## Abstract

Digit reduction is a major trend that characterizes horse evolution, but its causes and consequences have rarely been quantitatively tested. Using beam analysis on fossilized centre metapodials, we tested how locomotor bone stresses changed with digit reduction and increasing body size across the horse lineage. Internal bone geometry was captured from 13 fossil horse genera that covered the breadth of the equid phylogeny and the spectrum of digit reduction and body sizes, from *Hyracotherium* to *Equus*. To account for the load-bearing role of side digits, a novel, continuous measure of digit reduction was also established—toe reduction index (TRI). Our results show that without accounting for side digits, three-toed horses as late as *Parahippus* would have experienced physiologically untenable bone stresses. Conversely, when side digits are modelled as load-bearing, species at the base of the horse radiation through *Equus* probably maintained a similar safety factor to fracture stress. We conclude that the centre metapodial compensated for evolutionary digit reduction and body mass increases by becoming more resistant to bending through substantial positive allometry in internal geometry. These results lend support to two historical hypotheses: that increasing body mass selected for a single, robust metapodial rather than several smaller ones; and that, as horse limbs became elongated, the cost of inertia from the side toes outweighed their utility for stabilization or load-bearing.

## 1. Introduction

Digit reduction and loss is a repeated theme in tetrapod evolution, in groups as disparate as theropod dinosaurs, lizards, marsupials, rodents and ungulates [1–6]. Reduction from the ancestral state of five digits, or more in Devonian tetrapods [7], contributes to the remarkable diversity of limb form and function in living tetrapods. Evolutionary digit reduction requires interaction between development and selective pressures that drive adaptation. The developmental mode of digit reduction varies, even within mammalian orders [8,9], and the selective pressures that interact with these developmental changes are often associated with new ecological behaviours and locomotor modes [4,10,11]. In dipodid rodents, for example, repeated convergent evolution of reduced digits suggests selection for increased bipedality, with a concomitant shift to rapid, unpredictable locomotion for predator evasion [4,12].

One of the most extreme examples of digit reduction is the modern horse (genus *Equus*), which evolved monodactyly (a single toe) from an ancestral state of four digits in front and three behind [13]. All phalanges other than digit III are eliminated, and metapodials II and IV are vestigial ‘splint’ bones that taper off halfway down the length of metapodial III. In horses, the classic explanation for digit reduction is that of an adaptive response to the replacement of forests by grasslands, although the specific underlying driver for monodactyly has been debated. Shifting to hard turf and open spaces is suggested to select for long, slender legs to increase speed for predator escape [14], decrease the energetic cost of locomotion by reducing distal limb mass [15] or enhance stability for high-speed, straight-lined movements [16]. An additional hypothesis proposed for digit reduction in the horse lineage is that evolutionary increases in body mass produced greater bending forces on the limbs, and a single digit resists bending forces better than several smaller digits of the same total size [17,18]. We aim to test the body mass hypothesis by exploring how locomotion-related stresses in the metapodials change with the evolution of larger body sizes and reduced side digits.

Prior work on equid limb evolution has focused on the transition from digitigrade to unguligrade posture, generally using *Mesohippus* (tridactyl with large side digits), *Merychippus* (tridactyl with reduced side digits) and *Equus* (monodactyl) as exemplars for key stages of digit reduction. Using inferences from tendon scars and articular surfaces, *Mesohippus* has been reconstructed as subunguligrade with a digital pad that helps absorb forces, while *Merychippus* has been reconstructed as unguligrade with non-functional side digits (similar to *Equus*) [17,19,20]. These studies assume that as the foot becomes more upright and the central phalanges elongate, the side digits lose function. A mechanical investigation of digit reduction estimated bending forces on the third metacarpal in all three taxa [21]. Using external measurements and cross-sections (estimated from fractured specimens), mid-shaft bending stresses were calculated to be within the range found by *in vivo* experiments on mammals. Forces for *Mesohippus* were reduced by 50%, assuming that each side digit carried 25% of the load, but the side digits of *Merychippus* were assumed to play no functional role [21]. The only other test of load-bearing in side digits comes from a *Hipparion* trackway that shows contact from the side digits, supporting possible load-bearing or stabilizing functions [22].

