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Effects of size on Vervet (Cercopithecus aethiops) gait parameters A cross-sectional approach.

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AMERICAN JOURNAL OF PHYSICAL ANTHROPOLOGY 76:463-480 (1988)
Effects of Size on Vervet (Cercopithecus aethiops) Gait
Parameters: A Cross-Sectional Approach
JOEL A. VILENSKY, EVA GANKIEWICZ,AND DOUGLAS W.
TOWNSEND
Department of Anatomy, Indiana University School of Medicine ( J A V . ,
E.G.) and Department of Mathematical Sciences, Indiana-Purdw
University at Fort Wayne (D.W.T.),Fort Wayne, Indiana 46805
Primate locomotion, Allometry, Elastic similarity,
KEY WORDS
Dynamic similarity
ABSTRACT
A comparison of the values of certain temporal and spatial
locomotor parameters was made among ten different-aged (sized) vervet monkeys locomoting at nine identical speeds. Cycle and stance durations decreased
across speed for all the animals; at any one speed both parameters also varied
directly with body size. Stride length increased with speed for all the animals
and was greater in the larger animals. Swing duration and hindlimb support
length tended to be relatively consistent for each animal across speed, but varied
among the animals directly with body size. Hindlimb duty factor decreased with
speed for any one animal but showed no direct correlation with size. Hindlimb
angular excursion also showed no correlation with size, nor did it show a simple
relationship with speed. In terms of gaits and gait transitions, the data indicate
that vervets use a very wide variety of gait types, which are not easily correlated
with speed or body size. Furthermore, the data suggest the existence of a rungallop transition zone of speeds for these animals, rather than the existence of
a specific transition speed. Finally, the data were used to test intraspecifkally
the elastic and dynamic similarity models, both of which predict how locomotor
parameters will change with size in animals. The results are generally consistent
with the dynamic model.
In an earlier paper (Vilensky and Gankiewicz, 1986) we presented a preliminary
report on the effects of size on specific gait
parameters in vervets based on four different-aged (sized) animals locomoting at identical speeds. In the present report we greatly
expand on that paper by including more
animals (n = 10) and an additional parameter (hindlimb angular excursion). Furthermore, this report is the first of a pair that
will use similar methodologies to study the
effects of size on vervet locomotor behavior
from both cross-sectional and longitudinal
perspectives. That is, the animals used in
the present study are also part of a longterm ontogenetic investigation of the effects
of size on gait parameters within individuals.
The rationale for the present study is similar to that advanced in the earlier paper.
Specifically, although the relationship between body size and locomotor behavior in
0 1988 ALAN R. LISS, INC.
primates, as well as in other taxa, has been
studied previously (cf. Alexander and Jayes,
1983; Jungers, 1985a), these studies have
been almost entirely interspecifk. Thus there
are few data for single species other than
Homo sapiens detailing how locomotor parameters change with size. Such data are
important for understanding how young
(small) animals match the speeds of adult
(large) animals during travel. Additionally,
intraspecific studies eliminate the need to
consider the morphological and ecological
differences among species in determinations
of the effects of size on locomotor behavior.
Received May 22, 1987; accepted January 12,1988.
Address reprint requests to Joel A Viler&, Ph.D., Fort Wayne
Center for Medical Education, 2101 Coliseum Boulevard East,
Fort Wayne, IN 46805.
464
J.A. VILENSKY ET AL
Accordingly, in this report we test our data
against the most common models that predict how size affects locomotor parameters
(cf. Alexander and Jayes, 1983; Heglund et
al., 1974; McMahon, 1975, 1984).
MATERIALS AND METHODS
Some basic characteristics of the animals
used in this study are presented in Table 1.
The animals were assigned numbers based
on increasing body mass. All of the animals
except Nos. 7, 9, and 10 were born in captivity, and exact birth dates are known. All
are female except Nos. 1and 10. We did not
consider sex to have a specific effect on locomotor parameters, and thus we did not
segregate the males’ data from those of the
others. The lack of a gender effect on locomotor charcteristics of vervets has been previously documented (Hurov, 1979). Of the
animals listed in Table 1, Nos. 4, 5, 7, and
9 were the ones used in our prior study (Vilensky and Gankiewicz, 1986).However,none
of the data are identical for both studies (i.e.,
different filmings were used for the animals
in the two studies).
Each of the monkeys was trained to locomote on a motor-driven treadmill (1.17 m
x 0.43 m belt) that was enclosed in a Plexiglas cage. Food rewards were used to encourage the animals to locomote at nine
different speeds between 0.62 and 2.81 d s
(Table 2). Training sessions consisted of daily
10-20-min periods. Once an animal’s performance was satisfactory, it was maintained with twice weekly “maintenance”
sessions. Satisfactory performance entailed
the animal remaining in a relatively stationary position as the treadmill belt moved
at the different speeds.
Each animal was initially filmed when
training was completed. For all animals except Nos. 9 and 10, each was subsequently
filmed a t 6-month intervals until adulthood
was reached (for some animals this process
is still continuing). The filmings consisted of
10-20-s episodes at each of the nine speeds.
For the animals born in our laboratory (Nos.
1,2, and 4), training was begun at 3 months
of age. For the other animals, training usually began shortly after their arrival at our
lab. For the present study, the longitudinal
data from all the animals were scanned to
obtain data from all ten animals that were
relatively complete, and represented as diverse an assortment of body sizes as possible.
Thus the data from the animals were obtained over a number of filming dates.
Within a week subsequent to each filming
session, each animal filmed was anesthesized and measured. Specifically, the following measurements were determined (cf.
Schultz, 1929): mass, sitting height, trunk
height, thigh length, knee height, leg length,
foot length, upper arm length, forearm length,
and hand length.
