SOME PROPERTIES OF THE MAMMALIAN LOCOMOTORY AND RESPIRATORY SYSTEMS IN RELATION TO BODY MASS

J. exp. Bol. 164, 283-294 (1992) 283 Prnted n Great Brtan The Company of Bologsts Lmted 1992 SOME PROPERTIES OF THE MAMMALIAN LOCOMOTORY AND RESPIRATORY SYSTEMS IN RELATION TO BODY MASS BY IAIN S. YOUNG, RUTH D. WARREN AND JOHN D. ALTRINGHAM Department of Pure and Appled Bology, The Unversty, Leeds, LS2 9JT, UK Accepted 15 November 1991 Summary Vdeo and cn6 flms of mammals runnng at the trot-gallop transton were analysed to measure breathng frequences. Breathng frequency at the trotgallop transton (f h, n Hz) was shown to decrease wth ncreasng body mass (M, n kg) and was descrbed by the equaton / b =5.08M~ 14. The stffness of the thorax and daphragm of mce, rats, rabbts and wallabes was calculated and ths, together wth the mass of the vscera, was used to calculate the natural frequency of the system (nf u n Hz). The relatonshp between nf t and body mass can be descrbed by the equaton «/ t =5.02M~ 018. The sgnfcance of these results s dscussed n relaton to models of mechancal lnkage between respratory and locomotory movements. Introducton When a mammal s walkng or trottng, ncreases n speed are acheved through ncreases n strde frequency. At a certan speed, t becomes more effcent for the mammal to gallop rather than to trot, and t changes ts gat. Beyond ths trot-gallop transton, ncreases n runnng speed are acheved by ncreases n strde length, whle strde frequency remans almost constant (Heglund et al. 1974; Heglund and Taylor, 1988). Heglund et al. (1974) and Taylor (1985) have convncngly argued that the trot-gallop transton occurs at an allometrcally smlar speed and s sutable for comparng the mechancs of locomoton n terrestral mammals of varyng body sze. The relatonshp between strde frequency at the trot-gallop transton (f s, n Hz) and body mass (M, n kg) of terrestral mammals can be descrbed by the equaton (Heglund and Taylor, 1988): / s = 4.19M- 15. They reported a smlar relatonshp between body mass and the preferred gallopng speed (f p, n Hz): f p = 4A4M- 016. Altrngham and Young (1991) have shown that the cycle frequency for maxmum Key words: breathng, lnkage, locomoton, mammals, scalng, ventlaton.

284 I. S. YOUNG, R. D. WARREN AND J. D. ALTRINGHAM power output (f opt, n Hz) of mammalan daphragm muscle performng oscllatory work obeys a very smlar relatonshp to body mass: / opt = 4.42M- - 16. Ths smlarty suggested a lnkage between breathng and locomoton. It has already been observed n a number of terrestral mammals that breathng s synchronsed 1:1 wth body movement durng locomoton over a wde range of speeds (Bramble and Carrer, 1983; Attenburrow, 1982; Baudnette etal. 1987). Breathng frequency, lke strde frequency, s essentally maxmal at the trotgallop transton: at hgher runnng speeds, ncreases n ventlaton are acheved by ncreases n the depth of breathng (Woakes etal. 1987). If the respratory and locomotory systems are ndeed coupled to optmse performance, / s, / p, / opt and the breathng rate durng gallopng should all be descrbed by the same allometrc equaton. A lnkage between breathng and locomotory movements has not been systematcally nvestgated n terrestral mammals, and small mammals have been neglected completely. There s thus no publshed evdence for a relatonshp between breathng frequency durng gallopng and body mass that would allow us to test the above hypothess. The am of the present study was to measure breathng frequences n mammals of wdely dfferent szes and to look for evdence of couplng between respratory and locomotory movements n small mammals. Bramble and Carrer (1983), Baudnette et al. (1987) and Alexander (1989) have descrbed a vsceral pston mechansm n whch locomotory acceleratons cause oscllatons of the abdomnal vscera that, n turn, cause dsplacements of the daphragm and so drve breathng. The frequency and the magntude of these dsplacements wll be determned by the mass of the vscera and the vscoelastc propertes of the respratory system. Crawford (1962) found that dogs pant at very constant frequences, whch he suggested mght be the natural frequency of the respratory system. He found that the pantng frequency was the same as the 'natural frequency of the respratory