Can skeletal surface area predict in vivo foot surface area?

Abstract

The surface area of feet in contact with the ground is a key morphological feature that influences animal locomotion. Underfoot pressures (and consequently stresses experienced by the foot), as well as stability of an animal during locomotion, depend on the size and shape of this area. Here we tested whether the area of a skeletal foot could predict in vivo soft tissue foot surface area. Computed tomography scans of 29 extant tetrapods (covering mammals, reptiles, birds and amphibians) were used to produce models of both the soft tissues and the bones of their feet. Soft tissue models were oriented to a horizontal plane, and their outlines projected onto a surface to produce two‐dimensional silhouettes. Silhouettes of skeletal models were generated either from bones in CT pose or with all autopodial bones aligned to the horizontal plane. Areas of these projections were calculated using alpha shapes (mathematical tight‐fitting outline). Underfoot area of soft tissue was approximately 1.67 times that of skeletal tissue area (~ 2 times for manus, ~ 1.6 times for pes, if analysed separately). This relationship between skeletal foot area and soft tissue area, while variable in some of our study taxa, could provide information about the size of the organisms responsible for fossil trackways, suggest what size of tracks might be expected from potential trackmakers known only from skeletal remains, and aid in soft tissue reconstruction of skeletal remains for biomechanical modelling.

The surface areas of the skin of the foot in situ and of the foot's skeletal components are strongly correlated and thus should be predictable in terrestrial tetrapods. Skin surface area was approximately 1.67 times that of skeletal surface area (~ 2 times for manus, ~ 1.6 times for pes, if analysed separately). This trend was not affected by body mass and showed little evidence of being strongly affected by phylogeny. This predictability has potential in aiding with estimating the size and possible species of trackmakers in the fossil record, both by estimating the size of skeletal feet using footprints, and by estimating foot size, and therefore potential footprint size, from fossil feet.

Introduction

The surface area of tetrapod autopodia (feet) reflects several important biomechanical factors, including body mass (McMahon, 1975), habitat (Blackburn et al. 1999), speed (Segal et al. 2004), and bipedal or quadrupedal locomotory habits (Snyder, 1962). Foot surface area is determined by autopodial morphology and posture (Hildebrand, 1980; Full et al. 2002) and, in conjunction with the body mass and locomotory mode of an animal, determines underfoot pressure (Miller et al. 2008; Michilsens et al. 2009; Panagiotopoulou et al. 2012, 2016a,b; Qian et al. 2013).

For very large animals, such as rhinoceroses and elephants, foot surface area needs to be large, as a method of reducing underfoot pressure and avoiding injury to the foot, as well as avoiding sinking on soft ground (Falkingham et al. 2011a). However, foot contact area does not appear to scale isometrically with mass. Larger animals often have smaller foot contact areas than would be expected, and the relationship between foot contact area and mass differs between unguligrade, digitigrade and plantigrade animals (Michilsens et al. 2009; Chi & Roth, 2010). Large animals must compensate for their size with other mechanisms, such as fatty footpads, in order to reduce stress (Panagiotopoulou et al. 2012). Presumably the extinct sauropod dinosaurs, many times larger than extant elephants (Bates et al. 2016), used similar compensatory adaptations (Platt & Hasiotis, 2006).

Foot surface area is also reflective of an animal's posture and limb use (Biewener, 1989), with bipedal animals requiring feet large enough to support their bodyweight with half as many limbs as their quadrupedal counterparts (Gatesy & Biewener, 1991) and, in the case of birds, in a huge range of environments and ecological niches with different demands (Alexander, 2004). An animal's balance (e.g. keeping the body's centre of mass, CoM) close to the centre of pressure of feet – influenced by foot area) is also of vital importance, as the stability of an animal during locomotion is vital to its ability to catch prey, escape predators, migrate effectively, and avoid injury when overexerting itself and when moving on unstable ground (Hodgins & Raibert, 1991; Patla, 2003; Geyer et al. 2006; Birn‐Jeffery et al. 2014).

Foot surface area appears to correlate with relative speed during certain forms of locomotion. Body mass has a direct effect on maximum running speed, especially notable in large animals, as speed scales with body mass up to moderate sizes and then declines (Garland, 1983; Bejan & Marden, 2006), and the duration of foot contact with the ground also scales with body mass (Farley et al. 1993). The position and number of toes also tends to be a specialisation for terrestrial running, with a reduced number of toes present in both horses and ostriches (among other cursorial taxa; Coombs, 1978), reducing foot weight, a useful adaptation because heavier feet necessitate more energy usage to recover from a stride (Snyder, 1962; McGuigan & Wilson, 2003; Schaller et al. 2011). Peak plantar pressure and speed are demonstrably linked in humans (Rosenbaum et al. 1994; Segal et al. 2004; Pataky et al. 2008) and ostriches (Schaller et al. 2011); however, this link has not been fully explored in other terrestrial animals, especially quadrupeds.

Large feet have a potentially conflicting relationship with speed in that they will be more massive and thus have greater inertia, making them more difficult to swing quickly through the air (Taylor et al. 1974; Fedak et al. 1982; Kilbourne & Hoffman, 2013; Kilbourne & Carrier, 2016). Nonetheless, it is important that foot surface area and underfoot pressures evolve to allow an organism's locomotion to be energy efficient and its posture stable, while enabling sufficient bursts of speed if necessary. In other words, the surface area of the autopodia should be subject to selective pressures in the same manner as any other part of the locomotor system.