Here we significantly expand the beam bending approach by using modern three-dimensional imaging to capture the internal bone geometry of metapodial III from 13 fossil horse genera. The taxa in this study cover the breadth of the equid phylogeny and the full spectrum of body sizes and digit reduction, from the dog-sized, tetra/tridactyl *Hyracotherium* to the large, monodactyl *Equus*. Unlike prior studies, we also quantitatively account for the changing size of side digits through evolutionary time by scaling ground reaction forces relative to a continuous measure of digit state. Our study addresses the following three questions and associated hypotheses:

(1) How does stress on the centre metapodial change with evolutionary increases in body size? As quadrupeds tend to maintain similar long bone safety factors regardless of size [23,24], we hypothesized maximal metapodial III stresses to remain constant through evolution by adjusting its cross-sectional geometry to increase resistance to bending.

(2) Did side digits play a load-bearing role during horse evolution? If load is placed entirely on the centre metapodial, we hypothesized stress on metacarpal III to be high in species with load-bearing side digits and within normal ranges for species with non-load-bearing side digits. Likewise, if side digits share the load proportional to their size, we hypothesized stress on the centre metapodial to remain constant through evolution.

(3) Is the geometry of metacarpal III better or worse at withstanding bending forces than metatarsal III? In extant horses, the metatarsal experiences slightly higher bending forces than the metacarpal because it is less closely aligned to the ground reaction force [25,26]. Because the equid hindlimb shows reduced digits earlier than the forelimb, we hypothesized a more rapid increase in bending strength of metatarsal III relative to metacarpal III.

## 2. Material and methods

### (a) Specimens and internal geometry

This study uses adult metapodials (*n* = 26) from 12 fossil horse genera and *Tapirus bairdii* (figure 1; electronic supplementary material, methods and table S1). Tapirs are the most relevant comparative outgroup, as they are the only extant perissodactyls with similar distal limb morphology to early horses (but see [27] for discussion of varying morphology and locomotor styles within the genus). All specimens were micro-CT scanned using a Nikon Metrology (X-Tek) HMXST225 MicroCT system, reconstructed as a downsampled TIFF stack, and processed using the Bone Geometry function of the BoneJ (v. 1.0.0) plugin for ImageJ (v. 1.48v) [28,29]. In addition to bone length (*l*), we extracted from every slice the cross-sectional area (*A*), second moment of area about the mediolateral (*I*_{ML}, bending in the anteroposterior direction) and anteroposterior (*I*_{AP}, bending in the mediolateral plane) axes, and radius from the neutral axis in both directions (*y*_{AP}, *y*_{ML}; electronic supplementary material, figure S1). The mid-shaft slice of each specimen was then used for bending analysis (see below); if the exact midshaft slice was damaged or otherwise unsuitable, we chose the nearest suitable slice.

We tested the scaling of evolutionary changes in midshaft cross-sectional area (a measure of bone compressive strength) and second moment of area (a measure of resistance to bending). To correct for the effect of phylogeny, we calculated independent contrasts on log-transformed mass and internal geometry variables [30]. Using major axis regression in the R package smatr [31], we then tested whether the slopes of the mass versus internal geometry contrasts were significantly different from isometry (defined as a slope of 2/3 for cross-sectional area and 4/3 for second moment of area). Cross-sectional area and second moment of area were also plotted along the length of the bone, with genera coloured according to digit state, to assess how internal geometry changes with reduction in digits. For this comparison, second moment of area (*I*_{AP} and *I*_{ML}, mm^{4}) was size-corrected by taking the 4th root to provide a size-independent measure of shape, while retaining the evolutionary signal of increasing bone length [32]. Similarly, cross-sectional area (*A*, mm^{2}) was corrected by taking the square root.

