Effects of size on vervet (Cercopithecus aethiops) gait parameters A longitudinal approach.код для вставкиСкачать
AMERICAN JOURNAL OF PHYSICAL ANTHROPOLOGY 81:429439 (1990) Effects of Size on Vervet (Cercopithecus aethiops) Gait Parameters: A Longitudinal Approach JOEL A. VILENSKY, EVA GANKIEWICZ, AND DOUGLAS W. TOWNSEND Department of Anatomy, Indiana University School of Medicine, Fort Wayne, Indiana 46805-1499 (J.A.V., E.G.); Department of Mathematical Sciences, Indiana-Purdue University at Fort Wayne, Fort Wayne, Indiana 46805 (D. W.T.) KEY WORDS Primates, Locomotion, Ontogeny, Walk, Run, Gallop ABSTRACT Changes in the values of certain locomotor parameters were analyzed over a range of speeds for five immature vervet monkeys sampled at 6 month intervals over approximately a 3 year period. Lateral and diagonal sequence walking gaits and transverse and rotary gallops were commonly used. The monkeys switched from walking to galloping at long cycle durations for their mass, although, as a group, their transition speeds were in agreement with data from other mammals. However, for individual monkeys, transition speed was not consistently dependent on body mass. Cycle and stance durations generally increased with increasing size at each speed for each animal, with the greatest increases occurring at slower speeds. Swing durations increased slightly with size. For any particular individual, speed was highly predictable from cycle (or stance) duration and body mass (or age). However, the multiple regression equations for each animal were significantly different from each other, suggesting that no single equation is satisfactory for all of the individuals within a species. Vilensky et al. (1988) used a cross-sectional approach to investigate the effects of size on locomotion in vervet monkeys (Cercopithecus aethiops). In that paper we noted that some of the animals were also part of a long-term longitudinal study of the effects of size upon gait parameters within individual animals. The current report presents results of gait and temporal analyses of the longitudinal data. The primary purpose of the study was to determine whether relationships obtained from cross-sectional analyses can be applied to changes in locomotion during growth of individual animals. In a companion paper (Vilensky and Gankiewicz, 1990), we present a detailed analysis of the effects of size and speed on hindlimb joint displacement patterns in these animals. MATERIALS AND METHODS Table 1 presents some basic data for the animals. Each animal (A) was assigned a number and each filming date (see below) a letter code. Thus A1A refers to animal No. 1 filmed at an age of 1 year 2 months and a 0 1990 WILEY-LISS, INC. mass of 1.27 kg. Further, the table lists the number of O O ~ ”strides (see below) obtained for eac animal at each speed on each filming date. It is important to note that the animals used in the study were not genetically unrelated. All had the same father, and A1 and A2 had the same mother, as did A3 and A5. Data corresponding to AlD, A2B, A3A, A4A, and A5A were used in the crosssectional study (Vilensky et al., 1988). The same training and filming procedures used for the cross-sectional study were used in the present study. Briefly, each animal was trained to locomote on a motor-driven treadmill at nine speeds between 0.62 and 2.81 m/s. The animals were first filmed when training was completed and, subsequently, were filmed at approximately 6 month intervals. Within 1week after each filming, each animal was measured (see Schultz, 1929; Vilensky et al., 1988) to investigate how ontogenetic changes in gait parameters cor- “t Received March 29,1989; accepted June 1,1989 430 J.A. VILENSKY ET AL. TABLE 1 . Animal data Animal 1 2 3 4 5 Sex ~ i l date code F A F F F M B C D E A B C D E F A B C D E A B C D E F A B C D E ~Agei at ~filming ~ Years Months 1 1 2 2 3 1 1 2 2 3 3 0 1 1 2 2 0 0 1 1 2 2 0 0 2 8 2 8 2 0 6 0 6 0 6 10 4 10 4 10 5 10 5 11 5 10 4 10 1 4 1 2 10 4 M~~~ (kg) 1.27 1.59 1.82 2.09 2.22 1.31 1.56 1.79 2.24 2.52 2.50 1.14 1.62 1.79 2.12 2.27 0.64 0.99 1.27 1.32 1.45 1.73 0.73 1.32 1.54 1.77 2.00 0.62 0.89 - - 2 3 8 5 12 5 2 6 6 2 10 8 10 10 5 9 - 9 4 5 7 6 10 7 6 10 19 4 10 - - 9 10 9 3 9 6 2 2 10 10 10 9 6 9 8 9 No. of strides at each speed (m/s) 1.17 1.44 1.72 1.99 2.28 2.58 6 3 7 1 0 3 9 7 5 16 6 9 10 10 7 1 0 8 8 10 10 8 9 11 10 7 6 9 9 10 10 10 10 4 3 14 