consequence, many studies of postcranial growth in non-avian dinosaurs are restricted to simple comparisons of the proportions of limbs in the juveniles and adults (Russell 1970; Dodson 1980; Norman 1980) or, if statistical, then deal with obligatory quadrupedal (Lehman 1990) and bipedal (Smith 1998) dinosaurs. Only the study on Iguanodon bernissartensis (Norman 1980) presented evidence of an ontogenetic shift from bipedality to quadrupedality. However, the sample size in this study consisted of only four individuals, and the conclusions were based solely upon limb ratios. A more recent attempt to examine ontogeny and locomotion in the iguanodontian Dryosaurus lettowvorbecki from a biomechanic approach (Heinrich et al. 1993) purportedly revealed an ontogenetic shift from a quadrupedal to a biped stance. The methodology in this paper was a significant improvement upon the comparison of limb ratios. These studies demonstrate clearly that ontogeny provides a new and highly informative view on locomotion in the adult. The inclusion of juveniles in an ontogenetic study of locomotion is particularly relevant for those groups of dinosaurs whose stance is debated currently. Consideration of an ontogenetic dimension may reveal patterns that can explain the morphology of the adult better than comparisons of simple ratios between adults of different species. The relative bipedality or quadrupedality is uncertain for many prosauropods, the hadrosaurids, and basal iguanodontians sensu Weishampel and Heinrich (1992), such as Iguanodon and Dryosaurus. Many prosauropods have been interpreted as facultatively bipedal, defined as quadrupedal stance at slow speeds with a shift to a bipedal stance occurring only when moving quickly. Smaller prosauropods such as Thecodontosaurus may have been bipedal (Galton 1990; Benton et al. 2000), and larger prosauropods such as Riojasaurus were perhaps obligatory quadrupeds (Heerden and Galton 1997). Comparisons of limb ratios and proportions of the trunk and tail between hadrosaurs and quadrupedal dinosaurs and the slenderness of the metacarpals, the reduction of the carpals to only two small bones, and the mittenlike manus of a “mummified” hadrosaur (Osborn 1912) appeared to demonstrate that hadrosaurs were strict bipeds (Galton 1970). Acceptance of hadrosaurs as strict bipeds was crucial for an interpretation of the stance of the iguanodontian Iguanodon. Comparisons of limb proportions and hindlimb to forelimb ratios of hadrosaurs and the ornithopod Tenontosaurus (a probable quadruped) with those of Iguanodon mantelli and the larger I. bernissartensis suggested that I. mantelli was predominantly a biped, whereas I. bernissartensis was probably a quadruped (Norman 1980). Quadrupedality among iguanodontians is supported strongly by the presence of numerous adaptations for weight-bearing in the carpus and manus (Norman 1980) and trackways (Norman 1980; Moratalla et al. 1992, 1994; Pérez-Lorente et

al. 1997). However, this interpretation is challenged by biomechanical arguments that suggest a virtually habitual bipedal stance for I. bernissartensis (Alexander 1985; Christian and Preuschoft 1996). Trackways of large, quadrupedally walking hadrosaurs (Currie et al. 1991) have refuted the conclusion that these dinosaurs were strictly bipedal. Hadrosaurs are interpreted currently as facultatively bipedal. Individuals of different ontogenetic ages are required to test a hypothesis of an age-dependent stance. Furthermore, there should be a combination of biomechanic and morphometric analyses that extend beyond simple ratios of lengths of the forelimb and hindlimb or selected bones of the limbs. Limb ratios are an unsatisfactory method to examine postcranial growth because they reveal little biomechanical information and fail to capture the majority of shape information that may reveal allometric patterns. Mass accumulations with individuals at different growth stages are known for Iguanodon from the locality at Bernissart, Belgium (Norman 1986), hadrosaurids from Montana (Varricchio and Horner 1993), Alberta (Dodson 1971), and Alaska (Nelms 1989), and neoceratopsians such as Chasmosaurus mariscalensis from Texas (Lehman 1990) and several genera from Alberta and Montana (Sampson et al. 1997). The large sample sizes obtained from these bone beds provide data on intraspecific variation needed for an assessment of ontogenetic changes. A particularly impressive growth sequence is known for the hadrosaur Maiasaura peeblesorum from the Upper Cretaceous Two Medicine Formation of Montana (Fig. 1). The age of this formation has been dated recently to between 82.6 and 74.0 million years (Rogers et al. 1993), indicating that it straddles the Campanian– Maastrichtian boundary. Maiasaura first gained scientific notice in 1978 when a nest with egg shell and the disarticulated remains of more than a dozen nestlings were discovered in the Willow Creek Anticline near Choteau, Montana (Horner and Makela 1979). Soon afterwards, seven other nests were discovered on the same horizon as the nest of 1978, one of which contained the remains of additional, younger juveniles approximately 1 m in body length (Horner 1982). Three nesting horizons are currently known for Maiasaura in the Willow Creek Anticline (Horner 1994). Additional discoveries of Maiasaura in the Willow Creek Anticline include a virtually monospecific bone bed known as Camposaur on the eastern flank of the anticline (Fig. 1C). The Camposaur bone bed is one portion of a significantly larger deposit that is estimated at 3 km from east to west and 0.5 km from north to south and is one of the largest monospecific bone beds of dinosaurs in the world. This bone bed is an apparently catastrophic thanatocoenosis of thousands of individuals that span a three-fold size range from 3 m to over 7 m (Varricchio and Horner 1993; Schmitt et al. 1998). Other localities such as the Brandvold Site on the western flank of the Willow Creek Anticline and the Children’s Dig on the eastern flank are part of this larger deposit. Density of bones in the Camposaur bone bed is exceptionally high, yet all are disarticulated and unassociated and the majority are fragmented. When the Camposaur specimens are combined with the nestlings, a growth sequence exists for Maiasaura that occupies conservatively an order of magnitude in size. © 2001 NRC Canada

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Fig. 1. Geographic location of the Camposaur site. (A) Orthographic map showing state of Montana (hatched). (B) Location of the Willow Creek Anticline (hatched rectangle) in the Two Medicine Formation near the town of Choteau. (C) Topographic map of the Willow Creek Anticline corresponding to the rectangle in (B). The topographic map is adapted from the U.S. Geological Survey 7.5 min topographic map Watson Flats.

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This paper tests the hypothesis that there is an ontogenetic shift in stance for the hadrosaur M. peeblesorum by investigating the morphometric and biomechanic aspects of growth of the forelimb and hindlimb from nestling to adult. Morphometrics of external dimensions and cortical bone thickness of limb bones are based upon the bivariate model

of simple allometry (Huxley 1932; Shea 1985) and principal component analysis (PCA; Jolicoeur 1963). The forelimb and hindlimb are modelled as beams to identify any biomechanical changes during growth. Biomechanics of the adult manus are also studied to test the hypothesis that it would not have been capable of supporting even a small ÂŠ 2001 NRC Canada

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Fig. 2. Variables selected from forelimb and hindlimb of Maiasaura peeblesorum for morphometric analysis. (A) Left humerus in caudal and proximal (above) views. (B) Left ulna. (C) Left femur in medial view. (D) Left tibia in caudal view. (E) Left metatarsal II in medial and proximal (above) views. (F) Left metatarsal III in (from left to right and top to bottom) cranial, caudal, proximal, and distal views. (G) Left metatarsal IV in (from left to right and top to bottom) cranial, caudal, proximal, and distal views. Not drawn to scale.

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fraction of the body weight during locomotion, constituting the strongest morphologic evidence against quadrupedality in hadrosaurs.

bone or compaction of the sediments. Any specimens displaying deformations that would clearly compromise measurements were eliminated.

