The Tail of Tyrannosaurus: Reassessing the Size and Locomotive Importance of the M. caudofemoralis in Non-Avian Theropods



Unlike extant birds and mammals, most non-avian theropods had large muscular tails, with muscle arrangements similar to those of modern reptiles. Examination of ornithomimid and tyrannosaurid tails revealed sequential diagonal scarring on the lateral faces of four or more hemal spines that consistently correlates with the zone of the tail just anterior to the disappearance of the vertebral transverse processes. This sequential scarring is interpreted as the tapering boundary between the insertions of the M. caudofemoralis and the M. ilioischiocaudalis. Digital muscle reconstructions based on measurements of fossil specimens and dissections of modern reptiles showed that the M. caudofemoralis of many non-avian theropods was exceptionally large. These high caudofemoral mass estimates are consistent with the elevation of the transverse processes of the caudal vertebra above the centrum, which creates an enlarged hypaxial region. Dorsally elevated transverse processes are characteristic of even primitive theropods and suggest that a large M. caudofemoralis is a basal characteristic of the group. In the genus Tyrannosaurus, the mass of the M. caudofemoralis was further increased by dorsoventrally lengthening the hemal arches. The expanded M. caudofemoralis of Tyrannosaurus may have evolved as compensation for the animal's immense size. Because the M. caudofemoralis is the primary hind limb retractor, large M. caudofemoralis masses and the resulting contractile force and torque estimates presented here indicate a sizable investment in locomotive muscle among theropods with a range of body sizes and give new evidence in favor of greater athleticism, in terms of overall cursoriality, balance, and turning agility. Anat Rec,, 2010. © 2010 Wiley-Liss, Inc.

The associations between muscle mass, vertebrae morphology, and function have been well studied in the tails of extant mammals, particularly procyonids and primates, and tail biomechanics are better understood among mammals than any other group of terrestrial vertebrates (Dor,1937; German,1982; Lemelin,1995; Organ et al.,2009). However, in terms of mass and volume, most fully terrestrial mammals have unimpressive tails. Large terrestrial mammals, in particular, tend to have minimalist fly-swatter tails, and our own species, with nothing but a vestigial stub, is at the furthest extreme. As a result, when considering the relatively large tails of most non-avian dinosaurs, there has been a misleading tendency to regard tails as predominantly dead weight or, at best, as either defensive lashing weapons or (in bipedal taxa) as mere counterbalances for the crania. Modern reptiles represent the best modern analogs for the tails of most dinosaurs and demonstrate that large tails may serve a variety of consequential functions, including femoral retraction during the locomotive power stroke via the M. caudofemoralis.

The M. caudofemoralis is a tail muscle that inserts directly onto the fourth-trochanter of the femur, and acts as a femoral retractor. Extant mammals lack the M. caudofemoralis; instead, the gluteal muscles fill the role of primary limb retractors. Some mammals do have a muscle that is commonly termed the “M. caudofemoralis,” but this muscle is not homologous to the M. caudofemoralis of saurians and birds (Appleton,1928; Howell,1938). In modern Aves, knee flexion is more important to locomotion than femoral retraction (Gatesy and Biewener,1991; Carrano,1998; Farlow et al.,2000), and the M. caudofemoralis is greatly reduced in most birds and altogether absent in others (Gatesy,1990). In crocodilians and the majority of non-serpente squamates, however, the M. caudofemoralis is both the primary and the single largest retractor muscle of the hind limb (Snyder,1962; Gatesy,1990). Electromyographic studies of walking and running crocodiles have shown the M. caudofemoralis to be consistently active at all speeds, whenever femoral retraction occurs (Gatesy,1997).

The presence of large caudofemoral muscles in non-avian dinosaurs was noted as early as 1833, when Louis Dollo inferred their existence from the large femoral fourth trochanter of the herbivorous dinosaur Iguanodon (Dollo,1883). In Gatesy's1990 study of the M. caudofemoralis and its reduction in the lineage leading to extant birds, he argued that the muscle's gradual shrinkage resulted from a push towards overall tail weight reduction and from the tail's functional shift from locomotion to dynamic stabilization, with both trends relating to the evolution of flight (Gatesy,1990). Gatesy also argued insightfully that the M. caudofemoralis undoubtedly made the locomotion of most non-avian dinosaurs (perhaps, particularly the bipedal taxa) fundamentally different from what can be observed in any modern mammalian or avian analogue (Gatesy,1990).

Despite such arguments, the M. caudofemoralis has been undervalued in the majority of dinosaur biomechanical studies, and its contribution to locomotion has not been quantitatively analyzed. Moreover, the M. caudofemoralis has become a point of anatomical confusion, with different authors using different osteological correlates to infer its overall size and shape (Madsen,1976; Carpenter et al.,2005; Arbour,2009; Schwarz-Wings et al.,2009). As a consequence of this confusion, the tails of non-avian dinosaurs are commonly reconstructed with improbable muscle morphology and overly conservative masses, which appear altogether emaciated when compared to the tails of modern reptiles (Fig. 1).

Figure 1.

Tyrannosaurus dorsal silhouette (A) previously used in body-mass estimation (Modified from Paul,1997), compared with a modern Alligator dorsal silhouette (B) (Modified from Cong,1998). The basal bulge in the tail of the Alligator is primarily the result of a large M. caudofemoralis.

Here, basic caudal musculature of modern reptiles is used for more accurately reconstructing the muscle anatomy of dinosaur tails. The locomotive implications of the reconstructions are considered both qualitatively and quantitatively for non-avian theropods (the primarily carnivorous group of dinosaurs that gave rise to birds and for which the majority of previous locomotive biomechanical research has been done).