system' measured by mechancally ventlatng anaesthetsed dogs. He also estmated the stffness of the daphragm, and hence the natural frequency of the system, by measurng the dsplacement of the daphragm produced by the weght of the vscera, from X-rays of dog cadavers taken n the head-down poston. Ths produced qute dfferent estmates and suggested at least a second mode of vbraton of the respratory system. The present study estmates the natural frequency of a 'mass/sprng' system, where the vscera act as the mass and the elastc propertes of the thorax and the daphragm consttute the sprng. Ths s related to body sze, breathng frequency and strde frequency at the trot-gallop transton. Recent studes have shown that phylogenetc and ecologcal effects may be mportant n determnng many allometrc relatonshps (e.g. Gompper and Gttleman, 1991; Nee etal. 1991; Promslow, 1991). We have not entered ths controversy. Snce we can draw apparently sound and nformatve conclusons

Scalng effects n breathng and runnng 285 wthout consderng possble phylogenetc effects, we beleve ths valdates our approach n ths partcular case. We do not deny that phylogenetc and ecologcal effects may play a role, but we do not thnk that such effects would nfluence the conclusons drawn. Materals and methods Measurement of breathng rate The study was performed on mammals rangng n sze from Mongolan gerbls (Merones unguculartus) (0.073 kg) to whte rhnoceros {Ceratotherum smum) (1600 kg), runnng at speeds from just beyond the trot-gallop transton to a full gallop. The gerbl and horses (Equus caballus) runnng on a treadmll were just beyond the trot-gallop transton. Free-runnng horses were flmed exercsng on a lunge at speeds just beyond the trot-gallop transton. Greyhounds (Cans famlars) were runnng at a full gallop n a race. Rabbts (Oryctolagus cunculus, mxed domestc), rhnoceros and the remanng dogs (labrador and mongrel) were gallopng at some ndetermnate speed. Snce strde frequency at the preferred gallopng speed and at the trot-gallop transton are descrbed by very smlar allometrc equatons (Heglund and Taylor, 1988), t was not mportant to control the exact gallopng speed at whch measurements were taken. Ventlaton and strde frequences were derved from synchronzed recordngs of breathng flow and cn6 flm of racehorses exercsng upon a treadmll (full detals n I. S. Young, R. McN. Alexander, A. J. Woakes, P. J. Butler and L. Anderson, n preparaton). A battery-powered camcorder was used to flm the rderless, canterng standard-bred horses on cold days, so that the exhaled breath was also flmed. Smlar vdeo recordngs were made of exercsng dogs and freerunnng rabbts. The framng rate of the camcorder was checked by flmng a stopwatch and tmng the replay. Breathng frequency durng gallopng was obtaned from flm sequences n whch breathng was clearly vsble. Hgh-speed cne flm of racng greyhounds and runnng whte rhnoceros (courtesy of Professor R. McN. Alexander) was analysed on a photo-optcal data analyser, and the breathng rate was determned from respratory movements of the jaws (greyhounds) or nostrls (rhnoceros). To nvestgate the possblty of locomotor/respratory lnkage n small mammals, gerbls were traned to run on a treadmll. The frequency and phase of the breathng and locomotory cycles just beyond the trot-gallop transton were obtaned from vdeo flm, usng a NACHSV400 hgh-speed vdeo system (on loan from the SERC). Wth stroboscopc llumnaton, synchronsed to the frame rate of the vdeo system, respratory movements of the nose could be flmed. The vdeo flm was taken at 200 frames per second, and the tape was analysed on the vdeo processor frame by frame. Smaller mammals (gerbls-dogs) were weghed, and the masses of the horses were estmated by experenced owners, or measured n the case of those runnng

