Generation of digital sample.

All measurements were taken on 3D digital surface models. These were created by various scanning modalities. Most specimens were scanned using one of five instruments: at SBU, two different ScancoMedical brand machines were used (VivaCT 75, µCT40); at the AMNH Microscopy and Imaging Facility, a Phoenix brand v/tome/x s240 was used; and for specimens of Nasalis, Gorilla, Pan, and Pongo a GE eXplore Locus SP machine was used at the Ohio University µCT Facility. Some gorillas and a couple other large species were scanned with GE Medical CT scanner. A few specimen scans were generated with Breuckmann Structured light scanner provided to the New York Consortium in Evolutionary Primatology by funding of the National Science Foundation. Finally, several specimens were not scanned but measured manually with calipers (the measurements are quite basic: Fig. 1B) Specimens were mounted in foam or packed in cotton to prevent movement while scanning. Most specimens were scanned at a resolution of 39 microns or less. The highest resolutions used were on the order of 3–5 microns for the very smallest fossil specimens. The scanning resolution was usually high enough to result in an initial surface with 1–5 million faces, but all specimens were down-sampled to between 300,000 and 500,000 faces after fitting an initial surface to the data. See appendix for the original scan resolution of each specimen based on a microCT data set.

Measurements and Standard Regressions.

In most regards, our approach is traditional: we measure total length (TL) and distal segment length (DL) of the calcaneus [28], [33], [40] (Fig. 1B). Moyà-Solà et al. [7] used a slightly different approach, and split the anterior (distal) and posterior (proximal) halves of the calcaneus at the midpoint of the ectal facet. Unless selection acts differently on either side of the proximodistal midpoint of ectal facet (i.e., to stretch or compress each half in order to effect different degrees of calcaneal distal elongation), the patterns generated by their method, versus more standard methods should be equivalent. In addition, illustrations in Hall-Craggs [42] show the center of rotation of the astragalotibial joint to be anteriorly adjacent to the ectal facet. Regardless, we think the measurement landmark on the ectal facet used is of minor concern relative to the concern that the particular landmark of choice can be determined repeatably: i.e., the distal boundary of the ectal facet used here is very easy to repeatably locate in almost all included taxa. Instead of then using log-transformed raw data in our analyses, as in Moyà-Solà et al. [7], we calculated elongation ratios as described in the introduction: Calcaneal Elongation = ln(DL/TL).

Regardless of the variable of choice (raw measures or ratios), assessing allometric trends in fossil primates has been hindered previously by lack of body mass (BM) information on isolated calcanei (Moyà-Solà et al. [7] use species mean body mass and mean calcaneal segment lengths). We have generated a regression to estimate body mass based on cuboid facet area as represented by the product of the maximum mediolateral width (cuboid facet width: CW) and maximum dorsoplantar depth (cuboid facet depth: CD) of this facet from a taxonomically comprehensive sample of primates (Fig. 2B), which allows estimation of body mass for any calcaneus with a largely intact cuboid facet. The sample for this regression includes 129 individuals from all major clades (see Table S1 in File S1). Body mass data were obtained mainly from Smith and Jungers [43] with some data coming from Primates in Perspective [44] and Walker’s Mammals of the World [45]. Given a strong correlation between body mass and the calcaneal cuboid facet area one might question the wisdom of using mass estimates derived from measured variables instead of simply using the measured variables themselves. To explain our reasoning some reporting of results is necessary up front.

The equation derived from the linear relationship between logged body mass and logged cuboid facet area is the following: ln(BM) = 1.3274*ln(CW*CD)+3.0238, r² = 0.98. The obtained slope of 1.3274 of the regression and its confidence interval (95% CI: 1.29–1.36) excludes the value 1.5, which is the expectation for an isometric relationship between area and volume. Therefore, regressions of cuboid facet area (CW*CD) and calcaneal elongation directly would not be accurate representations of mass-related scaling of calcaneal elongation despite an excellent correlation between body mass and the area of the calcaneal cuboid facet. We therefore are obliged to use body mass estimates, rather than CW*CD as a covariate for calcaneal elongation. These estimates were used without Quasi-Maximum Likelihood Estimate (QMLE) correction [46]. We decided not to use the QMLE after comparing slopes and intercepts that resulted using both corrected and uncorrected data. Slopes were always either identical or the difference between slope estimates was never more than 0.5% (i.e., one half of one percent) of the standard error of the slope estimates. The difference between intercept estimates, likewise, was never more 50% of the standard error of the estimates (i.e., well within 95% confidence limits). Thus we found no reason to increase the number of estimated parameters by adding a QMLE correction. In Table S1 in File S1, we report anti-logged transformations of body mass estimates used in these analyses for individual specimens; in this case a QMLE correction is applied to give the reader an accurate sense of the estimates.

One might also worry about the phylogenetic specificity of this relationship. However, subdividing the sample into “prosimian” and anthropoid groups reveals no significant changes in slope or intercept (“prosimians” [n = 73, slope 95% C.I. = 1.299–1.395; intercept 95% C.I. = 2.875–3.159], anthropoids [n = 56, slope 95% C.I. = 1.320–1.435; intercept 95% C.I. = 2.541–3.015]). Thus, the taxonomically combined regression can be safely applied to any primate without having major concern about how its phylogenetic relationships might bias body mass estimates of the regression.