10 8 10 10 4 10 10 10 10 10 3 2 2 7 4 5 7 10 10 10 10 9 10 10 2 9 4 4 2 10 9 10 10 8 8 7 10 6 10 5 10 9 2 10 10 10 6 14 5 9 10 13 2 10 10 10 10 6 - - 4 10 10 10 2 10 7 8 10 4 4 8 10 10 10 19 7 5 10 9 6 10 10 10 2 7 10 10 5 10 5 10 10 10 10 10 2 6 2.81 - 6 10 14 10 2 10 10 10 10 10 9 3 6 10 10 10 9 20 20 8 2 2 10 10 2 10 10 10 - 10 3 12 16 9 9 2 9 10 10 2 10 10 10 10 related with changes in mass and body seg- duration x speed). When we compared the mean hindlimb and forelimb stance values ment lengths. The camera speed utilized for all the film- across the animals, the maximum mean difings was 100 frame&. As in the cross-sec- ference for any animal at any age across all tional study, the filmed strides were divided speeds was 0.02 s. Furthermore, there was into “good and “no good categories based on no overall trend for one set of limbs to have the amount of movement exhibited by the greater values than the other. However, at animal on the treadmill belt. Good strides the slower speeds, there was a tendency for were ones during which the animal moved the hindlimbs to have slightly greater stance less than 2.5 cm on the belt (i.e., remained (and therefore lesser swing) values than the relatively “motionless”as the treadmill belt forelimbs. Since even these differences were moved beneath). No data from a particular slight, only hindlimb data will be presented trial were analyzed unless there was a mini- here. The compiled parameters were analyzed mum of two good strides, and a maximum of initially in two basic ways: 1)The parame10 strides were analyzed for a specific trial. Hildebrand (1966) gait diagrams were ters were ualitatively examined across age, constructed for each stride. The diagrams speed, an animals. 2) When appropriate, from the same trial (i.e., at the same speed on least squares regression equations were the same date) for each individual were then computed. As in our previous paper, we normalized and averaged (see Vilensky and computed these equations using both raw Patrick, 1984; Vilensky et al., 1988). The (untransformed) and logarithmically transaverage stride for each trial was then used to formed (transformed) data. Although we determine gait type, cycle (stride) duration, recognize the value in presenting the results and absolute stance and swing durations for from both approaches (Smith, 1984; Vileneach limb. Mean stance and swing duration sky et al., 1988), for most of the data in this values for the forelimbs and hindlimbs were report we only present the results from the also determined, as was stride length (cycle transformed equations because graphs of the 1 R G R G R G R c, - w W G W R G c, W R w W A B E RG A RG B RG C 2 B D RG E RG F A B Animal 3 C D E 'D A B C 4 D E F A B 5 C D E W, =walk; R, =run; G, = gallop: D, =diagonal sequence; L, =lateral sequence;T,=transverse gallop;RG, =rotary gallop; 0,=walking trot; B, =both (k., both diagonal and lateral sequence walking or running gaits, or both transverse and rotary galloping gaits). See Table 1 for the precise ages associated with the filming date code letters (A-F) for each animal. ' 2.81 2.58 2.28 1.99 1.72 1.44 0.62 0.89 1.17 Speed Ws) 1 C D TABLE 2. Gaits used at each speed and age' 432 J.A. VILENSKY ET AL. data were nonlinear. For these regression pooled (i.e., whether all the data could be equations, the correlation coefficient (r)and considered to be sampled from the same percent standard error of estimate values population) we used Neter and Wasserman's (%SEE)are also presented (Smith, 1984). (1974) General Linear Test approach. In addition to simple regression equations, RESULTS we also computed multiple regression equaGaits tions relating various parameters for each animal and for all the animals combined. To Table 2 presents the gaits used by each determine whether the data could in fact be animal at each age and speed using the basic 0 c 0.00 ! -0.3 I -0.2 -0.1 0.0 0.1 0.2 0.4 0.3 0.5 LOG MASS (kg) Fig. 1. Log-logplot of body mass vs. transition speed (lowest galloping speed) for all five animals. Symbols and regression lines corresponding to each animal are noted, as are the r values associated with each line. Solid - -0.2- A1 A A 2 ..... A3 7 A4 +A5 v z 0 c s 3 n -I W 0 > V z 0 c_ h e corresponds to the equation presented by Heglund and Taylor (19881, which is based upon a variety of differently sized mammals. -0.3-- ---.* r=.87 - .+-+:.:'-A.-...