Materials and methods

Methods

Materials Specimens used in this study consist of the nestlings from the 1978 nest (Peabody Museum of Natural History at Yale University, housed formerly at Princeton University, designated by YPM-PU 22400), and excavations from Camposaur (Museum of the Rockies 005, designated by MOR-005). The 1978 nest and Camposaur are situated in Teton County, Montana, in section 30, T24N, R6W. Specimens from the Brandvold Site were too fragmentary to be included in the study. All specimens are housed in the Museum of the Rockies in Bozeman, Montana. Ideally, a thorough study of appendicular ontogeny should include the girdles as well as the limbs. Unfortunately, with few exceptions, available specimens of the girdles of Maiasaura are incomplete, usually distorted, and few in number. Accordingly, statistical analysis of postcranial ontogeny in Maiasaura is restricted to the humerus, ulna, femur, tibia, and metatarsals. Nestlings are combined with material from the bone bed for the humerus, all three metatarsals, femur, and tibia, but excluded for the ulna because available specimens are incomplete. The majority of postcranial elements from the Camposaur locality suffer from varying degrees of taphonomic distortion, often in different planes. External and internal features were examined for any gross distortions caused by permineralization of the

Selection of measurements Measurements used in the morphometric analyses are of two types: (i) distances between homologous, threedimensionally defined landmarks; and (ii) distances between extremal points. Extremal points are the traditional sort used in morphometrics and include such variables as diameters of shafts or openings (e.g., orbits), minimum circumference, maximum width of condyles, and points farthest from other points. Extremal points are kept to a minimum because information on their displacement is limited to the single dimension of the line that connects them, whereas displacements of homologous landmarks can be detected in two or three dimensions (Bookstein 1990). The variables used in the morphometric analyses excluding cortical bone thickness are shown in Fig. 2. Variables 11 for the humerus, 4 for the femur, 5 for the tibia, and 12 for metatarsal III are minimum circumferences of the shafts. For the ulna, variable 1 is the minimum diameter of the shaft, and the outer point on the olecranon for variable 4 is an extremal point. Additional extremal points are variables 2 and 3 for the femur and the point separating variables 2 and 3 for the tibia. All other points are landmarks of category 2 (sharp corners and maxima of curvatures) as defined by Bookstein (1990). As the proximal and distal ends of humeri, femora, tibia, and metatarsals are curved and were subject to biomechanical forces, great-

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Fig. 3. Locations of midpoints of shafts for the measurement of circumference and cortical bone thickness. (A) Left humerus. (B) Left tibia. (C) Left pes. (D) Metatarsal III of left pes. Not drawn to scale.

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est lengths of these elements include landmarks of category 2. Some curvilinear measurements are included and restricted to curved regions of a bone such as the lateral and medial shoulders of the humerus that are usually bent taphonomically. In these instances of taphonomic distortion, the curvature is either reduced or exaggerated, and the curved distance between a pair of landmarks is measured rather than the linear distance. If the bending is severe or if there is evidence of crushing, however, then the dimension could not be measured and the specimen is excluded. The following curvilinear distances are included in the morphometric analyses: variables 2 and 3 of the humerus, variables 2 and 3 of the tibia, variable 5 of metatarsal II, variables 2 and 5 of metatarsal III, and variables 6 and 11 of metatarsal IV. Cortical bone thickness is measured in four directions between extremal points at the same location on the shaft as the minimum circumference (Fig. 3). It was not possible to include cortical bone thicknesses of the ulna and femur in the morphometric analyses because it is too difficult to determine the boundary between the cortical bone and trabecular bone in the majority of specimens. Several dimensions are associated with a muscular scar or process and require further explanation. Variables 7, 8, 9,

and 10 of the humerus connect to a prominent and highly localized scar that was the likely insertion of M. latissimus dorsi (Dilkes 2000). Variable 3 of the femur is the size of the scar along the fourth trochanter, which was the probable insertion for M. caudifemoralis. The edges of this scar are clearly demarcated in all femora regardless of ontogenetic age. Midshaft of metatarsal III (Fig. 3) was chosen distal to the muscle scar of M. tibialis anterior (Dilkes 2000) for variable 12 and the measurement of cortical bone thickness. Technique for measurement The three-dimensional coordinates of landmark and extremal points on the majority of the bones were archived remotely by stereophotography for later retrieval. These stereophotographs were analyzed by the photogrammetry program GeoInter 3.2 (Rensberger 1988) to retrieve the X, Y, and Z coordinates of the landmark and extremal points. To judge the accuracy of the results, a complex control field with known X, Y, and Z coordinates was constructed around each bone when photographed. The base of this control field consisted of three pieces of 1.7 cm thick plywood (Fig. 4). Hinges connected the outer pair of boards to the middle piece so that they could be folded onto this middle piece for ÂŠ 2001 NRC Canada

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Fig. 4. Schematic drawing of board used for stereophotography. 75

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transportation. Holes were drilled in the boards at specific intervals. Aluminum pins 5, 8, 10, and 15 cm high were manufactured to fit into these holes. The X, Y, and Z coordinates of the tops of the pins provided the control field around the fossil. Stereophotographs were taken with a 35 mm Nikon FG camera equipped with a 50 mm lens and mounted on a tripod. Kodak Technical Pan (ASA 25) and TMax (ASA 100) black and white films were used. Landmarks, extremal points, helping points along curved surfaces, and the top of each aluminum pin were marked on black and white stereophotographs and their x and y coordinates digitized with a Summagraphics Pad. Helping points are nonhomologous point selected to describe a curved surface and were not included in any morphometric analysis. After calculation of X, Y, and Z coordinates of the landmarks, extremal points, and helping points, distances were calculated between selected pairs of points by Euclidean geometry. Lengths along curved surfaces were approximated by adding distances between helping points. Errors of calculated distances based upon three-dimensional coordinates of landmarks varied between 1 and 3% of the same distances measured with dial calipers. This margin of error is deemed to be within an acceptable range of repeatability errors. In view of the limited number of dimensions that could be measured on the femora, it was decided to use a set of large dial calipers to take all linear measurements for this bone. Minimal circumferences of the humerus, femur, tibia, and

metatarsal III were determined by measuring with a set of small dial calipers a thin nylon string wrapped around the shaft. Cortical bone thickness was also measured with dial calipers. Morphometrics Given the disarticulated nature of the nestlings and individuals from the Camposaur bone bed, it was not possible to identify any ontogenetic changes to the relative proportions of the skeleton. Accordingly, limb ratios cannot be calculated for Maiasaura. Data were transformed logarithmically to equalize variances of differently sized variables, render the data independent of scale, and linearize allometric relationships (Bookstein et al. 1985). Bivariate expressions of allometric growth were generated for the femur and tibia of Maiasaura because these bones tend to have greater damage and offer the fewest landmarks. Circumference of the humerus was analyzed bivariately because the sample size was considerably larger than that for the multivariate data set. Accurate measurements of the circumference of metatarsal III could be made for only a small subset of available specimens, so this dimension was also studied bivariately. Each variable to be analyzed bivariately, with the exception of the circumference of metatarsal III, was regressed against the maximum length of its respective bone. Circumference and cortical bone thicknesses of metatarsal III were regressed against the scores on the first principal component of a PCA because greatest length is not isometric (see Results). Growth lines for all bivariate data were calculated by reduced major axis regression, a method preferred (e.g., Rayner 1985; McCardle 1988) for reasons such as scale invariance, robustness in situations where data are not bivariately normal, and less bias when error variances are unknown. Isometry (size change without accompanying shape change) is interpreted when the regression coefficient (represented by k in the bivariate formula y = bxk) is 1.00. Isometry, in the sense employed in this paper, refers to those instances where the organ and body have the same rates of growth. Positive and negative allometry (shape change accompanying size change) exists if k > 1.00 and k < 1.00, respectively. Significance of the calculated k values was determined by t test. As multiple t tests were conducted for individual bones, the sequential Bonferroni procedure was applied to reduce possible type I errors (Rice 1989). The results were accepted as significant at the a/c level, where a is alpha (0.05) and c is the total number of comparisons. PCA (Jolicoeur 1963) was selected for multivariate analysis of the humerus, ulna, and three metatarsals. In the multivariate generalization of the bivariate formula y = bxk, the relative growth of a biological structure is described by the eigenvector (vector matrix of coefficients) of the first principal component of a variance窶田ovariance matrix of the logarithmically transformed dimensions of that structure. The coefficients of this eigenvector are proportional to the specific relative growth rates of the original dimensions. In a multivariate context, size is represented best as a linear combination of variables (Bookstein et al. 1985) with high positive correlations between the variables and the component. Body size of each individual is represented by its score on the first principal component: larger individuals will have higher scores on this axis. All components after the first ﾂｩ 2001 NRC Canada

