The effects of owl predation on the foraging behavior of heteromyid rodents

Summary Researchers have documented microhabitat partitioning among the heteromyid rodents of the deserts of North America that may result from microhabitat specific predation rates; large/bipedal species predominate in the open/risky microhabitat and small/quadrupedal species predominate in the bush/safer microhabitat. Here, we provide direct experimental evidence on the role of predatory risk in affecting the foraging behavior of three species of heteromyid rodents: Arizona pocket mouse (Perognathus amplus; small/quadrupedal), Bailey's pocket mouse (P. baileyi; large/quadrupedal), and Merriam's kangaroo rat (Dipodomys merriami; large/bipedal). Both kangaroo rats and pocket mice are behaviorally flexible and able to adjust their foraging behavior to nightly changes in predatory risk. Under low levels of perceived predatory risk the kangaroo rat foraged relatively more in the open microhabitat than the two pocket mouse species. In response to the presence of barn owls, however, all three species shifted their habitat use towards the bush microhabitat. In response to direct measures of predatory risk, i.e. the actual presence of owls, all three species reduced foraging and left resource patches at higher giving up densities of seeds. In response to indirect indicators of predatory risk, i.e. illumination, there was a tendency for all three species to reduce foraging. The differences in morphology between pocket mice and kangaroo rats do appear to influence their behavioral responses to predatory risk.     

An ecological comparison of the two arid-zone kangaroos of Australia, and their anomalous prosperity since the introduction of ruminant stock to their environment.

This paper discusses the interactions between the large and medium-sized marsupials, the introduced ruminant domestic stock, and the environment in the arid zone of Australia. The grazing of sheep and cattle has produced suitable subclimax pastures which today favor two sympatric kangaroos but not the smaller bandicoots and wallabies. Tall grass tussocks used as shelter by the latter have been grazed down by the ruminants, and replaced by "marsupial lawns" or xeric spinifex, depending on locality, thereby improving the food supplies for the plains kangaroo and the hill kangaroo, respectively. It is argued, however, that even these smaller marsupials benefited originally from the new grazing regime. Patchy grazing of the grasslands probably created edge effects and other early seral changes which improved the food supplies while leaving adequate shelter. Continued grazing by increasingly large numbers of sheep and cattle ultimately and critically removed the shelter and, therefore, eliminated the bandicoots and wallabies. There is evidence that the plains kangaroo, though generally abundant at the present time, is vulnerable to competitive displacement by sheep, cattle, rabbits, and, in one region, by the hill kangaroo when it invades the plains. The plains kangaroo with its diet of green herbage is most threatened during droughts because the other herbivores have finer-grained diets. Like the bandicoots and wallabies the plains kangaroo in at least two localities appears to have first increased in numbers and then decreased. Sheep and cattle numbers have generally done the same. It is postulated, therefore, that there may not be two opposing response curves for the large and medium-sized marsupials to the ruminant invasion of the inland plains, but, in the long run, only one: an initial numerical increase and then decline. Only the time-scale is different, taking 50 years or more for the plains kangaroo, but perhaps half that time or less for the bandicoots and wallabies. The hill kangaroo may be the ultimate winner because it requires the least nitrogen, and the spinifex it eats during drought has spread as part of the subclimax created by ruminants.     

Effects of hip torque during step-to-step transition on center-of-mass dynamics during human walking examined with numerical simulation

Besides the leg force actuator, humans also use a hip torque actuator during the step-to-step transition to redirect the velocity of CoM (Center of Mass). Although the leg force actuator has been widely studied, few researches analyze the hip torque actuator during the step-to-step transition. In this paper, we build a powered walking model which consists of a point mass linked with two compliant legs. Each leg has a spring and a damper in parallel. Two types of active actuators, the force actuator on the leg and the torque actuator at the hip, are added to simulate the leg force and hip torque actuator during the step-to-step transition. The cycle walk is solved by numerical simulations under different hip torque strength, and the energetics and stability are evaluated. The simulation results show that the hip torque actuator can reduce the energy cost and improve the stability of walking. Further analysis shows that the hip torque actuator can reduce mechanical works of both legs with small extra energy cost. To understand the principle of hip torque actuator, the CoM dynamics is analyzed. It is shown that the hip torque actuator is efficient on the redirection of CoM. Thus, it can improve the stability and reduce required forces of both legs, which decreases the energy cost. Our work provides a fundamental understanding of the hip torque during the step-to-step transition, and may help improve the design of bipedal robots and prosthesis.     