-- - -'*.' c'''L.' - - - -r=,5P_ ., y -,-$. - 0 . 4 - r -* _ _ _ _ _ _ _ ---i _ _ .... _ 3 .. I = : : L ~._....'.' .-+ _....... ......... r,..r - . -7- .,.=,..- ---; .=:.=:, v , ,, -o*5 _ l ...". ''' ~ r=.61 y- , , ' 0 l n 8z -0.6- / c 2 H e g l u n d a n d Taylor (1 988) c 3 2 -0.7- I 433 EFFECTS OF SIZE ON GAIT IN VERVETS terminology of Hildebrand (1966, 1977). Across the top of the table, each animal is listed with its filming date code letters (see Table 1).Across the side, speeds are listed, as well as walk, run, and gallop. The body of the table shows whether the animal walked, ran, or galloped a t that speed and age and, if so, the specific type of each gait used. For example, A1C used a lateral sequence walk at 0.62 m / s and a diagonal sequence walk at 0.89 m/S . Table 2 reveals that all of the animals except A4 used both diagonal and lateral sequence gaits during walking. Except for A1 (who galloped on only one occasion),running was used relatively infrequently. A5 was the only animal to use a walking trot, and A4 used only lateral sequence symmetrical gaits. Relative to asymmetrical gaits, Al, A2,and A3 used both rotary and transverse gallops while A4 and A5 used only transverse gallops. Figure 1depicts log-log plots of the lowest galloping speed (i.e., transition speed) vs. body mass for all of the animals, with the corresponding correlation coefficients and regression lines. The regression line relating the same two parameters from Heglund and Taylor's (1988) report for a wide variety of mammals is also shown (see Discussion). Although A3 and A4 exhibited good logarithmic relationships between body mass and transition speed, A2 and A5 did not (A1 galloped on only one occasion, and thus no 0.8T . regression line is shown.) Furthermore, at any particular body mass, the range of transition speeds was notable. Figure 2 presents a similar illustration of the relationship between cycle duration and mass at the transition speed. Again, a plot of the relevant equation from Heglund and Taylor (1988) is depicted. As is apparent, the relationship between these two parameters was highly inconsistent among the animals. Cycle duration Figure 3 depicts plots of speed vs. cycle duration for A5 at each age filmed. Plots for the other animals were similar. Over the speed range depicted, the relationship between speed and cycle duration is nonlinear. The r values for the data presented in this figure (transformed) ranged from -0.97 to -0.99. The r values of similar equations for all of the animals ranged from -0.95 to -0.99. Figure 3 also illustrates that for every increase in body size, there was a greater increase in the cycle durations at the slower speeds than at the faster speeds. This implies that, as an animal grows, the absolute value of the slope of the relationship between cycle duration and speed should increase. Accordingly, Figure 4 depicts the slopes of the log speed vs. log cycle duration equations, vs. body mass for each animal. The figure illustrates that the slopes (absolute value) are lower at the lower body masses; .---. .-..-. ..-.-.. \ E D . . . .. e-0 0.2 0.5 1 .o 1.5 2.0 C B A 2.5 3.0 SPEED (rn/s) Fig. 3. Plots of speed vs. mean cycle duration for A5. The different types of lines connecting the points correspond to successive ages (cf. Table 1). 434 J.A. VILENSKY ET AL. r\ 0 -0.2 0 W A3 a v, V A4 v) 0 v 9 a + A5 v n W A1 A A2 W r ' -0.41 + + v, A 0 0 1.o 0.5 1.5 2.0 2.5 3.0 MASS (kg) Fig. 4. Scatter plot of mass vs. the slope values from the log speed vs. log cycle duration equations for all five animals. The symbols corresponding to each animal are noted. 2.0 kg, the increases were minimal. Furthermore, in contrast to the slopes, all of the animals showed very strong individual relationships between the two parameters (r 3 0.91). The data described above suggest that, for any specific animal, speed may be predicted from cycle duration and mass. Accordingly, Table 3 presents multiple regression equations for each animal plus an equation based however, once a body mass of about 1.3 kg is reached, changes in slope relative to mass are not well defined. Because of this factor, only A4 and A5 had notable r values (r 2 10.841). Figure 5 shows the y-intercept values from the log-log cycle duration vs. speed regression equations, vs. body mass. The plot illustrates that, as body size increased, the intercepts also increased. However, above about CI 0 W -0.15 In v) ' -0.20 n 0 v -0.25 W u w z I -0.30 -0.35 W I 5 -0.40 Y v, 3 i- -0.45 T t ! = a t v+ + + v 0 v 0.5 A1 A A2 W A3 v A4 + A5 1.o 1.5 2.0 2.5 3.0 MASS (kg) Fig. 5. Scatter plot of mass vs. the y-intercept values from the log speed vs. log cycle duration equations for all five animals. The symbols corresponding to each animal are noted. 