The camera speed utilized for all the filmings was 100 frameds. This speed was verified by an internal timing device that marked
the film at 0.01-s intervals. Following processing, the films were analyzed by first dividing each trial into “good” and “no good
strides (left hindfoot contact to the subsequent left hindfoot contact constituted a
stride). Good strides were those in which the
animal’s rump moved no more than 2.5-cm
actual distance (i.e., the animal remained in
approximately the identical location as the
treadmill belt moved underneath it). This
process inherently reduced the number of
strides available for analysis, but it assured
that during good strides each animal’s limb
movements were highly comparable to those
that would have been used if the animal had
been locomoting overground at the speed
displayed on the treadmill speedometer. A
maximum of ten good strides was used for
analysis within any single trial (cf. Table 2);
no trial was analyzed unless a minimum of
two good strides was available.
Hildebrand (1966)gait diagrams were constructed for all the good strides. The diagrams from each trial were then normalized
and averaged, using the methodology described by Vilensky and Patrick (1984).This
procedure permitted the computation of an
average stride for each individual at each
speed. As is apparent from Table 2, at certain speeds some animals displayed more
than one type of gait. In these instances, the
Hildebrand gait diagrams were classified
prior to averaging and grouped accordingly.
Thus, for some animals a t some speeds, two
average strides were computed. Each of the
average strides was used to determine two
overall stride characteristics, gait type and
cycle (stride) duration, and two parameters
for each of the four limbs-absolute stance
and swing durations. Manipulation of these
data and the measurement data allowed
computation of the following additional parameters: mean forelimb and mean hindlimb stance and swing values; hindlimb and
forelimb duty factors (mean hindlimb or
forelimb stance durations + cycle duration);
stride length (cycle duration x speed); relative stride length (stride length + sitting
465
EFFECTS OF SIZE ON VERVET GAIT
TABLE 1. Sex, age, mass, sitting height, and hindlimb length of the animals
Animal No.
1
2
3
8
9
10
Sex
Age
Mass (kg)
Sitting height (cm)
Hindlimb length fcm)
M
F
F
F
F
F
F
F
F
4 mo
5.5 mo
9.5mo
22.5 mo
17.5 mo
30.5 mo
Adolescent
31.5 m o
Adult
Adult
0.71
0.84
1.13
1.33
1.56
1.84
1.90
2.07
2.61
4.10
27.0
27.0
31.0
33.4
36.8
38.1
38.0
38.9
41.2
48.5
16.6
17.1
20.4
24.3
21.9
25.8
24.4
26.5
27.1
32.1
M
height);l hindlimb support length (mean
hindlimb stance duration x speed); and relative hindlimb support length (hindlimb
support length + sitting height).
In addition to the above measurements,
we also determined the angular excursion of
the hindlimb of each animal at each speed.
This was ascertained by first projecting the
touchdown frame of the right hindfoot (the
right limb was closer to the camera) on a
rear-projection screen and determining the
inclination of a line connecting the estimated positions of the hip joint and the most
distal point on the foot. Next, the film was
advanced to the frame correspondingto right
hindfoot lift-off, and the inclination of a line
between the same two points was similarly
determined. Finally, hindlimb excursion was
then measured as the angle between the two
lines. Where possible, the described procedure was done for three strides at each speed.
These strides were chosen based upon their
closeness in terms of cycle duration to the
mean value for all the strides at that speed
and gait. The values for the three (or in the
cases where only two good strides were
available, two) strides were averaged; thus
a mean hindlimb angular excursion was determined for each animal at each speed for
which good strides were available.
The data were analyzed in two basic ways.
1) The parameters were qualitatively ex-
amined across speed and across size. 2) Where
appropriate, least squares regression equations were computed.2 We computed these
equations using both raw (untransformed)
and logarithmically transformed (transformed)data. Utilization of transformed values to compute the equations, in addition to
having strong historical precedent, generally resulted in a better fit. Furthermore, the
slope values of log-log equations are useful
because they indicate proportional changes
with size independent of scale. Thus, how a
trend compares with geometric similiarity
can be immediately ascertained (Smith,
1984). Despite these benefits, Smith (1984)
also described the misinterpretations that
can result from the use of transformed data
in regression equations. Because of these potential misinterpretations and because the
regressions equations using our raw data
generally also had high correlation coeficients, we chose to present the coefficients
from both sets of equations in this paper.
As part of our presentation of the regression coefficients, the standard errors of estimate (SEE)for the untransformed equations
and the percent standard errors of estimate
(%SEE) for the transformed equations are
listed. For the transformed equations, the
%SEE reveals the percentage range within
which 68% of the sample would fall for a
normal distribution of residuals (e.g., for a
'Consistent with our 1986 paper, we use relative stride length
to refer to the value determined by dividing absolute stride length
by sitting height. This is contrary to the definition of Alexander
and Jayes (1983) who consider relative stride length equal to
stride length divided by hip height. Our utilization of sitting
height as the denominator is based on the fact that sitting height
is clearly a better measure ofoverall body size than height, which
varies in different animals (e.g., plantigrade vs. digitigrade) and
with different joint angles.
There are differences of opinion as to which regression technique is most appropriate for allometric analyses. We have chosen,based on the rationale presented by Draper and Smith (1981)
and Jungers (1985b),to use the least-squares technique (model
I cf. Soh1 and Rohlf, 1981) rather than one of the model I1
techniques (major axis, reduced major axis, and Barlett's threegroup). Furthermore, because conclusions in the present study
are made only when correlation coefficients are high, use of any
of the regression techniques should have produced similar results
(Jungers, 198513).
J.A. VILENSKY ET AL.
%SEE of 5.0, 68%of the cases would lie between lines representing 95% and 105% of
the regression line; cf. Smith, 1984).