Scaling of elastic energy storage in mammalian limb tendons: do small mammals really lose out?

It is widely believed that elastic energy storage is more important in the locomotion of larger mammals. This is based on: (a) comparison of kangaroos with the smaller kangaroo rat; and (b) calculations that predict that the capacity for elastic energy storage relative to body mass increases with size. Here we argue that: (i) data from kangaroos and kangaroo rats cannot be generalized to other mammals; (ii) the elastic energy storage capacity relative to body mass is not indicative of the importance of elastic energy to an animal; and (iii) the contribution of elastic energy to the mechanical work of locomotion will not increase as rapidly with size as the mass-specific energy storage capacity, because larger mammals must do relatively more mechanical work per stride. We predict how the ratio of elastic energy storage to mechanical work will change with size in quadrupedal mammals by combining empirical scaling relationships from the literature. The results suggest that the percentage contribution of elastic energy to the mechanical work of locomotion decreases with size, so that elastic energy is more important in the locomotion of smaller mammals. This now needs to be tested experimentally.     

A collisional model of the energetic cost of support work qualitatively explains leg sequencing in walking and galloping, pseudo-elastic leg behavior in running and the walk-to-run transition

Terrestrial legged locomotion requires repeated support forces to redirect the body's vertical velocity component from down to up. We assume that the redirection is accomplished by impulsive leg forces that cause small-angle glancing collisions of a point-mass model of the animal. We estimate the energetic costs of these collisions by assuming a metabolic cost proportional to positive muscle work involved in generating the impulses. The cost of bipedal running estimated from this collisional model becomes less than that of walking at a Froude number (v2/gl) of about 0.7. Two strategies to reduce locomotion costs associated with the motion redirection are: (1) having legs simulate purely elastic springs, as is observed in human running; and (2) sequencing the leg forces during the redirection phase; examples of this sequencing are the ba-da-dump pattern of a horse gallop and having push-off followed by heel-strike in human walking.     

Differential design for hopping in two species of wallabies.

Hindlimb musculoskeletal anatomy and steady speed over ground hopping mechanics were compared in two species of macropod marsupials, tammar wallabies and yellow-footed rock wallabies (YFRW). These two species are relatively closely related and are of similar size and general body plan, yet they inhabit different environments with presumably different musculoskeletal demands. Tammar wallabies live in relatively flat, open habitat whereas yellow-footed rock wallabies inhabit steep cliff faces. The goal of this study was to explore musculoskeletal differences between tammar wallabies and yellow-footed rock wallabies and determine how these differences influence each species' hopping mechanics. We found the cross-sectional area of the combined ankle extensor tendons of yellow-footed rock wallabies was 13% greater than that of tammar wallabies. Both species experienced similar ankle joint moments during steady-speed hopping, however due to a lower mechanical advantage at this joint, tammar wallabies produced 26% more muscle force. Thus, during moderate speed hopping, yellow-footed rock wallabies operated with 38% higher tendon safety factors, while tammar wallabies were able to store 73% more elastic strain energy (2.18 J per leg vs. 1.26 J in YFRW). This likely reflects the differing demands of the environments inhabited by these two species, where selection for non-steady locomotor performance in rocky terrain likely requires trade-offs in locomotor economy.     