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principal component represent allometry-free biologic shape, random variation, and error (measurement and taphonomic). Thus, only the coefficients of the first component describe the implications of size change for shape, and the first component is described best as an allometric size variable (Bookstein 1989). In the present study, eigenvectors were normalized (i.e., summation of squared coefficients equals 1.00). Coefficients of the first eigenvector were rescaled by [1/(p)½]–1, where p is the number of variables, to create multivariate allometric coefficients (Leamy and Bradley 1982; Shea 1985). As with the bivariate formula, a multivariate allometric coefficient of 1.00 indicates isometry, a coefficient greater than 1.00 is positively allometric, and a coefficient less than 1.00 is negatively allometric. To judge the significance of components and the coefficients of an eigenvector, means and standard errors of the normalized allometric coefficients were estimated by the jackknife resampling method (Mosteller and Tukey 1977), a technique that has been shown to be useful in a PCA (Gibson et al. 1984; McGillivray 1985; Diniz-Filho et al. 1994; Peres 1994). A jackknife analysis entails the repeated computation of a sample statistic (e.g., variance) following the random omission of a single operational taxonomic unit (OTU). Hence, for n OTUs the sample statistic is recalculated n times with a sample size of n – 1. Pseudovalues, defined as yp = nyall – (n – 1)yi, are calculated, where yall is the sample statistic calculated with the full sample, and yi is the sample statistic calculated on the sample size of n – 1. The estimate of the variance is obtained by dividing the variance of the pseudovalues by n. The standard error is the square root of this variance estimate. The mean and standard error of these pseudovalues can aid in determining the accuracy of the sample statistic based upon the full sample. Significance of the principal components was assessed by the ratio of the jackknife estimate and its standard error for each of the coefficients of a component (Gibson et al. 1984). This ratio is designated by T (Marcus 1990). As the distribution of jackknifed variances is often highly skewed (Efron 1982), jackknifed estimates and T values will also be skewed. Thus, the t distribution suggested by Mosteller and Tukey (1977) and followed by Gibson et al. (1984) for testing the T statistic is incorrect. A value for T of 3.00 was chosen in the latter study to indicate a significant coefficient. A more conservative probability distribution is recommended by Marcus (1990), and followed in this paper, in which the significant T value is raised to 5.00. Only those components with a large number of significant coefficients were retained (Gibson et al. 1984). The standard errors for the coefficients of the first principal component allowed tests of isometry by t test. PCA was carried out with the statistical package NTSYS-pc (Rohlf 1990). Parameters for the bivariate allometric formula were calculated by a reduced major axis program written by K. Baia, formerly of the Biology Department, Erindale College, University of Toronto.

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Biomechanics The pattern of forces acting upon the humerus of an adult Maiasaura (Fig. 5) is shown at a stage that can represent either a quadrupedal stance or the midpoint of a step during quadrupedal locomotion. At this stage, the area of contact

Fig. 5. Lateral view of forelimb and trunk of Maiasaura peeblesorum to illustrate pattern of major forces acting upon the humerus. Compressive (Fc) and bending (Fb) forces are expressed by the following equations: Fc = G cos θ + Fm and Fb = G sin θ, where θ is the angle between the vector of G and the longitudinal axis of the humerus, and Fm is the force of the muscles that attach to the olecranon process.

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between the manus and ground is directly beneath the expanded glenoid tubercle of the scapula. The manus will exert a force on the ground that will, in turn, produce an equal, but opposite, force. This opposing force on the manus is the ground-reaction force (G), and it is restored as approximately parallel to most of the limb bones, as is true for © 2001 NRC Canada

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Fig. 6. Methods used for determination of the second moment of area for the shafts of the humerus and tibia of Maiasaura peeblesorum. The second moment of area is calculated for bending of the humerus about the neutral axes X and Y. Other variables are A (cross-sectional area), r (radius of medullary cavity), and R (radius of shaft).

and Biewener 1992) and loading that is at an angle to the long axis of the bone are responsible for these bending stresses. In the subsequent biomechanical analyses, it is assumed that bending was the primary source of stress on the limb bones of Maiasaura. Analysis of the bending of the humeral and tibial shafts under loading is based upon the equations of beam theory as outlined in a number of texts (e.g., Roark and Young 1975; Wainwright et al. 1976). Stresses produced in a beam that is bent about its neutral axis (an axis along which the material experiences neither compressive nor tensile stress) are expressed by the basic beam formula s=

My I

where M is the torque (moment) of the force that is producing the bending, y is the distance from the neutral axis to a point within the cross section of the beam (typically the outer edge to determine the maximum stress), and I is the second moment of area. When comparing two beams subject to the same torque, the stress can be minimized by maximizing the ratio I/y. Torque is the product of the force component (Fb) applied at the free end of the beam and the distance (L) from the free end to the plane of the cross section, at which the second moment of area is determined. Hence, the standard beam formula can also be expressed as s=

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large quadrupedal mammals such as horses (Biewener et al. 1983), though not for smaller mammals that tend to move with flexed limbs (Biewener 1983). When the head of the humerus is articulated with the glenoid, the long axis of the humerus is clearly articulated at an angle to the direction of G (Fig. 5). Consequently, as the manus was fixed upon the ground, the humerus was subject to torque that attempted to rotate it counterclockwise (when viewed left laterally) and flex the elbow. Collapse of the forelimb was prevented by the contraction of muscles, primarily M. triceps, that attached to the olecranon process. Since G acted at an angle to the humerus, not only was the whole humerus subject to torque about the glenoid, but also the shaft of the humerus experienced compressive and bending components of G (Fig. 5). Bone is stronger in compression than tension (Currey 1984), but bending is the major type of loading experienced by limb bones in tetrapods with an upright stance such as in mammals (Rubin and Lanyon 1982; Biewener and Taylor 1986), in contrast to the predominantly torsional strains in the limb bones of sprawling tetrapods (Blob and Biewener 1999). Curvature of the bone (Bertram

F b Ly I

Stress can be minimized by diminishing L in addition to maximizing I/y. In this study, the humerus and tibia are modelled as straight beams that are subject to stresses produced from ground-reaction forces during stance and locomotion. Although bending could occur at any point along the length of the humerus, it is assumed that the complex pattern of stresses produced by the attachment of the various appendicular muscles between the humeral head and the corner of the deltopectoral crest would contribute to the overall morphology of the bone. Since the relative proportions of stresses produced by muscular activity is unknown, it is not possible to separate the different influences of muscular stresses and bending stresses. Hence, beam theory is not applicable to this region of the humerus, and only the shaft from the distal condyles to the deltopectoral crest will be modelled as a beam. There is a slight curvature to the shaft of the humerus (Fig. 5), which implies that one should use the equations for the bending of a curved beam. However, the radius of this curvature is at least a magnitude larger than the depth of the beam, and thus in this situation any errors incurred by using the standard equations for a straight beam will be small (Roark and Young 1975). There is no detectable curvature to the shaft of the tibia at any growth stage. Cross-sectional outlines of the humerus and tibia were reconstructed from measurements of cortical bone thickness and circumference for the purpose of calculating I. The shafts of those few humeri that are undistorted have a virtually circular cross section. Others were restored with a circular ÂŠ 2001 NRC Canada