435 EFFECTS OF SIZE ON GAIT IN VERVETS TABLE 3. Multiple regression equations to predict speed (S) from mass (MI and cycle duration (CD)' Animal 1 2 3 4 5 Combined Equation r %SEE S = 0.25M .62CD-'.s4 S = 0.22M .53CD-2.04 S = 0.25M .38CD-2.13 S = 0.27M .39CD-'.99 S = 0.20M .49CD-".'8 S = 0.25M .44CD-2.02 0.99 0.97 0.99 0.97 0.97 0.97 7.2 12.1 8.9 10.7 12.7 11.5 'Speed is in m/s, mass in kg, and cycle duration in s. TABLE 4. Multiple regression equations to predict meed / S ) from age / A ) and cvcle duration (CDi' Animal Equation 1 2 3 4 5 Combined S = 0.26A .127CD-'.74 S = 0.12A *302CD-2.03 S = 0.17A .zozCD-2." S = 0.16A .195CD-2.00 S = 0.12A .267CD-2.21 S = 0.16A .224CD-1.9s r %SEE 0.97 0.97 0.98 0.97 0.97 0.97 12.6 12.1 9.6 11.0 12.0 12.8 'Speed is in m/s, age in months, and cycle duration in s. on the combined data for all of the animals. The r values indicate that the relationshi0 among the three parameters was very high. Similarly, because mass tended to be well correlated with age (r = 0.90 for all animals across all ages), equations with age substituted for mass also had high correlation coefficients (Table 4).Furthermore, because of the strong relationship between age and mass, the r value of the composite equations did not improve notably by using age and mass, as well as cycle duration, as independent variables. Hindlimb stance and swing durations Figure 6 depicts plots of hindlimb stance duration vs. speed for A5 at each age. The other animals had similar plots. These curves are very reminiscent of the cycle duration curves. In contrast, Figure 7 depicts hindlimb swing duration vs. speed for A5 at each age. None of the animals exhibited any consistent relationship between hindlimb swing duration and speed at any age. Figure 8 depicts mean hindlimb swing duration across all speeds for each animal for each date. The figure suggests a slight tendency for mean swing duration to increase with mass, although the variation at any particular mass is notable. Within animals, all except A5 exhibited good relationships (r b 0.79) between the two parameters. Stride length Figure 9 depicts stride length vs. speed for A5 at each age. As would be expected from the cycle duration data, stride length increased at almost every speed. Figure 9 also indicates that, at every age, this animal appeared to exhibit a linear relationship between stride length and speed. This was also true for all of the other animals at all ..--. .-..-. .-.-. ..-..c E D . .... B A U z E ,,, z1 0 $ 3I 0.3-- 0.2-- -- :. ,-I 4:; << -+-_- %- c 0.1 0.5 1.o 1.5 2.0 2.5 , 3.0 SPEED (rn/s) Fig. 6. Plots of speed vs. mean hindlimb stance duration. The different types of lines connecting the points correspond to successive ages (cf. Table 1). 436 J.A. VILENSKY ET AL. 0.26 em--. E *-..-. 0 .-.-. c 0.25 -0.24 -- ...... 0.23 -- h / ' \ , / B '.:- . ___---0 0.22 -0.21 -- 0.20 -- 0.190.18-- 0.17-- 0.16 ! 1.o 0.5 1.5 2.0 2.5 i 3.0 SPEED (rn/s) Fig. 7. Plots of speed vs. mean hindlimb swing durations for A5. The different types of lines connecting the points correspond to successive ages (cf. Table 1). v A v v +O A -i 6 rY 3 0 0.22 c3 z 0.21 t m a W * . I D v + A A 4 * A Z f 0.18 0.5 1.o 1.5 2.0 2.5 3.0 MASS (kg) Fig. 8. Scatter plot of mass vs. mean hindlimb swing duration for each animal across all speeds a t each age. Symbols corresponding t o each animal are noted. ages. Specifically, the lowest r value for the linear relationship between stride length and speed for any animal at any age was 0.97. Similar-sized comparisons In an attempt to reveal if variation in the length of a hindlimb segment could explain some of the observed variation in the temporal parameters at identical speeds among similar-"sized (in terms of total body mass) animals, Table 5 presents temporal and hindlimb segment length values for four of the animals (A4 twice) a t a similar overall body mass (1.25-1.33 kg) and at the same two speeds. This mass range and the two selected speeds were chosen to maximize the amount of data presentable in such a table. Clearly, a t the faster speed (2.81 d s ) limited variability among the temporal parameters precluded a meaningful comparison. At 1.17 mls, A5's temporal parameters were notably low (especially cycle duration). However, this difference was not intuitively related to 437 EFFECTS OF SIZE ON GAIT IN VERVETS 1.10- .