The degree to which potential and kinetic energy can be effectively exchanged in an inverted pendulum model depends on both the relative magnitudes of PE and KE fluctuations and their phase relationship. Potential energy fluctuations can be influenced by the amount of vertical displacement of the center of mass, which in turn can be influenced by the amount of limb flexion during stance phase. Increased limb flexion decreases the effective limb length and may reduce the vertical oscillation of the center of mass if other variables such as limb protraction and angular excursion remain equal. Therefore, we hypothesized that because cats walk with greater limb flexion than distance specialists, they may have lower mechanical energy recovery compared to long distance specialists because of reduced oscillations in the vertical position of their center of mass if the other variables that affect recovery such as amplitude of KE fluctuations and phase relationship between PE and KE remain unchanged. Accounting for limb compression is important for a full understanding of walking mechanics in animals. A recent study modeling human walking found that a pendulum model with completely stiff limbs that produced reasonable predictions of percent recovery did a poor job of predicting the force profile of actual human walking and that incorporating spring elements due to limb compression (flexion) produced a much closer match with empirical data 
Our data support the hypothesis that cats have a less effective pendular mechanical energy-saving mechanism than distance specialists. The average energy recovery (17.6±11.3% (s.d.), n
6) achieved by the cats was very low and their maximum energy recovery (37.9%) was substantially lower than the maximum energy recovery reported for distance specialists 
. Energy recovery values for trots were all relatively low suggesting a clear walk-trot transition (). Considering only walks, there was a statistically significant regression slope, but very poor predictive power in the relationship between velocity and recovery (linear fit: r2
0.002; quadratic fit: r2
6). Although previous studies on walking mechanics 
found a hyperbolic, curvilinear relationship between velocity and percent recovery with optimal mechanical energy recovery at a moderate speed in a small number of distance specialists, the cats in this study showed no evidence of such a relationship (). This suggests that velocity is not as good a predictor of mechanical energy recovery in cats as it has been found to be in distance specialists and other explanations must be sought for variation in recovery. Similar variability in energy recovery with respect to velocity has been documented in reptiles and amphibians 
and uniformly low energy recovery across a range of speeds was found in small mammals 
. It appears therefore that animals that do not specialize in long distance travel show a much less stereotyped pattern than that of distance specialists. However, previous studies did not explore the source of this variation.
Percent recovery of mechanical energy due to exchange of PE and KE vs. velocity for walking and trotting strides.
The timing of footfalls also can affect the magnitude of PE fluctuations. Diagonality is defined as the percentage of a stride by which ipsilateral (same side) feet follow one another. In a pacing gait, the ipsilateral front and hind feet strike the ground at the same time and the diagonality is 0%. In a trot, the ipsilateral front and hind feet strike the ground half the stride time apart, and the diagonality is 50%. For a stride with a diagonality of 25%, the contacts of the four feet are evenly spaced in time. It has been argued on theoretical grounds that if mass is evenly distributed between the forelimbs and hind limbs and an animal walks with a diagonality of 25%, the vertical position of its center of mass will move so little as to allow almost no energy exchange 
. This is because at the point in the stride when the front end is at its highest point, the hind end is at its lowest point and vice versa, so the front and back ends oscillate around the center of mass, resulting in zero PE fluctuation 
. It has been shown 
that dogs avoid this problem both by having more of their mass concentrated anteriorly and by consistently using a diagonality around 15% when walking.
Griffin et al.'s 
argument that dogs maintained high levels of recovery because of the mass distribution bias toward the forelimbs and because dogs chose diagonalities close to 15%, and that lower or higher diagonalities would lower mechanical energy recovery, is a logical conclusion but has not been fully tested because the dogs in this study used a narrow range of diagonalities. Cats are an ideal model in which to study the effect of diagonality on recovery. Like dogs, cats have a weight distribution pattern biased toward the forelimb 
. However, cats naturally use a wide range of diagonalities while walking (). Therefore the data presented here can be used to directly test Griffin et al.'s 
theoretically predicted relationship between footfall pattern and pendular energy recovery.
Percent recovery of mechanical energy due to exchange of PE and KE vs. diagonality for walking strides.