The pelvic and post pelvic musculature of a Basiliscus vittatus (brown basilisk), Caiman crocodilus (spectacled caiman), Chamaeleo calyptratus (veiled chameleon), Iguana iguana (green iguana), and Tupinambis merianae (Argentinean black and white tegu) were dissected. All specimens had been preserved via deep freezing and showed no signs of desiccation prior to dissection. Immediately following in situ observations and measurements, individual muscles were removed from each specimen and massed (Table 1). Epaxial muscles that were continuous into the pre-pelvic region were severed in line with the midpoint of the acetabulum.

Table 1. Caudal muscle mass of theropods and extant reptiles
  M. spinalisM. longissimusM. ilio- ischiocaudalisM. caudofemoralis
Caiman CrocodilusMass (g)1.49.6913.8
Spectacled caimanPercent4.1%28.4%26.6%40.8%
Tupinambis merianaeMass (g)3.922.512.213.3
Black and white teguPercent7.5%43.4%23.5%25.6%
Iguana iguanaMass (g)20.852.67049.2
Green iguanaPercent18.8%27.3%36.3%25.5%
Basiliscus vittatusMass (g)0.62.433.4
Brown basiliskPercent6.4%25.5%31.9%36.2%
Chamaeleo calyptratusMass (g)
Veiled ChameleonPercent9.1%27.3%36.4%27.3%
Ornithomimus edmontonicusMass (g)860244050509890
TMP 95.11.001Percent4.7%13.4%27.7%54.2%
Gorgosaurus libratusMass (g)390069001030017,300
TMP 91.36.500Percent10.2%18.0%26.8%45.1%
Tyrannosaurus rexMass (g)65200154200159400522200
BHI 3033Percent7.2%17.1%17.7%58.0%

Three advanced non-avian theropods are considered in this study: Gorgosaurus libratus (TMP 1991.36.500), Ornithomimus edmontonicus (TMP 1995.11.001), and Tyrannosaurus rex (cast of BHI 3033 currently on loan to the Smithsonian National Museum of Natural History). The specimens were chosen based on the completeness of the caudal series. Osteological dimensions of the femora, pelvic girdle, and caudal series were taken, and these measurements were later used in modeling digital skeletons. TMP 1991.36.500 is a juvenile; however, comparisons between the measurements of TMP 1991.36.500 and those of less complete but more mature Gorgosaurus specimens (TCM 2001.89.1 and AMNH 5458) indicate that proportions of the caudal skeleton varied little through ontogeny. Because both TMP 1991.36.500 and TMP 1995.11.001 are panel mounts, some measurements (such as transverse centrum width) could not be made for every vertebra in the series, and measurements had to be supplemented with those made on other similarly sized specimens (including AMNH 514, AMNH 5355, TMP 1999.33.1, and NMNH 2164). Likewise, the mounted skeleton of BHI 3033 was so large and difficult to reach that some measurements were supplemented with those made indirectly from photographs. Whenever possible, previously collected data on the original specimen of BHI 3033 were used to verify the accuracy of these measurements. Measurements were also made on published illustrations of other Tyrannosaurus specimens (Paul, 1996; Brochu,2002) and were used to supplement portions of the tail that were not preserved in BHI 3033.

Computer Modeling

Using the modeling software Rhinoceros (McNeel Robert and Associates,2007), the hips and caudal series of each of the three theropod specimens were digitally sculpted based on the skeletal measurements. Three-dimensional models of the various caudal muscles were then sculpted overtop of the digital skeleton, according to the osteological relations determined from the dissections. The volume of each restored muscle was then calculated by the software. Because muscle is known to have a fairly constant density of 1.06 g/cm3 (Mendez and Keys,1960), the muscle volume estimates could then be multiplied by this density value to obtain estimates of muscle mass.

To verify the accuracy of the restoration techniques used in sculpting the various theropod caudal muscles, digital skeletons were also made from measurements taken on three of the dissected reptiles: the Argentinean black and white tegu, green iguana, and spectacled caiman. Digital skeletons were not made for the brown basilisk and the veiled chameleon, because these specimens were too small to measure using the same methods and equipment. The same modeling techniques were then used to reconstruct the musculature and to estimate muscle volume and mass for the three extant reptiles, and these muscle mass estimates were then compared to the true muscle masses as measured during the dissections.


To evaluate the potential contribution of the M. caudofemoralis to femoral retraction, the digital muscle reconstructions of each theropod were used in combination with a series of standard biomechanical equations. First, M. caudofemoralis mass was calculated using a standard muscle density of 1.06 g/cm3 (Mendez and Keys,1960). Then, the physiological cross-sectional area (PCSA) of the M. caudofemoralis was calculated according to Eq. (1) (Sacks and Roy,1982; Snively and Russell,2007), where m is the total mass (the mass of one M. caudofemoralis, not the mass of the total bilaterally symmetric muscle set); σ is the pennation angle of the muscle fibers within the M. caudofemoralis and, based on measurements of the dissected specimens, is assumed to be approximately equal to 1.00 (0.95), d is muscle density (again, assumed to be 1.06 g/cm3), l is the average fascicle length within the M. caudofemoralis and was calculated for each taxa based on the digital model and close examination of the fascicles in the spectacled caiman specimen:

equation image(1)

Because calculating physiological cross-sectional area requires several assumptions, many authors favor the simpler method of measuring anatomical cross-sectional area (ACSA), which is simply the cross-sectional area through the muscle at its greatest width (Snively and Russell,2007). Anatomical cross-sectional areas were also measured from the digital models and compared to the calculated physiological cross-sectional areas. In all three instances, the two values varied only slightly from one another, as would be expected, given the assumed σ value of approximately 1 (Bamman et al.,2000) (Table 2).