286 I. S. YOUNG, R. D. WARREN AND J. D. ALTRINGHAM on the treadmll. Mean masses of the ndvdual greyhounds analysed were taken from Jayes and Alexander (1982) and of the three rhnoceros from Owen-Smth (1988). The numbers of anmals used n the analyss were as follows (wth mean mass n kg): gerbls 1 (0.073); rabbts 3 (2.72); dogs 4 (28.1); horses 6 (500); whte rhnoceros 3 (1600). Of the sx horses, three were free-runnng and three ran on the treadmll. Allometrc relatonshps were determned from speces means of body mass and breathng frequency. Mean breathng frequency±s.e. values for each speces are gven n the text. Values for each ndvdual are the means of at least sx expermental runs: ntra-ndvdual varaton was less than ntraspecfc varaton. Measurements were taken whle anmals were runnng steadly, wth no change n gat, when breathng frequency showed no tendency to ncrease or decrease. Measurements of the mechancal propertes of the ntact thorax Measurements were carred out on 11 mce (Mus musculus, whte laboratory, mean mass±standard error=0.026±0.001 kg), nne rats (Rattus norvegcus, whte laboratory, 0.23±0.02kg), one rabbt {Oryctolagus cunculus, laboratory, 4.5 kg) and four red-necked wallabes (Macropus rufogrseus, 16.13±1.25kg) of known mass. Mce and rats were klled by cervcal dslocaton, the rabbt by a fatal dose of KC1 when under anaesthetc (after use by other researchers for dfferent purposes). Wallabes were zoo specmens that had to be shot because of njury or llness. Fresh and prevously frozen specmens were used wth smlar results. In all cases, the vscera were removed from the abdomen and weghed. To measure the elastc propertes of the thorax and daphragm of mce and rats, the thorax was pnned down to a dssecton board (Fg. 1A). Awls pnnng the lumbar spne, the dorsal abdomnal musculature, the cervcal vertebrae and beneath the axllae prevented lateral movement of the trunk but allowed free movement of the rb cage. An sometrc force transducer (natural frequency 90Hz, complance errors <5 %), wth a large, blunt probe attached, and mounted on a mcromanpulator, was manoeuvred untl just touchng the abdomnal face of the daphragm and wthdrawn untl the force was zero. The end of the probe was modelled (from arsettng modellng clay) to make t as wde as possble so that, wthout touchng the rb cage, t would contact a large area of the daphragm, thus mnmsng stress concentratons. The resstng force of the thorax and daphragm was measured as the probe was moved aganst the daphragm n 0.5 mm ncrements. Measurements of stffness were obtaned from the rabbt and wallabes by dssectng out the thorax, together wth the ntact daphragm and mountng t daphragm uppermost n a stff-walled contaner (Fg. IB). The thorax rested upon ts vertebral column wth the anteror (rostral) processes of the frst thoracc vertebra cut to provde a flat base on the bottom of the contaner and the most posteror (caudal) thoracc vertebrae restng aganst ts sde. In the case of the wallaby, the bottom of the contaner was flled wth plaster of Pars to a depth of

Scalng effects n breathng and runnng 287 Probe Daphragm Awls Daphragm To osclloscope Force transducer Mcromanpulator Fg. 1. Expermental arrangement for testng the stffness of the daphragm and thorax n (A) the rat and mouse and (B) the wallaby and rabbt. Detals are gven n the text. about 2 cm to prevent slppage. Ths postonng allowed the rb cage and vertebral column to bend when the daphragm was loaded, wthout apparent mpedance by the walls of the contaner. The contaner was placed upon a pan balance, whch was then balanced to read zero, and loads were mposed upon the daphragm by brngng a round-ended probe upon a manpulator to bear upon ts upward facng surface. The dameter of the head of the probe was made as large as possble wthout touchng the rb cage, to reduce the rsk of stress concentraton. The loads upon the daphragm dsplaced the pan balance from zero; the weght requred to counter ths equalled the force upon the daphragm due to the mposed dsplacement, whch was measured on the verner scale of the manpulator. Daphragm dsplacement was plotted aganst force, and the gradent of the frstorder regresson lne, ftted to the lnear porton of the curve, was used to calculate the stffness of the sprng. Ths was then used to calculate the natural frequency (nf) of the mass/sprng system usng the followng equaton: nf t In (Thomson, 1981) where S s the stffness (N m~ L ) of the thorax and daphragm and A/ vs s the mass of the vscera n kg. The natural frequency was then plotted aganst body mass on logarthmc coordnates and a model 1, least-squares frst-order regresson ftted. Allometrc relatonshps were determned from speces means. Mean±s.E. values for each speces are gven n the text.