In addition to examining the parameters
themselves and utilizing regression techniques, the data were manipulated in appropriate ways to test the elastic and dynamic
similarity models regarding the effects of increasing size on locomotor parameters (in
Discussion).
RESULTS
i-
,g
C
a
Gaits
Table 2 depicts the number of strides analyzed and the specific gaits (Hildebrand,
1966)used by each subject at each speed.
Clearly, a wide variety of gaits was used
across the animals and across speeds. Unfortunately, neither body mass nor speed (nor
both together) can fully account for the gaits
employed. For example, animal No.4 exhibited only lateral sequence gaits before galloping at 1.44d s , while No.7 chose to use
only diagonal sequence gaits at the slower
speeds. Similarly, animal No. 8's use of runs
rather than gallops a t the higher speeds was
surprising.
In addition to inconsistent gait choices,
Table 2 also indicates various run-gallop
transition patterns. Intuitively, it would be
expected that smaller animals would gallop
at slower speeds than larger animals. It is
apparent from Table 2 that this is not always
the case. Furthermore, Figure 1 depicts a
plot of log transition speed (using lowest galloping speed) for each animal vs. log body
mass. Although the regression line indicates
Lo
z
2c
10
,200
0
2
150
1004
200
000
200
400
600
LOG MASS (KG)
Fig. 1. Plot of log body maas vs. log run-gallop transition
speed (lowest galloping speed; 1.72 m/s was used for animal No. 3) for all the animals that exhibited this transition.
467
EFFECTS OF SIZE ON VERVET GAIT
.9
.-.-._.#10
s
i
i
i
#9
---#8
..........#7
.8
-#6
---- # 5
--
-
84
---# 3
.7
___ # 2
- - - - #1
m
Z
2!I-
4,
.6
3
n
2
y1
U
>
u
r
.-
Z
2
z
1
{/,
I
,
,
,
,
,
, ,
.62 .89 1.17 1.44 1.72 1.99 2 . 2 8 2.58 2.81
SPEED ( M I S )
Fig. 2. Plot of speed vs. mean cycle duration for each of
the ten monkeys. The lines were drawn by connecting the
points corresponding to the mean cycle duration values
recorded for each animal at each speed for which data
were available. If a galloping and non-gallopingvalue were
available for a particular speed, only the galloping value
was plotted. The m w s indicate the lowest galloping speed
(run-gallop transition speed) for each animal.
a positive trend, the r value is poor (0.411,
and the spread is large (%SEE = 18.3).Computation of a n equation using raw values
resulted in a n even poorer fit (r = 0.31;
SEE = 0.34). It is noteworthy that five of
the animals exhibited a range of transition
speeds, where both gallops and runs were
exhibited. For example, animal No. 10 used
both runs and gallops between 1.72 and 2.28
d s . These animals thus appear to have the
potential to use symmetrical or asymmetrical gaits over a considerable range of speeds.
Cycle duration
Figure 2 depicts lines connecting the values corresponding to the mean cycle durations for each of the animals a t each speed.
For those speeds a t which both a symmetrical (non-gallop) and asymmetrical (gallop)
gait were recorded, the plotted values are
only for the latter. The minimum correlation
coefficient (absolute value) and maximum
SEE/%SEE value associated with the regression equation between speed and cycle duration for any particular monkey were: raw:
0.89, 0.068; transformed: 0.98, 5.7%. Obviously, an individual’s cycle duration is almost totally dependent on speed.
Furthermore, the higher r values for the
transformed equations suggest that cycle
duration decreases exponentially as speed
increases.
To determine how size influenced the cycle
duration vs. speed relationship, regression
equations between body mass and the y intercept and slope values from each individual monkey’s speed vs. cycle duration
equation were computed. The computation
based on the raw data resulted in a good
correlation coefficient (0.88) and a low estimate error for the intercepts (0.054). No significant relationship for the slopes was found.
A similar set of equations using the transformed data revealed a slightly higher correlation (0.911, while the %SEE equaled 6.7.
Again, no significant relationship for the
slopes was found.
The mean slope value for all the animals
( k 1SD) equaled -0.17 5 0.04 (raw) and
-0.49 2 0.07 (transformed). Thus all the
animals tended to reduce cycle durations at
the same rate with increased speed (in raw
terms, 0.17 s per d s ) ,but the larger animals
tended to have larger cycle durations than
the smaller animals a t identical speeds.
The above findings suggest that an animal’s speed is highly predictable if its cycle
duration and body size are known. We tested
this hypothesis by generating a multiple
regression equation using speed as the dependent variable and cycle duration and body
mass as independent variables in one case
and cycle duration and sitting height as independent variables in a second case. In both
cases the probabilities associated with all F
values were less than 0.0005. The actual
equations are:
Linear
Power
S=0.329M-5.039CD+3.479
(r = 0.90; SEE = 0.316)
S=0.26M05 CD
(r=O.98; %SEE=10.4)
S=0.054SH-5.045CD+2.128
S=0.0022SH’412CD-’’’’
(r=O.98; %SEE=11.2)
(r = 0.91; SEE = 0.230)
S
=
(s);
speed (mh); M = body mass (kg);CD
= sitting height (cm).
SH
=
cycle duration
468
J.A. VILENSKY ET AL
These equations (especially,the power equations) may be useful in field studies of vervets where speed is extremely difficult to
determine accurately while cycle duration
and mass or sitting height might be less so.
We would caution, however, that these equations are probably not accurate at very fast
galloping speeds when changes in cycle duration are minimal.
