Long-bone geometry in columnar-limbed animals: allometry of the proboscidean appendicular skeleton

Long-bone allometry in mammals has been analysed on a number of occasions, in order to determine, among others, the overall scaling patterns across a wide size spectrum and the relationship to theoretical models of bone allometry and stress (e.g. McMahon, 1973, 1975a, b; Alexander, 1977; Alexander et al., 1979a, 1981; Prothero & Sereno, 1982; Biewener, 1983; Economos, 1983; Bou, Casinos & Ocana, 1987; Bertram & Biewener, 1990; Christiansen, 1999). If animals simply scaled isometrically, skeletal stress might be expected to increase with mass^0.33 (M^0.33) (Biewener, 1990; Alexander & Pond, 1992), but this is not the case (e.g. Alexander et al., 1979b; Alexander, 1981; Biewener, Thomson & Lanyon, 1983, 1988; Biewener & Taylor, 1986; Biewener, 1990; Alexander & Pond, 1992). Size has a great influence on bone allometry (Bertram & Biewener, 1990; Christiansen, 1999), and there are a number of factors other than bone allometry that contribute to a mass-specific reduction of bone stress, such as limb postures and muscle mechanics (e.g. Biewener, 1983, 1989, 1990), in addition to a reduction in locomotor intensity with size.

Elephants differ markedly from other large mammals in that their limbs are kept near columnar during all forms of locomotion, and in their inability to perform true running with a suspended phase in the stride (Gambaryan, 1974; Alexander et al., 1979b; Hutchinson et al., 2003). This apomorphic and energetically efficient locomotor style (Langman et al., 1995) is reflected throughout their entire anatomy, both skeletal and myological (Fig. 1; Gambaryan, 1974; Alexander et al., 1979b; Mariappa, 1986; Haynes, 1991; Shoshani, 1995a), implying that it should be possible with some certainty to predict when this unusual mode of locomotion began to dominate in early proboscidean evolution, based on studies of comparative morphology.

Such a limb posture was clearly not present in moeritheres, and it was probably also not present in the larger, more elephantine Numidotherium either (Court, 1994, 1995). Although the morphology of the humerus and the femur of Numidotherium bear a substantial resemblance to the morphology of more derived proboscideans, there are several important differences in muscle scars (Court, 1994). With the exception of the enigmatic anthracobunids (Gingerich, Russell & Wells, 1990; Shoshani et al., 1995; Shoshani, 1995b), Numidotherium is either considered the most plesiomorphic proboscidean taxon (Court, 1995) along with Phosphatherium (Gheerbrant, Sudre & Capetta, 1996), or, alternatively, these two constitute the second most plesiomorphic taxon, following Moeritherium (Tassy, 1994, 1995a, b; Shoshani, 1995b; Gheerbrant et al., 1996). From the level of Deinotherium and onwards (e.g. see Tassy, 1994, 1995a) the apomorphic appendicular anatomy of extant elephants is clearly present, and, accordingly, a similar mode of locomotion is inferred.

A columnar stance precludes many of the postural and muscle mechanical adaptations for reducing bone stress utilized by other, flexed-limbed mammals. It is also reflected in the morphology of the long-bone diaphyses, especially the femur, which is distinctly larger in lateromedial than anteroposterior diameters in all proboscideans from the level of Deinotherium onwards, which is in contrast to most flexed-limbed mammals. This is a result of the columnar stance favouring axial compression and simple lateromedial bending over more complex bending and torsional moments (e.g. Carrano, 1998). Thus, if the limb bones of columnar-limbed proboscideans (Deinotheriidae and Elephantiformes; see Tassy, 1995a) scaled isometrically, skeletal stress could indeed be expected to increase with M^0.33, as noted above. As columnar-limbed proboscideans are precluded from using muscle mechanical and/or postural changes with increasing size, they either have to rely on osteometric changes exclusively in order to limit bone stresses to acceptable levels, or, alternatively, engage in less strenuous locomotor activity with increasing size, for which there can be no evidence for extinct forms.