Regressions of calcaneal elongation on estimated body mass were also run as ordinary least squares in the program PAST. It could be argued that reduced major axis is a more appropriate method for estimating relationships between variables analyzed here [47], since we are, at this point, modeling a relationship between two variables, instead of predicting one from the other. Nevertheless, we have two important reasons for using least squares in this study: 1) when assessing allometry using a ratio of two linear measurements (as we have done) the null hypothesis (isometry) is a slope of zero and/or no significant relationship between body mass and the ratio of interest. Therefore, when using ratios against body mass, least squares is the most conservative approach for testing for departures from isometry as it tends to underestimate the slope of a line when the correlation is low. OLS cannot necessarily be considered a conservative approach when using absolute measures against body mass: to demonstrate allometry between mass and another measurement it must be shown that the slope of the relationship is significantly different from what is predicted for isometric scaling. A slope of zero, or the lack of a significant relationship, actually implies allometry when regressing an absolute measure on body mass. Furthermore, for a positively allometric relationship, a poor correlation could cause the slope to drop enough to mimic isometry or negative allometry. This situation cannot result when using least squares to regress body mass against a ratio – poor correlations bring the slope towards zero (suggesting isometry) whether the true relationship is positive or negative allometry. Secondly, and more pragmatically relative to the design of our study, there is no well-tested code for phylogenetic RMA currently available.

Phylogenetic Methods.

Phylogenetic statistical methods use the pattern of connectivity and branch lengths in a phylogenetic tree to assess the presence of phylogenetic correlation of values in test variables, and to adjust standard error estimates on statistical tests to account for violation of the typical assumption in parametric tests that data points are metrically independent of each other.

It is intuitive and well-demonstrated [24] that different patterns of connectivity and the branch lengths of the phylogenetic distance matrix can result in different “phylogenetically adjusted” patterns. Nevertheless, it is generally acknowledged from simulation studies [24] that even when there are errors in the phylogeny, the results are more accurate than when assuming a “star phylogeny” ( = no phylogeny). In this study we utilize the “Phylogenetic Generalized Least Squares” (PGLS) [48] approach to incorporate phylogenetic information. We use this for three different specific analyses: 1) evaluation of trait correlation, 2) ANOVA on calcaneal elongation and distal segment length residuals from a phylogenetically-adjusted regression line, and 3) ancestral state reconstruction (ASR). The first two analyses were run using the caper [72] package implemented in R 2.15.0. The third was run using the Continuous module in BayesTraits 1.1B [70]. For all phylogeny-adjusted analyses, species mean values were used to represent each OTU of the sample.

The PGLS regressions and Bayesian reconstructions of continuous ancestral states presented here are each based on one of six different time-scaled phylogenetic trees of living and extinct primates, the overall topologies of which were computed by combining various source trees ([i.e., trees from previously published analyses, combined with new analyses performed specifically for this study [see below]) using the Matrix Representation with Parsimony (MRP) or “supertree” approach. MRP was used to combine the extant primate phylogeny of Springer et al. ([49], based on 61,199 base pairs from 69 nuclear genes and 10 mitochondrial genes) with the molecular analysis of Janečka et al. [50], the morphology-based trees of Tornow ([51], for omomyiforms; his Figure 10), Rose et al. ([52], for basal omomyiforms, their figure 13C), and Bloch et al. ([19], for plesiadapiforms; their Figure 4). These trees were combined with strict consensus topologies derived from de novo parsimony analyses of a matrix that has been used in several recent studies [52]–[57]; modified most recently by Gladman et al. [58] and Boyer and Seiffert (in press) that includes plesiadapiforms and several Paleogene primates (omomyiforms, adapiforms, and early anthropoids). This matrix was analyzed in PAUP 4.0b10 under various constraints so that the evolution of distal calcaneal elongation could be evaluated across several competing phylogenetic hypotheses: 1) with a molecular scaffold enforced, based on the results of Springer et al. [49], but with all extinct taxa unconstrained, 2) with the same molecular scaffold enforced, and adapiforms constrained to be more closely related to tarsiers and/or anthropoids than strepsirrhines [59], and 3) with the same molecular scaffold enforced, with tarsiers constrained to be more closely related to anthropoids than to any omomyiform [35], [52], [60], [61]. All parsimony analyses were performed (in PAUP 4.0b10 [62]) with random addition sequence and TBR branch-swapping across 10,000 heuristic search replicates. Some multistate characters were treated as ordered and were scaled so that transitions between “fixed” states in an ordered morphocline were equal to one step (polymorphisms were assigned their own state, intermediate between “fixed” states in each morphocline). MRP matrices were created and concatenated in Mesquite 2.75, and parsimony analyses were also run in PAUP 4.0b10.

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Figure 4. Plotting early fossil forms reveals allometric scaling within and between certain clades.

Different interecepts but similar slopes of scaling of distal calcaneal elongation index to body mass (as reconstructed from cuboid facet area) characterize different groups of early primates. There is a low- (based on Asiadapinae), intermediate- (based on all or subsets of the following taxa: Cantius, Notharctus, Smilodectes and Teilhardina) and high-elongation line (based on Omomyinae: see Table 2); see also Fig. 3B. The intermediate elongation line appears to be primitive, as the non-primate taxa plotting near the low line (some scandentians and plesiadapiforms) actually exhibit a non-significant relationship between mass and elongation. Dashed lines represent ordinary least squares lines for different groups. Adapiforms are represented by a line describing Cantius species only and one representing all notharctids. The gray area represents the space in between the mean for the two lines. Polygons: Red, Cantius and Teilhardina; Light blue, Notharctus; Dark blue, asiadapines; Yellow, Omomyines; Solid yellow, Omomys; Green, Anchomomys. Th, Tetonius homunculus. See Figure 3 caption for taxon abbreviations.

https://doi.org/10.1371/journal.pone.0067792.g004

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Figure 10. Modeling force magnification plot.