Foot surface area is also potentially influenced by Allen's rule (Allen, 1877; Allee & Schmidt, 1937), which supposes that warm‐blooded animals in cold climates will tend to have smaller feet compared with their relatives in warmer clines (Blackburn et al. 1999). This may or may not be due to causal links (i.e. natural selection) to reduce surface area exposed to the cold or it may be a reflection of adaptations in warmer climates to increase surface area to promote heat dissipation. This ‘rule’ may conflict with constraints imposed by keeping pressures low (i.e. foot areas large) to avoid sinking into soft substrates such as snow or sand. Allen's rule also potentially conflicts with the outcome of Bergmann's rule – the contentious but broadly supported tendency for ectotherms to be larger in colder climates (Clarke, 2017). Therefore, colder conditions will tend to correlate with increased body mass, implying a larger foot surface area while simultaneously selecting for smaller feet.

Some animals exhibit notable disparity in the size of fore‐ and hindfeet, which is apparent in their foot surface area: a condition known as heteropody. A previous study (Henderson, 2006) demonstrated that the ratio of fore‐ and hindfoot surface areas, in its subject animals, could match CoM position, e.g. an elephant has 40%/60% relative fore‐ vs. hindfoot surface area, and a CoM of 40% of the distance from the glenoid to the acetabulum. It would seem logical to assume that animals spread their bodyweight relatively evenly over their feet in order to reduce maximum pressure, excess tissue or substrate stress and strain (Cheung et al. 2005) and to prevent sinking when walking across compliant substrates (Falkingham et al. 2011a). However, this assumption runs contrary to pressure experiments showing higher mean peak pressures in elephant forelimbs (Panagiotopoulou et al. 2012). It is therefore worth exploring a possible correlation of the relative sizes of an animal's manus and pes, and CoM with both observations in mind, and worth considering possible implications of such a correlation across Tetrapoda.

Heteropody is a common occurrence in some extinct animals, such as sauropod dinosaurs, as indicated by trace fossil evidence (Lockley et al. 1994; Henderson, 2006). Preserved trackways from these dinosaurs indicate that often their fore‐ and hindfeet impressions differ in depth (Falkingham et al. 2011b, 2012), implying differential underfoot pressures. Determining foot surface area in these animals can be complex, however, and attribution of specific trackmakers to trackways is notoriously difficult (Farlow, 1992; Clack, 1997; Falkingham, 2014), partly because matching impressions of fully fleshed feet to skeletal remains would require accurate methods of predicting skeletal to skin foot morphology, which is currently difficult and largely speculative (Jannel et al. 2019). Indeed, matching the tracks of extant animals to the correct species is often not straightforward – as illustrated by the existence of field guides produced to help fieldworkers with this problem (e.g. Bang & Dahlstrøm, 2001).

For terrestrial and arboreal fauna, the substrate underfoot can have a noticeable effect on locomotion and on the way the foot moves in a step. Both substrate and autopodial tissue will be compressible to varying degrees, slightly altering foot contact area during stance (Gatesy et al. 1999; Gatesy, 2003; Falkingham & Gatesy, 2014b; Gatesy & Falkingham, 2017).

Palaeobiologists must rely on soft tissue data from extant animals to infer many facets of the morphology of extinct animals (Witmer & Thomason, 1995), because preservation of soft tissues is rare and only partial details about muscle and tendon structures can be inferred from the skeletal elements they interacted with. In this way, a study of the relationship of flesh and skeletal foot surface area should help to fill gaps in our understanding of the anatomy of extinct animals’ feet, as well as the interaction of foot structure and CoM, and would be particularly valuable for linking fossil trackways and supposed trackmakers. Here we aim to test whether skin and skeletal surface area are correlated across Tetrapoda and, if so, if their correlation is strong enough to form it a useful tool in the study of fossils and trackways.

Materials and methods

To compare skeletal and fully fleshed foot anatomy in extant animals, computed tomography (CT) scans of cadaveric autopodia from 29 species of tetrapod (one specimen of each except for Crocodylus moreletii and Osteolaemus tetraspis – see Supporting Information Data S1), covering amphibians, reptiles, birds and mammals, were analysed. The sex of individuals was unknown, and all but Crocodylus niloticus were adults. All specimens were museum or zoo‐donated specimens whose cause of death was unrelated to this study (and generally unknown).

mevislab (Heckel et al. 2009) was used to segment the scans into separate 3D models (OBJ format meshes) of the soft tissue and skeletal elements. The resultant meshes were then imported into autodesk maya 2018, where they were cleaned, aligned and re‐posed to the horizontal plane (Fig. 1). The aligned meshes were then processed using matlab (Mathworks Inc. Natick, MA, USA), where they were ‘flattened’ by setting the vertical component of each vertex to 0. This flattening produced 2D ‘silhouettes’ of the models, either as soft tissue of the foot or its skeleton, from which area was calculated using an alpha shape (see below).

Figure 1.

Projected area calculated from 3D models. (A) Hippopotamus left forelimb, soft tissue and bones reconstructed from CT data. (B) The soft tissue was cropped at a point representative of the area that would contact the ground during life. The bones were cropped based on the same posterior extent (Pose 1). The alpha shape (pink) and the convex hull (green) were used to determine (C) the underfoot area of the bones alone and (D) the soft tissue. (E) Bones were laid flat for a more repeatable approach (Pose 2). Where semi‐digitigrade animals were treated as digitigrade (Pose 2a), only bones in pink were used. Where semi‐digitigrade animals were treated as intermediate between digitigrade and plantigrade (Pose 2b), blue and pink bones were used. Where semi‐digitigrade animals were treated as plantigrade, all bones including those in green were used. (F) Alpha shapes for Poses 2a–c, where pink is 2a, blue is 2b, and green is 2c. (G–K) Distinctive foot morphologies in the dataset. Scale bar: (A–F, H–K) 10 cm, (G) 1 cm.