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cross section. A definite asymmetry between the relative thicknesses of the caudal and cranial sections of cortical bone suggested that bending along the shaft of the humerus should be studied along two neutral axes: one that is directed lateromedially (X), and a second that is directed craniocaudally (Y; Fig. 6A). The total I for the humeral shaft about each neutral axis was determined by dividing the cross section into 1 mm thick slices, for which the area was calculated graphically and then summing the I of each slice (Fig. 6A). A circular cross-sectional outline of the tibia was also reconstructed based upon undistorted specimens of different sizes. As there is little variation among the cortical bone thicknesses in any direction in the tibial shaft, I was calculated according to the formula for a thick-walled tube (Fig. 6B). The value of r (radius of medullary cavity) for each section was calculated based upon the average of the measured cortical bone thicknesses. Calculation of second moment of areas from reconstructions of cross sections rather than cross sections taken directly from specimens will introduce some error due to deviations from the assumption of circular cross sections. However, even the slight distortion evident in many specimens would introduce a larger error if not corrected. Furthermore, any error created through the use of reconstructions is probably small compared with the actual changes in cortical bone thicknesses and second moment of areas across the size range studied for Maiasaura. Units of I are linear dimensions raised to the power of four. Therefore, when regressed against length, the line of isometry will have a slope of 4.00. Positive and negative allometry are defined as greater than or less than 4.00, respectively. As an additional measure of the strength of the bone, surface area of the cross section was also calculated and regressed against greatest length. Since the surface area is proportional to the square of a linear dimension, isometry is present when the regression coefficient is 2.00, positive allometry exists when the coefficient is greater than 2.00, and negative allometry exists when the coefficient is less than 2.00.

Results

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In each of the PCAs, the first principal component accounted for at least 95% of the variance. Eigenvalues of each succeeding component attained a maximum in a few instances of only 2% and were usually less than 1%. In addition, there is a gradual decline in the eigenvalues beyond the first component. Both results suggest that those axes beyond the first component are not stable. Jackknife resampling provides additional support for this interpretation. All T values for the first principal component of each analysis are greater than 5.00. In contrast, few coefficients of the other components are greater than 5.00. Only two of the 10 coefficients for principal component 2 of the humerus have T values that are greater than 5.00, and two of the 13 coefficients for principal component 2 and one of the 13 coefficients for principal component 3 of metatarsal IV have T values that are greater than 5.00. The small and gradually declining eigenvalues and small number of significant coefficients for those components beyond principal component 1 demonstrate that the orientation of these axes within multidimensional space is

largely arbitrary, and any biological interpretations would be meaningless. Accordingly, only the first principal component is discussed. Results of multivariate and bivariate analyzes are summarized in Tables 1â&#x20AC;&#x201C;4. Patterns of allometry of external dimensions are also presented in Fig. 7. Graphs of regressions of cortical bone thickness, surface area of cross section, and second moment of area versus size are given in Figs. 8â&#x20AC;&#x201C;13.

Humerus There is a distal and lateral displacement of the deltopectoral crest during growth as shown by positive allometry of variables 4, 5, and 8 and negative allometry of variable 6 (Table 1; Fig. 7A). Minimum circumference of the shaft (variable 11) is negatively allometric (Table 2). Negative allometry of the length of the shaft is shown by variables 6 and 7. Caudal, lateral, and medial dimensions of cortical bone for the humerus exhibit positive allometry, whereas the cranial dimension is isometric (Table 3; Fig. 8). The second moment of areas for the humeral shaft along the X (lateromedial) and Y (craniocaudal) axes are isometric during growth (Table 4; Fig. 11). Surface area of the shaft is positively allometric (Table 4; Fig. 13A). Thus, the results indicate that the humeral shaft of an adult is stouter than that in a juvenile, but this stoutness has been achieved by a decrease in the relative width of the marrow cavity (Fig. 14). Nonetheless, there is evidence that the cortical bone of the humeri of large adults (7 m or greater in body length) is not markedly greater than that of smaller adults, indicative of a later ontogenetic expansion of the medullary cavity (Horner et al. 2000). Ulna Results are suggestive of a positively allometric increase in the craniocaudal diameter of the shaft (variable 1). However, none of the coefficients are significantly different from isometry (Table 1). Femur There is an allometric increase in the size of the fourth trochanter as shown by negative allometry of variable 2 and positive allometry of variable 3 (Table 2; Fig. 7C). The circumference of the shaft (variable 4) is negatively allometric. As the shaft is virtually cylindrical, negative allometry of its circumference implies negative allometry of the diameter. Tibia The circumference of the tibia is negatively allometric; all other measured external dimensions are isometric (Table 2; Fig. 7D). Given the cylindrical shape of the shaft, the negative allometry of the circumference demonstrates negative allometry of the diameter. All dimensions of cortical bone (Table 3) and the cross-sectional area for the tibial shaft (Table 4) are isometric. In contrast, the second moment of area of the tibial shaft is negatively allometric (Table 4).

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Metatarsals All measured variables for the second metatarsal are isometric (Table 1). The third and fourth metatarsals exhibit similar patterns of allometric growth (Tables 1, 2). Greatest

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Fig. 7. Summary of results of bivariate and multivariate morphometric analyses of external dimensions of limb bones of Maiasaura peeblesorum. Not drawn to scale.

length and some dimensions that are approximately parallel to the longitudinal axis are positively allometric, and only a single dimension of the distal condyle of the third and fourth metatarsals is negatively allometric. Circumference of the shaft of the third metatarsal is isometric (Table 2), and the caudal dimension of cortical bone thickness is positively allometric (Table 3).

Discussion

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The results demonstrate that the pattern of allometric growth for the forelimb was clearly different from that for the hindlimb. The distinctive patterns of morphometric change in the limbs are most likely due to stresses experienced by the limb bones during growth. Stresses on limb bones of terrestrial vertebrates are produced by gravity and the muscular forces required for moving the body. Bone can adjust to these stresses by (i) changing the mechanical properties of the bone material, (ii) changing the angulation of the long bones with respect to the direction of the vector of the ground-reaction forces, and (iii) changes in skeletal allometry. Any combination of these changes would maintain a similar safety margin (ratio of failure stress to functional stress) throughout a size range. Mechanical properties such as bending strength, compressive strength, and various elastic moduli (e.g., Youngâ&#x20AC;&#x2122;s modulus) of mature, compact bone in long bones are relatively invariant between species of terrestrial mammals and birds of different sizes (Biewener 1982; Currey 1984) and are not important factors in explaining the maintenance of skeletal stresses in animals of different sizes (Biewener 1990). However, the mechanical properties of growing bone in juveniles of mammals (Currey and Pond 1989) and birds (Carrier and Leon

1990) exhibit definite changes that are explained best as adaptive responses to changing functions. The rapidly growing young of mammals and birds are characterized by the presence of fibrolamellar bone, which has lower stiffness (i.e., lower Youngâ&#x20AC;&#x2122;s modulus) and lower strength due to its lower content of calcium and greater porosity (Currey and Pond 1989; Brear et al. 1990) than adult bone. Limb bones that are subject to locomotory stresses at an early age can adjust to these stresses either by increasing the mineralization of the bone (Currey and Pond 1989; Brear et al. 1990) or by increasing the amount of bone (Carrier and Leon 1990). Fibrolamellar bone is present in the cortical bone of the limb bones of Maiasaura at several stages of growth and becomes increasingly laminar in organization as the individual matures (Horner et al. 2000). Limb posture is an important means by which safety factors are maintained in quadrupedal mammals of greatly different sizes that have similar proportions (Biewener 1989, 1990; Bertram and Biewener 1990). Small mammals run in a semierect position, whereas larger mammals move with more upright limbs. Birds also show this size-dependent shift in limb orientation (Gatesy and Biewener 1991). There is a closer alignment between the axis of a limb and the ground-reaction force in the more vertically oriented limbs of larger tetrapods, which decreases the size of the moment arm of this force and, hence, both the torque about a joint and the bending stress imposed upon the long bone (Biewener 1989). Furthermore, the muscular force required to counter the torque is also diminished, which, in turn, decreases the compressive stress on the bone. Postural changes may have occurred during growth in Maiasaura, so large adults walked with more upright limbs. Unfortunately, it cannot be determined if the young of Maiasaura walked ÂŠ 2001 NRC Canada

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Fig. 8. Bivariate logarithmic plots of cortical bone thickness versus greatest length of humeri of Maiasaura peeblesorum. 75

Fig. 9. Bivariate logarithmic plots of cortical bone thickness versus greatest length of tibiae of Maiasaura peeblesorum.