We modeled the biomechanical significance of the empirically demonstrated allometry by assessing the scaling of the relative force needed to balance the load and lever arms of the calcaneus for a primate of varying body mass. We modeled this with three different “ancestral sizes” 10 g, 75 g and 1,000 g. For each starting weight we modeled the increase in relative effort required by the m. triceps surae muscles attaching to the calcaneal tuber for size increase with a constant load arm/lever arm ratio (upper, thin-dashed lines) and with the expected allometric change in load arm/lever arm ratios (lower, thick-dashed lines). We plot values up to 7 kg, the weight of the largest extant prosimians, and show that the observed allometry reduces the effort multiplication required by the animals’ hindlimbs by as much as a 9-to−4 ratio. Note also that evolving to smaller body sizes yields a diminished effort for constant and allometrically changing load arm/lever arm ratios. This opens the possibility for evolving “off” the line when body size decreases, without incurring extra effort on the muscular system (see text).

https://doi.org/10.1371/journal.pone.0067792.g010

Subfossil lemurs posed special problems for the MRP approach because not all have been included in bona fide phylogenetic analyses, leaving us with no option but to graft them onto the MRP supertrees in their most probable phylogenetic positions, given recent assessments of their morphology. The subfossil lemurid Pachylemur appears to be the sister taxon of the lemurid Varecia based on genetics [63] and morphology [64], [65]; as such we placed this genus mid-way along the Varecia branch. The only palaeopropithecid that has been included in a molecular phylogenetic analysis is Palaeopropithecus [66], and that study supported its proposed placement as an indrioid. We used the palaeopropithecid topology proposed by Jungers et al. ([67], i.e. (Mesopropithecus, (Babakotia, Palaeopropithecus))), and placed this clade as the sister group of extant indriids. Internodes within Palaeopropithecidae were spaced evenly, as there are currently no objective means for estimating divergence times within the family. Finally, the archaeolemurid Archaeolemur was placed as the sister group of palaeopropithecids and indriids, again following Jungers et al.’s [67] and Orlando et al.’s [66] placement of archaeolemurids with indrioids (note, however, that Orlando et al. did not resolve the relationships of archaeolemurids, palaeopropithecids, and indriids). Megaladapis was placed as the sister taxon of Lemuridae, following Orlando et al. [66], and was grafted onto the lemurid stem lineage at its mid-point. In other parts of the tree, some additional assumptions had to be made due to a lack of taxonomic overlap in the source trees: 1) not all of the tarsiids for which we have calcaneal measurements were included in the MRP analysis, so Springer et al.’s tarsier phylogeny was grafted onto the tarsiid branch following computation of the MRP supertree; 2) Gunnell’s [39] notharctine phylogeny did not show sufficient taxonomic overlap with other trees to allow for notharctines’ resolved placement relative to non-notharctine primates, so we assumed notharctine monophyly and grafted Gunnell’s consensus tree (his Figure 5 [39]) onto the Cantius abditus branch, and 3) the species of Chiropotes that we measured was not present in Springer et al.’s tree, so that genus was collapsed into a single OTU in our tree. Finally, in order to reconstruct ancestral character states on 1) a tree that would be consistent with the hypothesis of a plesiadapiform-dermopteran clade [68], [69], and 2) another tree that would be consistent with a closer relationship of carpolestid plesiadapiforms to primates than to plesiadapid plesiadapiforms [15], we also modified the primary supertree by 1) moving plesiadapiforms to join dermopterans in an arrangement matching that proposed by Beard [69], and 2) moving Carpolestes simpsoni to be the sister group of living primates to the exclusion of all other euarchontans, with all other relationships remaining consistent with the primary supertree.

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Figure 5. Plot of fossils with extant forms imposed shows similar allometric scaling relationships characterize in living taxa.

To better understand the phenetic associations of the fossils and to help consider the functional implications of their proportions, we plot them with extant taxa. Each data point represents an individual. Dark gray polygons represent species groups. Light gray polygons bound different extant prosimian radiations: Upper polygon, Galagidae; middle polygon, lemuriformes; lower polygon, Lorisidae. (see Figures 2 and 3 for taxon abbreviations). “IVPP” specimens are eosimiids from Shanguang fissure fills with taxon identifications given in Gebo et al. (2000).

https://doi.org/10.1371/journal.pone.0067792.g005

To convert the resulting supertrees into time-scaled phylogenies, we used the divergence times that Springer et al. [49] calculated using independent rates and soft bounds (their Text S2.4). The Ptilocercus-Tupaia divergence was not estimated in Springer et al.’s analysis; we placed this split at 61.8 Ma (i.e., the average of the mean divergence estimates calculated by Janečka et al. [50] and Roberts et al. [70]). Ghost lineages were minimized by placing extinct clades along stem lineages at successive 1 Ma intervals, working down from crown nodes. Within extinct clades, internodes were separated by 1 Ma unless adjacent sister taxa were geologically older. In the trees that recovered omomyiforms as paraphyletic with respect to tarsiids, the branch connecting Necrolemur to Tarsiidae was placed at 46 Ma because there is compelling fossil evidence that closer relatives of tarsiers were already present at ∼45 Ma (i.e., Tarsius eocaenus [71]). In order to evaluate whether a more recent haplorhine-strepsirrhine divergence (as implied by the molecular slowdown identified by Steiper and Seiffert [57]) had an impact on the reconstructed pattern of calcaneal evolution, we provided one additional modification of the primary supertree by adjusting the age of the primate crown node to reflect the ages of the oldest primate fossils (Teilhardina and Cantius) rather than the molecular divergence dates provided by Springer et al. [49]; divergence dates for more nested primate clades were the same as in the primary supertree.