### (b) Loading scenarios and conditions

To estimate bone stress, we simulated two loading scenarios: normal, steady-state forward locomotion (approximately trotting speed) and high-performance forward locomotion (rapid acceleration or jumping). Based on *in vivo* locomotion data on modern horses [25,26], the angle of each metapodial relative to the ground reaction force was set to 5° and 20°, respectively, for these two loading scenarios. For each loading scenario, either (i) a full body-weight load was applied to the centre metapodial (digit III) using reconstructed body mass values [33–36], matching the ground reaction force that medium-sized animals experience at a trotting gait, including extant horses [25,26,37]; or (ii) the body-weight load applied to metapodial III was reduced relative to the side digits bearing some of the load. The relative body-weight load applied to metapodial III was determined by a toe reduction index (TRI; see electronic supplementary material, methods and table S2). TRI is a ratio of side digit length to centre digit length in the proximal phalanx. The ratio ranges from 0, where no side toes are present (e.g. *Equus*), to 1, where all digits are of equal size (figure 1), using the simplifying assumption that load capacity correlates directly with digit size. For example, a TRI of 0 (e.g. *Equus*) produces a scaled load equal to the full body weight, whereas a TRI of 1 (all three digits equal in size) produces a scaled load of 1/3 body weight.

### (c) Beam bending

Using beam mechanics, we estimated the stress at the metapodial midshaft (electronic supplementary material, figure S1). We calculated bending in the anteroposterior direction, simulating forward locomotion, by combining stress from axial compression, 2.1and bending, 2.2

The muscle force *F*_{m} required to counteract the ground reaction force *F*_{grf} is defined as
2.3

where *r* is the moment arm of *F*_{m} and *R* is the moment arm of *F*_{grf}; *β* is the angle of *F*_{m} to the long axis of the bone; *θ* is the angle of *F*_{grf} to the long axis of the bone; and *h* (= *l*/2) is the height to the bone's midshaft, where the bone's total length is *l* (electronic supplementary material, figure S1).

Moment arms were taken from empirical values for the metapodial-phalanx joint in extant *Equus* (*r* = 30 mm and *R* = 100 mm for a 450 kg animal) [38,39] and scaled such that [23,40], where *M*_{body} was the reconstructed body mass of each genus [33–36]. Effective mechanical advantage (EMA), defined as *r*/*R*, scales proportional to *M*_{body}^{0.258}. With a starting point of *Equus* EMA = 30/100 mm = 0.3, we scaled EMA and back-calculated *R* for all taxa. The ground reaction force (*F*_{grf}) was set equal to a body-weight load for each species. In the first condition, the whole load was placed on the centre metapodial. In the TRI condition, that load was reduced proportional to TRI, as discussed previously. We chose a *β* of 0° to reflect that the muscle-tendon units act almost directly in line with the metapodials in extant horses [25,26].

Under a bending load, stress at the bone's midshaft cross-section will range from positive (tensile side of the bend; anterior, if *θ* is positive) to negative (compressive side of the bend; posterior, if *θ* is positive). We can therefore calculate the maximal stress on the anterior and posterior surfaces as , with axial compression reducing stress on the tensile surface ( and compounding stress on the compressive surface (). Safety factor was calculated as the ratio of the bone's fracture stress (approximately 200 MPa in compression and 170 MPa in tension [41]) to the maximal stress calculated in this study. When a metacarpal and metatarsal from the same specimen were available (*n* = 4), we assessed the ratio of maximal stress in the metacarpal versus metatarsal using the body-weight and TRI-scaled loading conditions.