Human hopping on damped surfaces: strategies for adjusting leg mechanics

Fast-moving legged animals bounce along the ground with spring-like legs and agilely traverse variable terrain. Previous research has shown that hopping and running humans maintain the same bouncing movement of the body's centre of mass on a range of elastic surfaces by adjusting their spring-like legs to exactly offset changes in surface stiffness. This study investigated human hopping on damped surfaces that dissipated up to 72% of the hopper's mechanical energy. On these surfaces, the legs did not act like pure springs. Leg muscles performed up to 24-fold more net work to replace the energy lost by the damped surface. However, considering the leg and surface together, the combination appeared to behave like a constant stiffness spring on all damped surfaces. By conserving the mechanics of the leg-surface combination regardless of surface damping, hoppers also conserved centre-of-mass motions. Thus, the normal bouncing movements of the centre of mass in hopping are not always a direct result of spring-like leg behaviour. Conserving the trajectory of the centre of mass by maintaining spring-like mechanics of the leg-surface combination may be an important control strategy for fast-legged locomotion on variable terrain.     

Merriam's kangaroo rats (Dipodomys merriami) voluntarily select temperatures that conserve energy rather than water

Desert endotherms such as Merriam's kangaroo rat (Dipodomys merriami) use both behavioral and physiological means to conserve energy and water. The energy and water needs of kangaroo rats are affected by their thermal environment. Animals that choose temperatures within their thermoneutral zone (TNZ) minimize energy expenditure but may impair water balance because the ratio of water loss to water gain is high. At temperatures below the TNZ, water balance may be improved because animals generate more oxidative water and reduce evaporative water loss; however, they must also increase energy expenditure to maintain a normal body temperature. Hence, it is not possible for kangaroo rats to choose thermal environments that simultaneously minimize energy expenditure and increase water conservation. I used a thermal gradient to test whether water stress, energy stress, simultaneous water and energy stress, or no water/energy stress affected the thermal environment selected by D. merriami. During the night (i.e., active phase), animals in all four treatments chose temperatures near the bottom of their TNZ. During the day (i.e., inactive phase), animals in all four treatments settled at temperatures near the top of their TNZ. Thus, kangaroo rats chose thermal environments that minimized energy requirements, not water requirements. Because kangaroo rats have evolved high water use efficiency, energy conservation may be more important than water conservation to the fitness of extant kangaroo rats.     

Bipedalism in lizards: whole-body modelling reveals a possible spandrel

This paper illustrates how simple mechanical models based on morphological, ethological, ecological and phylogenetic data can add to discussions in evolutionary biology. Bipedal locomotion has evolved on numerous occasions in lizards. Traits that appear repeatedly in independent evolutionary lines are often considered adaptive, but the exact advantages of bipedal locomotion in lizards remain debated. Earlier claims that bipedalism would increase maximal running speed or would be energetically advantageous have been questioned. Here, we use 'whole body' mechanical modelling to provide an alternative solution to the riddle. The starting point is the intermittent running style combined with the need for a high manoeuvrability characterizing many small lizard species. Manoeuvrability benefits from a caudal shift of the centre of mass of the body (body-COM), because forces to change the heading and to align the body to this new heading do not conflict with each other. The caudally situated body-COM, however, might result in a lift of the front part of the body when accelerating (intermittent style), thus resulting in bipedal running bouts. Based on a momentum-impulse approach the effect of acceleration is quantified for a mechanical model, a virtual lizard (three segments) based on the morphometrics of Acanthodactylus erythrurus (a small lacertid lizard). Biologically relevant input (dimensions, inertial properties, step cycle information, etc.) results in an important lift of the front part of the body and observable distances passively covered bipedally as a consequence of the acceleration. In this way, no functional explanation of the phenomenon of lizard bipedalism is required and bipedalism can probably be considered non-adaptive in many cases. This does not exclude, however, some species that may have turned this consequence to their benefit. For instance, instantaneous manipulation of the position of the centre of the body-COM allows stable, persisting bipedal running. Once this was achieved, the bipedal spandrel could be exploited further.     