Table 2. Cross-sectional area in the M. caudofemoralis among theropod taxa
 Mass (g)Average fascicle length (cm)PCSA (cm2)ACSA (cm2)PCSA/ACSA variation
Ornithomimus edmontonicus (TMP 95.11.001)494531.423141.038127.6751.105
Gorgosaurus libratus (TMP 91.36.500)865050.585153.254144.4861.061
Tyrannosaurus rex (BHI 3033)261,100129.6971804.2421794.4421.005

Specific tension (ST), also sometimes referred to as specific force (Brooks and Faulkner,1994), is a ratio of the strength of a muscle to its area and has been shown to vary among different muscles and among different taxa. Known ST values for hind limb muscles likely offer the best basis for estimating the ST value appropriate for the M. caudofemoralis of non-avian theropods. An overview of previously reported ST values that might be good analogs for the specific tension of the M. caudofemoralis of non-avian theropods is provided in Table 3. Estimates within the range of 25–35 N/cm2 would seem reasonable. Here, ST is assumed to be 25 N/cm2 for all the theropod taxa (certainly a conservative estimate).

Table 3. Summary of previously reported specific tension values for hind limb muscles of extant animals
AnimalMuscle(s)ST (N/cm2)Source
Domestic catCaudofemoralis31.2Brown et al. (1997)
HumanThigh average27.3–30.0Storer et al. (2003)
Quarter horseGluteus medius25.9Marx et al. (2005)
White rhinocerosHamstring34.4Marx et al. (2005)

The total contractile force (Ft) of the M. caudofemoralis was estimated by multiplying the calculated PCSA by the assumed ST (25 N/cm2):

equation image(2)

Although the calculated total contractile force of the M. caudofemoralis is useful as a comparable factor between taxa, a more accurate measure of its true contribution to locomotion is its capacity to generate torque. As outlined in Snively and Russell (2007), a muscle's torque-generating capacity is proportional to the force the muscle exerts in a direction orthogonal to its moment arm (the moment arm being measured from the joint's center of rotation to the muscle's insertion). This orthogonal force is here termed the effective force (Fe). The Fe of the M. caudofemoralis is calculated with the following equation, where θ is the angle between the vector of line of pull of the M. caudofemoralis and a vector orthogonal to the moment arm (for the M. caudofemoralis, the moment arm is the dorsal-ventral distance from the midpoint of the femoral head to the midpoint of the femoral fourth trochanter), calculated for a femur positioned perpendicular to the ground:

equation image(3)

Finally, the potential torque generation of the M. caudofemoralis is calculated with the equation:

equation image(4)

Here, ϕ is the angle between the vectors of the moment arm and the effective force (this angle is assumed to be 90° and the sinϕ is, therefore, equal to 1), and R is the length of the moment arm (again assuming a femur positioned perpendicular to the ground).

Abbreviations used: AMNH = American Museum of Natural History, New York, New York, USA; BHI = Black Hills Institute of Geological Research, Hill City, South Dakota, USA; FMNH = Field Museum of Natural History, Chicago, Illinois, USA; NMNH = Smithsonian Institution National Museum of Natural History, Washington, District of Colombia, USA; TCM = The Children's Museum of Indianapolis; TMP = Royal Tyrrell Museum of Palaeontology, Drumheller, Alberta, Canada


Caudal Musculature and Osteological Correlates of Extant Reptiles

The literature is filled with inconsistent and often redundant terminology schemes for the caudal muscles of reptiles. Following the recent scheme established by Arbour (2009), I will acknowledge four major paired muscle sets: the M. spinalis, M. longissimus, M. ilio-ischiocaudalis, and M. caudofemoralis. It should be noted that these four muscles form a good general, but overly simplistic, scheme, and subdivisions are clearly visible within many of these muscles, particularly in the posterior portions of the M. longissimus and M. ilio-ischiocaudalis. Like those of the limb, caudal muscles vary widely in size and relative proportions across reptilian taxa; however, the overall pattern of muscle insertions and positions remains relatively uniform (Figs. 2 and 3). The results presented here are based on the dissections of five taxa (one specimen each) and, combined with the previous literature, are intended to offer only a cursory overview of reptilian tail musculature.

Figure 2.

Sequential cross-sections through the tail of Tupinambis merianae. Tupinambis merianae was chosen to illustrate the anterior/posterior changes in muscle arrangement and morphology, because its tail is relatively unspecialized and its musculature is unremarkable in most respects. The cross-sections are anatomical abstractions, as they depict neural arches and hemal arches in the same vertical plane (these illustrations are similar in this way to those of Cong et al.,1998; Arbour,2009; Schwarz-Wings et al.,2009), but these views are preferable to ones that would omit either hemal or neural arches. A: Caudal vertebra 7; the M. caudofemoralis inserts across the lateral sides of the centrum and across the entire lateral face of the hemal arch. The M. ilio-ischiocaudalis is thin medially, but inserts across the entire ventral surface of the transverse processes, and only inserts onto the ventral tip of the hemal arch. B: Caudal vertebra 13; the M. caudofemoralis has begun to taper and the M. ilio-ischiocaudalis inserts across a ventral portion of the lateral face of the hemal arch. C: Caudal vertebra 18; the M. caudofemoralis is no longer present. The M. ilio-ischiocaudalis insets across the entire lateral face of the hemal arch and the lateral sides of the centrum. The transverse processes are absent. (Note, the posterior portion the tail is also a fat storage location in Tupinambis merianae; however, for simplicity, fat deposits have been not been shown).