Using the trees described above as input, three different sets of PGLS regressions were performed to determine how ankle elongation scales with body mass: 1) ln-transformed distal/total calcaneal length v. ln-transformed body mass as estimated from the cuboid facet area, 2) ln-transformed absolute distal calcaneal length v. ln-transformed body mass as estimated from the cuboid facet area, and 3) ln-transformed proximal calcaneal length v. ln-transformed body mass as estimated from the cuboid facet area. PGLS regressions in caper [72] employed the phylogenetic scaling parameter lambda (λ), a constant by which internal branch lengths are multiplied (λ of 0 would change all internal branch lengths to a length of 0). If trait evolution is well-modeled by Brownian motion, there will be a strong correlation between trait differences and branch lengths, and λ will approach 1.0. A λ value of 0 indicates that there is no correlation between trait values and branch lengths. In caper [72], other scaling parameters are available (δ, which adjusts overall path lengths, and κ, which adjusts individual branch lengths), but employing multiple branch length transformations simultaneously renders interpretation difficult; as such here we have only allowed λ to vary, and δ and κ were fixed as 1.

Phylogenetic ANOVA was used to assess whether significant among group variance in residual elongation values (Tables 1–2, Res A-B), exists for three different behavioral groups. The categorization for each taxon was determined through literature references [25], [72]–[77]. We treated animals that used acrobatic leaping behaviors from vertical or horizontal supports as a behavioral group, those that use primarily quadrupedal behaviors as another, and those that were slow-climbers or mainly terrestrialists as a third. We did not include animals that are committed to quadrumanual suspension (e.g., sloths, colugos, and presumably subfossil “sloth-lemurs”) in our analyses due to uncertainty about the demands that such behaviors place on the postcranium. Assignment of behavioral categories is described in more detail in Results. We report F statistics and P-values for these analyses. Post hoc comparisons were also executed. A sequential Dunn-Šidák adjustment to α = 0.05 was used to determine significance of P-values.

We used BayesTraits 1.1B to calculate means and 95% HPDs for ancestral states of both ln estimated body mass and the ratio of distal calcaneal segment length versus total calcaneal length. Mean values for each variable were used as the input data for each of the 117 OTUs in the primary supertree. Before reconstructing ancestral states, we ran several model tests to determine whether there were directional trends in the data given the input topologies, and whether inclusion of phylogenetic scaling parameters improved the likelihood of the reconstructions. For each tree, we ran two independent MCMC chains (10,050,000 iterations) for each of the following combinations: 1) non-directional model (model “A”, constant variance random-walk) with no scaling parameters; 2) non-directional model with parameter δ; 3) non-directional model with parameter κ; 4) non-directional model with parameter λ; 5) directional model (“model B”) with no scaling parameters; 6) directional model with parameter δ; 7) directional model with parameter κ; 8) directional model with parameter λ. The RateDev value was individually tuned for each analysis to achieve acceptances between 20–40%. The first 50,000 iterations were discarded from each chain as “burnin”, and the traces and mean log-likelihoods from the two independent chains were compared in Tracer 1.5 [78] to ensure convergence. Models for reconstruction of ancestral states were chosen by comparing harmonic means and averages of the mean log-likelihoods from each MCMC chain; i.e., models incorporating scaling parameters were only used for final reconstructions of ancestral states if the inclusion of a phylogenetic scaling parameter provided a log-likelihood that was 1.0 units greater than analyses that included no scaling parameters [79]. Ancestral reconstructions on each tree were based on two independent MCMC chains of 20,050,000 iterations (first 50,000 discarded as burnin, with the DataDev value tuned to achieve acceptances between 20–40%), using the distributions for the selected phylogenetic scaling parameters that were calculated in the previous step. Mean values and posterior densities for each reconstruction were taken from the combined results of the two independent MCMC runs.

Differences among primates with different degrees of leaping proclivity.