Accordingly, one would expect the ratio of circumference to the length of the limb long bones of columnar-limbed proboscideans to scale with significant negative allometry, becoming progressively stouter with size. Thus, as opposed to mammals as a group (e.g. Alexander et al., 1979a; Christiansen, 1999), they potentially could conform to McMahon’s (1973, 1975a, b) theory of elastic similarity, which predicts the bone length to scale with circumference^0.67 (C^0.67). Animals thus constructed are predicted to be subjected to similar degrees of physical deformation under gravity, independent of body size. Furthermore, Haynes (1991) suggested that the limb bones of mastodonts s.l. were consistently more massive than in elephantids, and presented some data on the subject. In this paper a large number of long bones from a variety of proboscideans are analysed in order to elucidate scaling patterns and possible phylogenetic differences.

MATERIAL AND METHODS

A total of 217 limb long bones were measured from 19 species of proboscideans, spanning a wide phylogenetic spectrum (Table 1; Fig. 2). Additionally, the lengths and circumferences of one humerus, three ulnae, five femora, and 11 tibiae of Mammuthus primigenius were taken from Germonpre (1993; not included in Table 1). Recently the forest elephant (Loxodonta africana cyclotis) has been discussed as potentially constituting a separate species (e.g. Barriel, Thuel & Tassy, 1999), but all specimens of the African elephant included in this analysis were from the savanna form (Loxodonta a. africana).

The data were transformed into logarithms (log₁₀) to ensure homoscedasticity and to linearize allometric scaling effects. Following logarithmic transformation, the scaling patterns of the included taxa were analysed with traditional regression methods and independent contrast regression. Each species was represented by the average value of the included long bones in the case of species with multiple specimens. A model-II (reduced major axis, RMA) analysis was preferred for traditional regressions, because of the inherent variability on both variables (Labarbera, 1989; Sokal & Rohlf, 1995). Traditional regression analyses do not, however, address the potential signal produced by the hierarchial phylogeny of organisms, as represented in a cladogram, implying that the error terms of a traditional regression analysis are correlated (e.g. Felsenstein, 1985; Grafen, 1989; Harvey & Pagel, 1991; Garland & Janis, 1993; Garland & Ives, 2000). The method of independent contrasts analysis takes this problem into account.

An RMA analysis was also preferred for independent contrasts analysis. Confidence limits were computed for the slopes and intercepts for traditional RMA analysis, and for the slope for the independent contrasts analysis. Independent contrast analysis produces regression through the origin and, thus, no intercept (e.g. Garland, Harvey & Ives, 1992; Garland & Janis, 1993). Hence, confidence intervals for the RMA slope were approximated using the standard error for the least squares regression slope, as in traditional regression analyses (Sokal & Rohlf, 1995; see also Garland & Ives, 2000). The confidence limits for the independent contrast RMA regression slopes were used to assess the possible difference between the computed slopes and theoretical slopes for geometric [Length (L) = C^1.00], elastic (L = C^0.67), and static (L = C^0.50) stress similarity. If the confidence limits did not include a value, they were deemed as significantly different. Additionally, for the traditional RMA equations significance tests were computed for the regression slopes and the three theoretical slopes. Significance levels were set at P = 0.05.

A phylogenetic tree was assembled from a variety of literature sources (Fig. 2). There is substantial disagreement in the exact topology of the various genera of ‘gomphotheres’ but in this analysis the results of Shoshani (1995b) were used (compare, e.g. with Tassy, 1994, 1995a). Traditionally, proboscidean taxonomy has been murky and riddled with synonyms. The synonymy of the included specimens follows Shoshani & Tassy (1995a). Serridentinus was considered a junior synonym of Gomphotherium, and Palaeoloxodon was considered a junior synonym of Elephas (but see Haynes, 1991; for a different opinion). Gomphotherium ojocaliensis, Gomphotherium pojoaguensis, Gomphotherium productus, and Trilophodon phippsi were considered junior synonyms of Gomphotherium productum. Mastodon andium and Cuvieronius humboldtii were considered junior synonyms of Cuvieronius hyodon. Mastodon ohioticus was considered a junior synonym of Mammut americanum. Parelephas and Archidiskodon were considered junior synonyms of Mammuthus. Mammuthus floridanus was considered a junior synonym of Mammuthus imperator and Mammuthus boreus was considered a junior synonym of M. primigenius.