Parasite and predator risk assessment: nuanced use of olfactory cues

Foraging herbivores face twin threats of predation and parasite infection, but the risk of predation has received much more attention. We evaluated, experimentally, the role of olfactory cues in predator and parasite risk assessment on the foraging behaviour of a population of marked, free-ranging, red-necked wallabies (Macropus rufogriseus). The wallabies adjusted their behaviour according to these olfactory cues. They foraged less, were more vigilant and spent less time at feeders placed in the vicinity of faeces from dogs that had consumed wallaby or kangaroo meat compared with that of dogs feeding on sheep, rabbit or possum meat. Wallabies also showed a species-specific faecal aversion by consuming less food from feeders contaminated with wallaby faeces compared with sympatric kangaroo faeces, whose gastrointestinal parasite fauna differs from that of the wallabies. Combining both parasite and predation cues in a single field experiment revealed that these risks had an additive effect, rather than the wallabies compromising their response to one risk at the expense of the other.     

Resolution of portions of the kangaroo phylogeny (Marsupialia: Macropodidae) using DNA hybridization

We generated a DNA hybridization matrix comparing eleven 'true' kangaroos (Macropodinae) and two outgroup marsupials, the rufous rat-kangaroo Aepyprymnus rufescens (Potoroinae) and the brush-tailed phalanger Trichosurus vulpecula (Phalangeridae). A small matrix included additional species of the genus Macropus (large kangaroos and wallabies). The results indicate that the New Guinean forest wallaby Dorcopsulus vanheurni, and the quokka Setonix brachyurus, represent successively closer sister-groups of other macropodines. The remaining taxa examined form two clades: the tree kangaroo Dendrolagus matschiei with die pademelons Thylogale and rock wallabies Petrogale, and Macropus including the swamp wallaby Wallabia bicolor. The smaller matrix of five Macropus species and Wallabia (with Dorcopsulus as an outgroup) pairs the red-necked wallaby M. rufogriseus and Parry's wallaby M. parryi, with the eastern grey kangaroo M. giganteus as their nearest relative; and associates the red kangaroo M. rufus and wallaroo M. robustus, with Wallabia as their sister-taxon. In the larger study, we found mat inclusion of both outgroups provided little resolution among the macropodines, judging by jackknife and bootstrap tests. When Aepyprymnus was deleted, the Dendrolagus-Thylogale-Petrogale association obtained; with Trichosurus eliminated instead, the Wallabia-Macropus group was recovered. Only analysis of the eleven ingroup taxa by themselves gave a topology which supported both major clades. Our findings suggest that, at least for DNA hybridization studies, when ingroup taxa are separated by very short internodes experimental error in outgroup-to-ingroup distances may seriously compromise determination of ingroup affinities as well as the position of the root. We recommend that in such cases separate analyses with the outgroups sequentially eliminated and rigorous validation of die topology at each step should be conducted.     

Elastic energy savings and active energy cost in a simple model of running

The energetic economy of running benefits from tendon and other tissues that store and return elastic energy, thus saving muscles from costly mechanical work. The classic “Spring-mass” computational model successfully explains the forces, displacements and mechanical power of running, as the outcome of dynamical interactions between the body center of mass and a purely elastic spring for the leg. However, the Spring-mass model does not include active muscles and cannot explain the metabolic energy cost of running, whether on level ground or on a slope. Here we add explicit actuation and dissipation to the Spring-mass model, and show how they explain substantial active (and thus costly) work during human running, and much of the associated energetic cost. Dissipation is modeled as modest energy losses (5% of total mechanical energy for running at 3 m s^-1) from hysteresis and foot-ground collisions, that must be restored by active work each step. Even with substantial elastic energy return (59% of positive work, comparable to empirical observations), the active work could account for most of the metabolic cost of human running (about 68%, assuming human-like muscle efficiency). We also introduce a previously unappreciated energetic cost for rapid production of force, that helps explain the relatively smooth ground reaction forces of running, and why muscles might also actively perform negative work. With both work and rapid force costs, the model reproduces the energetics of human running at a range of speeds on level ground and on slopes. Although elastic return is key to energy savings, there are still losses that require restorative muscle work, which can cost substantial energy during running.     