Skin models were oriented and posed so that only areas of the feet that would touch the ground during locomotion would be used upon flattening the models, and any parts of the models that extended past this area were removed (Fig. 1B). The extent of the soles of the feet were, for the most part, obvious from visible anatomy. In addition, from in vivo biplanar fluoroscopy studies, X‐ray images and photographs in situ, we made educated estimates of accurate positions for taxa (Astley & Roberts, 2014; Kambic et al. 2015; Bonnan et al. 2016; Panagiotopoulou et al. 2016a,b). For a more repeatable approach (Pose 2, see below), parts of the skin model extending past the functional foot area (the unguals for unguligrade animals, the digits for digitigrade animals, and the entire sole of the foot for plantigrade animals and semi‐digitigrade animals, so that the full extent of fatty foot pads were accounted for) were removed where present.

However, as these models were taken from CT scans, without the full weight of the animal deforming the foot underneath, the true shape of the foot during stance for many of these animals may have been slightly different, due to compliant soft tissues (Alexander et al. 1986; Gatesy, 2003). This is especially significant for those animals with large fatty foot pads such as Elephas and Ceratotherium, and less significant for the majority of ungulates, whose hooves are stiff and more resistant to deformation (Hinterhofer et al. 2000; Hutchinson et al. 2011).

Skeletal models were posed in one of two ways: Pose 1, matching the pose of skin models (Fig. 1B‐D) and Pose 2, with all bones aligned to the horizontal (Fig. 1E,F). For the latter pose, models were cropped proximal to the digits for digitigrade animals, proximal to the unguals for unguligrade animals, and proximal to the tarsals/carpals for plantigrade animals.

For large, semi‐digitigrade/subunguligrade animals (Elephas maximus, Ceratotherium simum and Hippopotamus amphibius), proximal foot elements are raised off the ground, supported by fatty foot pads, increasing the foot contact area. Therefore using only the phalanges, as for other digitigrade animals, would have severely underestimated the contact area. To explore this ambiguity, skeletal outlines were generated from just the digits (Pose 2a), the digits plus metatarsals (Pose 2b) and with the entire foot skeleton (Pose 2c). This analysis was designed to be more objective and repeatable in determining skin from skeletal surface area, particularly in extinct animals, where knowledge of in vivo foot posture may be lacking.

Results for area where left and right fore‐ or hindfeet were available were averaged (mean), as were area results for animals with multiple specimens and for Camelus, where both feet were unassigned as fore‐ or hindfeet.

It should be noted that our 29 animals studied include several ungulates, possessing large, keratinous hooves, much harder and stiffer than most other tissues categorised under ‘soft tissues’ in this study. While ungulate hooves have properties that distinguish them from other soft tissues, and take longer to decompose than softer tissues, they are also distinct from skeletal tissue, and are rarely preserved, especially in fossils (Pollitt, 2004; Saitta et al. 2017). In terms of comparisons between skeletal and fossil remains and the overall foot structure of living animals, hooves clearly are an important part of a living ungulate's foot structure and their ability to locomote; thus being able to predict their size from skeletal remains is as much of a part of the goal of this study as predicting the areas of softer tissues (Warner et al. 2013). In this sense, the term ‘soft tissue’ as used in this study refers to ‘non‐skeletal tissue’, with the hardness of these tissues largely irrelevant.

Initially, we attempted to calculate the 2D convex hull (a shape made by joining the outermost data points in a simplified representation of the data; see Fig. 1C,D, in green) of each silhouette, but we found via pose tests using bird feet that this method was extremely sensitive to pose, regardless of whether the digits were laterally spread or not (Supporting Information Tables S1–S7). Instead, 2D, tight‐fitting alpha shapes (where the outermost data points were joined in a shape that most closely fits the silhouette's true shape; Fig. 1C,D, in pink) were produced for each silhouette, and the area of these alpha shapes calculated. The alphaShape command in matlab uses an ‘alpha value’ to determine the maximum distance between edge points to bridge (a sufficiently large ‘alpha value’ will produce a convex hull). We used the automatically determined alpha value for each alpha shape, which is calculated based on the density of vertices in the model, as this produces the tightest fitting single shape for any given set of points. We set the hole threshold to be extremely large (larger than the foot as a whole) to remove any holes from the interior of the alpha shape. The surface area of the skeleton's alpha shape as a percentage of the skin's shape was then used to compare each organism.

The dataset was then run through PGLS (phylogenetic generalised least squares) regression analyses to assess the significance of the relationship between the variables and how much impact common ancestry between the animals studied affected the results (Felsenstein, 1985; Blomberg et al. 2012). This was accomplished using mesquite (Maddison & Maddison, 2003) to draw three simple trees (manually compiled ‘consensus’ phylogenies based on the most recent and broadly accepted phylogenies at the time of writing, within which the only major point of contention was the placement of Carnivora, Cetartiodactyla and Perissodactyla in relation to each other; Gauthier et al. 1988; Nery et al. 2012; Prum et al. 2015) connecting the organisms involved in this study. We then applied the Grafen method (Grafen, 1989) of branch length estimation to the trees, and ran PGLS via the Ape (Paradis et al. 2004), Geiger (Harmon et al. 2008), Nlme (Bliese, 2006) and Phytools (Revell, 2012) packages in R. Results for forefeet, hindfeet and all feet were each tested. The influence of body mass was also tested using PGLS to determine whether phylogeny, body mass or a combination of both factors had a significant effect on the relationship between skin and skeletal foot surface area. P‐values < 0.05 were considered significant. Body masses were taken from scan metadata where possible or estimated from the literature (e.g. Dunning, 1992) when such metadata were not available (Tables S1–S7).

