Gregory Paul's reply demonstrates that our study's critique(Ren et al., 2008) of how previous studies have dichotomized animal limb function into `flexed vs columnar' categories was on the mark. He again divides limb configurations into either `strongly flexed' or `highly extended' but where do the boundaries between these categories lie? Do large animals supposedly representing such categories, such as horses and elephants, differ appreciably from each other?
A quantitative approach is needed to shed light on this question, as postures are best described in terms of joint and segment angles. For example,the angles of limb joints/segments at mid-stance (approximately corresponding to maximal limb loading) in ambling elephants and trotting horses at equivalent size-normalized speeds are shown in Table 1. The data shown for horses are firmly validated with radiographic studies, as we cited. Horse and elephant thigh limb segment angles at mid-stance are quite similar whereas humerus segments may be slightly more protracted in horses (we repeat that elephant scapular motion remains to be measured). Furthermore, the wrist joint angles of running horses and elephants are almost identical. Elephants have∼30–60 deg. more flexed elbows, knees and ankles than horses do. Similar results hold for other instances in the stride cycle or other speeds. Where then do the supposed sharp divisions between `flexed' and`columnar/extended' limb orientations lie?
| Segment or joint | Elephant angle | Horse angle |
|---|---|---|
| Humerus | –32 | –50 |
| Elbow | 144 | 175 |
| Wrist | 189 | 185 |
| Thigh | 11 | 2 |
| Knee | 135 | 180 |
| Ankle | 108 | 170 |
| Segment or joint | Elephant angle | Horse angle |
|---|---|---|
| Humerus | –32 | –50 |
| Elbow | 144 | 175 |
| Wrist | 189 | 185 |
| Thigh | 11 | 2 |
| Knee | 135 | 180 |
| Ankle | 108 | 170 |
Average values from Ren et al. [Tables S1 and S2 in supplementary materialin Ren et al., 2008(Ren et al., 2008)] and Back et al. [fig. 4 in Back et al.,1995a (Back et al.,1995a); fig. 4 in Back et al.,1995b (Back et al.,1995b)], respectively
Quantitative data (Table 1)show that such dichotomies have no legs to stand on. Indeed, elephants' limbs could be said to be more flexed than horses' limbs during running –although we took a more cautious approach and described them as being roughly similar.
Paul repeats many of our points about the technical problems that face interpretation of elephant (and other large animal) locomotion. His approach(fitting a skeleton inside Muybridge's images of a single stride) is not equivalent to ours (in which six digital cameras captured 240 images per second at 1 mm accuracy, for 288 complete strides of 15 elephants, with joint landmarks palpated and visualized, and thorough statistical analysis). Our 3-D motion analysis approach is well accepted and validated as a reasonable standard (e.g. Back et al.,1995a; Back et al.,1995b) despite the technical flaws we discussed; his is unvalidated. Because Paul simply used Muybridge's data and did not provide a reliable method or quantitative results (unlike the other studies we discussed), we did not cite his small illustrations of an elephant in Paul and Christiansen [fig. 5D in Paul and Christiansen, 2000 (Paul and Christiansen, 2000)]. Likewise, we did not cite countless images of moving elephants in popular books. We felt all of these potential sources of data were too unreliable.
Paul has provided no new information on the problem of skin motion for experimental studies whereas we treated the subject cautiously with a statistical analysis of marker placement and a restraint from quantifying proximal joint angles, which are expected to have the worst artifacts. In addition, we used defleshed cadavers, which lacked such artefacts, to show that horse and elephant limbs have broadly similar flexibility.
Paul tries to argue that the two methods are more or less equivalent and the problems so difficult that it's anyone's guess how elephant limbs move;the issue is `open to question' and `cannot be verified or refuted.' We find this attitude disturbingly anti-scientific and quite misleading as it implies comparably accurate methodology.
Our method of quantifying foot skeletal joint angles was not flawed for the purposes of our analysis that was to estimate skeletal joint and segment angles, not to estimate the centre of pressure, which essentially all researchers have assumed would be more caudally positioned along the foot. Paul appears to conflate where the centre of pressure is with where the axis of foot motion is. The former is probably near mid-foot (our unpublished data); the latter is along the third digit. Estimating skeletal motion from the lateral side of the foot would underestimate ankle joint flexion and confuse ankle abduction and flexion. Motion of the short digits of elephants would not greatly change our results. Indeed our unpublished in vitroand radiographic data support the assumption that the toes move very little and that our markers were positioned on skeletal landmarks that enable approximation of ankle joint motion. Paul repeats descriptions of the same foot (and footpad) anatomy and function that we have described in three papers on that subject (Weissengruber et al.,2006; Hutchinson et al.,2008; Miller et al.,2008), so we do not see what he is critiquing. Again, he is providing no new information.
