Abstract
Speed estimations from trackways of Titanopodus mendozensis González Riga and Calvo provide information abo the locomotion of titanosaurian sauropods that lived in South America during the Late Cretaceous. Titanopodus ichnit were found at Agua del Choique, a newly discovered track site in the Loncoche Formation, Late Campanian-Ear Maastrichtian of Mendoza, Argentina. This speed study follows the hypothesis of dynamic similarity proposed b Alexander. As a refinement of this method, a complementary equation is presented here based on an articulate titanosaurian specimen collected in strata that are regarded as correlative to those that have yielded Titanopodus trac (Allen Formation, Neuquén Basin). This analysis indicates that hip height can be estimated as 4.586 times the leng of the pes track in derived titanosaurs. With an estimation of the hip height and the stride measurements, the spee is calculated. The study of two wide-gauge trackways indicates that Titanopodus ichnites were produced by medium sized titanosaurs (hip height of 211-229 cm) that khendricks@example.net km/h towards the south and southwest, followin in part, a sinuous pathway. These speeds and some taphonomic features of tracks (prominent rims, distorted elongate shapes) indicate the capacity of derived titanosaurs for walking effectively over a very wet and slippery substrate. In th ichnological record, the walking speeds of Titanopodus trackmakers are somewhat faster than those previously inferr for most sauropods.
INTRODUCTION
Important dinosaur tracksites have been described in South America, particularly in Chile (Casamiquela and Fasola 1968 , Moreno and Pino 2002 , Moreno et al. 2004 , Bolivia, and Brazil (Leonardi 1989 , Meyer et al. 2001 , Lockley et al. 2002 . In Argentina, dinosaur track sites are known from Salta, Neuquén, and Mendoza provinces.
In Salta (near eastern Puna), theropod and ornithopod tracks were discovered in the upper levels of the Yacoraite Formation (Maastrichtian) (Alonso 1980, Alonso and Marquillas 1986). In this province, sauroIn Neuquén (northern Patagonia), dinosaur have been found in the Picún Leufú and El C areas (Fig. 1) . These tracks were found in outcr the Candeleros Formation (Cenomanian), a unit characterized by deposits corresponding to mean rivers, poorly channeled ephemeral flows, and lakes. Titanosaurian tracks from this formation named Sauropodichnus giganteus (Calvo 1991, 1 Recently, a new tracksite, the first to be des from Mendoza Province, was discovered in th Campanian-Early Maastrichtian strata of the Lo
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BERNARDO J. GONZÁLEZ RIGA pod tracks were recently assigned to a new ichnotaxon named Titanopodus mendozensis (González Riga and Calvo 2009) . These tracks are an excellent example of the wide-gauge style of sauropod locomotion without impressions of manual phalanges. These features, together with the fossil record of the Loncoche Formation and equivalent units in Patagonia (Allen and Los Alamitos Formations), suggest that the Titanopodus trackmakers were, probably, saltasaurine or aeolosaurine titanosaurs. Titanosauria is a diverse sauropod clade that includes more than 50 species of worldwide distribution. However, studies of speed, gait and stance of these dinosaurs are scarce and most biomechanical aspects related to titanosaur locomotion are unknown. Only Sauropodichnus tracks, which have been attributed to basal titanosaurs, have been studied in this regard (Mazzetta and Blanco 2001, Calvo and Mazzeta 2004) . In this context, the objective of this paper is to study, for the first time, the speeds and stance of the Titanopodus trackmakers. This study is important for understanding the locomotion and behavior of the latest titanosaurs that lived during the Late Cretaceous.
MATERIALS AND METHODS
This paper is based on a dinosaur track site located at Agua del Choique, 14 km west of the city of Malargüe in Mendoza Province, Argentina (Fig. 1A) . At this paleoichnological outcrop, the author and his team discovered multiple track-bearing levels both in the Anacleto and Loncoche Formations.
In the upper section of the Anacleto Formation (Early Campanian), three levels with sauropod tracks were located in floodplain fluvial facies (Fig. 1B) .