---. c 1 .oo -- 0.90v F 0 5 1 0.80-- 0.700.60-- tY F ~1 0.50- 0.40-0.30 ! :/ 0.5 1.o I 2.0 1.5 3.0 2.5 SPEED (m/s) Fig. 9. Plots of speed vs. mean stride length for A5. The different types of lines connectingthe points correspond to successive ages (cf. Table 1). TABLE 5. Comparison of temporal and hindlimb segment parameters among animals (1.25-1.33 kg) at 1.17 and 2.81 m / s l 2.81 m/s 1.17 m / s Animal CD ST sw CD 1 2 4 4 5 0.48 0.49 0.47 0.47 0.43 0.27 0.31 0.27 0.28 0.26 0.21 0.19 0.19 0.20 0.18 0.34 0.33 0.33 0.34 - similar mass Body parameter (cm) KH FL ST - sw TL - 0.14 0.12 0.13 0.21 0.22 0.21 0.22 10.2 8.5 11.1 12.2 10.2 0.13 of 10.8 9.4 11.0 12.1 10.4 9.5 8.7 9.6 10.0 9.6 'CD, cycle duration; ST,hindlimb stance duration; SW, hindlimb swing duration; TL, thigh length; KH, knee height; FL, foot length. the variation in any of the values of the three listed hindlimb segment lengths. Comparisons of cross-sectional and longitudinal data The composite equation to predict speed from mass and cycle duration (Table 3) can be directly compared with the similarly derived equation -presented in our cross-sectional study: S = 0.26M0.5CDp1.96 . The equations are remarkably similar. For example, for a 2.00 kg animal with a cycle duration of 0.5 s, the equations give results of 1.38 and 1.43 d s . Despite the similarity between the two equations, it is evident from the individual equations presented in Table 3 that there were differences among the animals. Accordingly, a test for equality among the transformed versions of the individual equations led to rejection of the null hypothesis (equality among the planes associated witheachequation: P < 0,001).Asimilar test of the equations presented in Table 4 (using age instead of mass) produced identical results. Thus, although the composite equations presented here and in our earlier paper appear to be valid for vervets as a population, individual animals may deviate significantly from the population mean. In an attempt to determine whether the differences among the individual animals were due more to differences in swing durations than stance durations, we computed multiple regression equations to predict speed from mass and hindlimb stance duration (Table 6). Again, we tested for equality among the transformed versions of the equations. The results were identical. Thus, the animals differed among themselves in their relationships between speed, mass, and 438 J.A. VILENSKY ET AL. TABLE 6. Multiple regression equations to predict speed (S) from mass (MI and hindlimb stance IHST) duration' Animal 1 2 3 4 5 Combined Equation S = 0.24M S = 0.24M S = 0.26M S = 0.27M S = 0.24M S = 0.25M .464HST-1.'0 .324HST-'.'5 .zs'HST-'.'5 .3z1HST-'.M .393HST-'.0' .380HST-1.11 r %SEE 0.99 0.99 0.99 0.99 0.99 0.99 5.0 5.6 6.0 7.1 6.4 6.7 'Speed is in m/s, mass in kg,and hindlimb stance duration in s. stance duration as well as between speed, mass, and cycle duration. DISCUSSION Much of the longitudinal data reported here are consistent with those from our earlier cross-sectional analysis (Vilensky et al., 1988). As was found in that study, neither body size nor speed appears to account completely for gait choices among vervets. Vervets appear quite capable of using either diagonal or lateral sequence symmetrical gaits a t all walking speeds and at all the stages of development examined. However, the data do support the view of an overall preference for diagonal sequence symmetrical gaits, although individual animals may prefer the lateral sequence (e.g., A4). Relative to asymmetrical gaits, individual preferences were again evident (e.g., A4 and A5's exclusive use of transverse gallops), although as a group both transverse and rotary gallops were used. In contrast to the earlier report, the current data do not indicate a preference among younger animals for transverse rather than rotary gallops. One very interesting observation revealed by the gait data is the paucity of running gaits among the animals that regularly galloped (all but Al). Running is defined as a symmetrical gait in which stance duration equals less