288 I. S. YOUNG, R. D. WARREN AND J. D. ALTRINGHAM 1 1 1 10 "Gerbl -. - c u 3.. Dog Rabbt ""^> 2 PQ 1 - Horse " ^^P Rhnoceros - 1 0.01 0.1 10 100 Mass (kg) 1000 10000 100000 Fg. 2. Breathng frequency durng gallopng (fb) plotted aganst body mass. Data are speces means. 95% confdence lmts of the slope are shown. Model 2 lnear regresson. Results Breathng frequency In Fg. 2 (see also Table 1), breathng frequency (speces means) at the preferred gallopng speed (f b ) s plotted aganst body mass (M) on logarthmc axes. The relatonshp between f b and M may be descrbed by the allometrc equaton: / b = 5.08M- - 14, where/ b s n Hz and M s n kg. The 95 % confdence lmts about the slope are ±0.03, ^=0.96. The ntercept s 5.08±0.52Hz (ntercept±95 % confdence lmts at the mean). Summary data for ndvdual speces gven as [mean/ b (HZ)±S.E. (/V)] were as follows: gerbls=7.85 (1); rabbts=3.92 ±0.03 (3); dogs=3.20±0.11 (4); horses=2.10±0.04 (6); whte rhnoceros=2.02±0.03 (3). Lnkage of locomoton and breathng A rgorous analyss of the lnkage between locomoton and breathng has been performed on the horse (I. S. Young, R. McN. Alexander, A. J. Woakes, P. J. Butler and L. Anderson, n preparaton). Ths demonstrated a rgd 1:1 couplng (Fg. 3A), the possble mechancal benefts and underlyng mechansms of whch are dscussed by I. S. Young, R. McN. Alexander, A. J. Woakes, P. J. Butler and L. Anderson (n preparaton) and below n the Dscusson. Brefly, the phase relatonshp between the respratory and locomotory cycles ndcates that breathng may be asssted by flexon of the lumbo-sacral jont durng runnng, but s

Scalng effects n breathng and runnng 289 o- m o o---«o <>---- 500 ms o o - o 100 ms Fg. 3. Couplng of locomoton and ventlaton n a seres of consecutve gallopng strdes n the horse and the gerbl. (A) Expraton and forefoot fall n the horse and (B) openng of the nares and forefoot fall n the gerbl. In both, the begnnng of expraton/openng of the nares s denoted by the open crcles and the end of expraton/ closng of the nares by the closed crcles. The dashed lne shows expraton/the perod when the nares are open. Foot contact wth the ground s denoted by the blocked regons; R, rght forefoot; L, left forefoot. Tme s shown by scale bars for each speces. unlkely to be asssted by oscllatons of the vscera aganst the daphragm (I. S. Young, R. McN. Alexander, A. J. Woakes, P. J. Butler and L. Anderson, n preparaton). Analyss of the vdeo flm of the exercsng gerbl also showed a tght 1:1 locomotor/respratory couplng and a very smlar phase relatonshp. The nares opened at the same tme (or wthn 20 ms after) as the forelmbs mpacted wth the treadmll (Fg. 3B). The error nvolved n estmatng the tmng of the respratory events was small (<10ms). Errors n estmatng the tmng of lmb movements were smaller (<5 ms). Forelmb mpact concded wth the end of the flght phase of the strde. Durng the flght phase the back and lmbs were extended. After the forelmb mpact the back was flexed and the hndlmbs were drawn anterorly for the next strde. The observed tmng of the openng and closng of the nares was consstent wth the gerbl breathng out whle the back was flexng, and breathng n whle the back and lmbs were extendng. In the case of the rhno, the nares were observed to open and close once per strde, but flm qualty was not adequate for determnaton of the exact phase relatonshp wth locomotory movements. 1:1 couplng of breathng and locomoton n rabbts and dogs s already well documented (Bramble and Carrer, 1983). Natural frequency of the vscera, thorax and daphragm In Fg. 4, force versus dsplacement curves are shown for the rat daphragm, whch are typcal for all speces measured n ths experment. Stffness was