Skin surface area was plotted against skeletal surface area for all analyses, using the entire dataset, and then broken up into smaller groups: unguligrade, digitigrade, plantigrade, terrestrial, semi‐aquatic, erect posture, sprawling posture, mammals and birds. The plots were framed in terms of the predictability of skeletal area from skin area, to emphasise potential utility for trackmaker identification from fossils. However, these data are intended to be interpretable both ways, and the prediction of in vivo surface area from skeletal remains is of equal utility. For the purposes of these analyses, the digitigrade (Pose 2a) and plantigrade (Pose 2c) poses of semi‐digitigrade/subunguligrade (sensu Carrano, 1997) animals were added to their respective groups, whereas Pose 2b was used for the remaining groups, as it represents an intermediate pose: semi‐aquatic included amphibians, crocodilians and hippopotamuses; terrestrial did not include birds except for Dromaius novaehollandiae; and sprawling (here meaning non‐erect) posture included amphibians, lepidosaurs and crocodilians, although crocodilians use a range of limb postures spanning the sprawling‐to‐erect continuum (Gatesy, 1991; Reilly & Elias, 1998).

Results

For the Pose 1 analysis (approximate life position), projected foot skeleton surface area as a percentage of projected fully fleshed foot surface area (Fig. 2, above cladogram) was an average of 56% (both mean and median) for all organisms measured (three amphibians, four crocodilians, seven birds and 14 mammals), with means of 49% for amphibians (53% median), 47% for crocodilians (48% median), 68% for birds (67% median) and 55% for mammals (54% median) with an average standard deviation of 13%. Extremely similar results were found with bones oriented as in Pose 2. The smallest percentages of skeletal vs. fleshed surface area observed were in Equus species (Equus quagga at 34%, Equus ferus caballus 38%), Giraffa camelopardalis (38%), Crocodylus niloticus (38%) and Cryptobranchus alleganiensis (39%). However, besides Equus and Giraffa, other ungulates did not stand out as having particularly low skeletal areas relative to skin areas. Carnivorans had proportionately high skeletal calculated area. The highest skeletal areas relative to skin areas (as seen from the underside, and in two dimensions) were Coturnix at 83%, followed by Panthera leo persica and Ceratotherium simum, at 81% and 73%, respectively.

Figure 2.

Bar graph showing projected skin surface area as a percentage of projected skeletal surface area across all specimens in (A) Pose 1, with phylogeny for context and (B) Pose 2 (for elephant, rhino and hippo, main bar represents Pose 2b and additional bars show Poses 2a and 2c). Silhouettes from Phylopic. Mammalia data are in purple, Aves data in red, Crocodylia data in green, Lepidosauria data in blue, and Lissamphibia in yellow.

Where skeletal models were set flat (Pose 2), all unguligrade animals expressed lower skeletal area than skin surface area, compared with Pose 1 (Fig. 2). The zebra stood out most with just 22% skeletal representation.

Elephas, Hippopotamus and Ceratotherium showed considerable variability depending on which foot bones (Pose a/b/c) were used to predict skeletal area: Hippopotamus (37/76/100%), Ceratotherium (31/74/98%), Elephas (17/42/68%). A 100% skeletal surface area representation in the hippopotamus clearly suggests that treating these animals as plantigrade does not yield results representative of these animals’ foot morphology, or indeed results that are useful for predictive purposes, especially given the steep (subvertical) angle at which these animals position their feet in situ.

Carnivorans, particularly cats, typically do not have their digits extended fully when walking or standing, as such relative skeletal area calculated from Pose 2 (e.g. Panthera 93%, Vulpes 92%) generally produces higher relative skeletal areas than the more life‐like Pose 1 (e.g. Panthera 81%, Vulpes 70%).

Overall, mammalian data were highly variable (47% range from maximal to minimal values in Pose 1, over 80% range in Pose 2). Given that mammalian species dominated our study sample (followed by birds, then crocodilians), perhaps with more data the variability within other groups would increase to comparable levels. However, that mammalian feet have unusually high morphological disparity compared with other taxa in our sample, is reflective of their unusually high morphological disparity in terms of body size, foot anatomy and posture compared with other groups (Kubo et al. 2019).

Bird and crocodilian data were more consistent than mammals (25% range for birds in all analyses, 18% range for crocodilians). Dromaius, which was morphologically and functionally distinct from the other birds in the study in terms of being large and flightless, fell neatly within the range for birds.

Raw numbers for projected skeleton and projected skin surface area, calculated from Pose 1, were plotted as a log graph, and a power trendline fitted (Fig. 3). This plot, despite the variation seen in Fig. 2, showed a strongly positive correlation (R² = 0.99, P‐value < 0.05) in ‘Pose 1’ between skin and skeletal foot surface area. This correlation can be described with the equation y = 0.59x ^0.99 (where y = skeletal foot surface area and x = foot skin surface area). This skin and skeletal foot surface area's scaling relationship was close to isometry (slope of 1.0). Soft tissue surface area may therefore be predicted, on average, as approximately 1.67 times skeletal surface area. There were very few outlying animals; indeed, Elephas and Ceratotherium were the only animals that diverged notably from the linear trendline. If the three largest animals were removed from the dataset, or the three smallest, the strength of the correlation was unaffected, but soft tissue area predictions from skeletal area decreased (Tables S1–S7). If both groups were removed, the predicted value decreased further.

Figure 3.

Log₁₀ plots for projected skin surface area against projected skeletal surface area (mm²) in (A) Pose 1 for all limbs, (B) Pose 1 for forelimbs, (C) Pose 1 for hindlimbs, Silhouettes from Phylopic. All numbers rounded to two significant figures. Mammalia data are in purple, Aves data in red, Crocodylia data in green, Lepidosauria data in blue, and Lissamphibia in yellow.