Prior to this study the question of whether and how distal elongation of the ankle reflects leaping proclivity had been answered in very general terms using an impressively comprehensive sample [7]. Results from our analyses suggest a functional association between presence/degree of leaping specialization and calcaneal elongation, at least among prosimian primates. The signal from our phylogenetic ANOVA of elongation residuals, while weak at the scale of all prosimians, suggests significant differences among leapers (greatest calcaneal elongation), arboreal quadrupeds (intermediate calcaneal elongation) and slow climbers/terrestrialists (low calcaneal elongation). We suggest that this signal appears weaker than it should due to 1) limited knowledge of the phylogenetic history of prosimians, 2) imperfect behavioral categories and 3) the limits on ecological diversity across prosimians primates, that if it were greater, would add statistical power to our analyses. Within clades striking correlations between calcaneal elongation residuals and behavior are apparent. For instance, calcaneal elongation residuals in cheirogaleids is strongly correlated with differences in leaping proclivity among taxa described by Gebo [74], with Cheirogaleus major leaping the least (6% of locomotor bouts) and having the lowest residual (0.032), Cheirogaleus medius leaping more (21%) and having a higher residual (0.048), Mirza coquereli leaping more yet (27%) and having a higher residual yet (0.162) and Microcebus murinus leaping most (38%) and having the highest residual (0.182). The relationship clearly applies across lorisiforms (Fig. 11). However, even on the smaller scale of galagos included in Gebo’s [74] study, there is some variation that matches previously identified behavioral differences: Galago senegalensis leaps more than any other galago (63%) and has the highest residual (0.442). However, variation in leaping reliance among other galagos, as documented by Gebo [74], is not correlated with calcaneal elongation residuals (this is not including Euoticus, whose lower residual yet is predicted by its use of large diameter supports and claw-clinging [76], see Fig. 11). Among larger-bodied taxa the relationships generally hold: within non-cheirogaleid, non-indriid lemuriforms, Daubentonia is the least specialized for leaping [75] and has the lowest residual value (0.028), while Varecia is slightly more acrobatic according to Gebo [74] (leaps were 21–25% of the locomotor bouts) and its residual is higher (0.048). Lemur catta leaps more frequently when on the ground (55%) than Eulemur (44%), but less while in the trees (22% v. 30–37%). Nevertheless Lemur and Eulemur are both more leaping reliant overall than Varecia and have accordingly higher residuals (0.072–0.076). Lepilemur is a more committed leaper (no data in Gebo [74] though) and has a higher residual yet (0.106). Another group for which the relationship appears to break down slightly is Hapalemur that leaps more (56% – although it should be noted that this value is close to that for Lemur catta on the ground), but has residuals similar to those of other lemurids that leap less (0.070–0.072). Interestingly, Hamrick [99] has noted that Hapalemur also lacks predicted adaptations for vertical clinging in its wrist. Therefore some unappreciated aspect of Hapalemur’s ecology or evolutionary history may have muted the development of adaptations to vertical clinging and leaping. Overall the correlation is striking when considering leaping behavior on a finer scale than done in our phylogenetic ANOVA and looking within groups.

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Figure 11. Box plots of residual elongation.

We plot species mean values for residual elongation from the all primate line (Residual A from Table 1). The distribution of values within clades corresponds very well to degree of agility of locomotion. For fossils the variation corresponds with locomotor agility hypotheses based on additional skeletal features [30]. When these residual data sets are examined with phylogenetic ANOVA, a strong relationship between elongation and behavior is revealed (Table 7) meaning that calcaneal elongation is broadly related to behavior in contrast to the conclusion of Moyà-Solà et al. [7]. See previous figures for taxon abbreviations.

https://doi.org/10.1371/journal.pone.0067792.g011

Going back to the exceptions (some galagos and Hapalemur), an important point to consider here is that “average leaping reliance,” as documented by Gebo [73] as a percentage of all locomotor bouts observed, is neither a sufficient or necessary condition for the hypothesis that an animal will exhibit adaptations for leaping. Many assumptions underlie the expectation for such a correlation. Another behavioral variable that may conceivably correlate with morphology as well or better than documented leaping reliance is “leaping performance.” For example, two species of the same size may use leaping with similar frequency, but one may consistently leap farther than the other, or, when stressed, have a maximum leaping distance that is significantly farther. It should be noted that such definitions of performance are not necessarily expected to correlate with energetic efficiency in a behavior so coarsely defined as “leaping.” However, if one were to specify “leaping” more narrowly in terms of substrates used and distances covered, measurements of “energetic efficiency” might be more closely equivalent to “leaping ability” in terms of achievable leaping distances. Studies that evaluate leaping performance in a sample broad enough to be relevant here have not yet been done. Finally, “leaping reliance” may be defined not only as frequency during daily routines, but also by its recruitment for locomotion fulfilling particular, critical roles. That is, a small percentage of total daily locomotion may serve in predator evasion, or alternatively, in ambushing prey. However, if a species has been observed to use leaping during most predator evasion or predation events, one could reasonably hypothesize that these events put a strong selection pressure on high leaping performance, even if leaping is a small part of the daily routine.

Previous studies have led to the conclusion that after a certain size threshold, there is no longer a benefit bestowed by ankle elongation to large leapers [31]–[33]. Some of the discussion above notes patterns in our data on lemurids that suggests against this. Furthermore, several additional lines of evidence show that while allometric constraints reduce the degree of elongation in large taxa, offsets between behavioral categories still exist. For example, while Gebo and Dagosto [33] concluded that the indriid foot was primarily adapted for climbing, not leaping, we note that the calcaneus of Indri indri is a strong positive outlier to lemuriform regressions as well as “all primate” regressions. This is true whether one considers the calcaneal ratio, or the absolute length of the distal calcaneal segment relative to body mass (Table 1, Res A–B). This suggests a leaping effect on residual calcaneal elongation in Indri. On the other hand the position of other indriids contradicts the general trend (they are committed leapers, but have low residuals) and has been difficult to explain [33]. However, it is well-documented by the sub-fossil record that known indroid outgroups to the extant Indriidae were not leapers [100]. Furthermore, it is even possible that more than one clade within crown Indriidae has adapted to leaping independently, and that different clades have increased leaping specialization at different times (i.e., some more recently than others). A debated hypothesis that, if true, would add plausibility to this idea is that Mesopropithecus, judged to be anti-pronograde due to an intermembral index greater than 100 [100], is the sister taxon to extant Propithecus [101] (and probably Avahi as well). If an independent behavioral transition to leaping happened very recently in Avahi and Propithecus, compared to Indri [66], then some aspects of the skeleton may still be “adapting” in those taxa. Strong phylogenetic co-variance in calcaneal elongation residuals demonstrated by our analyses (Table 7, Fig. 11) in fact implies that this is a reasonable expectation.