The split ages between the various nodes were determined using minimal ages of the various fossil taxa included (Fig. 2). In some cases a taxon was present much later than the inferred split age between itself and its inferred sister taxon, implying long ghost lineages, e.g. the Pleistocene Mammut and more advanced taxa, such as Gomphotherium and Archaeobelodon, which are known from the Early Miocene (∼18 Mya). Primitive mammutids (Eozygodon and Zygolophodon; not included in the present study) are also from the Early Miocene (Saunders, 1995).

The split age between Palaeomastodon and the Elephantoidea (e.g. Tassy, 1994, 1995a) was determined by the age of Palaeomastodon, from the Late Eocene of El Fayum in Egypt. However, phylogenetic analyses indicate that the deinotheres are the sister taxon to Elephantiformes (Palaeomastodon and Elephantoidea), but even the earliest and most plesiomorphic deinothere, Prodeinotherium, is only Early Miocene in age, implying a substantial ghost lineage. The age of 45 Myr for the split between Deinotheriidae and Elephantiformes was arbitrary, as the most plesiomorphic taxon included in the analysis (the deinotheriid Deinotherium) was a lot younger than the following taxon (Elephantiformes), thus rendering the direct computation of split ages impossible. The lineage leading from Deinotheriidae to Elephantiformes was arbitrarily set at 5 Mya.

The inferred age for the Elephantidae (in this analysis equivalent to Loxodonta, Mammuthus, and Elephas) of 9 Mya predates fossil discoveries (e.g. Haynes, 1991; Todd & Roth, 1995; Shoshani, Golenberg & Yang, 1998), but is indicated in the study of molecular phylogeny by Thomas et al., (2000). The more advanced species of Mammuthus are all Pleistocene, and the inferred age of 2 Mya for Mammuthus meridionalis predates its fossil record by around 500 Kya. As the included species of Mammuthus are very closely related and morphologically very similar, a rather short split age of 500 Kya was inferred, but this is arbitary because they were approximately contemporaneous. Traditionally, a sister group relationship between Elephas and Mammuthus is inferred, with Loxodonta forming the sister taxon to both, but recently a sister group relationship between Loxodonta and Mammuthus has been inferred (Barriel et al., 1999; Thomas et al., 2000). In this analysis the traditional topology was followed, as this is supported by a variety of analyses (e.g. Tassy, 1994, 1995a; Kalb, Froehlich & Bell, 1995; Shoshani et al., 1998).

The current tree (Fig. 2) differs in one aspect from the trees normally used in comparative analyses using independent contrasts, in that most of the included taxa are not extant. Thus, when assigning age to a clade based on the age of fossils (e.g. the two species of Gomphotherium) and analysing tip data, these are not really ‘tip’ data in a strict sense, as this would imply that the data are from animals with separate evolutionary paths for the past 18 Myr. This is, however, not the case. Thus, for the fossil taxa, the inferred split ages were the oldest occurrence of the group and the tips represent the youngest occurrence of the species, following the assumption that individuals assigned to the same species are morphologically similar. Accordingly, the tips for Loxodonta and Elephas maximus are extant, and for Cuvieronius, Stegomastodon, Mammut, and M. primigenius they are Pleistocene/Holocene, but for some taxa (e.g. ‘gomphotheres’) they are lot older.

Independent contrast analysis requires that the included branch lengths, whether they are either real (in years) or arbitrary (e.g. all set to 1), be properly standardized, such that the common variance of the contrasts is independent of branch length (Garland et al., 1992; Garland & Janies, 1993). This was evaluated by visual examination of scatterplots of absolute values of the standardized contrasts to their corresponding standard deviations, and by computing the correlation coefficient (r) between the two. The branch lengths were evaluated as properly standardized when the correlation was ≤ 0.05. In addition to raw (i.e. unmodified) branch lengths, a variety of branch-length transformations were used, including log, square root, cube root, Grafen’s rho method (rho values of 2–9), Grafen’s arbitrary method, Pagel’s arbitrary method, and Nee’s arbitrary method. The branch-length transformation that resulted in the lowest correlation between the absolute values of the standardized contrasts and their corresponding standard deviations was chosen for the analysis of regression using independent contrasts.