When the forelimb and hindlimb results were calculated separately, the equations differed noticeably (y = 0.52x ^0.99 and y = 0.64x ^0.98, respectively); although the difference in slope was not statistically significant, and R² values remained ~ 0.99 (Fig. 3). However, soft tissue area was ~ 2 times skeletal area in the forelimb, but only ~ 1.56 times in the hindlimb. See Table 1 for full list of formulae, R² values, p values, and confidence intervals based on coefficient estimates and standard error, all rounded to two significant figures (and see Tables S1–S7 for slope uncertainties for all poses, and for all limbs, forelimbs and hindlimbs.).

Table 1.

Regressions and confidence intervals for main analyses

Analysis	Linear regression	Linear R²	Log regression	Log R²	95% CI	P‐value
Pose 1 ‐ All limbs	y = 0.51x + 146.71	R² = 0.94	y = 0.59x 0.99	R² = 0.99	1.922 ± 0.06186	<2.2E‐16
Pose 1 ‐ Forelimbs	y = 0.45x + 641.27	R² = 0.92	y = 0.52x 0.99	R² = 0.99	1.916 ± 7.887E‐02	3.27E‐15
Pose 1 ‐ Hindlimbs	y = 0.59x − 292.02	R² = 0.97	y = 0.64x 0.98	R² = 0.99	1.9229 ± 0.0632	<2E‐16
Pose 2a ‐ All limbs	y = 0.20x + 1303.8	R² = 0.82	y = 0.87x 0.91	R² = 0.99	3.9266 ± 0.3584	1.93E‐11
Pose 2a ‐ Forelimbs	y = 0.21x + 1345.4	R² = 0.85	y = 0.69x 0.93	R² = 0.97	3.9614 ± 0.3954	8.68E‐09
Pose 2a ‐ Hindlimbs	y = 0.19x + 1177.4	R² = 0.79	y = 1.06x 0.89	R² = 0.96	4.1603 ± 0.4157	2.08E‐10
Pose 2b ‐ All limbs	y = 0.48x + 436.75	R² = 0.87	y = 0.58x 0.98	R² = 0.97	1.856 ± 0.1199	5.98E‐15
Pose 2b ‐ Forelimbs	y = 0.52x + 410.47	R² = 0.89	y = 0.47x 0.10	R² = 0.97	1.7074 ± 0.1388	3.39E‐10
Pose 2b ‐ Hindlimbs	y = 0.44x + 535.85	R² = 0.89	y = 0.71x 0.96	R² = 0.97	2.029 ± 0.139	4.83E‐14
Pose 2c ‐ All limbs	y = 0.74x − 700.51	R² = 0.93	y = 0.49x 1.00	R² = 0.97	1.279 ± 6.225E‐02	<2.2E‐16
Pose 2c ‐ Forelimbs	y = 0.79x − 1120.2	R² = 0.95	y = 0.40x 1.02	R² = 0.97	1.211 ± 6.473E‐02	3.03E‐13
Pose 2c ‐ Hindlimbs	y = 0.69x − 228.13	R² = 0.92	y = 0.57x 0.99	R² = 0.97	1.333 ± 7.677E‐02	8.04E‐16

CI, confidence interval.

For all flat pose analyses (Pose 2), heavier animals remained the outliers, with Elephas, Hippopotamus and Ceratotherium diverging most from the trendline (Fig. 4). Similar to the Pose 1 analysis, Pose 2b suggested high predictability, with soft tissue as approximately 1.67 times skeletal surface area. Regressions for Pose 1 and Pose 2b were statistically similar. The analysis treating semi‐digitigrade/subunguligrade as plantigrade (Pose 2c) suggested soft tissue as approximately 2.04 times skeletal surface area, and semi‐digitigrade as digitigrade (Pose 2a) resulted in soft tissue as 1.05 times skeletal surface area. Interestingly, the hindlimbs‐only regression for Pose 2b was significantly different from its equivalent with both fore‐ and hindlimbs and forelimbs‐only (Table 1).

Figure 4.

Log₁₀ plots for projected skin surface area against projected skeletal surface area for (A) Pose 2a for all limbs, (B) Pose 2b for all limbs, (C) Pose 2c for all limbs. Silhouettes from Phylopic. All numbers rounded to two significant figures. Mammalia data are in purple, Aves data in red, Crocodylia data in green, Lepidosauria data in blue, and Lissamphibia in yellow.

Phylogenetic generalised least squares results (e.g. for all feet, in ‘Pose 1’, with Carnivora and Perissodactyla in a single clade) produced a correlation of −0.171 between the predictor and the intercept, and a Pagel's lambda value ~ 1, with an adjusted R ² of 0.92: t‐statistic 18.06, residual standard error (SE) 12 005, 29 degrees of freedom (DF), 26 residual). Similar results were found when running the same tests on fore‐ and hindfeet separately, with the other two phylogenetic tree arrangements. When skeletal elements were laid flat, variable adjusted R², Pagel's lambda (though all ~ 1) and t‐statistics were found, with higher standard error (15 686.49 SE, 28 DF, 26 residual) in Pose 2a) (Tables S1–S7). Despite these variations, this still suggests that phylogeny is not the main driver of the correlations found.

Separate regressions for unguligrade, digitigrade, plantigrade, terrestrial, semi‐aquatic, erect posture, sprawling posture, birds and mammals, all showed strong correlations (Tables 2, S1–S7, Supporting Information Fig. S1). Equations for all the analyses varied, with opposing regressions (e.g. sprawling vs. erect posture, or terrestrial vs. semi‐aquatic) statistically different from each other (Table 2, equations and R ² values rounded to two significant figures). Although R ² values suggest high correlations for these regressions, the lack of data points in each of them (particularly those with the highest R ² values) suggests their predictive value is relatively low at present. There are potentially functional reasons why, for example, sprawling animals, semi‐aquatic animals and birds would have stronger correlations and more predictable foot morphologies, but the lower scores in groups with more data points suggest that high correlation in groups with few data points may be an artefact, and should be viewed with caution.