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Fig. 10. Bivariate logarithmic plots of cortical bone thickness versus score along principal component 1 of metatarsal III of Maiasaura peeblesorum.

Fig. 11. Bivariate logarithmic plots of second moment of area versus greatest length of humeri of Maiasaura peeblesorum.

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with more flexed limbs because there are no clear osteological constraints on the degree of flexion of the hip or knee. Allometry is a means of compensating for the weakness of fibrolamellar bone in order for limbs of young birds to function at a very early age (Carrier and Leon 1990). It is

also important in the phylogenetic size increase of terrestrial mammals. Geometric similarity (i.e., proportions remain similar throughout the size range) has been reported for mammals across a size range from a shrew to an elephant (Alexander et al. 1979) and within Carnivora (Bertram and Biewener 1990). A number of studies (Prothero and Sereno ÂŠ 2001 NRC Canada

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Fig. 12. Bivariate plot of second moment of area versus greatest length of tibiae of Maiasaura peeblesorum.

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1982; Economos 1983; Bertram and Biewener 1990; Cole 1992) have shown that very large mammalian species such as the ceratomorphs (extant tapirs, rhinoceroses, and the extinct members of this clade) and large bovids depart from geometric scaling and often show pronounced positive allometry of long bone dimensions. Skeletal allometry in very large species produces more robust bones for dealing with stresses beyond those that can be accommodated by a change in posture (Biewener 1990). Although the above allometric patterns in large mammals are phylogenetic rather than ontogenetic, the principle is the same in both instances. Gravity imposes far greater stresses on larger individuals, whether that size increase is phylogenetic within a lineage or ontogenetic. The positively allometric growth of the deltopectoral crest of the humerus can be related to ontogenetic changes in either the probable size or attachment sites of pectoral muscles. Scars that have been associated phylogenetically with a common insertion of M. deltoides clavicularis and M. scapulohumeralis anterior (Dilkes 2000) are concentrated along the caudal surface of the deltopectoral crest nearest the distal corner in all observed growth stages. Thus, the distal and lateral ontogenetic shift of the distal corner of the deltopectoral crest suggests a distal shift in the attachment site of these muscles. Contraction of these muscles will elevate and protract the humerus in conjunction with other muscles with similar actions such as M. deltoides scapularis and M. latissimus dorsi. In addition, a more distally positioned attachment site may act to offset bending moments acting upon the humeral shaft as the pectoral limb is elevated by decreasing the distance between the deltopectoral crest and the distal condyle (Currey 1984). Musculus latissimus dorsi is a particularly interesting muscle of Maiasaura, because there is a clear change in the morphology of its insertional scar on the humerus, which suggests an ontogenetically increasing usage of the muscle.

The humerus of an embryonic Maiasaura has an ill-defined shallow pit at the caudal end of a groove on the caudal surface of the deltopectoral crest. This pit and groove have much sharper boundaries in a nestling and are accordingly more easily identified (Figs. 15A, 15B). During growth, this scar for M. latissimus dorsi changes from a pit to a prominent bump composed of highly fibrous bone (Figs. 15C, 15D). According to a customary assumption of proportionality between the rugosity of a muscle scar and the force produced by its muscle, an adult of Maiasaura used M. latissimus dorsi more consistently than a nestling. The tension produced by M. latissimus dorsi would be greater in individuals older than a nestling, and additional bone was laid down for better anchorage of the tendon. However, empirical support for this assumption is limited, and it is not valid in those instances where muscle scars are faint or absent (Bryant and Seymour 1990). For Maiasaura, the scar for M. latissimus dorsi is one of the most readily identifiable scars at all stages of growth and is the only one that exhibits morphological changes during growth. Depending upon the craniocaudal extent of the likely origin of M. latissimus dorsi from the fascia of the dorsal vertebrae, middle and posterior fibres may have acted to propel the trunk forwards if an individual moved quadrupedally. Elevation of the forelimb and propulsion of the trunk are likely plesiomorphic actions of M. latissimus dorsi (Jenkins and Goslow 1983). The entire cranial surface of the deltopectoral crest has a continuous muscle scar from the probable insertion of M. supracoracoideus and M. pectoralis (Dilkes 2000). A positively allometric increase in the size of this scar suggests a probable corresponding allometric increase in the size of at least one of these appendicular muscles. When a terrestrial tetrapod moves quadrupedally, M. supracoracoideus and M. pectoralis act primarily during the propulsive stage (Jenkins and Goslow 1983). Musculus supracoracoideus is a stabilizer of the shoulder joint in tetrapods. Musculus pectoralis is one of a group of postural muscles that helps to support terrestrial vertebrates with erect posture by preventing collapse of the limbs. Possible ontogenetic enlargement of either M. supracoracoideus or M. pectoralis in Maiasaura may be correlated with quadrupedal locomotion through increased muscular moments needed for postural support and stabilization of the shoulder joint. In addition, relatively larger attachment areas for one or both of these muscles suggest a greater range of lever arms for the muscle fibres. Those fibres with lever arms significantly different from the distance from the glenoid to the origin of the muscles will tend to generate maximum torque later during flexion and thus continue flexion beyond the point at which other fibres reach their maximum torque (Mameren and Drukker 1979). Since the forelimb remains in contact with the ground during quadrupedal movement, the trunk is moving forward relative to the forelimb during propulsion and the angle between the trunk and forelimb is changing continually. Hence, the positively allometric increase in the attachment area for this pair of postural muscles suggests that in the adults different parts of the muscles will generate maximum torque at different times throughout the propulsive stage and serve to stabilize the shoulder. For the femur, positive allometry of the fourth trochanter indicates a corresponding increase in the relative size of M. ÂŠ 2001 NRC Canada

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Fig. 13. Bivariate plots of surface area of shaft versus greatest length of humeri and tibiae of Maiasaura peeblesorum. 75

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caudifemoralis (Dilkes 2000) during growth. As the primary femoral retractor muscle, allometric enlargement of M. caudifemoralis would increase the moment generated by this muscle and would, in turn, correlate with the significantly greater mass of the adult. Positive allometry of several longitudinal dimensions and the isometry or negative allometry of the proximal and distal ends of the third and fourth metatarsals indicate that the pes of an adult of Maiasaura is more slender than that of a juvenile. A more slender pes in a heavier animal might suggest that the bending stresses experienced by the metatarsals would be disproportionately larger. However, it is likely that the large heel pad that is shown clearly in tracks of hadrosaurs (Langston 1960; Currie et al. 1991) would have dissipated much of the force generated by the pes striking the ground (Alexander et al. 1986). This pad likely reduced the peak magnitude of bending stresses. According to beam theory, the main factors that determine the ability of a beam to resist bending are I and L. As one would conclude intuitively, a short (small L) and wide (large I) cylinder is less easily bent than one that is long and narrow. Growth of I for the humeral shaft of Maiasaura is isometric, which is unexpected because if there is a disproportionate increase in stresses on the forelimb due to an ontogenetic delay in its use, then I should show a similar allometric increase. However, positive allometry of cortical bone width and cross-sectional area implies that the humeral shaft of an adult is more resistant to bending stresses than that in a juvenile, even though its value of I maintains the same proportion to size. Negative allometry of L (variable 6 for the humerus in Table 1) will reduce stress further. In contrast, the nearly consistent pattern of isometry for cortical bone dimensions and cross-sectional surface area of the tibial shaft and metatarsal III and the negative allometry of I for the tibia suggest that isometric growth was sufficient in the hindlimb to withstand ontogenetically increasing locomotory stresses. Two explanations may be offered for the dramatically different patterns of allometry in the forelimb and hindlimb. One explanation is that individuals of Maiasaura were