Regression analyses (traditional and independent contrasts RMA analyses) were also performed for the Elephantidae group alone, comprising eight terminal taxa (see Fig. 2). However, analyses were only performed for the humerus and the femur, as these were the only two bones represented by nearly all the included species (seven species each, see Table 1).

RESULTS

The suggestion made by Haynes (1991) that the limb long bones of mastodonts s.l. were more massive at any given overall length than those in elephantids is corroborated here. A simple comparison of proportions (Fig. 3) reveals that gomphotheres (s.l.) do indeed have significantly larger diaphysial circumferences at any given overall bone length compared with elephantids. This generalized comparison is somewhat biased, however, in that it compares a paraphyletic (‘gomphotheres’) clade to three monophyletic clades. Haynes (1991) also suggested that Mammuthus, on average, had more massive long bones than either E. maximus or L. africana, and this is less evident from a simple morphometric comparison. In fact, there does not appear to be consistent differences in the ratio of diaphysial circumference to bone length for either the femur or the humerus between Elephas, Loxodonta, and Mammuthus (Fig. 3). A seemingly thicker diaphysis will automatically result as a consequence of greater overall bone lengths, providing that the bones scale with negative allometry, as the large species of Mammuthus were considerably larger than extant elephants. This pattern is easily verified in Figure 3.

Branch lengths for the total sample of proboscideans were properly standardized (Fig. 4) using a log transformation for the humerus (r = 0.025), the cube root for the ulna (r = 0.01), and the square root for the tibia (r = 0.028). For the radius and the femur, Nee’s and Pagel’s arbitrary transformation, respectively, resulted in the lowest correlation of all the transformation methods used. However, they still showed slight signs of significance, because the correlation coefficient for the radius was 0.085, and for the femur it was 0.052. This slight correlation is, however, not evident from a visual inspection of the scatterplots (Fig. 4C). For the subset of the Elephantidae, the branch-length transformations that resulted in the lowest correlation between the absolute values of the standardized contrasts to their corresponding standard deviations were Nee’s arbitrary transformation method for the humerus and a square root transformation for the femur. However, both showed slight signs of correlation, as the correlation coefficients were both > 0.05 (0.086 for humerus and 0.119 for femur).

The limb long bones of the total sample of proboscideans scale somewhat differently than expected, both for traditional RMA analysis and independent contrasts RMA analysis (Table 2; Fig. 5). All traditional RMA slopes for forelimb bones are significantly different from elastic similarity (Table 1). The two hind-limb slopes are neither significantly different from geometric similarity nor from elastic similarity, and apart from the tibia slope, all other fore- and hind-limb slopes either approach or exceed 1.00. All slopes are significantly different from the extreme allometry predicted by the theory of static stress similarity (see McMahon, 1973, 1975a for details). The correlation coefficients are unimpressive, owing to the markedly greater diaphysial circumferences at any given length of some (‘mastodonts’) compared with those of other (elephantids) included species, as noted above, introducing substantial scatter about the regression line.

Unusually, the independent contrasts RMA slopes have correlation coefficients that either equal or even exceed the corresponding correlation coefficients for the traditional RMA analyses (Table 2). Normally, correcting for the phylogenetic signal will lower correlation coefficients, as some of the purported ‘correlation’ (i.e. adaptation) is actually a result of synapomorphies and not convergences, as would be required for true adaptation. In this case the massive diaphyses of more plesiomorphic proboscideans at any given bone length were corrected for by the independent contrasts analysis, and, thus, the correlations between bone length and circumference were increased. The slopes of the independent contrasts analyses are also unanimously lower than the traditional RMA slopes, although for the tibia only negligably so (Table 2; Fig. 5), and the confidence intervals about the slopes exclude 0.67 in only one case (humerus). All confidence intervals include 1.00, except the tibia. Overall, both traditional RMA and independent contrasts RMA slopes are lower for the hind-limb long bones than for the forelimbs, but they all fail, however, to comply with the expected elastic similarity scaling.