Also in Figure 2, arrows indicate the rungallop transition speed (lowest galloping
speed) for each animal. In general, there is
no marked change in the slope of the lines
at this transition. Furthermore, there was
relatively little variation among all the animals regarding their cycle durations at the
run-gallop transition. Specifically, the mean
cycle duration at the transition to galloping
was 0.42 s, with a standard deviation of
0.05 s (for animal No. 3, an intermediate
value between the cycle durations at 1.44
and 1.99 d s was used in the computation).
These results suggest that the value for cycle
duration at the run-gallop transition within
a species may not vary greatly with body
size. Accordingly, the correlation coefficient
at the run-gallop transition speed between
cycle duration and body size was not significant using either raw or transformed data.
To determine the effect of size on cycle
duration at specific fured speeds, regression
equations were computed between body mass
and cycle duration at each of the speeds used
in this study (Table 3). Clearly, the correlation coefficients were strong at all speeds
for both the raw and transformed equations,
and the SEE and %SEE values were low.
Additionally, as speed increased, both the
slope and the intercepts generally decreased. Interestingly, at 2.28 m/s both the
raw and transformed slopes reached their
lowest value and remained at that value
across the final two speeds. Finally, the slope
values shown for the transformed data are
all less than one, indicating that the ratio
between the body masses of two animals of
different sizes will be greater than the ratio
between their cycle durations at any speed
(assuming the larger animal's mass is the
numerator).
Fore us. hindlimb stance and swing values
The mean value of the absolute differences
between the fore and hindlimb stance and
swing values for all the animals across all
the speeds was approximately 0.01 s (i.e.,
one frame of film). Since this difference was
so small, and because there was no overall
trend for one set of limbs to have greater
value than the other, the forelimb data will
not be discussed below. It should be noted,
however, that at the slower speeds there was
a tendency for the differences to be greater
than at the faster speeds; when differences
were apparent at these speeds, the hindlimb
stance values were almost always greater
than the forelimb stance values (and vice
versa for the swing values).
Hindlimb stance duration
As with cycle duration, regression equations of speed vs. hindlimb stance duration
were associated with high correlation coefficients and low estimate errors for each animal (minimum r, maximum SEE/%SEE:
raw, 0.91,0.063;transformed, 0.99,7.4).Also
as with cycle duration, correlation coefficients were computed between body mass
and the slope and y intercept from each animal's speed vs. hindlimb stance duration
equation. Body mass was fairly well correlated with the y intercepts using raw data
(r = 0.86; SEE = 0.044). No significant relationship was found for the slopes. Transformed values had better results for the
intercepts (r = 0.98;%SEE = 3.3),and again
no significiant relationship for the slopes.
The mean slope values and the associated
standard deviations from all the body mass
vs. hindlimb stance duration equations
equaled -0.17 5 0.03 (raw) and -0.90
k 0.05 (transformed). These findings indicate that hindlimb stance duration tended
to decrease across speed at a similar rate,
regardless of body size, although a specific
animal's value at a set speed depended principally on some aspect of its mass. The untransformed slope value of this decrease is
the same as that found for cycle duration,
0.17 s per d s . Table 3 depicts the regression
coefficients for the raw and transformed
equations between body mass and hindlimb
stance duration at specific speeds. The depicted r values indicate that differences in
body mass account for most of the variation
in stance duration at all the tested speeds.
Furthermore, as speed increased, the y intercepts and slopes of the equations based
on the raw data clearly decreased. For the
eauations based on transformed data. the
s6pe values showed an initial increase followed by a subsequent decrease, while the
EFFECTS OF SIZE ON VERVET GAIT
intercepts consistently decreased, except
across the last two speeds.
Hindlimb swing duration
For hindlimb swing duration, only two of
the animals (Nos. 3 and 6) showed significant correlation coefficients (P < 0.05) between this parameter and speed using raw
data. A negative correlation coefficient also
was shown by No. 6, using transformed data.
Thus, in general, there was no overall relationship between hindlimb swing duration
and speed. There was, however, a positive
relationship (raw: r = 0.90, SEE = 0.012;
transformed: r = 0.91, %SEE = 5.2) between the mean hindlimb swing duration for
each animal across all speeds and body mass.
Thus larger animals had longer overall hindlimb swing durations. The mean swing durations ( 2 1SD) in seconds across all speeds
for each animal equaled: No. 1,0.203 & 0.013;
No. 2, 0.185 t 0.010; No, 3, 0.21 -t- 0.024;
No. 4, 0.219 2 0.012; No. 5, 0.211 -+ 0.008;
No. 6, 0.226 2 0.026; No. 7, 0.251 0.018;
No. 8, 0.226 2 0.012; No. 9, 0.247 ? 0.005;
and, No. 10, 0.269 2 0.013.
Table 3 depicts the regression coefficients
for the relationship between hindlimb swing
duration and body mass at each speed. As
would be expected from the above, the r values were generally good at most speeds. The
slope and y intercept values of the equations
based on raw data remained consistent across
speeds. The slope values from the transformed equations varied unsystematically
across speeds, while the intercepts remained
virtually constant.
*
469
0.024 at 0.62 d s ; 0.637 ? 0.016 at 0.89 ml
s; 0.589 f 0.023 at 1.17 d s ; 0.528 2 0.045
at 1.44 mls; 0.481 f 0.039 at 1.72 mls; 0.440
2 0.034 at 1.99 d s ; 0.423 2 0.026 at 2.28
mh; 0.389 -c 0.025 at 2.58 d s ; and, 0.383
k 0.015 at 2.81 d s .