In the middle section of the Loncoche Formation (Late Campanian-Early Maastrichtian), two different levels with dinosaur tracks were found (Fig. 1B) . One of them occurs in a yellow grey calcareous sandstone and pertains to Titanopodus mendozensis (González Riga and Calvo 2009) . The other track level is located 80 cm above the former and is exposed only in crossProvince, this Formation is comprised by marginal marine facies (e.g., tidal flats, deltas, sabkhas deposits) that were produced by a shallow transgression of the Atlantic Ocean that covered central-northern Patagonia (Gonzá-lez Riga and Parras 1998). In the Ranquil-Có and Calmu-Co sections, the Loncoche Formation has yielded a varied association of fossil fishes and reptiles (González Riga 1999, Previtera and González Riga 2008) . These vertebrate assemblages are associated with ancient tidally dominated deltaic deposits and include a mixture of terrestrial vertebrates (dinosaurs and snakes), together with freshwater taxa (e.g. turtles, fishes), as well as marine or littoral forms (plesiosaurs and rays). Parras et al. (1998) recognized two depositional environments in the Agua del Choique area. The first is attributed to a river-dominated delta and lake setting, and the second corresponds to a river-dominated delta that changed to a tide-dominated delta. A detailed environmental analysis of the Titanopodus track site, including sedimentological and paleopalynological data, is presently in progress and will be published elsewhere.
The Titanopodus level dips 12 degrees towards the northeast (80 • ). It extends across three areas. Area A (35 • 26 55.2 S; 69 • 44 2.0 W) includes approximately 160 tracks in four principal trackways (AC-1 to AC-4 in this paper). Area B is located 234 m to the south of area A and comprises around 100 tracks partially covered by sediments. Area C is located 150 m south of area B and includes more than 50 tracks (González Riga and Calvo 2009) . In this paper we analyze trackways from area A.
The trackways were photographed and mapped, and some tracks were cast with plaster under the abbreviation of IANIGLA-PV.
The first method for estimating the speed of dinosaurs was proposed by Alexander (1976) , who supported his analysis using the hypothesis of dynamic similarity. According to this hypothesis, the movements of animals with geometrically similar shapes, even if they are different in size, are dynamically similar only when they move with equal values of the Froude number. This number is a non-dimensional parameter used where in-SPEED OF TITANOSAUR SAUROPODS Dynamically similar movements (i.e., those with equal Froude numbers) require equal values of relative stride length (S/H where S is stride length). The relationship between the relative stride length and the Froude number allows one to estimate speed. On this basis, Alexander (1976) proposed the following equation:
( 1) In this formula, the S and H values are entered in meters and V is solved in meters per second. Although refinements to the method have been proposed This method involves the measurement of length (S) and the estimation of height at the hi The parameter S is the distance among corresp points on successive prints of the same foot, and ily measured in trackways. In contrast, the esti of H is difficult because it is related with the len the hind foot print (L) through some mathemati tios. This parameter is tested for derived titanos this paper.
Alexander (1976) has pointed out that exta restrial mammals change from a walk to a run "main" -2011/2/10 -16:13 -page 282 -#4
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BERNARDO J. GONZÁLEZ RIGA and Wade 1984), Alexander's (1976) observations on the gaits of extant vertebrates were extended to define three different gaits in dinosaurs: walk (S/H < 2.0), trot (S/H between 2.0 and 2.9), and run (S/H > 2.9). Finally, the equation (1) is limited to estimating the speed at which a particular trackway was made and cannot be used for estimating the top running speed of a dinosaur (Coombs 1978).
INSTITUTIONAL ABBREVIATIONS
IANIGLA-PV -Instituto Argentino de Nivología, Glaciología y Ciencias Ambientales, Colección Paleovertebrados, Argentina. MUCPv -Museo de Geología y Paleontología, Universidad Nacional del Comahue, Argentina.
RESULTS AND DISCUSSIONS

ANALYSIS OF ANATOMICAL EVIDENCES
An estimation of the height at the hip joint (H ) is the first step for calculating the speed of a given dinosaur. Alexander (1976) , following the skeletal proportions of the diplodocid sauropod Apatosaurus, considered that H is four times the length of the pes footprint (L). He estimated similar values (e.g., L = 0.23 − 0.38H ) for many bipedal dinosaurs of a wide range of sizes, both theropods and ornithopods. Thulborn (1990) claimed that the assumption of H = 4L is likely to be incorrect for two reasons. First, the H/L ratio varies in systematic fashion among dinosaur taxa. Second, the H/L ratio certainly changes during ontogeny, on account of the allometric growth that prevails in terrestrial vertebrates. This author supposed that juveniles have relatively larger feet (and therefore smaller H/L ratio) than do adults of the same taxon.