Another more recently posited hypothesis based on molecular data places the Paleopropithecidae as a sister group of indriids, and places archaeolemurids as sister of these two clades [66]. Regardless of when or how many times leaping evolved in extant indriids, this suggests a long evolutionary history of non-leaping, slow-climbing, and/or terrestrialism in the indrioid clade. If the ancestral indriid was a slow climber and/or terrestrial and had calcanei with extremely low elongation ratios [certainly a possibility given that such a condition exists in certain subfossil species (Table 2)], then all extant indriids may indeed have experienced increases in elongation that cannot be explained by allometry and reflect increased leaping compared to their ancestors. While such changes can only be appreciated with analyses that extensively sample subfossil lemur morphology, the limited subfossil data in our study show that residual elongation in extant indriids is greater than that in Archaeolemur, Paleopropithecus, and Mesopithecus, which are reconstructed as semi-terrestrial, antipronograde, and slow-climbing, respectively [100] (see Fig. 11). While Babakotia actually has high residual calcaneal elongation, as stated in the methods, we do not have specific predictions for the elongation constraints of inverted quadrupeds, and/or highly specialized, sloth-like quadrumanous suspensory taxa. It may be that quadrumanous suspension allows and/or selects for greater elongation than is possible/useful for pronograde and orthograde animals of similar size in some situations. The fact that Cynocephalus volans has the greatest degree of elongation among non-primate euarchontans, despite also being the most massive in this group, may reflect a similar functional correlation. Comparison of elongation in sloths to that of other xenarthrans could provide data to test this idea. On the other hand, Babakotia and Paleopropithecus have the lowest residual distal calcaneal segment lengths of any sampled euprimate (see Table 1, Res. B: −0.726 and −0.634, respectively). The only other primates with similarly low residuals are the hylobatids (Table 1). Avahi (−0.109), Propithecus (−0.008), and Indri (0.156) are all much higher.

Our explanation for the muted pattern of distal calcaneal elongation among indriid leapers as a consequence of recent and potentially multiple transitions to leaping from non-leaping indrioid ancestors, if correct, is most likely still only part of the story. This muted pattern is plausibly also contingent on, or driven by, 1) indriid leaping specializations first evolving in an ancestor of a larger size than the ancestral galagos and 2) the lack of evidence for any pronounced lineal decreases in body mass among indrioids [the evolutionary situation in which our model (above) suggests that increases in tarsal elongation can be most profound]. Our ASRs suggest that the ancestral galagid was around 250 g, while the nodes of the indrioid clade are reconstructed as having been between ∼1,500–2,000 g (Tables S2–S7 in File S1) with little variation and no obvious trends. These data begin to reconcile ideas about body size limits for “ankle powered leaping” with apparent paradoxes such as different structural solutions for leaping employed by taxa of similar body mass (i.e., Avahi and Otolemur). While our study suggests there is no strict body size “cut off” for a tarsal-lengthening effect from leaping specialization, a strong tarsal-elongation response to frequent leaping selection would appear to be most likely in small-bodied lineages rather than large ones given the constraints of the observed allometric line and the finding that (according to our model) tarsal elongation can happen most easily during lineal decreases in body mass.

Ancestral state reconstructions.

Among available non-euprimate eurchontans no clear allometric trend is present (Table 2). Taxa exhibiting values for calcaneal elongation that are on the low end of euprimates (for their body masses) are the plesiadapoid plesiadapiform Carpolestes simpsoni, tupaiid tree shrews, and the dermopteran Cynocephalus volans. Looking at the nodal trend leading from the base of Euarchonta to Euprimates shows predominantly body size increases and minimal elongation increases (Tables S2–S7 in File S1). While all reconstructions of the ancestral plesiadapoid have significantly larger body size and lower elongation than C. simpsoni, we note that poor taxon sampling of more primitive species may be driving this pattern. If more primitive, much smaller (and much older) carpolestids such as Elphidotarsius florencae, and more basal, small plesiadapoids such as Chronolestes simul could have been sampled, the ASR for plesiadapoid body mass would likely have been much smaller. Likewise if one assumes that the ankle morphology of C. simpsoni is similar to those of both E. florencae (a distinct possibility) and the most primitive plesiadapoids, then the overall trend in plesiadapoid evolution leading to C. simpsoni would be reconstructed as paralleling that leading to the euprimate ancestor more than can be inferred from our results (Fig. 9A: note right-most dashed arrow). This possibility can only be directly addressed through new fossil discoveries.

Regardless of the accuracy of the plesiadapoid ASR in our analysis, C. simpsoni has a higher elongation residual than any estimate for the euprimateform node or any nodes more basal, suggesting corresponding functional differences in C. simpsoni. The hindlimb skeleton of C. simpsoni does not exhibit obvious potential correlates of leaping [15]. Instead, the most striking aspects of C. simpsoni, which distinguish it from other plesiadapiforms, are its euprimate-like divergent and seemingly opposable hallux, and short non-hallucal metatarsals [15]. The grasping hallux and tarsifulcrimating foot of both euprimates and C. simpsoni appears to have happened coincident with an increase in distal calcaneal elongation. These acquisitions may have happened in parallel or may be homologous [15]. The combination of features in C. simpsoni is consistent with Moyà-Solà et al.’s [7] hypothesis that a moderate amount of calcaneal elongation in euprimates is a function of development of a specialized hallux and tarsifulcrumating foot, not leaping. More specifically, by analogy with C. simpsoni (which shows no other obvious correlates of leaping), we can explain increasing elongation as a result of compensation for evolution of tarsifulcrumation alone in any primate lineage that does not exceed the elongation residual values seen in C. simpsoni.