Figure 3.

Lateral view (anterior left and posterior right) of the dissected tail of Tupinambis, with all muscles, except the M. caudofemoralis, removed. Highlighted regions correspond to cross-sections in Fig. 2.

On the basis of the dissections, the arrangement and osteological insertion sites of the caudal muscles are as follows.

M. spinalis.

The M. spinalis is the most dorsal of the caudal muscles and is present along the full length of the tail. The M. spinalis inserts onto the dorsal tips and the full lateral surfaces of the neural spines.

M. longissimus.

Composing the primary bulk of the epaxial tail musculature, the M. longissimus is also present along the full length of the tail and may be difficult to distinguish from the M. spinalis. This distinction becomes more difficult posteriorly, when subdivisions in the two muscles become increasingly independent. The M. longissimus has two strong dorsoventrally stacked subdivisions that are distinguishable in even the most anterior of cross sections. These two subdivisions are often regarded as separate muscles, with the more ventral subdivision retaining the name M. longissimus, and the more dorsal subdivision occasionally referred to as the M. tendinoarticularis (although this term has also been applied to the M. spinalis). There is no clear osteological indicator of the level at which these two M. longissimus subdivisions meet, and the functional differences between the two are currently unknown. Attempts herein to subdivide the M. longissimus of theropods would, therefore, be both highly speculative and ultimately uninformative.

Anteriorly, the M. longissimus inserts onto the full dorsal surfaces of the transverse processes and to the lateral faces of the neural arches. Posteriorly, after the transverse processes have terminated, the lateral faces of the neural arches are the only osteological insertion points of the M. longissimus. Throughout its anterior/posterior length, the M. longissimus is separated dorsally from the M. spinalis by a septum that stems from the lateral edges of the pre-zygapophyses and extends lateral at an often strongly dorsally inclined angle. [Note: Consistent with convention the large lateral projections of caudal vertebra are herein referred to as “transverse processes.” However, as originally argued by Romer (1956), the majority of these projections are probably homologues with the ribs of the dorsal series and are not true transverse processes. The term “caudal ribs” is likely more accurate for all but the most posterior caudal vertebra]. Both the M. longissimus and M. spinalis are continues into the dorsal region (Organ,2006).

M. ilio-ischiocaudalis.

Consistent with its nomenclature, the M. ilio-ischiocaudalis is composed of two major subdivisions: the m. iliocaudalis and the m. ischiocaudalis, with the former originating from the ilium and the later from the ischium. The M. ilio-ischiocaudalis is relatively thin anteriorly, where it attaches dorsally to the lateral tips and ventral surfaces of the transverse processes, raps around the M. caudofemoralis, and attaches ventrally both to the ventral tips of the hemal spines and to its bilaterally symmetric muscular doppelgänger that raps around from the other side. Posteriorly, the M. ilio-ischiocaudalis increases in relative thickness as the thickness of the M. caudofemoralis diminishes. After the disappearance of the M. caudofemoralis, the M. ilio-ischiocaudalis inserts onto the full lateral surface of the centrum and the hemal spines.

M. caudofemoralis.

Unique among the caudal muscles, the M. caudofemoralis is not partitioned by conical myosepta, and its overall form more closely resembles a limb muscle rather than an axial muscle. The primary caudofemoral tendon attaches the M. caudofemoralis to the fourth trochanter of the femur, and the auxiliary caudofemoral tendon (present in most extant reptiles but absent in birds) also anchors the M. caudofemoralis to the knee joint (Fig. 4).

Figure 4.

The anterior end of the M. caudofemoralis, its insertion onto the fourth trochanter of the femur, and the auxiliary tendon that inserts at the knee joint, seen in (A) Caiman (oblique dorsolateral view, anterior top, and posterior bottom) and (B) Tupinambis (oblique posterolateral view, anterior upper right, and posterior bottom left).

The M. caudofemoralis is composed of the m. caudofemoralis brevis, which fills the brevis fossa and may also insert across the anteriormost caudal vertebra, and the m. caudofemoralis longus. Throughout its anterior/posterior length, the m. caudofemoralis longus inserts medially onto the lateral faces of the caudal vertebra. However, the insertion of the m. caudofemoralis longus across the lateral faces of the hemal spines varies across the caudal series (Fig. 2). The M. caudofemoralis does not extend down the entire length of the tail (in none of the dissected reptiles did the M. caudofemoralis extend across even half of the tail's total length). Rather, the M. caudofemoralis extends posteriorly down the caudal series with a gradual reduction in overall size, then reaches a point where it begins to rapidly taper, and, shortly thereafter, terminates (Fig. 3).

Prior to the taper point, the M. caudofemoralis' medial insertion extends ventrally across the entire lateral face of the hemal arches. As it tapers, the M. caudofemoralis' medial insertion shrinks dorsally; correspondingly, the ventral insertion of the M. ilio-ischiocaudalis expands dorsally, and the M. ilio-ischiocaudalis begins to insert across an increasing proportion of the lateral faces of the hemal arches. Past the termination of M. caudofemoralis, the M. ilio-ischiocaudalis inserts across the entire lateral faces of both the hemal arches and the centrum. As they are no longer needed to provide dorsal insertion points for the M. ilio-ischiocaudalis, the transverse processes are usually no longer present after the M. caudofemoralis termination. However, because the transverse processes also serve as lateral insertion points for the M. longissimus, they may (as is the case in the Argentinean black and white tegu) remain present well after the M. caudofemoralis has terminated.