quadrupedal throughout life, but the percentage of mass carried by the forelimbs increased during growth. An alternative explanation is that juveniles may have walked predominantly as bipeds, but adopted an increasingly quadrupedal stance as they matured. Both explanations require the use of the forelimb for quadrupedal locomotion. The primary difference resides in the stage of growth at which quadrupedal locomotion is introduced. It is important to note that neither explanation restricts the forelimb to locomotion; each states merely that the strains encountered during locomotion are most likely to be the primary factor responsible for the observed allometric growth pattern. Hadrosaurs probably used their forelimbs for other behaviors such as manipulation of vegetation while foraging and the construction of nests. These activities would certainly place stresses upon the bones, but any strains experienced would be transitory and in the case of nest building would likely apply solely to the sexually mature adults. The first explanation for the different growth patterns of the forelimb and hindlimb requires a cranial shift of the centre of mass during growth so that the forelimb carries a steadily increasing proportion of the body mass. Although no published calculation of the centre of mass for a hadrosaur is available, it has been estimated for the iguanodontian Iguanodon (Alexander 1985), which has a body shape similar to that of a large hadrosaur. It was found that the centre of mass was situated virtually above the pelvis, and only a small percentage of the body mass was likely supported by the forelimbs. Presumably the forelimbs of adult hadrosaurs also supported only a small percentage of the body mass. Without a reasonably accurate estimate of the relative locations of the centres of mass of a juvenile and an adult of Maiasaura and the magnitude of the increase in mechanical loading on the forelimbs, it is unknown whether any ontogenetic shift in the centre of mass occurred and if it could reasonably account for the differing allometric responses of the forelimb and hindlimb to mechanical loads. The second and more likely explanation is that the forelimbs were not used for locomotion until later in life. Given the likelihood that the forelimb only supported a ÂŠ 2001 NRC Canada

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Table 1. Normalized and multivariate allometric coefficients and jackknife estimates of coefficients of the first principal axis of the principal components analyses of selected limb bones of Maiasaura peeblesorum. Element

Variable

Normalized coefficient

Jackknifea

Multivariate allometric

Humerus (N = 24)

1 2 3 4 5 6 7 8 9 10 1 2 3 4 5 1 2 3 4 5 6 7 8 9 10 1 2 3 4 5 6 7 8 9 10 11 1 2 3 4 5 6 7 8 9 10 11 12 13

0.314 0.294 0.298 0.334 0.342 0.297 0.305 0.346 0.309 0.319 0.488 0.433 0.430 0.441 0.442 0.315 0.290 0.325 0.321 0.319 0.313 0.329 0.327 0.310 0.311 0.331 0.293 0.266 0.263 0.311 0.258 0.286 0.317 0.316 0.327 0.336 0.298 0.259 0.262 0.280 0.281 0.256 0.295 0.296 0.249 0.262 0.268 0.306 0.286

0.318 0.286 0.299 0.341 0.344 0.308 0.311 0.351 0.297 0.318 0.491 0.435 0.424 0.448 0.443 0.312 0.286 0.321 0.325 0.318 0.316 0.329 0.324 0.307 0.315 0.338 0.300 0.272 0.259 0.314 0.262 0.283 0.318 0.315 0.329 0.330 0.298 0.258 0.254 0.274 0.282 0.257 0.304 0.300 0.250 0.260 0.259 0.308 0.290

0.99 0.93 0.94 1.06b 1.08b 0.94b 0.97b 1.10b 0.98 1.01 1.09 0.97 0.96 0.99 0.99 1.00 0.92 1.03 1.02 1.01 0.99 1.04 1.03 0.98 0.98 1.10b 0.97 0.88 0.87 1.03 0.85b 0.95 1.05 1.05 1.08b 1.11b 1.08b 0.94 0.95 1.01 1.01 0.92 1.07b 1.07b 0.90b 0.95 0.97 1.11b 1.03

Ulna (N = 14)

Metatarsal II (N = 14)

Metatarsal III (N = 15)

Metatarsal IV (N = 18)

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(0.003) (0.011) (0.014) (0.006) (0.004) (0.006) (0.003) (0.011) (0.014) (0.009) (0.027) (0.025) (0.015) (0.028) (0.012) (0.007) (0.013) (0.014) (0.011) (0.020) (0.007) (0.007) (0.018) (0.007) (0.012) (0.008) (0.008) (0.031) (0.020) (0.023) (0.015) (0.026) (0.011) (0.013) (0.008) (0.011) (0.007) (0.011) (0.015) (0.015) (0.009) (0.015) (0.008) (0.008) (0.008) (0.023) (0.018) (0.010) (0.016)

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Note: N, number of individuals. a Standard error is given in parentheses. b Significantly different from 1.00 at P = 0.05.

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Table 2. Reduced major axis regressions for the humerus, metatarsal III, femur, and tibia of Maiasaura peeblesorum. Element

Variable

Humerus Femur

11 2 3 4 2 3 4 5 12

41 23 23 23 19 19 26 48 10

0.99 0.99 0.99 0.99 0.96 0.97 0.99 0.99 0.99

–0.81 –0.36 –2.06 –0.76 –2.09 –1.85 –1.07 –0.99 –0.04

0.96a 0.92b 1.11b 0.95b 0.99 1.03 0.95 0.97b 1.03

Tibia

Metatarsal IIIc

Note: b, y intercept; k, regression coefficient; r, correlation coefficient. a Significantly different from 1.00 at P = 0.05. b Significantly different from 1.00 at P = 0.05 after sequential Bonferroni correction. c Circumference regressed against scores on the first principal component (PC1).

Table 3. Parameters of reduced major axis regressions for cortical bone thicknesses of the humerus, tibia, and metatarsal III of Maiasaura peeblesorum. Element

Dimension

Humerus

Dorsal Ventral Lateral Medial Anterior Posterior Lateral Medial Anterior Posterior Lateral Medial

16 16 16 16 18 18 18 18 10 10 10 10

0.97 0.99 0.97 0.97 0.98 0.98 0.99 0.98 0.98 0.97 0.95 0.96

–5.35 –3.79 –5.75 –4.93 –3.45 –3.53 –3.53 –3.50 –2.75 –3.72 –2.68 –3.29

1.29a 1.08 1.39a 1.25a 1.00 1.00 0.99 1.01 1.09 1.33b 1.12 1.24

Tibia

Metatarsal III

Note: Each dimension was regressed against greatest length, with the exception of metatarsal III where the independent variable was the score along PC1. a Significantly different from 1.00 at P = 0.01. b Significantly different from 1.00 at P = 0.05.

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minor amount of the body mass, any delay in the adoption of quadrupedal locomotion would generate a pattern of strains greatly different and significantly greater in magnitude from the earlier pattern. It is generally accepted that dynamic rather than static mechanical loading will stimulate the formation of new bone (Lanyon and Rubin 1984; Lanyon 1992), and even a brief period of dynamic loading is sufficient (Forwood et al. 1996). Transitory or static loads will not affect bone mass. Although there is evidence for both a threshold response to dynamic strains and a linear increase in bone formation with the magnitude of the strain (Rubin and Lanyon 1985; Turner et al. 1994), it appears that bone will respond more to a change in the strain rather than simply an increase in the absolute magnitude of strain. Furthermore, the amount of bone formation is directly proportional to the rate of change in strain: a large change in the rate of strain will stimulate more formation of bone than a

Table 4. Parameters of reduced major axis regressions for cortical bone surface area (SA) and second moment of area (I) of the shafts of the humerus and tibia of Maiasaura peeblesorum. Element Humerus Ix Iy SA Tibia I SA

k 25

16 16 16

0.99 0.99 0.99

–11.74 –11.69 –5.81

4.00 3.99 2.147a

18 18

0.99 0.99

–11.50 –4.68

3.86b 1.94

Note: The subscripts x and y for I of the humerus correspond to the axes defined in the text and shown in Fig. 6A. a Significantly different from 2.00 at P = 0.05. b Significantly different from 4.00 at P = 0.05.