After evolution of the lineage representing the ancestral stock of crown primates (represented by the ASR for the Euprimate node in our analyses: see Fig. 9A), subsequent further elongation (beyond that seen in C. simpsoni) is reconstructed as having occurred along branches leading to the ancestral strepsirrhine and haplorhine lineages (Fig. 9A, B). This further elongation therefore exceeds the amount explainable by acquisition of a tarsifulcrumating foot.

Other authors have suggested that the didelphid Caluromys might be the best available analogue for early euprimates [10], [11], [98]. A cursory look at didelphids does not provide any support for Moyà-Solà et al.’s [7] hypothesis. Despite increased specialization of the hallux and greater prehensility compared to some of its relatives, the arboreal marsupial Caluromys philander does not exhibit increased actual or a higher residual calcaneal elongation [n = 3, ln(DL/TL) = −1.40±0.05; ln(CW*CD) = 1.53±0.15 (body mass estimate using equation derived from primates = 161 g); residual from all primate allometric line = −0.68±0.04] compared to its more generalized scansorial relative Monodelphis brevicaudata [n = 3, ln(DL/TL) = −1.30±0.06; ln(CW*CD) = 0.56±0.08 (body mass estimate using equation derived from primates = 45 g); residual from all primate allometric line = −0.62±0.07]. At the very least, this suggests phylogenetic dependency on whether the hallucal grasp complex is functionally correlated with the distal calcaneal segment length.

If C. simpsoni is reconstructed as the sister taxon of euprimates to the exclusion of other plesiadapoids (Table S7 in File S1; Fig. 9A, note left-most dashed arrow), its position in the phylogeny makes it a contributer to the basal trend of gradually increasing elongation relative to body mass – which could relate to selection for both/either improved grasping and/or leaping early in primate evolution. Undoubtedly the large differences in the reconstructed evolutionary history of body size change implied for the lineage leading to C. simpsoni is greatly influenced by missing data on small-bodied early plesiadapoids such as Chronolestes simul, Pronothodectes matthewi, and Elphidotarsius florencae.

The trajectories in both haplorhine and strepsirrhine lineages suggest significant functional/behavioral shifts associated with increasing elongation, because these increases do not follow the allometric slope identified earlier in this study. Haplorhines evolved mainly by increasing elongation at the same size as the ancestral euprimate, while strepsirrhines evolved mainly by increasing in body size with only slight increases in elongation compared to the ancestral euprimate. Nonetheless, improved leaping in both clades is suggested by the fact that they both approach, rather than parallel, the “all euprimates” regression line (thereby acquiring greater “body-size standardized” elongation than hypothetical taxa represented by more basal nodes). This pattern is also clear on a plot of residual elongation against node depth (Fig. 9B). The evidence for parallel evolution of elongated tarsals is consistent with the long known fact that omomyiforms have increased their foot length by significantly lengthening bones of the foot beyond the transverse tarsal joint (cuneiforms and cuboid) possibly beyond the degree exhibited by extant cheirogaleids in many cases [30].

It is important to note that the ancestral state reconstructions here suggest that calcaneal elongation as seen in the early fossils Teilhardina, Anchomomys or Cantius, or leaping proficiency as seen in even “generalized” modern strepsirrhines, was not a synapomorphy of Euprimates. This is especially relevant given uncertainties about the functional significance of nails compared to claws and the observation that anatomical details of distal phalanges exhibited by early omomyiforms [52] differ markedly from those of early adapiforms [102]. If nails are particularly relevant in improving leaping performance then we might even expect that non-hallucal nails evolved in parallel with improved leaping in two major clades of euprimates (possibly from a common ancestor having a more “Carpolestes-like” foot). A leaping adaptation for nails remains plausible since specialized hallucal grasping alone does not explain the loss of claws (as specialized graspers Caluromys, Petaurus, and many other marsupials retain large non-hallucal claws, while also sporting a large, divergent opposable hallux with a nail). Furthermore, the idea that nails evolved to aid grasping in large-bodied arborealists [103] cannot be entertained given the presence of nails in 30 g Teilhardina and the lack of fossil evidence for more basal euprimates having been any larger than this.

Another implication of the ancestral state reconstructions is that the evolution of notharctines is not explained by decreased elongation due to increasing body size from an animal similar in size and ankle proportions to Teilhardina. In other words, the alignment of Teilhardina with notharctines along the “all euprimates” regression line would appear to be coincidental relative to the phylogenetic history of the two groups. This also means that it is difficult to talk about “behavioral equivalence” in these two taxa relative to the allometric line. This perspective, that Teilhardina and Cantius have achieved ankle elongation in parallel and cannot be equated or contrasted behaviorally, would be further supported if future discoveries of Teilhardina show the typical omomyiform pattern of cuneiform elongation. This raises the question of “for what clades does the allometric relationship explain reconstructed evolutionary change?” There are several. The evolution of adapines from an asiadapine-like ancestor could be explained by increases in body mass with allometrically expected decreases in elongation. Notharctine evolution starting with known Cantius is explained by increases in body size with allometric decreases in ankle length. Likewise, Omomyinae have followed an allometrically predicted decrease in ankle elongation from a smaller-bodied, more basal tarsiiform. Finally, the morphological change in anthropoid calcaneal proportions can be explained by the allometric expectation of decreasing ankle elongation from an eosimiid-like ancestral haplorhine.