Evidence for the Posterior Taper Point and Ventral Boundary of the M. caudofemoralis in Non-Avian Theropods

Caudal 14 is the last transverse process-bearing vertebra of Ornithomimus TMP 1995.11.001 (Fig. 5). The transverse process is located at roughly the centrum's dorsoventral midpoint. Hemal arch 13 (positioned between caudal vertebra 13 and 14) is displaced slightly, with its posterior end tilted dorsally. A groove or scar is apparent running across its lateral face.

Figure 5.

Lateral view (anterior right and posterior left) of the M. caudofemoralis termination point of Ornithomimus TMP 1995.11.001. Caudal vertebra 14 bears the last transverse processes, which sit at roughly mid dorsal/ventral height. Hemal arch 13 (between caudal vertebra 13 and 14) is displaced slightly, with its posterior end tilted dorsally. Hemal arch 13 has a strong grove or scar across its lateral face. Reproduced from Arbour,2009.

The scar seen on hemal arch 13 is part of a continuous diagonal sequence of scars that runs anteroventral to posterodorsal across hemal arches 10–14 parallel to the axis of the tail (Fig. 6). This scar sequence coincides with the rapid decent of the transverse processes from an elevated height above the centra (a full 19.8 mm above at caudal vertebra 1) to the mid-centrum elevation seen on caudal vertebra 14. Together, the descending transverse processes and hemal arch scarring are here interpreted as demarcating the boundaries of the tapering M. caudofemoralis. Under this interpretation, the hemal arch scar is regarded as the insertion point for the skeletogenous septum that divided the M. caudofemoralis from the M. ilio-ischiocaudalis, and the anteroposterior ascent and eventual posterior disappearance of this scar is, therefore, taken to mark the M. ilio-ischiocaudalis' gradual dorsal intrusion and eventual usurpation of the M. caudofemoralis.

Figure 6.

Lateral view (anterior right and posterior left) of caudal vertebra 10–17 of Ornithomimus TMP 1995.11.001. Arrows point to the anterior edges of the M. ilio-ischiocaudalis/M. caudofemoralis septum scarring, visible on hemal arches 11–14 and the posterior end of hemal arch 10. Reproduced from Arbour,2009.

The M. ilio-ischiocaudalis/M. caudofemoralis septum scarring disappears anteriorly, reaching the ventral tip of hemal arch 10. The scar does not reappear on any of the more anterior hemal arches, and this is interpreted as evidence that, prior to the taper point, the M. caudofemoralis inserted across the entire lateral surfaces of the hemal arches. This is in contradiction to some restorations that have shown the M. caudofemoralis of dinosaurs riding high on the caudal series (see Arbour,2009; for one example), but is entirely consistent with the morphology seen in all of the dissected reptiles.

TMP 1995.11.001 displays the M. ilio-ischiocaudalis/M. caudofemoralis septum scar sequence more clearly than any of the other fossil specimens examined in this study; however, the scar sequence is by no means a feature unique to TMP 1995.11.001 or to Ornithomimus. The scars of TMP 1991.36.500 (Gorgosaurus), which, although faint, are unambiguously present (Fig. 7). The M. ilio-ischiocaudalis/M. caudofemoralis septum scars have not gone unnoticed by previous authors. For instance, although no explanation for the structure is offered, Brochu (2002) notes it existence in his wonderfully thorough description of the Tyrannosaurus specimen FMNH PR2081.

Figure 7.

Lateral view (anterior right and posterior left) of caudal vertebra 13-8 of Gorgosaurus TMP 91.36.500. The last transverse process is present on caudal vertebra 12. Although fainter than TMP 1995.11.001, the M. ilio-ischiocaudalis/M. caudofemoralis septum scarring is visible on hemal arches 11-7. Arrows point to the anterior edges of the scarring.

Evidence for the Lateral Boundary of the M. caudofemoralis in Non-avian Theropods

To model the M. caudofemoralis of theropods, the muscle's extent must be defined in all dimensions. The femoral fourth trochanter is the muscle's anteriormost insertion point. The transverse processes cap its dorsalmost limit, and the ventralmost margins of the hemal arches indicate its ventral extent. Both the M. ilio-ischiocaudalis/M. caudofemoralis septum scars and the rapid descent of the transverse processes mark its posterior taper point. What remains is determining the lateral extent of the M. caudofemoralis.

Traditionally, the lateral width of the caudal transverse processes has been used as a correlate for the girth of the M. caudofemoralis in all saurians. However, this method is without sound anatomical basis. As described, and contrary to the depictions and descriptions of Caldwell (2006), Arbour (2009), Schwarz-Wings et al. (2009), and various others, the M. caudofemoralis does not attach to the lateral tips or ventral surfaces of the transverse processes. Rather, both are insertion points of the M. ilio-ischiocaudalis (the near vertical caudal transverse processes of some advanced abelisaurids are a possible exception).