In bipedal dinosaurs, Alexander (1991) and Thulborn and Wade (1984) proposed some refinements to this estimation using allometric equations in some cases. Alternatively, Henderson (2003) studied other methods using computer models. In contrast, recommendations for quadrupedal dinosaurs are less clear because, in many In this paper, as refinements of previous studies, I estimate the hip height of derived titanosaurs using anatomical and ichnological lines of evidence.
First, it is important to analyze the anatomical proportions of the probable trackmakers. The ichnological features of Titanopodus indicated that its trackmakers were sauropods of wide-gauge stance where both manus and pes prints were well separated from the midline, as is described in titanosauriforms (Wilson and Carrano 1999) . In trackway AC-1 (Fig. 2 , holotype of Titanopodus), the total width of the trackway is about 125-132 cm, and the inner trackways width is about 40 cm. This feature can be carefully analyzed following the manus and pes trackway ratios (MTR and PTR) proposed by Romano et al. (2007) . These indices are defined as the ratio of the track width measured transversely to the midline (side width, SW ) relative to the total width of the trackway (overall width, O W ) as follows: T R = SW/O W × 100. In the present case, trackway AC-1 shows MTR and PTR values of 22.09 and 31.32 per cent, respectively. These values indicate that Titanopodus has a very wide-gauge trackway in comparison with other known trackways. Moreover, the absence of impressions of manual phalanges and the Late Cretaceous age of these ichnites indicate that the trackmakers were, probably, derived titanosaurs.
In Argentina, almost all Late Campanian-Maastrichtian sauropods correspond to Aeolosaurini and Saltasaurinae titanosaurs. The aeolosaurines include Aeolosaurus rionegrinus from the Angostura Colorada Formation (Powell 1987) . The named species of saltasaurines comprise two forms from the Allen Formation: Bonatitan reigi (Martinelli and Forasiepi 2004) and Rocasaurus muniozi (Salgado and Azpilicueta 2000), and one species from the Lecho Formation: Saltasaurus loricatus (Bonaparte and Powell 1980) .
It is important to consider that, in the same strata that have yielded Titanopodus tracks (precisely the Allen Formation, a lateral equivalent of the Loncoche Formation and also deposited in the Neuquén Basin), two saltasaurine titanosaurs have been found: Bonatitan Obviously, we cannot definitively identify the trackmaker of Titanopodus to the genus level; however, Among these titanosaurs, an interesting spe for studying the appendicular skeleton is that La Invernada taxon (MUCPv-1533). It was disc 230 km south of the Titanopodus tracksite and pre the caudal series and fore-and hind limbs, the la cluding a complete and articulated left pes (Go Riga et al. 2007 .
The forelimb of MUCPv-1533 includes fi ticulated metacarpals, which form a semi-tubul U-shaped vertical structure, as in other sauropod church 1994, Wilson and Sereno 1998, Wilson This particular morphology limited tensional st the forearm, and was related to the gigantism o quadrupedal dinosaurs (Bonnan 2003) . This spe preserves no evidence of manual phalanges, as most all derived titanosaurs (Salgado et al. 1997 (Salgado et al. , et al. 2007 . A partially similar condition is ob in Epachthosaurus from the Late Cenomanian Turonian of Chubut Province, Argentine Pat (Martínez et al. 2004) , and Opisthocoelicaudia fr Maastrichtian of Mongolia (Borsuk-Bialynicka In these two species, no manual phalanges are p with the exception of a vestigial element fused distal surface of metacarpal IV.
In the ichnological record, the semi-tubular ture of the sauropod metacarpus is preserved, i cases, as a characteristic crescent shape of manu (e.g., Farlow et al. 1989 , Lockley 1991 , Santos 1994 , Calvo 1999 , Lockley et al. 2004 In particular, the manus tracks of Titanopodus a strongly asymmetrical crescentic contour and e no evidence of manual phalanges (Fig. 3B-C) asymmetry is in agreement with the manus specimen MUCPv-1533, where the metacarpals II are very robust elements in comparison with laterally-positioned metacarpals (Fig. 3D) . This metry is absent in the Patagonian titanosaur Epa saurus (Fig. 3E) The pes of MUCPv-1533 is also typically asymmetrical, relatively short and wide (Fig. 3F) . Metatarsals III and IV are the longest elements; the phalangeal formula is: 2-2-2-2-0, and the first three digits carry sickle-shaped unguals (González Riga et al. 2008 In a preliminary reconstruction of the hind limb, I assume a semi-plantigrade posture, with an angle of (2005) proposed a similar disposition (45 • ) for sauropods in general, following the hypothesis that these dinosaurs had an elastic plantar pad. There are no detailed studies of these postural aspects in titanosaurs, but it is possible that, within a single pes, different metatarsals had differing inclinations, as in modern elephants. In these mammals, the digitigrade pedes are functionally plantigrade (Miller et al. 2007 ) due to the presence of a fatty foot pad that acts in a fashion analogous to highheeled shoes in humans.