Redundant or complementary? Impact of a colonizing species on community structure and function

Recent studies suggest that species with similar functional traits will have similar effects on ecosystems, but evidence for redundancy of species impacts is limited. Here we use a long‐term experiment to gain insight into functional relationships within a desert rodent community. Experimental removal of kangaroo rats, Dipodomys spp., coupled with the recent, serendipitous colonization of a single species of large pocket mouse Chaetodipus baileyi yielded treatments that differed in the diversity of large granivorous rodents present. We evaluated functional overlap of C. baileyi and the other resident large granivores (i.e. the kangaroo rats) by comparing total energy use of granivorous rodents and total abundance and species richness of small granivores across treatments before and after the arrival of C. baileyi. We found that C. baileyi almost completely compensated for the changes in these key ecosystem‐level properties caused by kangaroo rat removal, but it differentially impacted the population dynamics of individual small granivorous rodent species. Thus, its effects were largely complementary, rather than redundant, to those of the missing kangaroo rats. Although short‐term or single‐measure analyses may suggest redundancy, our results support the longstanding dictum that niches of coexisting species are often similar but rarely, if ever, identical.     

Passive bipedal walking with phasic muscle contraction

The existence of self-organizing walking patterns is often considered the result of a mechanical system interacting with the environment and a (neural) oscillating unit. The pattern generators might be thought of as an indispensable component for the existence of limit cycle behavior. This paper shows that this is not a necessity for the existence of a self-organizing bipedal walking pattern. Stable walking cycles emerge from a simple passive bipedal structure, with an energy source inevitably present to sustain the oscillation. In this work the energy source is chosen to be phasic muscle contraction. A two-dimensional model is composed of two legs and a hip mass, symbolizing the trunk. The stance leg stiffness is generated by two muscles. The hip stiffness is generated by four muscles. Muscle activation is caused by two reflex-like trigger signals, without feedback control. Human equivalent model parameters such as geometry and mass distribution were assumed. With return map analysis, the model is analyzed on periodic behavior. Stable walking cycles were found and could be manipulated during walking by varying the muscle or reflex parameters, forcing the oscillation to converge to a new attractor. Received: 5 November 1998 / Accepted in revised form: 26 March 1999     

Biomechanical modeling and sensitivity analysis of bipedal running ability. I. Extant taxa

I used a simple mathematical model of the inverse dynamics of locomotion to estimate the minimum muscle masses required to maintain quasi-static equilibrium about the four main limb joints at mid-stance of fast running. Models of 10 extant taxa (a human, a kangaroo, two lizards, an alligator, and five birds) were analyzed in various bipedal poses to examine how anatomy, size, limb orientation, and other model parameters influence running ability. I examined how the muscle masses required for fast running compare to the muscle masses that are actually able to exert moments about the hip, knee, ankle, and toe joints, to see how support ability varies across the limb. I discuss the assumptions and limitations of the models, using sensitivity analysis to see how widely the results differed with feasible parameter input values. Even with a wide range of input values, the models validated the analysis procedure. Animals that are known to run bipedally were calculated as able to preserve quasi-static equilibrium about their hindlimb joints at mid-stance, whereas non-bipedal runners (iguanas and alligators) were recognized as having too little muscle mass to run quickly in bipedal poses. Thus, this modeling approach should be reliable for reconstructing running ability in extinct bipeds such as nonavian dinosaurs. The models also elucidated how key features are important for bipedal running capacity, such as limb orientation, muscle moment arms, muscle fascicle lengths, and body size. None of the animals modeled had extensor muscle masses acting about any one joint that were 7% or more of their body mass, which provides a reasonable limit for how much muscle mass is normally apportioned within a limb to act about a particular joint. The models consistently showed that a key biomechanical limit on running ability is the capacity of ankle extensors to generate sufficiently large joint moments. Additionally, the analysis reveals how large ratite birds remain excellent runners despite their larger size; they have apomorphically large extensor muscles with relatively high effective mechanical advantage. Finally, I reconstructed the evolution of running ability in the clade Reptilia, showing that the ancestors of extant birds likely were quite capable runners, even though they had already reduced key hip extensors such as M. caudofemoralis longus.     