Stride and hindlimb support length
Because stride length is totally determinable from cycle duration and speed (i.e., stride
length = cycle duration x speed), it will not
be discussed in detail here. Briefly, as would
be expected, stride length was longer in the
larger animals, and the parameter increased
with speed. Interestingly, regression equations using raw values had correlation coefficients equally as high as transformed ones
for the relationship between stride length
and speed for the animals. Because in some
field situations stride length might be easier
to measure than cycle duration, we computed the following equations in order that
speed could be predicted using stride length,
rather than cycle duration, as an independent variable. In both cases, the probabilities associated with all F values were less
than 0.0005. The equations are:
S= -0.344M 3.915SL- 0.533
(r = 0.97; SEE = 0.16)
Linear
Power
S=3.78M-0473SL'
(r = 0.96; %SEE= 10.0)
s=-0.054SH+3.96dSL+0.772
(r=0.95; SEE=0.17)
S= 368.55SH-1-345SL1889
(r=O.96; %SEE=11.0)
+
SL
=
stride length (m).
Similar to stride length, hindlimb support
length is also fully determinable from temporal data (i.e., hindlimb support length =
Hindlimb duty factor
hindlimb stance duration x speed). This
As would be predicted from the previous parameter tended to remain relatively confindings for cycle and stance durations, there stant across speed, although all but one anwere strong negative relationships and low imal showed their lowest value at .62 d s .
error values between duty factor and speed Four of the animals also showed their highfor each of the animals across speed (mini- est support length values at their highest
mum r, maximum SEE/%SEE: raw, 0.90, speeds. Across animals, support length var0.057; transformed, 0.96, 7.6). A test for cor- ied directly with body size and was signifirelation between the y intercepts of the in- cantly correlated (raw and transformed) at
dividual regression equations (between duty all speeds.
To depict the stride and support length
factor and speed) and body mass indicated
no significant correlation, as did a test be- characteristics of the group relative to speed,
tween the slopes and body mass. Further- Figure 3 shows the mean relative stride and
more, it is apparent from Table 3 that the hindlimb support length ( & 1SD) values at
relationship between hindlimb duty factor each speed for all the animals. Mean relative
and body mass was poor at all speeds. The stride length clearly increased linearly with
mean duty factor values ( Ifr 1SD) for all the speed. Furthermore, the variability in this
monkeys at each speed equalled: 0.690 2 parameter also increased with speed. Intu-
0.09
0.09
0.08
0.07
0.06
0.05
0.04
0.04
0.04
m+
0.28
0.29
0.28
0.26
0.26
0.22
0.21
0.21
0.21
0.62
0.89
1.17
1.44
1.72
1.99
2.28
2.58
2.81
-0.47
-0.50
-0.50
- 0.35
- 0.39
- 0.43
- 0.44
-0.28
- 0.20
Y'
0.56
0.45
0.38
0.35
0.32
0.32
0.31
0.29
0.28
*Based on raw data.
'Based on transformed data.
m = slope; y = y intercept; r
0.62
0.89
1.17
1.44
1.72
1.99
2.28
2.58
2.81
m*
(ds)
Speed
=
0.06
0.04
0.03
0.02
0.02
0.02
0.02
0.03
0.02
%SEEt
6.9
3.8
4.2
4.7
4.0
4.7
5.7
6.2
4.2
SEE*
mass
0.07
0.06
0.05
0.05
0.04
0.03
0.02
0.02
0.02
mi
0.30
0.31
0.33
0.37
0.34
0.32
0.25
0.26
0.24
=
0.93
0.95
0.94
0.90
0.91
0.93
0.94
0.94
0.98
r'
0.94
0.99
0.97
0.91
0.93
0.96
0.96
0.98
0.99
0.04
0.02
0.02
0.02
0.02
0.01
0.01
0.01
0.004
%SEEr
6.4
2.8
5.0
9.4
7.6
5.4
3.0
2.8
1.4
=
0.02
0.03
0.02
0.02
0.02
0.02
0.02
0.01
0.02
m'
0.20
0.24
0.20
0.17
0.19
0.13
0.17
0.12
0 19
0.03
0.02
0.01
0.02
0.02
0.02
0.02
0.02
0.01
%SEEt
11.7
6.7
6.7
7.9
7.9
7.9
8.9
10.2
6.4
percent standard error of estimate
~
0.20
0.51
0.82
0.18
0.18
0.90
0.85
0.19
0.85
0.18
0.20
0.79
0.73
0.20
0.20
0.58
0.18
0.90
y'
rt
-0.68
0.70
-0.70
0.90
-0.70
0.87
-0.68
0.76
-0.69
0.82
-0.66
0.67
-0.67
0.65
-0.69
0.58
-0.69 - 0.86
Body mass vs.
hindlimb swing duration
m*
y*
r*
SEE*
standard error of estimate; %SEE
-0.85
-0.92
-0.92
- 0.37
- 0.49
- 0.59
- 0.69
- 0.77
- 0.82
Y'
0.37
0.28
0.21
0.17
0.14
0.13
0.13
0.11
0.11
Body mass vs.
hindlimb stance duration
m*
y*
r*
SEE*
Y'
mT
0.02
0.02
0.05
0.11
0.08
0.10
0.03
0.05
0.03
-0.17
-0.20
-0.24
-0.31
-0.34
-0.38
-0.39
-0.42
-0.43
0.67
0.62
0.57
0.48
0.45
0.41
0.42
0.37
0.37
0.43
0.60
0.55
0.50
0.42
0.49
0.11
0.40
0.29
r'
0.30
0.50
0.65
0.63
0.50
0.65
0.22
0.39
0.38
0.02
0.01
0.02
0.04
0.04
0.03
0.03
0.03
0.02
%SEE'
3.5
2.1
3.3
7.6
8.4
6.4
6.4
6.9
4.2
Body mass vs.
hindlimb duty factor
y*
r*
SEE*
0.01
0.01
0.01
0.02
0.02
0.02
0.003
0.01
0.005
m*
us. cycle duration, hindlimb stance and swing durations, and hindlimb duty factor
correlation coefficient; SEE
O.&i
0.92
0.95
0.96
0.96
0.96
0.92
0.84
0.94
rt
0.92
0.98
0.97
0.95
0.97
0.93
0.86
0.89
0.94
Body mass vs.
cycle duration
y*
r*
TABLE 3. Regression coefficients of body
471
EFFECTS OF SIZE ON VERVET GAIT
itively, it would be expected that the smaller
animals would have higher relative stride
lengths, especially at the high speeds. This
was not necessarily the case, as only at 0.89
d s were both the raw and transformed relative stride length and body mass values
signficantly correlated. Relationships were
also significant at 1.17 and 2.81 d s , using
only transformed values.