In the graphic reconstruction of the specimen MUCPv-1533 (Fig. 4) , the acetabulum (e.g., the hip joint) is located 197 cm above the ground.
ESTIMATION OF HIP JOINT HEIGHT
Based on the reconstruction of the titanosaur hind limb (Fig. 4) , the hip joint height can be expressed as an equation:
In this equation, F is the femur length, A f is the distance between the proximal end of the femur and the horizontal axis of movement of the femoral head (∼7% of the femur length), K e (Knee) is the space for the femoral-tibial articulation (preliminarily, I assumed a value of ∼3% of the femur length), T is the tibia length, A is the height of the astragalus, Mt is the length of the metatarsal III, a is the inclination of the metatarsals (usually interpreted as 40-50 • ), and Php is the height of a hypothetical pad located ventral to the phalanges, following Gallup's (1989) reconstruction of the pes of the titanosauriform Pleurocoelus. In this formula, I assume that Php is 50% of the dorsoventral diameter of the first phalanx of digit III (see Php in Fig. 4) .
Also included in this reconstruction is an elastic plantar pad (as a heel) that distributes the weight transmitted through the pes. Obviously, the development of this plantar pad can modify the reconstruction of the length of the pes track. I assume that the track length (L) can vary by about 5% depending on different interpretations of this plantar pad ( P L). Other feature is the According to this analysis, the Titanopodus tracks were produced by medium-sized titanosaurs. Sizes and anatomical proportions are estimated in based on the equation 3 and ichnological data. Trackways AC-1 and AC-4 were produced by sauropod specimens that had a hip height (H ) of 211 cm and 229 cm, respectively (Fig. 5) . The ratio of glenoacetabular distance to hip joint height (G AD/H ) is useful for estimating the body length and relative anatomical proportions. According
In trackway AC-1 (18.5 m long; 27 ichnites), one titanosaurian individual khendricks@example.net km/h towards the southwest (193-224 degrees) . In trackway AC-4 (46.2 m long; 71 ichnites), a slightly larger titanosaur khendricks@example.net km/h following a sinuous pathway towards the south (176 degrees), southwest (224 degrees), south (172 degrees) and, finally, again the southwest (253 degrees).
The stride values (245 cm for the pes) and the pes length are larger than those from trackway AC-1 (235 cm), but length) in comparison with the best preserved prints that reach 46 and 50 cm in trackways AC-1 and AC-4, respectively. In elongated and distorted tracks, the presence of prominent rims indicates high water content in the substrate and some degree of sliding of the pedes during locomotion. Thus, the Titanopodus trackmakers moved at moderate speed, indicating their capacity to effectively walk over very saturated substrates. The ratio of stride length to hip height (S/H ) reaches values of 1.11, indicating that the gait is a walk (not a trot or run), after the definitions of Alexander (1976) and Thulborn and Wade (1984) .
The estimated speeds of sauropods generally never surpass 7.2 km/h (Thulborn 1990) . For example, the sauropod trackmakers of Rotundichnus muenchehagensis from the Lower Cretaceous of Germany show ranges from 3.1 to 4.5 km/h (Lockley et al. 2004 ) (although these authors used the ratio H = 5L to calculate the speed in these wide-gauge trackways). Another study of speed in a wide-gauge sauropod trackmaker was made using ichnites from the Candeleros Formation of northern Patagonia. In this unit, the Sauropodichnus trackmakers reached speeds of only 1.7-2.3 km/h (Mazzetta and Blanco 2001) , indicating a very slow pace in a medium-sized basal titanosaur. In contrast, according to this analysis, the walking speeds of Titanopodus trackmakers (4.9 km/h) are somewhat faster than those previously inferred for most sauropods. 

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