by Toby White

Working with his Footsteps:Holtz (1995)

In 1995, Tom Holtz published a now classic paper: \"The arctometatarsalian pes, anunusual structure of the metatarsus of Cretaceous Theropoda.\" Holtz (1995)[fn1] In this paper, Holtz described in some detail a peculiar arrangement of theme tatarsals -- the three foot bones that attach to the ankle joint - in tyrannosaurids, ornithomimids and various other theropod dinosaurs from the late Cretaceous of Asia and North America.

This essay looks back at that article with the benefit of hindsight. That is, the aspects of the paper discussed here are not always matters that could have been seen when it was published. In most respects, this paper has held up extremely well. However,it is useful to assess the present status of the ideas and conclusions for which this paper is still so often cited. Theropods functionally have three digitson their feet.

The \"arctometatarsaliancondition\" describes a special arrangement of the foot in which metatarsals (\"Mts\") IIand IV make contact at the joint with the leg bones, and Mt III is reduced to a splint, or disappears altogether at the same level.See Fig. 1.But why does anyone care about the feet of theropods? There are two main reasons. The first is phylogenetic. The relationshipsof the advanced theropods were, and remain, very unclear. The arctometatarsalian condition initially seemed to be such a strange and unique arrangement that it could be used to answer a good many questions about the familytree of late Cretaceous theropods.

Second, the speed and agility of dinosaursis still a contentious issue. Special structures of the feet might give us a handleon how fast and how active they may havebeen.Holtz\'s paper is, roughly speaking, addressed to three corresponding points.First, he describes the arctometatarsalian foot and presents statistical data to show how the properties of this arrangement are genuinely different from the plesiomorphic (underived or primitive) condition. Second,these conclusions are discussed in light of an earlier assertion (Holtz (1994)) that the Arctometatarsalia -- the theropods sharingthis condition -- formed a distinct, related group of dinosaurs.

This point is not taken up in much detail in this paper, since Holtz had discussed it elsewhere. Third, Holtz discusses the possibility that the arctometatarsalian foot represents a biomechanical improvement reflecting a more active, fast-moving lifestyle than could be achieved with oldfashioned Jurassic models.Figure 3 illustrates (not very accurately, tobe sure) a generalized theropod leg. Themetatarsals are the \"foot bones\" which, in abipedal human, would articulate with the ankle joint.However, the equally bipedal theropod dinosaurs had nothing one could call a heel.Bipedal dinosaurs were digitigrade. That is,they walked on their toes.

The metatarsals attached directly to the distal tarsals, the astragalus and calcaneum at the distal end of the tibia and fibula. The metatarsals thus formed the important physical link between the weight - bearing surfaces of the phalanges (toe bones) and the leg bones that balanced that weight. The tibia, fibula, and distal tarsals are referred to collectively as the epipodiale (or, sometimes, epipodium).The metatarsals and phalanges are,collectively, the pes.Figures 1(a) and 3 represent the primitive condition found, for example, in the Jurassic Allosaurus. In these dinosaurs, the metatarsals were three roughly equal bones

.In arctometatarsalian, late Cretaceous forms, such as Tyrannosaurus, the configuration is quite different, as will be seen in figs. 1(b) and 2. Here, Mts II and IV actually lie next to each other proximally,where they contact the distal tarsals. Theupper part of Mt III lies behind Mts II andIV. However, Mt III is not merely \"covered\"by Mts II and IV when viewed from the front. Metatarsal III is actually reduced toa splint as it approaches the epipodiale. Fig.2A. In some cases, Mt III may dis appearaltogether. In the middle section of the arctometatarsalian foot (fig. 2B), Mt III is small and flattened between the other metatarsals.

II
Standing Toe to ToeThe Arctometatarsalian Condition

The inner faces of Mts II and IV may also be bent in such a way that Mt III is locked into position between the two larger bones on each side. This variation occurs, for example, in Tyrannosaurus. In other cases,(Avimimus), Mts II and IV are fused together at the top, which also has the effect of locking Mt III into place. Finally, the lower, distal section of the arctometatarsalian foot is superficially similar to the primitive foot. Fig. 2C.Metatarsal III lies in front of Mts II and IV and extends more or less straight out in front of the leg.