When viewed casually in most reptile dissections the transverse processes are easily mistaken for an M. caudofemoralis insertion point, because the portion of the M. ilio-ischiocaudalis that attaches to the transverse processes is usually quite thin. Adding to this confusion is the high profile and commonly cited 1923 reconstruction by Alfred Romer of the hip and hind limb musculature of Tyrannosaurus, in which the M. caudofemoralis is clearly, but incorrectly, shown attaching to the lateral tips of transverse processes (Romer,1923). Romer does comment in the same manuscript that there is a lack of good tail muscle data available for crocodiles—the analogue on which he most heavily relied—and, 4 years later, he did correct himself when reconstructing the hip and hind limb musculature of ornithischian dinosaurs (Romer,1927). Nonetheless, his Tyrannosaurus reconstruction remains the one to which most researchers have paid attention.

The transverse processes also do not appear to be good indirect indicators of the M. caudofemoralis' lateral extent. The spectacled caiman, for example, had the relatively largest M. caudofemoralis of any of this study's extant reptiles, but the lateral widths of its transverse processes, relative to other aspects of its caudal vertebrae, were only average. In contrast, the dissected Argentinean black and white tegu specimen had among the relatively smallest caudofemoral muscles, but the relatively widest transverse processes. The dissections also revealed that the width of the M. caudofemoralis varies relative to the length of the transverse processes across the caudal series of the same individual, with the caudofemoral muscles extending well beyond the lateral tips of the transverse processes at the anterior base of the tail, and usually extending well short of the tips at and near the taper point.

Recognizing that the transverse processes do not bear a M. caudofemoralis insertion and that they are not good indicators of its lateral width is important, because this has dramatic implications for the overall shape of the hypaxial region of the tail. Figure 8a shows a restored cross-section through the anterior tail base of Allosaurus from Madsen (1976). Madsen's reconstruction follows the traditional restoration method, and assumed a caudofemoralis that inserted onto the ventral surfaces of the transverse processes and that did not bulge past their ventral-most tips. As a result, the tail is widest dorsal to its midpoint, at or just below the level of the transverse processes, producing an inverted tear-drop shaped cross-section. For comparison, the widest portion of the tail of a modern caiman is at roughly mid-hypaxial height (Fig. 8b).

Figure 8.

Comparison of anterior caudal cross-section reconstructions for (A) Allosaurus (Modified from Madsen,1976), with greatest width assumed to be roughly equal to the lateral extent of the transverse processes and (B) Caiman, reconstructed based on dissection and showing greatest lateral extent to be at roughly mid hypaxial height.

Muscle Reconstruction

In creating this study's reconstructions (Figs. 9, 10, 11, 9–11), the vertical cross-section of the M. caudofemoralis was treated as elliptical in overall shape—consistent with the M. caudofemoralis in all the dissected specimens—and was modeled across the caudal series (Fig. 10) by tracing an arc from below the medioventral base of the transverse process to the ventral tip of the hemal arch.

Figure 9.

Tyrannosaurus BHI 3033 in dorsal view with M. caudofemoralis musculature reconstructed and in lateral view with full caudal musculature reconstructed. Skeletal image Modified from Paul, 1989.

Figure 10.

Prior to the anterior tapering of the M. caudofemoralis longissimus, its lateral margin was reconstructed at each vertebra, as shown, by tracing a symmetric arch from below the medioventral base of the transverse process to the ventral tip of the nearest hemal arch.

Figure 11.

Modeling sequence for the tail of Tyrannosaurus BHI 3033. A: Skeleton model constructed based off dimensional measurements. B: Model with M. caudofemoralis longissimus sculpted overtop of the skeleton model. C: Full muscle restoration with M. spinalis, M. longissimus, and M. ilio-ischiocaudalis visible.

Comparisons, based on the dissected reptile specimens, between mass predictions for the M. caudofemoralis derived from digital reconstruction models and the M. caudofemoralis masses actually measured, confirm the accuracy of this restoration technique (see Table 4). All predicted M.caudofemoralis masses are within 6% of the true mass and slightly lower than the true value. This is probably because, at the anterior-most base of the tail, the M.caudofemoralis has a more extensive lateral bulge that diverges from the overall shape seen more posteriorly. The mass estimates presented here are, therefore, conservative.

Table 4. True M.caudofemoralis mass versus estimated mass, based on digital models, in the extant reptiles
 True mass (g)Modeled mass (g)Accuracy
Caiman crocodilus13.812.997−5.8%
Tupinambis merianae13.312.692−4.6%
Iguana iguana49.248.194−2.0%

The measured tail muscle masses of the dissected extant reptiles and the estimated tail muscle masses of the three theropods are presented with the percentages of total tail muscle mass (Table 1). These percentages offer one way to quantify the relative size of the different tail muscles across the various taxa.

Among the extant taxa, the spectacled caiman (the only crocodilian considered in this study) had the highest percentage of its tail muscle mass contributed by the M. caudofemoralis. The brown basilisk had the second highest caudofemoral percentage. Given the caiman's closer phylogenetic relation and the basilisk's bipedal running style, the large M. caudofemoralis found in both of these taxa could be taken as indirect support for a large M. caudofemoralis in bipedal non-avian theropods.

Among the three extinct taxa, Tyrannosaurus had the largest relative (and absolute) M. caudofemoralis. However, all three theropods were estimated as having substantially larger caudofemoral muscles than any of the modern reptiles. Given that the M. caudofemoralis is the primary retractile muscle of the hind limb, and given the numerous advanced locomotive adaptations present in non-avian theropods, this high relative investment in caudofemoral mass should, perhaps, not be surprising. But the osteological features associated with this caudofemoral bulk-up do merit special note. Two such features are readily identifiable from this study: the strong dorsally inclined angle of the transverse processes and the elevation of the transverse processes on the neural arch (Fig. 12).