small change (O’Connor et al. 1982; Turner et al. 1995). Bones of mature and growing terrestrial animals will apparently maintain their architecture over a range of daily dynamic strains, but will change their shape and mass when subjected to unusual dynamic loading that is different from these normal daily strains (Mosley et al. 1997). This adaptive modelling and remodelling is necessary to maintain the functional loading within specific limits to prevent damage (Keller and Spengler 1989; Biewener and Bertram 1993). Thus, a sharp increase in the use of the forelimbs of Maiasaura for locomotion as an individual grew in size would lead to dramatic increases in stresses, and the shaft of the humerus apparently adjusted to these new stresses. The probable allometric increases in the size of postural muscles and the lever arms of protractor muscles that attach to the humerus are also consistent with this explanation. The results presented herein of an age-dependent preference for stance agree with those based upon ontogenetic changes in limb ratios for I. bernissartensis (Norman 1980). There are some intriguing changes to the cross-sectional shape of the shaft of the humerus that merit comment. A nestling has a humerus with an elliptical and offset marrow cavity, whereas the marrow cavity of an adult humerus better approximates a hollow cylinder (Fig. 14). In contrast, the cross-sectional shape of the tibial shaft remains essentially a symmetrical hollow cylinder from nestling to adult. A beam that has a more cylindrical cross-sectional shape is stronger and stiffer and thus more resistant to torsional stresses (Roark and Young 1975). The change for the humerus shaft might then indicate an enhanced resistance to torsion or that both craniocaudal and mediolateral bending generated significant stresses. Either way, the change in cross-sectional shape of the shaft is consistent with adaptive remodelling to a pattern of stresses that a forelimb would experience if the animal was a quadruped. In addition, the variability in the cross-sectional shape of the bipedal nestling is seemingly greater than that of the quadrupedal adult (Fig. 14). This observation is similar to the findings of Biewener and Bertram (1994) on the effect of use and disuse on growing bone. They noted increased variation in cross-sectional shape of the tibia in those birds that were denervated. Their conclusion was that in the absence of normal functional loading, the usual degree of relative resorption and deposition required to maintain a specific bone shape is disrupted. As a © 2001 NRC Canada

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Fig. 14. Representative cross sections of the shafts of humeri of Maiasaura peeblesorum. (A) Two nestlings. (B) Two adults. 75

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result, the variability of the cross section is greater. The differences in the variability of cross-sectional geometries of juvenile and adult humeri of Maiasaura may have a similar explanation. The decrease in the variability of the crosssectional shape of the shaft of the humerus and its more symmetrical geometry supports the hypothesis that the forelimb of Maiasaura did not experience a consistent pattern of strains until some time after the individual began to move about on its hindlimbs. The hypothesis of an age-dependent change from predominantly bipedality to quadrupedality in Maiasaura is contrasted by the results of a biomechanical study of femoral growth in the basal iguanodontian D. lettowvorbecki (Heinrich et al. 1993). It was proposed that juveniles of Dryosaurus were quadrupedal and underwent a shift to bipedality early in life, perhaps within the first several months after hatching. This transition was thought to be due to changes in the proportions of the body during growth. Although no hatchlings of D. lettowvorbecki are known, juveniles of the related ornithopods Orodromeus makelai and M. peeblesorum have heads that appear to be larger relative to their bodies than in the adults. It was concluded that the juveniles of D. lettowvorbecki probably had similar proportions. With their relatively larger heads, the centre of mass was far cranial to the hips, and quadrupedality was necessary to reduce stresses on the femur. As the individual matured, its head became relatively smaller and the tail relatively larger and the centre of mass moved closer to the pelvis. Bipedality was now the normal stance, as the heavier tail could counterbalance the trunk and head. Data presented in this paper and additional factors suggest that any change in stance for D. lettowvorbecki may not have been from quadrupedal to bipedal. It is now possible to make more accurate statements about the relative propor-

tions of a juvenile D. lettowvorbecki because a juvenile of Dryosaurus altus has been described recently (Carpenter 1994). Although a different species, the postcrania of adults of D. lettowvorbecki and D. altus are very similar (Galton 1981) and it is unlikely that the juveniles would differ greatly. The skull of a juvenile of D. altus is not nearly as large relative to the femur (Carpenter and Alf 1994), as had been suggested for D. lettowvorbecki by Heinrich et al. (1993, their Fig. 9). Consequently, the centre of mass may not have been located a great distance cranial to the pelvis in juveniles. The femur of D. lettowvorbecki has a pronounced craniocaudal curvature. Curvature of a long bone increases bending stresses for a bone under axial compression in the direction of the curvature (Bertram and Biewener 1988). Femoral curvature is present in all known growth stages of D. lettowvorbecki (Galton 1981) and the juvenile D. altus (Carpenter 1994); hence, it is reasonable to propose that the craniocaudal femoral curvature of D. lettowvorbecki would have enhanced stresses in this direction relative to other directions throughout ontogeny. Heinrich et al. (1993) found a significant increase in the ratio of the maximum I and the minimum I between the small- and medium-sized groups of D. lettowvorbecki, which they interpreted as evidence for a dramatic increase in bending stresses that accompanied a shift from quadrupedality to bipedality. As the direction of this ratio is nearly the same as the femoral curvature, it is possible that the observed changes in biomechanics may represent an adjustment to the craniocaudal stresses created by the curvature of the femur. Weight-bearing and the forelimb of hadrosaurs The hypothesis of age-dependent selection of stance in Maiasaura advanced in this paper and trackways of quadrupedal ÂŠ 2001 NRC Canada

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Fig. 15. Development of the muscle scar on the humerus of Maiasaura peeblesorum that is attributed to M. latissimus dorsi (Dilkes 2000). (A, B) From a nestling. (C, D) From an adult. l.d., M. latissimus dorsi.

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ornithopods attributed to hadrosaurs (Currie et al. 1991) are seemingly at odds with the general consensus that the forelimb of hadrosaurs shows no clear adaptations for weight-bearing. Thus, there is an apparent mismatch between the combined evidence from morphometrics, biomechanics, and ichnology and the morphology of the skeleton that should be addressed. At the heart of all discussions of the possible functions of the forelimb in hadrosaurs has been the manus. Earlier inter-

pretations (e.g., Leidy 1858; Cope 1883) of hadrosaurs as strictly aquatic swamp dwellers received a significant boost following the discoveries by Charles M. Sternberg in 1908 and 1910 of two â&#x20AC;&#x153;mummifiedâ&#x20AC;? hadrosaurs that have a mitten-like manus. Strictly aquatic habits for hadrosaurs were supposedly demonstrated by the presence of skin that completely covered the manus and extended between the digits to create webbing and the absence of tubercles or calluses on the skin impressions (Osborn 1912). Additional ÂŠ 2001 NRC Canada

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Fig. 16. (A) Midpoint cross-sectional outline of articulated metacarpals II–IV of an adult of Maiasaura peeblesorum. (B) Hypothetical elliptical outline with length and width equivalent to that of (A). Second moment of area of (A) was calculated by the same method as for the humeral shaft of Fig. 6, whereas the second moment of area for the elliptical outline was determined by the given formula. Bending is assumed to occur along the lateromedial axis X–X. Variables a and b are the maximum and minimum radii of the ellipse, respectively.