We showed how elephant ankles dorsiflex, then plantarflex during the stance phase (as in most other mammals with spring-like ankles), exhibiting classic spring-like kinematics. Paul provides no evidence or coherent argument to falsify our measurements; the statement that elephant ankles are `too short and inflexible' is a non-sequitur. Precisely how long would they need to be and what kind of quantitative motion would they need to exhibit to be spring-like? Specifically, how much more `functionally columnar' is an elephant's foot than a horse's foot, if the skeletal kinematics are less columnar in elephant feet? Certainly more data on foot mechanics for elephants and other large animals would be useful and our ongoing studies are fulfilling this need.
Whereas few studies have provided reliable new data, we cited numerous studies (e.g. Paul and Christiansen,2000) that have talked about elephant locomotion without measuring or carefully considering empirical data. Some studies hung elaborate ideas about broader patterns in animal locomotor evolution on tidy categories like`flexed' and `columnar.' In our introduction, we first cited some antiquated notions about elephant limbs as being inflexible or simply column-like and then noted `ridiculous as those fallacies may seem to contemporary scientists,elephant posture and gait remain misunderstood, partly because of their strange anatomy and partly because of little rigorous measurement of elephant locomotion' [p. 2735 in Ren et al. (Ren et al., 2008)]. That sentence summarizes the current dialogue quite well.
Morphology can matter; indeed we agree with Paul that the locomotor differences between elephants and other animals may hinge upon anatomy and other factors, so we suspect that there is much more to the mystery than simple dichotomies and qualitative anecdotes. For example, Fig. 1 supports the inference that previously perceived differences in posture between `cursorial' horses and `graviportal' elephants are largely due to different limb proportions,i.e. relative lengths of the proximal and distal limbs, not more flexed limbs in horses.
![Mid-stance limb orientations for ambling elephants and trotting horses at Froude numbers ∼1; individual data (not averaged, thus joint angles do not perfectly match those presented in Table 1), respectively, from Ren et al. [see fig. 11 in Ren et al., 2008(Ren et al., 2008)] and Back et al. [see fig. 4 in Back et al.,1995a (Back et al.,1995a); see fig. 4 in Back et al., 1995b (Back et al.,1995b)].](https://cob.silverchair-cdn.com/cob/content_public/journal/jeb/212/1/10.1242_jeb.025098/3/m_jeb025098f1.jpeg?Expires=1716301803&Signature=oW5lvLiueoqbhsWxX-WzpEpfwLEGP7-8~PuxIQ5wC3aR9pHwTKw-vFqCa4C~OGrhUEdJSlxSDAfniC3fTKY0NYoSL7E1gU-lkCY0YoLn1kxTvYrAMsXsNMqGB~kTsSBaLtY4vciFMQmyBHH3pSv8xzJryTCC26mjeEQ6jZvsYrnAxnJKX0de~aikiXrYlAl9BdlGBc5~ot9hxYYJ~Laj9FCW4cvoBITCBeTA1RMVanoY-ONjuMYSlm09AC1i7yy1iNs98t0J68zbTT2Km~aOciZD6iNGqi4hWUKlbjwHiLCojAeIbMdDHXR-4YfROV3m5Z-SV~6xZ--qsIFVcdYTAg__&Key-Pair-Id=APKAIE5G5CRDK6RD3PGA)
Mid-stance limb orientations for ambling elephants and trotting horses at Froude numbers ∼1; individual data (not averaged, thus joint angles do not perfectly match those presented in Table 1), respectively, from Ren et al. [see fig. 11 in Ren et al., 2008(Ren et al., 2008)] and Back et al. [see fig. 4 in Back et al.,1995a (Back et al.,1995a); see fig. 4 in Back et al., 1995b (Back et al.,1995b)].
Mid-stance limb orientations for ambling elephants and trotting horses at Froude numbers ∼1; individual data (not averaged, thus joint angles do not perfectly match those presented in Table 1), respectively, from Ren et al. [see fig. 11 in Ren et al., 2008(Ren et al., 2008)] and Back et al. [see fig. 4 in Back et al.,1995a (Back et al.,1995a); see fig. 4 in Back et al., 1995b (Back et al.,1995b)].
Gait analysis of elephants and other large animals needs more data but Paul offers none. Ideas about animal locomotion are not enough, especially when weighed down with ponderous conceptual baggage and antiquated methodology. To contribute to animal locomotor science, researchers must generate novel data with reliable methods. We stand by our original methods and data.