In this way, the foot remains three-toed. However the middle toe no longer connects directly with the ankle. Instead, it connects with the two outer toes, through Mts II and IV. In addition, Mt II is almost triangular in cross-section, and theinner edges of Mts II and IV have a smooth, beveled surface on which two of the faces of the triangle rest. Most researchers would have been satisfied with this type of general description.However, Holtz went further - much further. He created a database of leg measurements from dozens of theropod fossils of all kinds, in an effort to put some quantitative rigor behind the usual descriptive prose. In a way, the database itself may be the most lasting accomplishment of his paper. Vertebratepaleontology has long been dominated by elaborate descriptive works on single specimens.Beginning in the mid - 1980\'s, phylogenetic taxonomy introduced statistical and computer-based methods for comparativean alysis of numerous specimens of different species.

This type of data is used to create a character matrix for mathematically estimating the most probable evolutionary tree connecting the specimens. Holtz had previously worked, and continues to work,in this area. In his 1995 paper, he applies this character matrix technique back on to the traditional business of descriptive paleontology, a subtle reversal of method which may have interesting long-termimplications. Using this character matrix, Holtz argued that the arctometatarsalian condition is a distinct and separate arrangement from the primitive, Allosaurus-style foot.

This is an important prerequisite to any phylogenetic discussion of the condition. If the arctometatarsus were simply one end of a continuum of foot arrangements, it would be hard to draw any conclusions about evolutionary relationships. Over the onehundred million years which separate Allosaurus from Tyrannosaurus, it is reasonable to expect that continuously variable characteristics will wander back and forth with some frequency, based on local selective pressures or simply random genetic drift. So, for example, overall body size, tail length, and even arm length are not very useful in tracing such long-term evolutionary movements. The problem is not just theoretical.A number of theropod dinosaurs have feet which might be viewed as intermediate between the primitive and arctometatarsalian states.

For example, many theropods havefeet with metatarsal III lying somewhatanterior to its neighbors, or even somewhat reduced near the ankle joint.In order to determine whether the arctometatarsus was just \"more of the same\" or a really new arrangement, Holtz graphed a number of different leg measurements against each other for arctometatarsalian and primitive theropods.He calculated the equations for the lines which best fit each distribution and tested to see if the lines were statistically different.This method should not only reveal whether the arctometatarsus was in fact aqualitatively unique character, but how it affected (or, more exactly, was correlated with) the overall shape and mechanics of the leg in each case.

As expected, Holtz found that the lines describing the relationships between leg measurements were significantly different between the primitive and arctometatarsalian groups. Metatarsals II and IV are flatter inarctometatarsalian species. Importantly, arctometatarsalian theropods had longer legs than primitive theropods of the same size. At least in mammals, longer leg length is correlated with speed, as the animal gets more distance with each stride. The foot itself was thinner, lighter and more gracile. Since the foot is swung forward at the distal end of the leg, it must be moved further than any other part of the body in running.

Therefore, a small weight reduction in the foot translates into both alarge energy savings and greater speed.What is more, the longer the leg, the more difference this makes. Thus, Holtz\'s statistics indicated that the arctometatarsalian theropods were significantly different from the Jurassic models, and may have been faster and more energy-efficient in motion.

III
Footing the BillPhylogenetic Consequences

Prior to the 1995 paper, Holtz had arguedthat the arctometatarsalian condition was also a hallmark of a family of dinosaurs, which he called the Arctometatarsalia after their most distinctive feature. In fact, he had originally defined the Arctometatarsalia as the first theropod to acquire the arctometatarsalian condition, and all of its descendants. Holtz felt that the Arctometatarsalia were a clade: that is, a single organism and all ofits descendants. As originally proposed,Holtz suggested that this group included at least the Tyrannosauridae, Ornithomosauria, Troodontidae, Avimimusand Elmisauridae.