Table 2.

Regressions and confidence intervals for analysis subgroups

Analysis	Linear regression	Linear R²	Log regression	Log R²	95% CI	P‐value
Unguligrade	y = 0.36x − 593.56	R² = 0.95	y = 0.27x 1.01	R² = 0.97	2.6121 ± 0.2903	0.000844
Digitigrade	y = 0.19x + 1823.1	R² = 0.83	y = 2.02x 0.84	R² = 0.97	4.336 ± 0.537	2.02E‐06
Plantigrade	y = 0.74x + 1128.3	R² = 0.96	y = 0.35x 1.06	R² = 0.99	1.29686 ± 0.08747	1.25E‐07
Terrestrial	y = 0.45x + 491.99	R² = 0.91	y = 0.68x 0.96	R² = 0.91	1.9998 ± 0.1769	4.25E‐08
Semi‐aquatic	y = 0.77x + 408.03	R² = 1.00	y = 0.42x 1.02	R² = 0.99	1.30129 ± 0.02233	4.26E‐09
Erect Posture	y = 0.48x + 588.49	R² = 0.89	y = 0.94x 0.93	R² = 0.95	1.8517 ± 0.1486	1.37E‐10
Sprawling Posture	y = 0.51x − 19.70	R² = 0.99	y = 0.50x 0.99	R² = 1.00	1.96139 ± 0.06779	1.13E‐07
Birds	y = 0.59x + 32.25	R² = 1.00	y = 0.87x 0.96	R² = 0.99	1.69386 ± 0.01636	1.59E‐09
Mammals	y = 0.48x + 903.78	R² = 0.87	y = 0.57x 0.98	R² = 0.91	1.8353 ± 0.2018	9.87E‐07

Body mass had no significant effect on relative skin/skeletal areas. This was unsurprising because Ceratotherium results indicated more skeletal representation than other large animals such as Elephas, and percentage of skeletal vs. non‐skeletal (skin) area results for small animals did not appear to skew towards either obviously high or low skeletal representation (Tables S1–S7).

Discussion

Projected skeletal surface area as a percentage of projected skin surface area varied between the organisms studied, most notably in mammals, which yielded both the lowest and second highest values (Fig. 2). Bird feet are all similarly digitigrade in their posture and are largely made up of skeleton (with three major digits and consistent phalangeal numbers), skin and connective tissue, so their more consistent percentages are not surprising considering that some of the mammals in this dataset had hooves, fatty footpads and a wide range of foot anatomies and postures (from plantigrade to unguligrade). PGLS results suggested that the correlation between skin and skeletal foot surface area in all poses, as well as being very strong, still held with phylogeny taken into account. This suggestion was supported by Figs 3 and 4.

Equus and Giraffa stood out in this dataset for having an especially low relative skeletal surface area. All extant horses have one toe with a large, keratinous hoof (Bowker et al. 1998), so this was perhaps to be expected. Giraffes also have relatively small feet and gracile legs compared with other animals of similar size, and a combination of high body mass and high running speeds, which contribute to an overall unique morphology (Van Sittert et al. 2015). Pose 2 resulted in a lower relative skeletal area across unguligrade animals, though none as extreme as either Equus species. By focusing on ungual bones, it became clear that the keratinous sheath that forms the hoof dominates the ‘silhouettes’, with skeletal tissue only represented by the very tip of the toe, so this is to be expected. Non‐unguligrade ungulates – Ceratotherium, Hippopotamus, Camelus dromedaries and Vicugna pacos – did not yield similar results to unguligrade ungulates, and varied significantly from this group, as well as from each other.

For Crocodylus niloticus, the fact that Crocodylia have relatively thin, long, digital bones, somewhat similar to human phalanges, that converge to form a surprisingly robust foot, could have some effect (Ferraro & Binetti, 2014). Furthermore, joint range of motion studies have suggested an unusual wrist function and resultant manus posture in crocodilians favouring rigidity, which could affect potential foot contact area (Hutson & Hutson, 2014). This rigidity could potentially aid in swimming, with the stiff foot acting in a flipper‐like fashion to push through water efficiently, which smaller crocodilians tend to rely upon (Seebacher et al. 2003). Furthermore, the Crocodylus niloticus specimen used was the only juvenile in this study, and its phalanges were small and spaced far apart in some cases, so this result could be an artefact of ontogeny, or of the quality of the models used. Further studies on the effect of ontogeny on skeleton to skin surface area ratio could elucidate this further. Indeed, in future studies, consideration should be given to levels of ossification of manus and pes bones. For example, our Cryptobranchus CT scan was missing wrist bones on all feet when segmented because these elements were cartilaginous in the specimen scanned, and were indistinguishable from soft tissue. Such ossification is likely to vary across species and across ontogeny.

At the other extreme, where skeletal surface area was high (most closely approaching projected skin surface area), several birds (most notably Coturnix, Accipiter nisus and Alectoris chukar) along with carnivorans and Ceratotherium (as well as Hippopotamus in Pose 2b and 2c) stood out the most. For birds, this is understandable considering their relative lack of musculature and fat in their feet. For carnivorans this could be explained by their claws, extending beyond the main body of the foot, by the resting position of their digits in vivo, and by their footpads, for which stiffness scales directly with body mass, whereas foot contact area lags behind (Chi & Roth, 2010). This scaling allows carnivorans to maintain relatively small feet that are light enough to be moved quickly (Kilbourne & Hoffman, 2013; Kilbourne & Carrier, 2016).