The prediction that diagonality influences mechanical energy recovery is supported by our results. Cats in this study often used footfall patterns with diagonality close to 25% and had low energy recovery when they did. In walking gaits, energy recovery was significantly, inversely correlated with diagonality (linear fit: r2
0.5417, p<0.001, n
5) (). This supports Griffin's 
model and is consistent with other studies that found recoveries that were low and/or highly variable in animals that also used gaits with a high diagonality 
A second important factor that can influence mechanical energy recovery is the phase relationship between PE and KE fluctuations. Phase relationships are typically computed by identifying peaks in the energy fluctuations, but clear energy peaks are often not readily apparent. In these cases the phase relationship can be characterized by calculating congruity, the product of the derivatives of PE and KE with respect to time 
. Congruity is positive when PE and KE change in the same direction and negative when they change in opposite directions. This can be expressed as a percentage of the stride during which congruity is positive. A high percent congruity indicates that PE and KE fluctuate largely in phase allowing little mechanical energy recovery, whereas a low percent congruity is associated with out of phase PE and KE fluctuations and high energy recovery.
The cats in this study had a strong, significant relationship (r2
6) between recovery and congruity, thus changes in phase of PE and KE fluctuations explain the vast majority of the variation in recovery (). This contrasts with our prediction that the magnitude of vertical oscillations of the center of mass would be the primary influence on mechanical energy recovery; our data reject this hypothesis. No relationship was found between energy recovery and the maximum vertical displacement of the center of mass during a stride (linear fit r2
6). Therefore, diagonality appears to influence energy recovery not through its effect on vertical oscillations of the center of mass as theoretically predicted, but through an effect on the phase relationship between PE and KE fluctuations.
Percent recovery of mechanical energy due to exchange of PE and KE vs. percent congruity for walking strides.
In this study, there was also a clear association between crouched posture and diagonality. The cats in our study used a wide range of postures from very crouched (Video S1
) to relatively extended (Video S2
), and the adoption of these different postures was not associated with walking speed. We found a significant curvilinear relationship between diagonality and normalized hip height (quadratic fit: r2
0.5455, p<0.001, n
3) (). During crouched strides in which the hip was held relatively close to the substrate, cats used higher diagonalities. It is likely that evenly spaced footfalls increase stability 
and are thus helpful during stealthy approach to prey. However, by choosing such diagonalities during crouched gaits, cats sacrifice energetic efficiency. The reduced mechanical energy recovery that results from this footfall pattern may be compensated somewhat by decreased collisional energy losses. In a numerical simulation of stiff-legged walking 
, it was found that collisional energy loss due to the change in direction of the center of mass was lowest when limb phase (diagonality) was 25%.
Diagonality vs. mean normalized hip height during stance phase for walking strides.
The data presented here suggest ways in which animals can balance complex and sometimes conflicting performance criteria when walking. Some animals may gain the greatest selective advantage by reducing metabolic energy costs by reducing muscular contribution whereas others gain the greatest advantage by avoiding detection while avoiding predators or stalking prey. Those animals may be unable to achieve high levels of mechanical energy recovery as a result of choosing more diagonal footfall patterns and more crouched postures which tend to increase the congruity of PE and KE fluctuations, but may gain stability during stealthy walking by choosing this kind of gait and posture. This novel study of cats highlights these compromises very clearly. The strong associations found between posture and diagonality, and between diagonality and mechanical energy recovery within this single species demonstrates that cats tune their behavior to different critical demands depending on the locomotor context. Cats provide a good comparison with distance specialists such as canids because they consistently walk with their limbs in a more flexed posture, which as we have seen here within cats, is associated with poorer mechanical energy exchange through its effect on footfall pattern. Dogs tend to use lower diagonalities and have higher energy recovery 
than cats and it seems likely that this is due at least in part to their more extended posture. Little is yet known about the relationship between pendular energy recovery and the metabolic costs associated with walking, particularly in the more poorly studied non-distance specialists. If fluctuations in PE and KE are small to begin with, the cost of supplying this energy through muscular work may be small. Although further study is needed regarding the metabolic costs of reduced pendular exchange during walking, the consistent differences between the results found here and those reported for distance specialists suggest the possibility of an evolutionary tradeoff between energetic efficiency and stealthy locomotion, highlighting the importance of the interplay of conflicting performance goals to evolutionary outcomes.