Figure 12.

Anterior view of caudal vertebra 1 of Ornithomimus NMNH 2164. Note the dorsally angled transverse processes, and the dorsal elevation of the transverse processes above the centrum, which create an expanded hypaxial region.

The caudal transverse processes of all the dissected extant reptiles protrude at flat, fully horizontal angles. Anterior vertebrae with dorsally angled transverse processes are present in many theropod taxa, and the angled transverse processes would have provided an expanded hypaxial region that the M. caudofemoralis could have filled. However, angled transverse processes are not characteristic of all theropod taxa (they are absent in both Tyannosaurus and Gorgosaurus), and, when present, usually only occur on the first three or four caudal vertebra.

More important, then, would seem to be the elevation of the transverse processes on the neural arch, above the centrum. This too creates a greatly expanded hypaxial region (at the expense of the epaxial region), and the M. caudofemoralis is the only muscle that is likely to have filled this space. Dorsally elevated transverse processes are found in even primitive theropods, including Coelophysis and Herrerasaurus. This suggests that a large M. caudofemoralis is a basal characteristic of the group and appears to have remained present in nearly all non-avian theropod lineages (the character appears to be absent in the highly derived and specialized tails of Paraves). Elevated transverse processes are not only present on the anteriormost tail vertebra of most non-avian theropods, but remain elevated down the series, until rapidly descending at the taper point.


Interpreting the results of the biomechanical calculations performed for each of the three theropods (Table 5) is hindered by the lack of analogous data available for modern animals with muscles of equivalent size. The data can most confidently be used to compare different theropod taxa, but it should be noted that the high torque estimates calculated for all three theropod taxa are consistent with what would generally be predicted for muscles of their size based on what is known about the physiology of smaller modern taxa.

Table 5. Summary of estimated biomechanical data for the M. caudofemoralis of the theropods
 Ornithomimus (TMP 95.11.001)Gorgosaurus libratus (TMP 91.36.500)Tyrannosaurus rex (BHI 3033)
Mass (g)49458650261,100
PCSA (cm2)141.038153.2541804.242
Total contractile force (N)2820.7623065.08236084.831
Effective muscle pull (N)2820.4803064.77536081.223
Moment arm (m)0.0810.1470.505
Torque (Nm)228.459449.60318208.028


Among the three theropods examined here, an intriguing comparison can be made between the estimated M. caudofemoralis masses of Tyrannosaurus BHI 3033 and the juvenile Gorgosaurus TMP 1991.36.500. As tyrannosaurids, the taxa are closely related, and one might be surprised by the substantially larger tail mass percentage that the M. caudofemoralis of Tyrannosaurus is predicted to comprise (58.0%) compared with that of Gorgosaurus (45.1%). However, this discrepancy in relative M. caudofemoralis mass makes sense when considering the absolute body mass discrepancy between the two tyrannosaurids.

Based on mass estimates of other Gorgosaurus specimens (Paul,1988), the body mass of TMP 1991.36.500 can be estimated as roughly 400 kg, and the mass of BHI 3033 has been estimated as in the range of 3,800–4,500 kg (Stevens et al, 2008; but see Bates et al.,2009 for an alternative interpretation). The need for relatively larger locomotive muscles in absolutely larger taxa has been well established (Biewener,1989; Roberts,1998). A muscle's strength is largely a factor of its cross-sectional area, and locomotive muscles must be strong relative to the mass of the body they are trying to accelerate. Simple isometric growth of any animal would result in a three-fold increase in body mass (as mass is largely a function of volume) and only a two-fold increase in the strength of its muscles. Hence, the general rule that larger animals require relatively larger muscles to achieve the same speeds as smaller animals.

That is not to suggest this relatively enlarged M. caudofemoralis estimation indicates that Tyrannosaurus could have achieved the same degree of cursoriality as a juvenile Gorgosaurus or other smaller tyrannosaurids. Indeed, the relatively shorter metatarsals of Tyrannosaurus (among other anatomical features) testify that it could not (Holtz,1995). Nonetheless, it seems likely that the high relative M. caudofemoralis mass of Tyrannosaurus did evolve as partial compensation for its colossal body size, and it is worth noting how this increased M. caudofemoralis mass was achieved. The higher M. caudofemoralis mass estimation for Tyrannosaurus is not the result of relatively more dorsally angled or elevated transverse processes, but of more ventrally elongated hemal arches, which means that the hypaxial musculature was increased without decreasing the size of the epaxial musculature.

The expanded masses and high contractile force and torque estimates for all three theropods confirm previous assertions that the M. caudofemoralis was indeed a muscle of fundamental importance to non-avian theropod locomotion. These results have implications for the ongoing discussion of the potential locomotive abilities of non-avian theropods. For instance, in their assessment of the cursoriality of Tyrannosaurus, Hutchinson and Garcia (2002) assumed a total femoral retractor muscle mass of 297 kg for each leg of a 6,000 kg Tyrannosaurus. Here, the mass of the M. caudofemoralis alone has been conservatively estimated as 261 kg for each femur of a Tyrannosaurus previously estimated to have weighed as little as 4,500 kg, which implies that the M. caudofemoralis should have a mass of 348 kg in a 6,000 kg individual. Hutchinson and Garcia (2002) did not provide mass estimates for individual limb muscles, making it difficult to assess how this new M. caudofemoralis data affects their total estimation. However, it can surely be assumed that the mass of the other femoral retractors (the M. adductor femoris, M. puboischiofemoralis externus, and M. ischiotrochantericus) in a 6,000 kg Tyrannosaurus would weigh at least 25 kg. Under this assumption, the 297 kg estimation appears to be off by over 25% (and is conceivably off by as much as 45%). This by no means accounts for the 80% of total body mass that Hutchinson and Garcia (2002) assert must have been invested in the limb retractors, in order for Tyrannosaurus to have been capable of rapid locomotion. Nonetheless, the new M. caudofemoralis data does suggest that Tyrannosaurus should have fallen towards the higher end of Hutchinson and Garcia's (2002) advocated speed range, and the data are consistent with the faster locomotive estimates advocated by other authors using different speed estimating techniques (Bakker,1986; Paul,2000; Sellers and Paul,2005).