Notharctines.

Gebo [30], Rose and Walker [104], Gebo et al. [40], Fleagle and Anapol [105], Schmitt [106], Silcox et al. [107] and others have interpreted a similar range of locomotor behaviors for early North American notharctines. Most authors suggest that Notharctus and Smilodectes exhibit some degree of VCL leaping with increased leaping proclivities compared to Cantius, the most basal notharctine. Previous studies of the calcaneus added little to these interpretations. For instance, Gebo et al. [40] documented that Notharctus exhibited less calcaneal elongation than Cantius. While this is true, it appears to contradict the general conclusion about notharctine behavioral differences outside of an allometric context. As we have shown, most of the difference in calcaneal elongation among early North American notharctines can be explained by body size differences. However, if one examines the residual calcaneal elongation values (Table 1; Fig. 11), Notharctus actually exhibits a higher elongation residual (indicating more elongation for its body size) than all species of Cantius. Smilodectes exhibits less elongation than Notharctus, which actually is consistent with locomotor interpretation based on analyses of the humeral head [106]. Therefore an allometric treatment of calcaneal elongation returns a pattern broadly consistent with that from other regions of the skeleton and indicative of more leaping in Notharctus than in Cantius [30], [106], [107]. Comparing residual calcaneal elongation of these fossils with that of extant taxa, shows the fossils to exhibit less residual calcaneal elongation than most arboreal quadrupedal, leaping and vertical clinging and leaping primates. This likely indicates that leaping behaviors were not as effective in any early Eocene adapiforms. This is consistent with a recent analysis of body proportions by Gingerich [108], showing Notharctus to be most similar to Cheirogaleus and well-separated from leapers it has been compared to previously like Lepilemur and Avahi. Therefore, despite the possibility that differences between Notharctus and extant leapers are results of clade shifts in morphology that are not reflected by behavior, the fact that the rest of the skeleton lacks leaping specializations decreases the likelihood of this for us. By extension, Cantius and Smilodectes would also be considered ineffective or infrequent leapers. The inference for these latter taxa could be tested with analyses of more complete skeletal material.

Asiadapines.

Rose et al. [37] argued that early Eocene (∼53–54 mya) adapiforms Marcgodinotius and Asiadapis from Gujarat, India, could be reconstructed as active arboreal quadrupeds with some leaping proclivities based on phenetic similarity to Cantius. For the calcaneus, taking a phenetic approach to a locomotor reconstruction is problematic given the results of this study. Given the small body size of asiadapines compared to Cantius, the similar levels of calcaneal elongation equate to very low residual calcanael elongation suggesting a slow-climbing lifestyle (Table 1; Figs. 4, 5, 6, 7, 11). What is unclear from our ancestral state reconstructions is whether asiadapines have reverted to smaller body size and shorter ankles from a larger-bodied, longer-tarsaled ancestor (as implied by ASRs based on the maximum parsimony supertree – Table S2 in File S1) or whether the common ancestor of asiadapines and its sister taxon had body-mass and elongation proportions more similar to asiadapines. If the former scenario is true, this definitely suggests a decreased emphasis on leaping in these taxa relative to the general strepsirrhine stem. If the latter is true, it is more difficult to reconstruct their locomotor repertoire relative to other primates. However, in either case, short ankles at such small body size would appear to suggest relatively ineffective leaping. Turning to other features of the asiadapine skeleton: although astragalar depth and a strong posterior trochlear shelf (present in asiadapines and Cantius) may demonstrate leaping, this has never been broadly demonstrated aside from contrasts between lorisids and other strepsirrhines. Furthermore, the femur does not demonstrate leaping proclivities beyond what might be expected in a mainly quadrupedal Cheirogaleus. One feature not mentioned by Rose et al. [37] which suggests against leaping is the very distal position of the third trochanter (it is positioned distal to the lesser trochanter). This morphology is reminiscent of other taxa which lack prosimian-like specializations for leaping such as sciurid rodents, plesiadapiforms [109], and basal stem catarrhines [110].

In sum, we think Rose et al.’s [37] interpretation of these taxa could be correct, depending upon how the morphology of asiadapines compares to the ancestors they share with other strepsirrhines. However, in the context of our analysis the available data seems to suggest that compared to notharctines including early Cantius, asiadapines were less specialized for and probably less effective at leaping.

Adapines.

Various authors [30], [111] have interpreted Adapis and Leptadapis as cautious slow-climbers and possibly lorisid-like. Our results corroborate this perspective.

Anchomomys.

Roig et al. [112] and Moyà-Solà et al. [7] made a different allometry-based argument for the lack of specialized leaping in Anchomomys frontanenysis. Their study was apparently motivated by the seemingly high degree of calcaneal elongation in this small-bodied adapiform. Their conclusion was thus somewhat surprising given the qualitative appearance of strong elongation in this bone. In our analyses, Anchomomys exhibits moderate residual calcaneal elongation compared with other early euprimates: it is higher than in any notharctines, Teilhardina and Tetonius, yet lower than in Absarokius and omomyines (Table 1, Fig. 11). This suggests to us that the Anchomomys lineage experienced selection for greater improvements in leaping compared to lineages of notharctines, Teilhardina, and Tetonius, though we would not argue that it was a specialized vertical clinger and leaper and are basically in agreement with Roig et al. [112] and Moyà-Solà et al. [7] on this point.