The spring-mass model for running and hopping

A simple spring-mass model consisting of a massless spring attached to a point mass describes the interdependency of mechanical parameters characterizing running and hopping of humans as a function of speed. The bouncing mechanism itself results in a confinement of the free parameter space where solutions can be found. In particular, bouncing frequency and vertical displacement are closely related. Only a few parameters, such as the vector of the specific landing velocity and the specific leg length, are sufficient to determine the point of operation of the system. There are more physiological constraints than independent parameters. As constraints limit the parameter space where hopping is possible, they must be tuned to each other in order to allow for hopping at all. Within the range of physiologically possible hopping frequencies, a human hopper selects a frequency where the largest amount of energy can be delivered and still be stored elastically. During running and hopping animals use flat angles of the landing velocity resulting in maximum contact length. In this situation ground reaction force is proportional to specific contact time and total displacement is proportional to the square of the step duration. Contact time and hopping frequency are not simply determined by the natural frequency of the spring-mass system, but are influenced largely by the vector of the landing velocity. Differences in the aerial phase or in the angle of the landing velocity result in the different kinematic and dynamic patterns observed during running and hopping. Despite these differences, the model predicts the mass specific energy fluctuations of the center of mass per distance to be similar for runners and hoppers and similar to empirical data obtained for animals of various size.     

Lipid metabolism by rat lung in vitro. Effect of starvation and re-feeding on utilization of [U-14C]glucose by lung slices

1. The incorporation of [U-(14)C]glucose into several lipid components of lung and liver slices, and the activities of glucose 6-phosphate dehydrogenase (EC 1.1.1.49), 6-phosphogluconate dehydrogenase (EC 1.1.1.44), ;malic' enzyme (EC 1.1.1.40) and NADP-isocitrate dehydrogenase (EC 1.1.1.42) of the cell cytosol were examined in normal, starved and re-fed rats. 2. Lipogenesis and the activities of these enzymes in liver were decreased markedly in rats starved for 72h. Re-feeding starved rats on a fat-free diet for 72h resulted in the well documented hyperlipogenic response in liver, particularly in its ability to convert glucose into neutral lipid, and increased activities of glucose 6-phosphate dehydrogenase, ;malic' enzyme and 6-phosphogluconate dehydrogenase to values approx. 700, 470 and 250% of controls respectively. 3. Approx. 70% of the total label in lung lipids was present in the phospholipid fraction. Hydrolysis of lung phospholipids revealed that lipogenesis from glucose was considerable, with approx. 40% of the total phospholipid radioactivity present in the fatty acid fraction. 4. Incorporation of glucose into total lung lipids was decreased by approx. 40% in lung slices of starved rats and was returned to control values on re-feeding. Although phospholipid synthesis from glucose was decreased in lung slices of starved rats, the decrease proportionally was greater for the fatty acid fraction (approx. 50%) as compared with the glycerol fraction (approx. 25%). 5. The activities of lung glucose 6-phosphate dehydrogenase, 6-phosphogluconate dehydrogenase and NADP-isocitrate dehydrogenase were not affected by the dietary alterations. ;Malic' enzyme activity was not detected in lung cytosol preparations. 6. The results are discussed in relation to the surface-active lining layer (surfactant) of the lung.     

Livestock guardian dogs as surrogate top predators? How Maremma sheepdogs affect a wildlife community

Use of livestock guardian dogs (LGDs) to reduce predation on livestock is increasing. However, how these dogs influence the activity of wildlife, including predators, is not well understood. We used pellet counts and remote cameras to investigate the effects of free ranging LGDs on four large herbivores (eastern gray kangaroo, common wombat, swamp wallaby, and sambar deer) and one mesopredator (red fox) in Victoria, Australia. Generalized mixed models and one‐ and two‐species detection models were used to assess the influence of the presence of LGDs on detection of the other species. We found avoidance of LGDs in four species. Swamp wallabies and sambar deer were excluded from areas occupied by LGDs; gray kangaroos showed strong spatial and temporal avoidance of LGD areas; foxes showed moderately strong spatial and temporal avoidance of LGD areas. The effect of LGDs on wombats was unclear. Avoidance of areas with LGDs by large herbivores can benefit livestock production by reducing competition for pasture and disease transmission from wildlife to livestock, and providing managers with better control over grazing pressure. Suppression of mesopredators could benefit the small prey of those species. Synthesis and applications: In pastoral areas, LGDs can function as a surrogate top‐order predator, controlling the local distribution and affecting behavior of large herbivores and mesopredators. LGDs may provide similar ecological functions to those that in many areas have been lost with the extirpation of native large carnivores.     