The name was certainly a linguistically appropriate one. The term\"arctometatarsalian\" was originally derived from arcere, meaning to close up, confine,or lock away. [fn2] However, Latin writers also used the word arctous to mean \"northern.\" [fn 3]. As Holtz points out, the arctometatarsalian foot is in fact a northern foot. That is, it is identified almost exclusively with theropods from the late Cretaceous of Asiamerica, the present North America and eastern Asia. However, it is normally not considered good practice to define a clade in terms of a characteristic. If additional information suggests that the characteristic evolved more than once, the definition becomes impossible to use since it no longer defines a clade. For example, if the arctometatarsalian foot evolved twice, then the last common ancestor of all arctometatarsalian dinosaurs would nothave the defining characteristic. Such a group is said to be \"polyphyletic\" and is not a valid clade.

As matters turned out, this is exactly what happened. In the 1995 paper, Holtz had already concluded that the arctometatarsalian foot might have evolved more than once. In a later paper (Holtz(1996)), he amended the definition of the group to \"all theropods more closely related to Ornithomimus than to birds.\" [fn 4] In this analysis Holtz hypothesized that the group contained only Ornithomimosauria,Tyrannosauridae and Troodontidae. Fig. 4.More recent work by Sereno (1999),among others, suggests that troodonts are much more closely related to birds. Sereno asserts that even the tyrannosaurids are more closely related to birds than to ornithomimids. If so, \"Arctometatarsalia\"is simply another name for the Ornithomimosauria. See fig. 5.Few taxonomists would be bold enough to claim that the relationships of the advanced Theropods are settled. In particular, the position of the Tyrannosaurs is still unclear.

The Arctometatarsalia may well describe a clade containing Tyrannosaurus as well as Ornithomimus and its close relatives. Still, there is little doubt that the original,broad concept of the Arctometatarsalia has itself been squeezed down. What, then,happened to the significant differences Holtz found between the arctometatarsalian and primitive theropods? The answer may lie in the way the statistic alanalysis was performed. For the most part,Holtz takes the measurements from the arctometatarsalian species and plots the data pair-wise, i.e., he plots it two variablesat a time. [fn 5] He calculates the line whichbest fits this data. He then repeats this process for the data from primitive theropods.

Finally, tests to see whether the two lines are statistically different in position and slope. This method has several logical limitations. First, it assumes that the arctometatarsalian specimens are a group, and asks whether that group is different from other theropods.It does not test whether the existence ofthe arctometatarsalian condition isnecessarily the best way to split the sample population of theropods. Thus, the analysis cannot be used to draw phylogenetic conclusions, nor does Holtz attempt to doso. In fact, if the data had been used in anattempt to draw a \"natural\" dividing line,Avimimus and the elmisaurids might wellhave fallen away from the other arctometatarsalian forms. [fn 6]Second, and perhaps more interestingly, Holtz uses a form of linear regression. However, there is no clear indication that the best fit is, in fact, a straight line. Eyeball estimates should not be confused with rigorous number-crunching, but there is at least a visual hint that the data for arctometatarsalian and primitive forms would converge at large size if the data were fitted without the constraint of linearity.

The limb proportions of small arctometatarsalian dinosaurs are dramatically different from other smalltheropods. The difference in proportionsbetween a large Allosaurus and aTyrannosaurus is, at least, not quite so obvious.Finally, the data on arctometatarsalian dinosaurs is dominated by ornithomimids(29 specimens) and tyrannosaurids (37 specimens).Troodonts, elmisaurids and Avimimus together are represented by only 8 specimens, and only 3 of these were complete enough to be included in most of the calculations. As a result, it is not possible to draw firm conclusions about these groups.What is impressive is that, despite the vast difference in size and form, both among the ornithomimids and between them and the tyrannosaurids, the data for these groups do tend to form a neat, if not always linear, pattern. Athlete\'s Foot: the Biomechanics of the Arctometatarsalian Condition Holtz\'sbiomechanical treatment of the arctometatarsalian foot is interesting andc onvincing.