The correlation coefficients for the intraspecific elephantid analyses (E. maximus, L. africana, and M. primigenius) are generally considerably higher than for the total sample, and the slopes are also nearly unanimously lower, sometimes significantly so, although the moderate correlations of the total samples often preclude assumptions of significance. The humeral slope for all proboscideans is significantly different from that of Loxodonta (0.05 > P > 0.02) and Elephas (0.01 > P > 0.001), but not from that of Mammuthus (0.40 > P > 0.30), owing to the rather poor correlation coefficient of the latter (r = 0.832). None of the other slopes of the total samples are significantly different from the corresponding slopes for Elephas, Loxodonta, or Mammuthus. The femur slopes for the two non-elephantids (G. productum and M. americanum) are not significantly different from the total sample (0.90 > P > 0.80 and 0.30 > P > 0.20, respectively). For Mammut this is undoubtedly because of a low sample size and a high variance, as its slope is a lot lower (Table 2).

The intraspecific analyses presented in Table 2 are more in accord with the expected pattern of significant negative allometry, probably because of the markedly higher correlation coefficients, especially in the samples of extant elephants. For E. maximus, the humerus, ulna, and femur scale with significantly negative allometry, but the tibia scales nearly perfectly isometrically. All slopes, save for the humerus, are, however, significantly different from elastic and static stress similarity. Curiously, L. africana is markedly different from E. maximus, as all of its long bones are very similar to the slope for elastic similarity, and all are significantly different from geometric similarity. The humerus and the tibia scale with such negative allometry as to be statistically indistinguishable from static stress similarity (Table 2). The slopes for Loxodonta are, however, not so low as to be significantly different from the corresponding slopes for Elephas in the case of the humerus (0.40 > P > 0.30), the ulna (0.50 > P > 0.40), and the femur (0.30 > P > 0.20), but the two tibia slopes (Elephas L = C^1.008 vs. Loxodonta L = C^0.658) are significantly different (0.05 > P > 0.02). No analysis was carried out for the radius in L. africana because of the limited amount of data (N = 4; Table 1).

The long bones of M. primigenius in general also scaled with negative allometry, and in the case of the femur significantly so (Table 2). However, as in E. maximus, the tibia slope was almost perfectly isometric (L = C^1.033). The slopes of M. primigenius bones were rather similar to the corresponding slopes for E. maximus (humerus, 0.50 > P > 0.40; ulna, 0.90 > P > 0.80; tibia, P > 0.90). The considerably lower femoral slope for Mammuthus (L = C^0.597) compared with that of Elephas (L = C^0.786) was not significantly different (0.20 > P > 0.10) from the latter, owing to the rather low correlation coefficient in Mammuthus. The slopes in Mammuthus were not significantly different from the corresponding slopes in Loxodonta (humerus, 0.40 > P > 0.30; ulna, 0.70 > P > 0.60; femur, 0.70 > P > 0.60), not even the apparently markedly higher tibia slope for Mammuthus (L = C^1.033 compared with L = C^0.658 for Loxodonta; 0.20 > P > 0.10). The ulna sample for Mammuthus is a restricted one (N = 6, not 7), because one value (log length, 2.8241; log circumference, 2.4997) was an outlier. This specimen was from Germonpre (1993) and is thus not included in Table 1. The correlation coefficient including this specimen was r = 0.771 and the RMA slope was 0.952, compared with r = 0.928 and an RMA slope of 0.773 (Table 2) excluding this outlier.

The intraspecific femur slopes of the two non-elephantids G. productum and M. americanum were somewhat different from each other (Table 2), with that of Mammut being distinctly negatively allometric. However, low sample sizes and a low correlation in the case of Mammut precludes assumptions of significance (0.40 > P > 0.30). The higher slope for Gomphotherium was only significantly different from the extreme negative allometry slope of static stress similarity (Table 2), but not from either elastic or geometric similarity. In Mammut the rather low sample size and moderate correlation precluded assumptions of significance from any of the three hypothetical slopes (Table 2), although the slope was almost significantly different from geometric similarity. The slope for the femur of Gomphotherium was not significantly different from that of E. maximus (0.80 > P > 0.70), L. africana (0.40 > P > 0.30), and M. primigenius (0.30 > P > 0.20). The latter non-significant difference should probably be ascribed in part to a low sample size, implying wide confidence limits. The femur slope of Mammut was considerably lower, and more in accord with those of Loxodonta and Mammuthus (Table 2), and conversely it was not significantly different from them (0.80 > P > 0.70 and P > 0.90, respectively), but was not significantly different from the higher slope of Elephas (0.30 > P > 0.20) either.