290 I. S. YOUNG, R. D. WARREN AND J. D. ALTRINGHAM 0.4-0.0 0.000 0.002 0.004 0.006 0.008 Dsplacement (m) 0.010 0.012 Fg. 4. Force-dsplacement curves for rat thorax/daphragm. Model 1 least-squares lnear regresson lnes are ftted to the lnear regon of curves (rlled symbols). Symbols refer to dfferent ndvduals. determned from these characterstc 'J-shaped' curves by fttng a model 1, leastsquares lnear regresson (all /^>0.98). Stffness values for the four speces gven as [mean±s.e. NITT^AO] were as follows: mouse=23.2±5.6 (11); rat=41.6±11.8 (9); rabbt=576 (1); wallaby=1060±230 (4). A logarthmc plot of the natural frequency of the vscera, thorax and daphragm (speces means) as a functon of log body mass gves a relatonshp descrbed by the equaton: n/ t = 5.02AT 018, where the 95 % confdence lmts about the slope s ±0.09, r 2 =0.97. The ntercept was 5.02±1.26Hz (ntercept±95 % confdence lmts at the mean) (Fg. 5, Table 1). Summary data for ndvdual speces were as follows [mean nf t (HZ)±S.E. (N)]: mouse=10.48±0.06 (11); rat=5.78±0.31 (9); rabbt=4.02 (1); wallaby=3.05±0.28 (4). Dscusson The followng varables all show a smlar dependence on body mass n terrestral mammals: strde frequences at the trot-gallop transton (/j) and the preferred gallopng speed (f p, Heglund and Taylor, 1988), breathng frequency durng gallopng (f b, ths study), oscllatory work frequency for maxmum muscle

Scalng effects n breathng and runnng 291 10 10 Fg. 5. Natural frequency of the thorax/daphragm (n/ t ) plotted aganst body mass. Data are speces means. 95 % confdence lmts of the slope are shown. Model 2 lnear regresson. power output of the daphragm (f opt, Altrngham and Young, 1991) and the natural frequency of the daphragm, thorax and vscera (nf t, ths study) (Fg. 6, Table 1): / s = 4.19M- 15, / b = 5.08M- 14, / opt = 4.42M- - 16, n/ t = 5.02AT 018. The slopes and ntercepts n these fve relatonshps are not sgnfcantly dfferent from each other (Table 1, comparson of 95 % confdence lmts). Smlarty of the slope ndcates that all fve varables scale n the same way wth body mass. Smlarty of the ntercept ndcates a 1:1 lnkage between them. It has been suggested that couplng between respraton and locomoton could be due to a mechancal lnkage (Bramble and Carrer, 1983; Baudnette et al. 1987; Alexander, 1989). Ths lnkage may be attrbutable to a ventlaton mechansm drven by locomotory movements. Bramble and Carrer (1983) descrbed three possble mechansms that may be responsble for ths lnkage: the vsceral pston, flexon of the back and loadng of the thorax by the forelmbs. Alexander (1989) suggested that breathng may be drven by the vsceral pston mechansm n the wallaby and by flexon of the back n the horse. The experments by I. S. Young, R. McN. Alexander, A. J. Woakes, P. J. Butler and L. Anderson (n preparaton) on the horse also ndcate that back flexon, rather than the vsceral pston mechansm, s assstng breathng.