than 50% of cycle duration (Hildebrand, 1966). Rather than run, vervets appear to prefer to switch directly to a gallop. This corresponds to the fact that primates tend to shift to a gallop at a higher cycle duration than other similarly sized mammals (cf. Fig. 2; Vilensky, 1987). In contrast to cycle duration, the vervets, as a group, tended to switch to a gallop a t the speeds predicted from the Heglund and Taylor (1988)equation (Fig. 1).However, within the group, body mass alone was not a very good predictor of transition speed. Accord- ingly, at any particular body mass value, the range of transition speeds was notable. Thus, although the Heglund and Taylor equation is probably accurate across mammalian species of widely differing body sizes, it is again suggested (Vilensky et al., 1988) that the notion of Stein et al. (1986) of a transition speed zone is more appropriate for a particular individual than that of a consistent transition speed that is solely dependent on body mass (Heglund et al., 1974; McMahon, 1984). One goal of measuring the animals subsequent to each filming was to investigate whether changes in the temporal parameters during growth were more highly correlated with a particular measurement (e.g., thigh length) than with overall body mass. Unfortunately, within individuals, segment lengths were so well correlated with body mass that it was impossible to separate the effects caused by changes in segment length from those caused by changes in overall body mass. Furthermore, as exemplified by Table 5, even at nearly identical body masses the variation in temporal parameters was not associated clearly with differences in hindlimb segment lengths among the animals. The r values associated with the multiple regression equations indicate that speed can be extremely well predicted (regardless of gait) for any particular individual based on mass (or age) and cycle (or stance) duration. Nevertheless, the relationships among these variables are sufficiently labile among individuals to preclude using the same equation for every individual within the population. These differences in the equations are especially noteworthy considering that the animals were genetically related. Furthermore, even animals that were very similar in the overall range of body mass values (e.g., A1 and A3) had notably different equations. Thus it does not appear that our results are due to the animals not all being similarly sized when we began the study. Based on these findings, we must rescind our prior suggestion (Vilensky et al., 1988) that the equations we presented would be useful in field situations to predict a specific animal's speed. Rather, the value of these equations seems now to be more for comparisons across species than within species. This investigation demonstrates that each individual vervet monkey appears to utilize a uni ue relationship in determining precisely ow it will use its limbs to generate the R EFFECTS OF SIZE 01N GAIT IN VERVETS propulsive forces necessary to achieve locomotion across increasing speed and increasing size (i.e., growth). The factors that govern this relationship may be neurological, psychological, and/or morphological. Clearly, however, there is no one optimal solution for all the animals of a particular species. ACKNOWLEDGMENTS We are grateful to Mr. G. Duncan and Ms. P. Wilson for assistance during filming, to Ms. J. Kettelkamp for analyzing some of the data, to two anonymous reviewers for constructive comments on the original version of this paper, and to Ms. D. Jackson for typing the many drafts of the manuscript. Funds for this study were supplied by the Indiana University School of Medicine. LITERATURE CITED Heglund NC, and Taylor CR (1988) Speed, stride frequency and energy cost er stride: How do they change with body size and gaitfJ. Exp. Biol. 138:301-318. Heglund NC, Taylor CR, and McMahon TA (1974) Scaling stride frequency and gait to animal size: Mice to horses. Science 186:1112-1113. 439 Hildebrand M (1966) Analysis of symmetrical gaits of tetrapods. Folia Biotheor. 6:9-22. Hildebrand M (1977) Analysis of asymmetrical gaits. J. Mammal. 58: 1 31-156. McMahon TA (1984)Muscles, Reflexes and Locomotion. Princeton, NJ: Princeton University Press. Neter J , and Wasserman W (1974) Applied Linear Statistical Models. Homewood, IL: Richard D. Irwin, Inc. 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