## 3. Results

### (a) Metapodial internal geometry

After phylogenetic correction, metapodial *A* (resistance to axial compression) shows strong positive allometry (figure 2*a*; electronic supplementary material, table S3). Metapodial *I*_{ML} (resistance to bending in the anteroposterior direction) also shows strong phylogenetically corrected positive allometry (figure 2*b*; electronic supplementary material, table S4). For each metapodial specimen, cross-sectional geometry variables remain consistent along the length of the bone with a typical peak near the articular ends (figure 2*c*; electronic supplementary material, figures S2 and S3). As TRI decreases in fossil equids, size-independent resistance to anteroposterior bending increases, as shown by the higher values of size-corrected *I*_{ML} for lines of warmer colour (figure 2*c*). *Tapirus*, the outgroup, has significantly greater resistance to bending relative to equids with similar TRI values, perhaps reflecting adaptation to a larger body mass (closer to *Equus* than to more basal taxa). *Equus* metacarpals show the greatest size-independent resistance to bending, followed by *Pliohippus* and the hipparionine horses. The lowest size-independent resistance to bending is *Hyracotherium*. Results are similar for resistance to mediolateral bending (electronic supplementary material, figure S2*b*), with higher overall values of *I*_{AP}, reflecting the slight anteroposterior cross-sectional flattening of most metapodials in this study (figure 1).

### (b) Metacarpal stress during normal (trotting) locomotion

During normal locomotion, the posterior metapodial surface experiences the greatest load due to the combination of bending and axial compression (electronic supplementary material, figure S4). The metacarpals in all taxa studied maintained a safety factor of at least 1.7, even without accounting for the side digits bearing some of the load (mean safety factor 3.1 ± 1.1; table 1). The average posterior surface stress during normal locomotion supporting a body weight load is −70.1 ± 21.1 MPa, higher than would be expected for trotting locomotion [25]. After scaling the load by TRI to account for side digits distributing the load, the average posterior surface stress is reduced to −31.6 ± 7.4 MPa, yielding a higher and more consistent safety factor (6.7 ± 1.6) across taxa.

### (c) Metacarpal stress during performance (acceleration/jumping) locomotion

During performance locomotion (figure 3), the anterior metacarpal surface is loaded in tension and the posterior surface loaded in compression. Without scaling for TRI, many fossil taxa approach or surpass the tensile fracture stress of bone on the anterior surface and/or the compressive fracture stress on the posterior surface (black bars). Most tridactyl taxa exhibit posterior surface stresses within approximately 50 MPa of fracture stress. The exceptions are the later, hipparionine horses (especially *Pseudhipparion* and *Cormohipparion*), as well as *Pliohippus* and *Equus*, which all exhibit stresses closer to −100 MPa (a safety factor of 2). When accounting for the side digits by scaling the load relative to TRI, maximal stress is below −100 MPa for almost all taxa (maximum −109 MPa for one specimen of *Mesohippus,* a safety factor of 1.8). Average posterior surface stress is −67.7 ± 19.5 MPa, providing a safety factor of 3.2 ± 0.9. On the anterior surface, tensile stress averages 29.6 ± 14.2 MPa for all taxa. In all cases, adjusting for TRI leaves maximal stresses within or below the safety factor range of 2–4 found during terrestrial locomotion in birds and mammals [42].

### (d) Metacarpal versus metatarsal maximal stress

In *Mesohippus*, *Equus* and extant *Tapirus*, metatarsal stresses range from 7 to 33% higher than metacarpal stresses under performance conditions with weight scaled by TRI (up to 25.5 MPa difference; table 2). In *Archaeohippus*, metacarpal stress is 8% higher than metatarsal stress (a 3.2 MPa difference). Results are similar for a non-scaled load, but with higher magnitudes. Overall, results for all metatarsals follow the same pattern as metacarpals, with similar safety factors (electronic supplementary material, figure S5).

## 4. Discussion

### (a) Simulated stress matches *in vivo* stress in *Equus*

Results for a Pleistocene fossil *Equus*, with maximal metacarpal stresses of −34 MPa for normal trotting locomotion and −70 MPa for performance locomotion, are similar to maximal *in vivo* stress from living *Equus* (−31 MPa during forward locomotion and −53 MPa for jumping [25]). After reducing the forces on the metacarpal relative to side digit proportions, mean safety factor during performance locomotion for all taxa (3.2 ± 0.9) aligns closely with experimentally determined safety factor values from 2 to 4 across a wide range of mammalian species [40,42]. Furthermore, *Mesohippus* and *Equus* metacarpal stresses agree with those calculated in 1985 by Thomason, who used more simplifying assumptions and less detailed three-dimensional geometry but incorporated estimates of foot posture (which we did not) [21]. During trotting locomotion with the side digits bearing proportional load, we calculate a posterior midshaft stress of −34 MPa for *Equus*, and −34 MPa and −45 MPa for two *Mesohippus* specimens in this study, which agrees with Thomason's results of −48.3 MPa in *Equus* and −33.4 MPa in *Mesohippus* [21].