Considering the results of this study in the context of such biomechanical studies points out the large gaps in our current understanding of how tail muscularity is involved in terrestrial locomotion. The M. caudofemoralis has been treated herein as the only tail muscle involved in femoral retraction, but this is likely a gross oversimplification, and the case can be made for the partial involvement of other caudal muscles in femoral retraction as well. Studies of walking and running alligators demonstrate that during retraction of the right femur, the tail consistently swings to the left, and vice versa (Reilly and Elias, 1998). Given the electromyography evidence showing that during retraction of the right femur, the right M. caudofemoralis retracts, one might instead have predicted the tail to swing towards, not away from, the right side. Pelvic rotation is partially responsible for this tail motion, but the left caudal muscles also retract to pull the tail leftwards and do, thereby, add to the right M. caudofemoralis' femoral pull. The elongate zygapophyses of Tyrannosaurus would likely have reduced the overall lateral flexibility of the tail, but the assistance of other caudal muscles in femoral retraction remains plausible, and the recruitment of muscle sets with no direct connections to limb bones has been well documented in extant animals, such as the intercostal muscles in running dogs (Carrier,1996) or neck muscles in galloping horses (Gellman et al.,2002).

Elasticity is another complication likely to have improved the tail's locomotive contribution. Tails are naturally rich in tendons and septa, which are excellent stores of elastic energy. Elastic elements within the tails of both large and small non-avian theropods may have greatly improved locomotive efficiency beyond what would be estimated based on the limb musculature of most modern birds and mammals.

In addition to considerations of absolute speed, large caudofemoral muscles also have implications for previous estimates of theropod centers of mass and, are therefore relevant to Hutchinson and Garcia's 2002 study and to Hutchinson's2004 follow-up, which found via numerous sensitivity analyses that repositioning the axial center of mass more posteriorly had the potential to significantly decrease the estimated muscle mass needed by Tyrannosaurus to achieve higher speeds and to support its own bulk. Obviously, a larger M. caudofemoralis mass results in a more posterior position of any center of mass estimation (although the center of mass would also be determined by the dorsoventral angle of the torso and by the amount of curvature in the neck). The similar enlargement of any of the other hind limb retractors would have a largely neutral effect on the axial center of mass. With its center of mass positioned closer to its hips, a theropod's leg muscles would be relatively less strained in supporting its weight, and the animal's overall balance and turning agility would be improved, as it would be less front-end heavy and its rotational inertia would be reduced.

The last point that should be made is primarily an artistic one. The current prevalent fashion among paleoartists is to depict the tails of most dinosaurs, but particularly theropods, as relatively unmuscular and laterally compressed. This is true not only of depictions made strictly for aesthetic purposes but also of those intended to support scientific research, such as estimations of mass (for example, Paul,1997; Bates et al.,2009). The less-than-robust tail depictions are consistent with the more traditional tail muscle restoration technique described. They are also likely the result of the recent trend towards depicting more lightly built and more fleet-footed theropods, because skinny laterally compressed tails have a more aerodynamic and superficially more athletic appearance. In reality, skinny tails are not more athletic. Because the M. caudofemoralis is the primary retractor muscle of the hind limb, a slim-tailed theropod would be inherently slower than one with a large, muscular tail.

In overall appearance, the tails of most non-avian theropods likely resembled those of their modern crocodilian relatives, with relatively larger hypaxial muscles (and relatively smaller epaxial muscles) but without (in most cases at least) dorsal osteoderms. At the anterior base, the tails of most non-avian theropods would have been as broad or broader laterally as they were tall dorsoventrally. At and near the transition point, the tails would be laterally compressed, and towards the posterior tip, the tails would, as the neural spines and hemal arches steadily shrunk, return to being roughly round in cross-section (Fig. 13).

Figure 13.

A fully rendered reconstruction of BHI 3033 created by Scott Hartman to illustrate the appearance of a Tyrannosaurus with a tail of appropriate beefiness.


This research was made possible by the financial support of the Dinosaur Research Institute. We wish to thank John Acorn, Victoria Arbour, Robert Bakker, Robert Holmes, Pierre Lemelin, and Eric Snively for their repeated council and for many fruitful discussions about dinosaur tails. We also wish to extend our gratitude to Mike Brett-Surman, Chris Norris, and Brandon Strilisky for their indispensable assistance in navigating the enormous storerooms of their respective institutions. Scott Hartman merits our gratitude (and envy) for his stunning artistic skills and talents, which were graciously lent to this project. Special thanks are also owed to Joe Barter for his hospitality and assistance in recording tail measurements. Lastly, we thank Michael Caldwell for his unhesitating willingness to sacrifice many tails from his sizable frozen reptile collection.