Relative hindlimb support length clearly
increased across the slower speeds and then
remained rather constant for all the remaining speeds, except the fastest, a t which
there was a notable increase. It is interesting that at all but the slowest speed, relative
hindlimb support length hovered around 1.OO,
that is, each animal propelled itself one sitting height per hindlimb stance duration.
Hindlimb excursion
Table 4 presents the angular excursion
values of the hindlimb for each animal at
each speed plus mean values. The italicized
numbers in the table indicate values during
galloping. It is obvious from the table that
size had no consistent effect on hindlimb angular excursions. In terms of relationships
with speed, it appears to be important to
differentiate between symmetrical and
asymmetrical gaits. During the former, the
data indicate a general increase occurring
primarily during slower speeds. At the rungallop transition there is usually a decrease
followed by a subsequent increase as speed
increases. It is noteworthy that unusually
high values were found for No. 10's angular
excursions at 2.58 d s relative to his other
values. The excursions given are for a rotatory gallop (98")and a left-lead transverse
gallop (94"). A value more consistent with
the other galloping data for that animal was
found for a right-lead transverse gallop (68O)
a t the same speed. However, the right-lead
strides had previously been eliminated as
"no good' and were therefore not used here.
as well as the transformed data. Despite the
fact that in our case the results were similar,
we find value in this dual approach. The
equations based on the raw data were unquestionably easier to interpret (e.g., the
finding that cycle and stance durations decrease 170 msec for every meter per second
increase in speed for all animals). The transformed data, however, generally had better
fits and thus probably better reflects the true
biological relationships. Analyses of data from
higher speeds will probably confirm this to
be the case (Fig. 2). Additionally, the coefficients for the transformed equations are
more comparable with those from previous
studies.
Gaits and gait transitions
Previous reports describing vervet gaits
have indicated that diagonal sequence gaits
3.00-
2.902.802.702.602.50-
RELATIVE
2.402.302.20W
u
2.10-
2
2.00-
Z
9
n
1.90-
Lu
b
I-
1.80-
5
1.70-
LL
1.60-
W
I
1.501.401.30-
1.20-
I
RELATIVE HINDLIMB SUPPORT LENGTH
DISCUSSION
Methods
The vast majority of recent studies investigating the consequences of body-size
differences in animals (whether inter- or
intraspecifically) use only logarithmically
transformed data for analyses (cf. Smith,
1984). However, in accord with Smith's illustration of the misinterpretations that can
result from this approach, we chose to compute regression equations using the raw data
,801
.70
.62 .89 1.17 1.441.72 1.99 2.282.582.81
SPEED (M/S]
Fig. 3. Plot of relative stride length (upper bars) and
relative hindlimb support length (lower bars) 2 1 SD for
all the animals at each speed. Relative stride length =
stride length + sitting height and relative hindlimb support length = hindlimb support length + sitting height.
J.A. VILENSKY ET AL
472
A
.*ooj
.700,600,500.400-
,300(3
9
,200-
,000
. '
O
O
"
l
B
-.loo-
- .I 5 0 -.200-.250-
-.300-.350-.400-.450-SO0
I
I
I
I
LOG FROUDE NUMBER
Fig. 4. Plots of: A) log E'roude number vs. log stride length
+ hip height and B) log Froude number vs. log hindlimb
duty fador. Froude number = velocityz + (gravity x
height), r = correlation coefficient.
are strongly predominant in all but very
young animals (Wells, 1974; Hurov, 1979,
1982;Vilensky and Gankiewicz, 1986).However, Hurov (1979)reported that under overground conditions (i.e., not a treadmill environment) one adult female used lateral sequence gaits 50% of the time. The data
presented in Table 2 also show lateral sequence symmetrical gaits to be relatively
common. Furthermore, there is no clear association of lateral sequence gait utilization
with size or speed. Additionally, in accord
with prior reports (Hurov, 1979, 1985; Vilensky and Gankiewicz, 1986), none of the
vervets used a running trot type of gait at
any speed. Finally, the great overall variability in gait utilization shown in Table 2 is
noteworthy. Although previous reports have
also discussed the large amount of variability present in primate gaits (Hildebrand,
1967; Rollinson and Martin, 1981), whether
primates truly have greater variability in
gait selection than other cursorial mammals
is not clear. Stuart et al. (1973) noted that
cats may use a variety of support patterns
that are not completely related to speed; Vilensky and Patrick (1984) similarly showed
that cats can markedly vary their locomotor
behavior at a single speed.
Relative to asymmetrical gaits, as we reported previously (Vilensky and Gankiewicz, 1986),younger vervets apparently favor
transverse over rotatory gallops, while older
individuals are adept at either. However,
young infants (under 6 months of age) are
also capable of using the rotatory sequence
(Hurov, 1979).Young animals' preference for
transverse gallops has also been noted in
cats (Peters, 1983).
The prevailing view of the trot-gallop
transition in mammals is that it is a repeatable event, the speed of which is solely
EFFECTS OF SIZE ON VERVET GAIT
dependent on body mass (i.e., it is virtually
free of any effects due to training or motivation; Heglundet al., 1974;McMahon, 1984).