Body mass seemed to have little general effect on the relationship between skin and skeletal foot surface area. Previous studies have found a scaling relationship between body mass and foot contact area that is not significantly different from isometry (Michilsens et al. 2009), implying that the ratio of skeleton to soft tissue in the foot was not affected by this scaling effect. The scaling relationship between the ratio of skin to skeletal foot surface area was at best trivially different from isometry – a sensible result given that the variables are two facets of the same structure (i.e. the manus or pes), and therefore their structure and development are intrinsically linked. Despite this result, the largest animals in our dataset were the most outlying (much less so when plotted logarithmically; Fig. 3). It is notable that these largest animals, namely, Elephas, Ceratotherium and Hippopotamus, were also the only semi‐digitigrade/subunguligrade animals in our data. These animals both had the largest feet in the study and possess fatty foot pads to reduce loads on their individual toes and spread out underfoot pressure due to their large body masses (Hutchinson et al. 2011; Regnault et al. 2013). The divergence of these data appears to be influenced by their foot posture as well as their large size, with the adaptation of a semi‐digitigrade posture potentially occurring specifically to support their large bodyweights.

It may be worth considering that beyond a certain weight threshold, specialised foot morphologies are necessary for weight support and locomotion, and thus successively heavier animals may have more disparate soft tissue structure and foot posture adaptations to cope with increased load (Hutchinson et al. 2011). This has implications for the inherent predictability of our methods for very large extinct animals, such as sauropod dinosaurs, especially where foot posture is loosely inferred and little information about soft tissue structure is available. Follow‐up studies on semi‐digitigrade foot postures and how they support loads differently to other foot postures, as well as similar studies to this, using additional heavy and semi‐digitigrade animals, would increase understanding of this variation of foot form and function. Contrary to the semi‐digitigrade animals in our study, the giraffe, an unguligrade animal, was the largest other tetrapod (< 1500 vs. ≥3000 kg in larger individuals of the semi‐unguligrade taxa), and deviated little from trendlines.

The strength of the correlation between skin and skeletal foot surface area, despite variations seen in Fig. 2, implied sufficient reliability to predict one from the other (Fig. 3). Despite this, birds only appeared above the trendline (Fig. 3). Perhaps a more accurate correlation could be achieved for birds alone with a larger avian dataset (with a wider range of foot sizes), which would allow more accurate predictions of bird foot surface area, and of foot surface area for animals with similar pedal anatomy to birds (such as non‐avian theropod dinosaurs). Although our main results could be refined with a much larger tetrapod dataset, it appears that foot surface area can be predicted from foot skeletal surface area, with soft tissue generally predictable as approximately 1.67 times skeletal foot surface area, as demonstrated in Poses 1 and 2b. However, when analysed separately, manus and pes presented differing ratios, with soft tissue surface area of the former being predicted as ~ 2 times skeletal area but just ~ 1.56 times for the pes. This correlation could potentially be used to estimate skeletal foot surface area of animals from their footprints, and its inverse used to predict skin‐on‐foot surface area of extinct animals from their skeletons, and even of cadavers from skeletons, with potential forensic applications.

For Pose 2, Elephas, Ceratotherium and Hippopotamus were tested in three different poses. Their foot anatomy is unusual in that they have a foot posture with most foot elements far off the ground, but also have fatty pads which give them a large foot surface area. With this in mind, all foot elements being in line with the horizontal plane, as in Pose 2c, is highly unrealistic. Pose 2a is perhaps more realistic than 2c, but assumes that fewer foot elements are supportive during stance than is accurate in vivo. The most representative position for semi‐digitigrade would arguably be Pose 1, as this did not force these animals into an unrealistic foot posture. However, Pose 1 and Pose 2b both result in the same 1.67 times skeletal surface area value, and the intermediate nature of Pose 2b tests a pose in between digitigrade and plantigrade. Pose 2b, then, is perhaps the best repeatable method. If, despite this, our other methods were chosen to predict foot surface area, skin surface area would be equal to 1.05 times skeletal surface area for Pose 2a, and 2.04 times skeletal surface area for Pose 2c. The variability in these analyses does reveal that altering the results of the largest animals in the study alters the equation used. Therefore, this method would perhaps be best applied to smaller and non‐semi‐digitigrade animals. However, variation in area results is to be expected when fundamentally changing the number of skeletal elements in an analysis.

Where data were divided into smaller groups for analysis, strong correlations were found in results for plantigrade animals, semi‐aquatic animals, sprawling posture and birds (Table 2). Selective pressures potentially could drive a need for similar foot anatomy across these groups, and therefore predictable foot structures, such as adaptations for perching, swimming and supporting bodyweight when feet are not directly under the body. Yet, considering that these groups were also the groups with the fewest data points, we cannot draw any definitive conclusions from these results.

In terms of methods used, we found that convex hulls are highly sensitive to foot pose, such as the size of inter‐digital angles (Tables S1–S7), a result consistent with previous findings (Cholewo & Love, 1999). This could be the cause of wide error margins if these hulls were used for predictive purposes. This is especially relevant in re‐posed foot models, where inter‐digital angles are manipulated to resemble in vivo arrangements, and in animals that have long, thin digits, such as crocodilians. Alpha shapes produced more consistent, ‘tight‐fitting’ outlines for area calculation, a much more accurate measure of the real scope of foot surface area for these models.