292 I. S. YOUNG, R. D. WARREN AND J. D. ALTRINGHAM Table 1. Coeffcents a and b for the general allometrc equaton y=am b, where y s the frequency n (Hz) of the varables n column 1 and M s body mass (n kg) Coeffcent a Exponent b Mean Mean (95 % confdence (95 % confdence r 2 Varable lmts) lmts) (d.f.) Strde frequency at trot-gallop transton (f s )* Strde frequency at preferred gallopng speed (f p )* Breathng frequency durng gallopng (f b ) Oscllatory work frequency for maxmal daphragm power output (f op t)t Natural frequency of vscera/daphragm/ thorax system (n/ t ) 4.19 (3.78, 4.65) 4.44 (4.08, 4.84) 5.08 (3.94, 6.56) 4.42 (3.42, 5.97) 5.02 (4.14, 6.59) -0.15 (-0.12, -0.18) -0.16 (-0.13, -0.18) -0.14 (-0.10, -0.17) -0.16 (0.14, -0.05) -0.18 (-0.09, -0.27) 0.87 0.90 0.96 (3 d.f.) 0.98 (I d.f.) 0.97 (2 d.f.) Data are expressed as mean, wth upper and lower 95 % confdence lmts on the slope (b) and on the coeffcent a. The r 2 values and degrees of freedom (d.f.) are also gven. *Data from Heglund and Taylor (1988). tfrom Altrngham and Young (1991). u. 10 10 1 Mass (kg) 10 4 Fg. 6. Regresson lnes for strde frequency at the trot-gallop transton (/j,), preferred gallopng speed (f p ), breathng frequency at the trot-gallop transton (f b ), oscllatory work frequency for maxmum muscle power output of the daphragm (f opt ) and the natural frequency of the daphragm and thorax (n/ t ), all plotted aganst body mass.

Scalng effects n breathng and runnng 293 In the vsceral pston mechansm, the vscera are regarded as a mass suspended on an nternal sprng, representng the daphragm and the thorax. Durng runnng, acceleratons act upon the trunk, causng dsplacements of the vscera relatve to the body wall. The sze and phase of these oscllatons depend on the mass of the vscera and the vscoelastc propertes of the vscera and the respratory system. Alexander (1989) suggested that the vsceral pston could drve ventlaton f ts natural frequency were tuned to the frequency of the movements of locomoton. Flexon of the back and the resultng forward sweep of the pelvs wth each strde push the vscera towards the daphragm, compressng the lungs (Alexander, 1989; I. S. Young, R. McN. Alexander, A. J. Woakes, P. J. Butler and L. Anderson, n preparaton). For ths mechansm to operate, back flexon must have the same frequency as breathng. As nertal losses are mnmsed at the natural frequency of a sprng/mass system, the back flexon mechansm may operate more effcently f the predcted natural frequency of the daphragm/thorax/vscera has the same frequency as strde and breathng. Strde frequency, breathng frequency and the predcted natural frequency of the daphragm/thorax/vscera have been shown to obey the same allometrc relatonshp. Ths s consstent wth the hypothess that the vsceral pston and the back flexon mechansms could be assstng ventlaton. The mechancal propertes of the respratory system allow ether of these mechansms to operate, but the evdence from Alexander (1989) and I. S. Young, R. McN. Alexander, A. J. Woakes, P. J. Butler and L. Anderson (n preparaton) shows that the precse phase relatonshp between locomotory movements and breathng wll determne whch (f ether) of these mechansms may assst breathng. In addton to passve mechancal propertes, the actve propertes of the respratory muscles must constran the normal physologcal operaton of the respratory system. Immedately after the trot-gallop transton, strde frequency (Heglund and Taylor, 1988) and breathng frequency (Bramble and Carrer, 1983) are essentally maxmal, ncreasng only slghtly wth speed. Increases