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osteological evidence for aquatic hadrosaurs included the small size of the forelimb relative to the hindlimb, the slenderness of the metacarpals, poor articulation of the phalanges, and the presence of only two hoof-like unguals (Brown 1908, 1912). Lull and Wright (1942) interpreted hadrosaurs as bipedal, aquatic herbivores that used their forelimbs for support only when resting along a shore, and Sternberg (1965) stated that hadrosaurs were capable of some quadrupedal walking along the shores of swamps or rivers. The prevalent opinion of hadrosaurs as aquatic dinosaurs was overturned by Ostrom (1964) and Galton (1970), who amassed a wide array of evidence to support a new interpretation of hadrosaurs as bipedal, terrestrial herbivores. Ostrom pointed out that the evidence presented by Osborn (1912) showed only that hadrosaurs were not quadrupedal; it did not show that they were aquatic. As further evidence in favor of only bipedal walking, Ostrom argued that the reduction of carpal ossification to only a pair of small bones implied a weak carpus that was incapable of supporting a significant portion of body mass. Galton agreed that hadrosaurs were bipedal except when resting, but noted that reduction of the carpus did not necessarily indicate a weak joint, since the ceratopsid Monoclonius also has only two carpals. A poorly ossified carpus, slender metacarpals, and poorly articulated phalanges are certainly valid observations for the hadrosaurian manus, but other features of the manus that can be interpreted as adaptations for weight-bearing have been neglected in the descriptions by Brown (1912) and Parks (1920) and more recently Nelms (1992). The ground-reaction force would exert a torque about the carpus if that force was inclined relative to the metacarpals. Without the presence of a complex of ossified carpals to virtually lock the manus and antebrachium to the carpus as described in I. bernissartensis (Norman 1980), or at least limit mobility, even a slight misalignment of the axis of the manus with the ground-reaction force could lead to its collapse. Thus, the manus of hadrosaurs would be at a continual risk of failure as the vector of the ground-reaction force changed during locomotion. Use of the forelimb at any point during locomotion would then be excluded or, at best, restricted to a quadrupedal stance. However, the presence of prominent muscle scars on metacarpals III and IV identified phylogenetically as likely attachment sites for extensor and flexor muscles (Dilkes 2000) suggests that these muscles could have acted to constrain flexibility of the carpus and,

hence, replaced functionally the carpals. Contraction of these muscles would help to counter any rotation of the metacarpals about the carpus by stretching the tendons and decelerating the manus rapidly as it contacted the ground. Although it is not possible to estimate the relative proportions of tendon and muscle fibres in the flexor muscles, it is likely that the length of the tendon was significant because tendons typically transmit the force of muscles in the manus and pes of terrestrial vertebrates. An alternative hypothesis that the extensor and flexor muscles served to manipulate the manus is less likely because the slight curvature of the articular surfaces on the metacarpals and the antebrachium implies a limited range of flexion and extension. A larger range of flexibility was possible between the metacarpals and phalanges and between the individual phalanges, but the soft tissue impressions of the mummified hadrosaur and trackways show that digits II–IV were held together and only digit V could move independently. The three primary metacarpals (II–IV) were united firmly in life as shown by the close apposition between the metacarpals along their entire lengths. In addition to their tight connection, the metacarpals join along a narrow arc, with metacarpal III situated cranial to its neighbours to produce a semicircular cross section (Fig. 16A). The significance of this arrangement can be seen readily when one models the metacarpals as a beam that is bent along the X–X axis. This axis lies within a transverse plane and is the axis along which bending is most likely to occur while the animal is standing or moving. The second moment of area for a cross section through the middle of the three metacarpals can be compared to the second moment of area of a hypothetical manus in which the metacarpals are aligned transversely as an ellipse (Fig. 16B). The method that was used for calculating the second moment of area of the shaft of the humerus (Fig. 6) was also used to calculate the second moment of area for the actual cross section of the metacarpals. A formula was used to calculate the second moment of area for the hypothetical elliptical cross section (Fig. 16B). The second moment of area along the X–X axis for the actual cross section is approximately 39% greater than that of an ellipse with the same length and width. Furthermore, the ratio I/y is approximately 15% larger for the actual cross section than for the elliptical cross section. Thus, the articulation of the metacarpals along an arc produces a structure that is stiffer and subject to less bending strain than one with © 2001 NRC Canada

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an elliptical cross section. The strong union between metacarpals II–IV and their articulation along a curved rather than a transverse plane are interpreted herein as adaptations for weight-bearing. The statement by Brown (1912) that the phalanges of the hadrosaurian manus are articulated loosely was probably a reference to the absence of the type of interphalangeal articulation found in the pes, where rounded distal condyles fit relatively snugly into proximal concavities on the succeeding phalanx. Interphalangeal joints in Maiasaura and other hadrosaurs consist of contact between flat or rounded surfaces with little evidence for constraints on direction of mobility. However, as digits II–IV of the manus were enclosed in skin, interphalangeal movement was probably limited. The greatest degree of flexibility probably occurred between the metacarpals and the first phalanges. The articular surfaces on the distal condyles of the metacarpals are extensive and notably are larger on the cranial surface than on the caudal surface (Dilkes 1993), contrary to the statements of Nelms (1992) that the distal ends of hadrosaurid metacarpals are flat. The greater cranial portion of the articular surface implies that the manus could be hyperextended, which is compatible with a role of support. Curvature of the distal condyle of metacarpal III is modest, but more pronounced for the distal condyles of metacarpals II and IV (Dilkes 1993). Furthermore, the distal condyles of metacarpals II and IV face outwards from the middle metacarpal III as a consequence of the curved structure of the manus. Hence, the digits spread apart to create a larger surface area for contact with the ground. The webbing between the digits that earlier researchers thought was an adaptation for paddling through the water are probably displaced digital pads (Bakker 1986). Well-preserved manus prints (Currie et al. 1991; Currie 1995) show that the pads of digits II–IV were substantial relative to the unguals and spread out as the manus contacted the ground. As with the large heel pad of the pes, the digital pads of the manus would absorb and dissipate impact forces. Tendons within the manus would also stretch and further dampen the peak stress.

reduced number of carpals was apparently reinforced against collapse by the strong attachment of flexor tendons onto the caudal faces of metacarpals III and IV, metacarpals II–IV were united firmly and articulated in an arc configuration that was more resistant to bending than if the metacarpals were aligned in a transverse row, hyperextension was possible at the metacarpal–phalangeal joints, the phalanges were bound together by skin and probably ligaments, and the manus had a broad contact with the ground.

Acknowledgments This paper is a revised portion of a doctorate thesis submitted to the Department of Zoology at the University of Toronto. I wish to thank my thesis supervisor Dr. Robert Reisz for his support throughout my research and Dr. John Horner for the opportunity to study M. peeblesorum. Comments from Drs. R. Reisz, J. Horner, C.S. Churcher, C. McGowan, and D.H. Collins are greatly appreciated. Numerous discussions with Dr. J. Horner and Mr. Matt Smith on hadrosaurian anatomy, myology, and biomechanics helped to clarify my ideas. Comments and suggestions by Dr. Hans-Dieter Sues (Department of Palaeobiology, Royal Ontario Museum) were very helpful. I also thank Dr. N.C. Collins (Department of Zoology, Erindale College, University of Toronto) for his critical reading of the statistics and alerting me to the Bonferroni test. I am grateful to Dr. John Rensberger (Thomas Burke Memorial Museum, University of Washington) for providing a copy of the photogrammetry program GeoInter 3.2 and his advice on its operation. Many of the specimens incorporated into this study were found during fieldwork at the Camposaur site in the summers of 1988–1990. This fieldwork was aided greatly by the many individuals who participated in the Museum of the Rockies Paleontology Summer Field School, and I wish to thank them for their efforts. Partial support for my research was provided by a postgraduate scholarship from the Natural Sciences and Engineering Research Council of Canada and two research grants from the Geological Society of America.

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Since the first description of an articulated forelimb of a hadrosaur, several different lines of evidence have been used to argue that the forelimb was at best a paddle for swimming or could support only a small fraction of weight when on land. Quadrupedal walking was virtually excluded. Although present opinion is that hadrosaurs were facultative bipeds, possible ontogenetic variability in the relative importance of bipedality and quadrupedality has been considered only rarely for ornithopods. Furthermore, the contradiction between an assumption of quadrupedality (even if limited) as indicated by trackways and the apparent lack of any clear adaptations for weight-bearing in the forelimb has not been addressed. Results from the present study have revealed a dichotomy in the morphometrics of growth in the forelimb and hindlimb of M. peeblesorum that is consistent with a hypothesis that the preferred stance changed from bipedality to quadrupedality during growth. There are numerous features in the manus of hadrosaurs that can be interpreted as adaptations for weight-bearing. The carpus with its

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