In general, he makes two points.First, he argues that the arctometatarsalian foot could not be used as a device for spreading force over time. Instead, he argues that the specialization served to direct the forces in space. He then uses avariety of assumptions to calculate thestresses on the bones of the foot in moderately fast motion and finds that these forces were not significantly greater in arctometatarsalian feet, even though the leg was both longer and more slender than underived feet. Thus the arctometatarsalian foot represented a truly improved design:greater speed at no additional energy cost. Previous authors had suggested that the arctometatarsalian foot worked with \"snap ligaments\" analogous to those of some modern ungulates.That is, they proposed that Mt III was either(a) rotated out of the plane of Mts II and IV at mid-step or (b) pushed up wards relative to Mts II and IV. In either case, the ground force exerted at mid-step would go into stretching the ligaments which held MtIII to the rest of the foot.

These ligaments would then snap back andhelp lift the leg off the ground for the nex tstep. Holtz believes that this is unlikely because the complicated surfaces of metatarsal III would not allow it to move significantly relative to II and IV, either vertically or by rotation. He also points out that the proximal portions of the metatarsus in Elmisaurus and Avimimus are at partially fused, making any relative motion impossible. Rather than spreading force over time, Holtz bases his model on the idea that the arctometatarsus served to redirect forces in space. Specifically, Holtz asserts that the most likely function of the wedge-shaped distal portion of Mt III was to distribute the force experienced by Mt III laterally, onto the shafts of Mts II and IV. Fig. 6.

Since Mts II and IV are flattened, they are well-suited to withstand lateral forces --forces acting across the long axis of the ellipse. He notes that advanced theropods also have well developed condyles at the distal ends of the distal tarsals -- at the base of the astragalus and calcaneum. Thus, Mts II and IV could direct force more efficiently and more sensitively to the upper leg than MtIII -- which terminates between the astragalus and the calcaneum. Holtz provides a detailed quantitative model based on similar studies of living animals.It is not clear whether the mechanics of theropod locomotion are sufficiently similar to the model animals to place much faith in his detailed results.

However, this does not appear to have been the intent. Rather, the model shows that the stresses placed on the bones of the arctometatarsalian foot are similar to those placed on the bones of underived theropod feet and that the numbers are within the range which bones can be expected to tolerate well. These observations have held up well. As Holtz emphasizes, nothing in the study compels any conclusions about the absolute speed of advanced predatory dinosaurs. What the study does justify are the conclusions that (1) arctometatarsalian dinosaurs were probably faster than their Jurassic cousins and (2) they had evolved a very special adaptation for movement which required some degree of speed. The inescapable conclusion is that predatory dinosaurs experienced some fairly significant selective pressure for increased speed -- that speed was important to their mode of living. We cannot conclude from Holtz\'s work that arctometatarsalian theropods had any particular speed or activity level.

However,his paper provides a firm foundation for the conclusion that Cretaceous theropods used speed, probably over substantial distances,for hunting or some other significant purpose.fn 1 The article appears in the December,1994 issue of the Journal of Vertebrate Paleontology. However, Holtz himself has pointed out that the issue was not actually published until January, 1995 and is appropriately cited to that year.fn 2 To be precise, \"arctometatarsalian\" isderived from arctus, the passive participleof arcere. Hence a phrase from the Inquisition: murus strictus seu arctus, i.e.,solitary confinement.fn 3 The original derivation is from Greek mythology. Arctos was the son of Callistoby Zeus. Hera was enraged by this eventand turned Callisto into a bear. Zeus then cast Callisto into the night sky as a constellation, the Great Bear - the traditional signpost for celestial North.Arctos became her guardian (i.e. Arcturus).The full story is apparently yet moreillogical, but this is the usual explanation for the origin of words such as \"arctic.\"fn 4

In taxonomy, the phrase \"closer than \" means having a more recent common ancestor.Thus, the Arctometatarsalia are organisms whose last common ancestor with Ornithomimus was more recent than their last common ancestor with birds.fn 5 To be more precise, Holtz plots ratios and log transformations of the variables,apparently for biostatistical reasons.

Thus,for example, one of the most dramatic difference is found in a plot of total limb length divided by femur length against the logarithm of femur length.fn 6 It is not suggested that this would even be a worthwhile exercise. Conventional cladistic parsimony analysis, using a wide variety of characters, is the appropriate model for drawing phylogenetic conclusions.

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