n ventlaton are acheved by ncreasng ts depth; daphragm muscle should therefore be operatng at ts maxmal n vvo frequency and stran durng gallopng. If systems evolve towards optmum desgn, then t s not unexpected that daphragm muscle should produce ts maxmum power output at the gallopng frequency (Altrngham and Young, 1991), when the demands on the respratory system are greatest. In concluson, the results of ths study extend the sze range of anmals n whch a 1:1 strde to breathng frequency rato s observed durng gallopng to nclude the gerbl at one end of the range and the rhnoceros at the other. We also show that the gerbl mantans a constant phase relatonshp between locomoton and ventlaton, ndcatng mechancal lnkage. The observed mechancal propertes of the respratory system support the hypothess of optmal desgn n the processes drvng respraton durng locomoton. We would lke to thank Professor R. McN. Alexander for many helpful dscussons, and comments on the manuscrpt, and Chrs Smth for techncal

294 I. S. YOUNG, R. D. WARREN AND J. D. ALTRINGHAM assstance and cream eggs. Thanks also to Professor John Kessler and Professor Tm Pedley, and the SERC, for the use of the hgh-speed vdeo camera system. The manuscrpt was substantally mproved by the suggestons of two referees. I.S.Y. was supported by a SERC grant. References ALEXANDER, R. MCN. (1989). On the synchronsaton of breathng wth runnng n wallabes (Macropus spp.) and horses (Equus caballus). J. Zoo, Lond. 218, 69-85. ALTRINGHAM, J. D. AND YOUNG, I. S. (1991). Power output and the frequency of oscllatory work n mammalan daphragm muscles: the effects of anmal sze. J. exp. Bol. 157, 381-389. ATTENBURROW, D. P. (1982). Tme relatonshp between the respratory cycle and lmb cycle n the horse. Equne Vet. J. 14, 69-72. BAUDINETTE, R. V., GANNON, B. J., RUNCIMAN, W. B., WELLS, S. AND LOVE, J. B. (1987). Do cardorespratory frequences show entranment wth hoppng n the Tammar wallaby? J. exp. Bol. 129, 251-263. BRAMBLE, D. M. AND CARRIER, D. R. (1983). Runnng and breathng n mammals. Scence 219, 251-256. CRAWFORD, E. C. (1962). Mechancal aspects of pantng n dogs. J. appl. Physol. 17, 249-251. GOMPPER, M. E. AND GITTLEMAN, J. L. (1991). Home range scalng: ntraspecfc and comparatve trends. Oecologa 87, 343-348. HEGLUND, N. C. AND TAYLOR, C. R. (1988). Speed, strde frequency and energy cost per strde: how do they change wth body sze and gat? J. exp. Bol. 138, 301-318. HEGLUND, N. C, TAYLOR, C. R. AND MCMAHON, T. (1974). Scalng strde frequences to anmal sze: mce to horses. Scence 186, 1112-1113. JAYES, A. S., ALEXANDER, R. MCN. (1982). Estmates of mechancal stresses n leg muscles of gallopng greyhounds (Cans famlars). J. Zool., Lond. 198, 315-328. NEE, S., READ, A. F., GREENWOOD, J. J. D. AND HARVEY, P. H. (1991). The relatonshp between abundance and body sze n Brtsh brds. Nature 351, 312-313. OWEN-SMITH, N. R. (1988). Megaherbvores - The Influence of Very Large Body Sze on Ecology. Cambrdge: Cambrdge Unversty Press. PROMISLOW, D. E. L. (1991). The evoluton of mammalan blood parameters: patterns and ther nterpretaton. Physol. Zool. 64, 393-431. TAYLOR, C. R. (1985). Force development durng sustaned locomoton: a determnant of gat, speed and metabolc power. /. exp. Bol. 115, 253-262. THOMSON, W. T. (1981). Theory of Vbratons wth Applcatons. 2nd edton. London: Allen & Unwn. WOAKES, A. J., BUTLER, P. J. AND SNOW, D. H. (1987). The measurement of respratory arflow n exercsng horses. In Equne Exercse Physology, vol. 2 (ed. J. R. Gllespe and N. E. Robnson), pp. 194-205. Davs, CA: ICEEP Publcatons.