Patterns of mechanical energy change in tetrapod gait: pendula, springs and work

Kinematic and center of mass (CoM) mechanical variables used to define terrestrial gaits are compared for various tetrapod species. Kinematic variables (limb phase, duty factor) provide important timing information regarding the neural control and limb coordination of various gaits. Whereas, mechanical variables (potential and kinetic energy relative phase, %Recovery, %Congruity) provide insight into the underlying mechanisms that minimize muscle work and the metabolic cost of locomotion, and also influence neural control strategies. Two basic mechanisms identified by Cavagna et al. (1977. Am J Physiol 233:R243-R261) are used broadly by various bipedal and quadrupedal species. During walking, animals exchange CoM potential energy (PE) with kinetic energy (KE) via an inverted pendulum mechanism to reduce muscle work. During the stance period of running (including trotting, hopping and galloping) gaits, animals convert PE and KE into elastic strain energy in spring elements of the limbs and trunk and regain this energy later during limb support. The bouncing motion of the body on the support limb(s) is well represented by a simple mass-spring system. Limb spring compliance allows the storage and return of elastic energy to reduce muscle work. These two distinct patterns of CoM mechanical energy exchange are fairly well correlated with kinematic distinctions of limb movement patterns associated with gait change. However, in some cases such correlations can be misleading. When running (or trotting) at low speeds many animals lack an aerial period and have limb duty factors that exceed 0.5. Rather than interpreting this as a change of gait, the underlying mechanics of the body's CoM motion indicate no fundamental change in limb movement pattern or CoM dynamics has occurred. Nevertheless, the idealized, distinctive patterns of CoM energy fluctuation predicted by an inverted pendulum for walking and a bouncing mass spring for running are often not clear cut, especially for less cursorial species. When the kinematic and mechanical patterns of a broader diversity of quadrupeds and bipeds are compared, more complex patterns emerge, indicating that some animals may combine walking and running mechanics at intermediate speeds or at very large size. These models also ignore energy costs that are likely associated with the opposing action of limbs that have overlapping support times during walking. A recent model of terrestrial gait (Ruina et al., 2005. J Theor Biol, in press) that treats limb contact with the ground in terms of collisional energy loss indicates that considerable CoM energy can be conserved simply by matching the path of CoM motion perpendicular to limb ground force. This model, coupled with the earlier ones of pendular exchange during walking and mass-spring elastic energy savings during running, provides compelling argument for the view that the legged locomotion of quadrupeds and other terrestrial animals has generally evolved to minimize muscle work during steady level movement.     

A comparative collision-based analysis of human gait

This study compares human walking and running, and places them within the context of other mammalian gaits. We use a collision-based approach to analyse the fundamental dynamics of the centre of mass (CoM) according to three angles derived from the instantaneous force and velocity vectors. These dimensionless angles permit comparisons across gait, species and size. The collision angle Φ, which is equivalent to the dimensionless mechanical cost of transport CoT_mech, is found to be three times greater during running than walking of humans. This threefold difference is consistent with previous studies of walking versus trotting of quadrupeds, albeit tends to be greater in the gaits of humans and hopping bipeds than in quadrupeds. Plotting the collision angle Φ together with the angles of the CoM force vector Θ and velocity vector Λ results in the functional grouping of bipedal and quadrupedal gaits according to their CoM dynamics—walking, galloping and ambling are distinguished as separate gaits that employ collision reduction, whereas trotting, running and hopping employ little collision reduction and represent more of a continuum that is influenced by dimensionless speed. Comparable with quadrupedal mammals, collision fraction (the ratio of actual to potential collision) is 0.51 during walking and 0.89 during running, indicating substantial collision reduction during walking, but not running, of humans.