### (b) Stress on the centre metapodial decreases with increasing body mass

When a body-weight load is placed on MCIII, its midshaft stress decreases as body mass increases through evolutionary time (figure 3, black bars). This result is in contrast with living vertebrates from mice to elephants, which show similar limb safety factor regardless of body mass [40]. Changes in internal geometry explain this pattern: resistance to bending and axial compression in the third metapodial shows strong positive allometry in the equid lineage (figure 2*a*,*b*). Because cross-sectional area and second moment of area increased, total stress during locomotion is reduced as body mass increases. Not only is this pattern of safety factor unexpected, it suggests that many tridactyl taxa could not have safely loaded only metapodial III during high-performance locomotion (figure 3, black bars that approach or surpass the red line of fracture). These results point to evolutionary compensation by the centre digit for increasing body mass and shrinking side digits, but also suggest that the side digits played a necessary role in earlier taxa. Alternatively, bending resistance in the centre digit could have increased in response to increasing body mass, which then relaxed selection for load-bearing side digits. Postural changes in the angle of the metapodial to the ground reaction force could also influence safety factor as side digits were reduced and body mass increased. Although we do not account for postural changes in this study, less upright posture in earlier equids would probably increase the reconstructed stresses, as larger ground reaction force angles would lead to greater bending moments and larger muscle forces.

### (c) Load-bearing side digits are critical in most tridactyl taxa

When side digits are load-bearing, metapodial midshaft stress remains approximately constant through equid evolution (white bars, figure 3). Estimated metacarpal safety factor is biologically feasible and consistent (average safety factor of 3.2 ± 0.9). Even during more demanding locomotion such as acceleration or jumping, midshaft stress does not change with digit reduction or increasing body mass—consistent with bone stresses determined for extant quadrupeds [40].

We expected *Pliohippus* to have sufficient safety factor at high performance even without accounting for the side digits because the population of *Pliohippus pernix* from Ashfall, the source of our specimen, contains both tridactyl and monodactyl individuals [43]. Such variation would seem to suggest that the biomechanical role of the side digits for weight support, if any, was not critical during locomotion. Under the high-performance scenario, the *Pliohippus* metacarpal had a safety factor of 2 without side digits and 4 when scaling by TRI. These results bracket the *Equus* safety factor of 2.9 but are similar to the hipparionine horses, whose side digits probably did provide utility, as discussed in the next section. However, *Pliohippus* shows the highest size-independent resistance to anteroposterior bending after *Equus* and *Tapirus* (figure 2). Our results do not definitively show that the side digits of *Pliohippus* at Ashfall were without weight support function, but support the possibility.

### (d) Metacarpals resist bending slightly better than metatarsals

We hypothesized that the bending performance of metacarpals and metatarsals might be decoupled because of the asymmetrical nature of digit reduction between the forelimb and hindlimb. With ground reaction force equivalent to one body-weight—which both the metacarpal and metatarsal experience during faster locomotion in extant *Equus* [25,26]—and similar angle deviations between bone and GRF alignment of 5° or 20°, the metatarsals of fossil horses generally showed slightly higher stresses than the corresponding metacarpals from the same specimens. These differences were small in magnitude, ranging from +25.5 MPa to −3.2 MPa in the metatarsal relative to metacarpal (a maximum of 33% difference). Our results do not account for a greater body weight load in the forelimb or a greater angle in the hindlimb [26], which could produce greater loads in the metacarpal or metatarsal respectively, but the values for both are within experimental results for extant *Equus* [25,26]. We therefore do not find strong support for evolutionary decoupling of the stresses experienced by the metacarpal and metatarsal.