Although this may be true on a gross level
(i.e., mouse to horses), it is not necessarily
true within a species. Specifically, although
some of the smaller vervets exhibited a transition earlier than some of the larger animals (Table 2), other factors clearly
predominated. For example, animals No. 7
and No. 10 galloped at 1.72 m/s, while animal No. 6 did not gallop until 2.28 mfs. Similarly, animal No. 8 did not gallop a t all.
Furthermore, there is evidence that this
phenomenon is not confined to primates. Melt
et al. (1983)reported that dogs were able to
undergo a trot-gallop transition regardless
of actual speed, and Vilensky and Gankiewicz (1985) found no relationship between
size and galloping speed for two kittens over
a 9-month period. Finally, it may be that in
vervets the run-gallop transition occurs at
a relatively similar cycle duration for all individuals.
Despite the fact that our data indicate that
body mass is not a very important determinant of transition speed, we did compare
our data with an equation derived by Hurov
(1985)to predict run-gallop transition speeds
from body mass in vervets. The comparison
reveals that Hurov’s equation would tend to
underestimate transition speeds for our animals. Compared with our speeds, Hurov’s
estimates would be 0.11to 0.91 m/s less than
those exhibited. Accordingly, in our 1986 paper, we questioned whether he could accurately measure overground speed using his
methodology. We also compared our rungallop speeds with the equation presented
by Heglund et al. (1974) for all mammals.
This equation overestimated the actual
speeds in three animals and underestimated
them for the others.
In contrast to the traditional view of the
run-gallop transition, and more in accordance with our data, Stein et al. (1986) suggested that a transition zone of speeds exists
for an animal. Within this zone, a variety of
gaits can be utilized without compromising
stability. For our animals, one-half exhibited ranges where both runs and gallops were
used. Most interesting were the cases of the
smallest and largest animals. No. 1 began
galloping at 1.44 m/s but also exhibited running gaits at both 1.99 and 2.58 m/s. No. 10
exhibited both a run and a gallop over a range
of three speeds (1.72-2.28 m f s i before using
only gallops. Based on these findings, it is
47 3
reasonable to suggest that Stein et al.’s view
of a transition zone of speeds may be more
appropriate than the traditional view.
Temporal parameters
The extremely high correlation coeficients between cycle duration and speed for
each animal leave little doubt that cycle duration, in contrast to gait selection, is almost
totally determinable from speed for a specific individual. Across individuals, the data
strongly suggest that some aspect of body
size is determining the precise value of a
specific individual’s cycle duration a t a certain speed. Initially, for this report, we had
hoped t o use our measurement data to ascertain if the influence of body size could be
attributed more to certain body segments
than to others. However, all segment lengths
were so well correlated with each other, as
well as with body mass, that we could not
differentiate among them.
Our results regarding the effects of size
on cycle duration in vervets are in agreement with our previous findings in this species and also in kittens (Vilensky and
Gankiewicz, 1985,1986).However, they are
divergent from a report by Goslow et al. (1973)
who found that three cats of slightly different body sizes (2, 2.5, and 3 kg) locomoting
at similar speeds could not be differentiated
in their locomotor parameters by their bodysize differences. The findings of Goslow et
al. are probably attributable to the relatively
slow filming speed used (64 frame&) and
the fact that the speed of the cats could not
be accurately controlled (i.e., the cats ran
overground).
Similar to our findings in vervets, Vilensky et al. (1987)reported that cycle duration
a t particular speeds in human children is
significantly correlated with stature. Accordingly, Beck et al. (1981) indicated that
cadence at set speeds in human children is
dependent on age, being highest in the
younger children and lowest in the older
children. Additionally, Sutherland et al.
(1980)reported that children walk with faster
cadences than adults. Finally, Alexander et
al. (1977) reported for a variety of African
ungulates that maximum stride frequency
and mean stride frequency during galloping
are smaller in larger animals. This would be
in agreement with our findings. However,
they also stated that maximum frequency
was better correlated with the height of the
animals’ hindquarters than with body mass.
Our analyses on the vervets show, on the
474
J.A. VILENSKY ET AL.
contrary, that body mass is overall a slightly
better predictor of cycle duration at a specific
speed than a linear measure.
Heglund et al. (1974) stated that the stride
frequency of a galloping animal is virtually
constant. Thus they proposed that the trotgallop transition occurs at an animal’s maximum sustainable stride frequency. Furthermore, they proposed that the trot-gallop
transition speed is a physiologically similar
speed for different-sized animals. Accordingly, McMahon (1975) hypothesized that
muscle stress is the same in homologous
muscles in different-sized animals at this
transition. As is apparent from Figure 2,
Heglund et al.’s hypothesis (and therefore
probably McMahon’s as well) is not correct
for vervet monkey^.^ Clearly, for these animals, there are regular decreases in cycle
duration once galloping begins. Furthermore, the vervets showed a poor relationship
between stride frequency at the run-gallop
transition and body size. This was surprising because, both across a wide variety of
mammals and across different primate species, there appears to be a good relationship
between body size and stride frequency at
the galloping transition (Alexander and Maloiy, 1984; Heglund et al., 1974). On the contrary, our data indicate that intraspecifically,
the gallop transition generally occurs at a
similar value for all animals. Interestingly,
Hurov (1985) found that interlimb timing
intervals at the run-gallop transition appeared to be independent of body size for
vervets; Pennycuick (1975), in a comparison
of the locomotor behavior of adult and calf
gnus (Connochaetes taurinus), found that
during cantering (slow galloping)gnu calves
used stride frequencies that were much less
than would be expected for their size. Thus,
within a species, body size does not seem to
be a good predictor of galloping stride frequency.