Inevitably, models derived from CT scans, such as those we used, ignore certain in vivo factors such as foot deformation during contact with the ground. While we attempted to stick closely to the in situ positions of feet (Pose 1) and aimed for a more objective iteration of our analysis by laying bones flat to remove subjectivity (Pose 2), deformation is a very difficult issue to control for. Collection of the data needed to take this into account would require advanced in vivo imaging techniques such as biplanar fluoroscopy (i.e. ‘XROMM’; Brainerd et al. 2010; Gatesy et al. 2010); however, such techniques remain limited in the size of potential subjects (e.g. Panagiotopoulou et al. 2016a,b) and can be expensive and time‐consuming to conduct. Despite this issue, deformation of the foot should generally not be significant enough that it should diminish the usefulness of this study or the predictability of the methods employed here, as even in soft footpads, foot contact area does not maintain constant stress with body mass, and larger body mass can lead to increased foot stiffness (Chi & Roth, 2010). Combining this methodology with XROMM data for elephants and other animals with large, fatty foot pads, however, would be advantageous in determining the overall effect of deformation on the predictability of these methods and on foot surface area in general, as this particular aspect of foot anatomy is the most prone to deformation with bodyweight, due to its high compliance (Hutchinson et al. 2011). Overall, CT scans are a reliable resource for studies like these, and their utility in determining foot surface area could potentially contribute to future studies on animal locomotion and posture if used in conjunction with in vivo loading, centre of mass and pressure data. However, as in this study, where quality of the models varied, results could potentially be limited by the fidelity of the scans available, and therefore, more scans available for each animal to have the option to pick and choose the most complete and highest quality, as well as more computing power and high‐end software, would be a boon to future studies.

Most studies concerning underfoot areas and pressures have focused on humans and other primates. Adaptations for arboreal locomotion have resulted in large functional differences between the forelimb and hindlimb in primates (Schmitt & Hanna, 2004). Such differences would make them an interesting subject for a follow‐up study.

Assigning specific trackmakers to fossilised trackways is a difficult task (Falkingham, 2014). It is our hope that these results could be used to constrain potential trackmaker identity. However, as an extrapolation from a bivariate plot, with a number of variables unaccounted for such as soft tissue and substrate compliance, the applications of Fig. 3 and its predictions are currently limited, and such identifications of trackmakers must be undertaken cautiously.

When predicting the skeletal surface area of the feet of extinct animals, and identifying trackmakers, the many complexities of footprint formation must be taken into account. The shape of footprints is determined not only by foot anatomy, but also dynamics of the limbs and substrate consistency (Padian & Olsen, 1984; Minter et al. 2007; Falkingham, 2014). Underfoot pressures (Hatala et al. 2013), centre of mass position (Castanera et al. 2013) and style of locomotion (Hatala et al. 2016) all contribute to variations in limb dynamics, and consequently the morphology of a track. Given that foot size and shape is the focus of this study, the findings herein concern matters of critical importance to footprint formation and trackmaker identification, relating as they do to both anatomy and dynamics.

When trying to model footprint formation and dynamics of extinct animals, centre of mass and underfoot pressures of the animals in question are determining factors. When considering these factors, the difference between manus and pes size and pressure is of great importance. Disparity between the cranial and caudal parts of the body is especially notable, as previous biomechanical models have often underestimated mass in the cranial half of the body (see Discussion in Allen et al. 2009). Simply put, taking into account the differences between soft tissue area in manus and pes could make a notable difference in estimations of underfoot pressures and simulations of footprint formation. As an example, when the skeletal remains of Plateosaurus engelhardti feet were laid flat, and their skin areas predicted from alpha hulls, estimated manus skin area was 32% of pes area when using the 1.67 multiplier from combined analyses, and 40% of pes area using the separate multipliers (2 for manus, 1.6 for pes). Using body mass and centre of mass calculations from Allen et al. (2013), these results predicted manus underfoot pressure of 80% pes pressure when combined, and 64% when separate (Tables S1–S7). This effect should also be considered in the inverse when considering trackmaker anatomy from fossil footprints. In this way, this method is a useful tool to consider in digital reconstruction and trackmaker identification.

Conclusions

The surface areas of the skin of the foot in situ and of the foot's skeletal components are strongly correlated and thus should be predictable in terrestrial tetrapods. Skin surface area was approximately 1.67 times that of skeletal surface area (~ 2 times for manus, ~ 1.6 times for pes, if analysed separately). This trend was not affected by body mass and showed little evidence of being strongly affected by phylogeny. This predictability has potential in aiding estimation of the size and possible species of trackmakers in the fossil record, by estimating both the size of skeletal feet using footprints and foot size, and therefore potential footprint size, from fossil feet.

Author contributions

Research and analysis were conducted by E.C.S. Manuscript and figures by E.C.S., with contributions from P.L.F., J.R.H. and D.M.W. The majority of the CT scans used were provided by J.R.H. Research was part of a PhD by E.C.S., supervised by P.L.F., D.M.W. and J.R.H.

Supporting information

Table S1‐S7. Additional data including P‐values for all analyses, calculated soft‐tissue and skeletal areas, approximate body masses for all animals, data for analyses with smallest and largest taxa removed, and demonstration of utility using Plateosaurus engelhardti. Table S1. Phylogenetic comparative tests for all limbs in all poses. Table S2. Area (mm²) measurements for all animals and proportions of skeleton to skin surface area (%). Table S3. Body mass for each subject animal, source of data, and F‐ and P‐values for GLS with body mass as a predictor of correlatory power for all poses. Table S4. Slope uncertainties for all poses and combinations of limbs. Table S5. List of taxa used with common names and Latin names. Table S6. Examples of results with large and small animals removed. Table S7. Example of study utility using Plateosaurus engelhardti.

Fig. S1. Plots for projected skin surface area against projected skeletal surface area in Pose 1 and Pose 2, presented as sub‐groups by phylogeny and ecology.

Data S1. Top‐down projections of models used in study, showing alpha shapes and convex hulls.