DISCUSSION

Overall, most of the produced regressions were negatively allometric, as expected, although often insignificantly so, owing to low sample sizes and/or moderate correlation coefficients. Thus, proboscideans appear, in general, to compensate osteologically for the increased bone stresses associated with increasing body size. Extant elephants also appear to engage less, or at least less frequently, in strenuous physically activity if they are really large, with the exception of sparring bulls. The reason for this may, however, be primarily ethological rather than imposed by strictly physical constraints. If extended to interspecific relationships, a reduction of physical activity with size would also imply that long-bone scaling across a wide size spectrum could result in regression slopes that need not follow the theory of elastic similarity. Really huge mammoths may not have been able to perform fast ambling for strictly physical reasons, although the extreme resemblance of the skeleton to those extant elephants makes this suggestion rather dubious. Such inferences are, however, unlikely to ever be verified for extinct animals.

The heterogeneity of long-bone proportions between more archaic ‘gomphotheres’ and elephantids (Fig. 3), of course, implies that analysis of samples encompassing a wide phylogenetic spectrum will result in substantial residual variances and scatter about the regression lines, and even when taking phylogeny into account the correlation coefficients barely exceeded 0.90. The question remains, however, why some proboscideans apparently were endowed with considerably more massive long bones than others, as their mode of peak locomotion may be inferred not to have differed to any large extent from that of extant elephants, consisting of ambling with rather columnar limbs, and limb mechanics favouring axial compression and mediolateral bending moments at all gaits.

Haynes (1991) suggested that some proboscideans might have had more sturdy limbs because of a more aquatic lifestyle but dismissed this as unlikely, but he also suggested that it could be the result of some extinct proboscideans having engaged in more strenuous physical activities than extant elephants. This is possible, and certainly in accord with the results of the present study, as the ‘gomphotheres’ did not attain the huge body sizes of many elephantids, including extant forms (e.g. Pilla, 1941; Wood, 1981; Blashford-Snell & Lenska, 1996; Christiansen, 2004). However, even if engaging in more strenuous and/or more frequent locomotor activity, it is highly unlikely that ‘gomphotheres’ were able to run in the traditional sense, i.e. including a suspended phase in the stride. Such differences in locomotor mechanics would imply major morphological differences from extant elephants. For this there is little morphological evidence, and it seems unlikely because of the great similarity of the appendicular skeleton of these forms to that of extant elephants. There is ample fossil evidence of elephant-sized animals, dinosaurs and various mammals alike, to strongly suggest that true running at a body mass of numerous metric tons is feasible, providing that it was evolutionary important to adapt to doing so (see e.g. Paul & Christiansen, 2000; Christiansen & Paul, 2001 for details). The fact that ‘gomphotheres’ showed no signs of evolving these anatomical traits suggests that increased locomotor activity was not a driving force in their evolution.

One possible explanation is that most primitive proboscideans, such as ‘gomphotheres’, had considerably more elongate bodies than the taller and more compact elephantids. Thus, they could have had a considerably greater body mass at any given shoulder height than, for instance, extant elephants. Some also appear to have been sturdier overall, e.g. Mammut, where practically every bone in the skeleton is considerably more massive than in, for instance, E. maximus (Warren, 1852; Osborn, 1936, 1942; Miller, 1987; Haynes, 1991; Christiansen, 2004). Support of a greater body mass would imply thicker long bones, providing that the safety factors were kept within the same levels as extant animals. Whether or not they were actually so massive as to warrant such sturdy long bones compared with elephantids is still a largely unexplored question, and is likely to remain so, as the actual body masses are unavailable for fossil animals.