### (e) Evolutionary timing and the loss of functional side digits

Based on our results, side toes were critical for load-bearing to some extent through at least *Parahippus,* the genus at the base of the grazing adaptive radiation. At that point in equid evolution, the distal limb had been significantly elongated and the digits were reduced; *Parahippus* had a TRI of 0.61, reduced from 0.89 in *Hyracotherium*. At that time, true grasslands were part of the North American flora [44] and may have been spreading significantly [45], which could have provided selective pressure for reduced distal limb mass to save on costs of locomotion over large home ranges [15] or reduced the need for lateral stability [16]. Later, some hipparionine horses (*Pseudhipparion* and *Cormohipparion*) evolved a centre metacarpal that may have been robust enough to maintain an acceptable safety factor without load-bearing use of the side digits (figure 3, black bars). Although these genera show reasonable safety factors under the conditions of our analysis, a trackway attributed to the closely related genus *Hipparion* shows ground contact by the side digits [22], which would provide a greater safety factor for the centre metacarpal (approximately 4 instead of 2). As Thomason [17] points out, the contact of side digits in the trackway also supports a possible stabilizing function for the side toes, as argued by Shotwell [16]. Selection for stabilization could be separate from any need for stress reduction via load-bearing, and as such would be unrelated to safety factor in the traditional sense.

## 5. Conclusion

Our beam analysis indicates that fossil horse metapodials maintained a similar safety factor throughout evolution when accounting for TRI. Furthermore, as digits were reduced and body mass increased, the centre metapodial changed in its internal geometry, showing allometric increases in cross-sectional area and second moment of area relative to body size. According to our results, side digits were necessary for load-bearing in earlier taxa, including *Parahippus*, to avoid unsafe levels of stress in the centre metapodial. The mechanism of support could be directly through ground contact or, as has been suggested previously, indirectly via interdigital ligaments [17]. Our results support the hypothesis that increasing body mass was a potential driver of digit reduction because a single, robust digit could resist the increased bending forces better than three smaller digits of the same total bone mass [46] (see electronic supplementary material, methods and table S5). However, other factors were probably involved. In combination with increasingly parasagittal limb motion and lengthened distal limbs, the reduced side digits—with their reduced mechanical function—could have incurred sufficient inertial penalty to distal limb motions to either decrease speed or increase energetic cost [17,21]. Thus, selection may have been for a combination of increased strength and decreased inertia, or one followed by the other.

## Ethics

All research conducted for this study was performed on skeletal and fossil specimens that are reposited in accredited museums. No live animals were used.

## Data accessibility

All data, code and results needed to replicate this study are available from Dryad: http://dx.doi.org/10.5061/dryad.4v130 [47]. The main results and supplemental methods have been uploaded as part of the electronic supplementary material. CT scan data have been reposited with the museums that hold copyright to the original specimens; requests to use scan data should be made directly to those museums.

## Authors' contributions

All authors conceived and designed the study. B.K.M. collected the data, wrote the code, analysed the data and drafted the manuscript. All authors interpreted the data, edited the manuscript and gave final approval for publication.

## Competing Interests

We have no competing interests.

## Funding

Funding was provided by the Ashford Foundation, the Harvard Department of Organismic and Evolutionary Biology, and a Sigma Xi Grant in Aid of Research. B.K.M. was supported by a NSF Graduate Research Fellowship (no. DGE1144152) while this work was conducted.

## Acknowledgements

For assistance with collections access we thank J. Chupasko, J. Cundiff, M. Omura, M. Renczkowski and C. Capobianco at the Harvard MCZ; J. Galkin and A. Gishlick at the AMNH; P. Holroyd at the UCMP; G. Corner and R. Secord at the UNSM; R. Otto at Ashfall Fossil Beds; and J. Head. J. MacLaren contributed TRI data. A. Parker assisted with data processing. We thank two anonymous reviewers and the Biewener and Pierce labs at Harvard for feedback on this work.

## Footnotes

Electronic supplementary material is available online at https://dx.doi.org/10.6084/m9.figshare.c.3833713.

- Received May 26, 2017.
- Accepted July 12, 2017.

- © 2017 The Author(s)

Published by the Royal Society. All rights reserved.