The hindlimb stance duration vs. speed
data showed a pattern similar to the cycle
duration vs. speed data for each individual.
Specifically, the mean absolute slope values
from the untransformed equations of both
cycle and stance durations vs. speed were
3Despite the fact that Heglund et al. (1974) stated that stride
frequency remains “nearly”constant once galloping begins, their
Figure 1 clearly shows increases in this parameter, with increased speed for the two smaller animals tested (mouse and
rat). Thus, although the data for the vervets tend to contradict
the statement of Heglund et al., our results are not necessarily
in conflict with their findings.
identical (0.17). Also similar, at any particular speed, body weight accounted for the
vast majority of the differences in hindlimb
stance duration. Accordingly, Melt et al.
(1983) reported for dogs that stance durations at particular speeds are strongly dependent on limb length; Vilensky et al. (1987)
and Beck et al. (1981) reported that stance
durations at particular speeds in human
children are dependent upon stature and age,
respectively.
For the raw and transformed cycle duration and stance slope values depicted in Table 3, there is an overall decrease with
increasing speed. Thus, the magnitude of the
influence of body size on cycle and stance
duration is generally less at faster speeds
than at slower ones. “his finding should serve
to emphasize that it is imperative to consider speed in any discussion of the effects
of size on locomotor parameters.
Swing durations were generally constant
across speeds for each individual, but they
were higher in the larger animals. The comparative invariance of swing duration across
speed is a well-reported phenomenon in
quadrupeds (cf. Grillner, 1975). There has
been some data for dogs and cats, however,
indicating that at least across slow speeds,
swing duration decreases slightly with increased speed (Melt et al., 1983; Melt and
Kasicki, 1975; Halbertsma, 1983). Only two
monkeys showed a significant trend toward
decreasing swing duration with increasing
speed. Thus our results are in general agreement with classical studies, with the cautionary note that individual animals may not
follow the typical pattern.
The effects of body size on swing duration
in quadrupeds has previously been addressed in two studies by us (Vilensky and
Gankiewicz, 1985; 1986) and in Goslow et
al.’s (1973) study on cats. In our studies (one
on kittens and the other on vervets) there
was some tendency for swing t o increase
slightly with size. Goslow et al. found no differences that could be correlated with size.
Again, in the current study we demonstrate
that, across speeds, size has a notable effect
on absolute swing duration.
For adult humans, swing duration generally decreases with increasedwalking speed
and remains comparatively constant during
running (cf. Vilensky, 1987). Across different-aged children, it clearly increases with
body size at similar speeds (Beck et al., 1981;
Vilensky et al., 1987).
EFFECTS OF SIZE ON VERVET GAIT
The strong curvilinear relationship between duty factor and speed found for the
monkeys also has been reported for a wide
variety of other quadrupedal mammals
(Biewener, 1983; Goslow et al., 1973) and for
humans (Vilensky and Gehlsen, 1984).
Biewener (1983) also found that at identical
speeds larger animals tend to have larger
duty factors. Our reports support this finding, in the sense that animal No. 1 always
had a smaller duty factor than animal No.
10; but, as evidenced by Table 3, across all
the vervets the relationship was poor. Accordingly, Beck et al. (1981) reported that
for children of varied ages (2-14 years) relative stance duration (i.e., duty factor) a t
similar speeds did not vary consistently with
age. Thus, at least intraspecifically in vervets and humans, size alone is not a good
predictor of duty factor.
Biewener (1983) also reported that the
mean duty factor ( 1SD) for a wide variety
of mammals at the trot-gallop transition
equaled 0.41
0.02. In contrast, corresponding values for the vervets were 0.46 ?
0.03. Similarly, Reynolds (1987) reported that
non-human primate duty factors at the
run-gallop transition ranged from 0.42 to
0.48. Thus primates appear to have slightly
higher duty factors a t the gallop transition
than most mammals.
*
*
Spatial parameters
Similar to our findings on stride length,
Pennycuick (1975) found that both raw and
transformed equations for large African herbivores are equally good for predicting the
relationship between stride length and speed.
Linear relationships based on raw data have
been reported for dogs and a variety of nonhuman primates (Blaszczyk and Dobrzecka,
1985; Reynolds, 1987).
Previous studies have documented that
non-human primates have longer than expected stride length for their body sizes (Alexander and Maloiy, 1984; Reynolds, 1987;
Vilensky, 1980). Our results support these
findings. Specifically, a t their run-gallop
transition speeds, the vervets had stride
lengths that were between 62% and 97%
greater than expected based on the equation
presented by Heglund et al. (1974). Furthermore, even a t a specific speed (1.1 d s ) ,
Reynolds (1987) showed that, compared with
other mammals, primates have longer than
expected stride lengths. Interestingly, Rey-
475
nolds’ equation for interspecific scaling of
stride length in primates a t 1.1 m / s (stride
length = 0.538 mass0.286)is reasonably close
to the intraspecific equation computed for
the vervets at 1.17 m/s (stride length = 0.527
masso.280,r = 0.96, %SEE = 4.5). Thus, inter- and intraspecific scaling of stride length
in primates may be quite similar.
As would be expected from the absolute
stride length data, mean relative stride length
for all the animals increased with speed (Fig.
3). Furthermore, variability in relative stride
length also tended to increase with speed.
The intuitive explanation for this would be
that, as speed increased, the smaller animals had to increase their stride length relatively more than the larger animals.
However, this was only mildly true, that is,
body size was not a very good predictor of
relative stride length, even a t the fastest
speed.
Support length has received considerably
more attention in the animal locomotion literature than stride length. Most important,
it has been considered to remain rather constant during symmetrical gaits and then to
increase during galloping (Grillner, 19811.
We found no dramatic increases during galloping. Accordingly, we suggest in our earlier paper (Vilensky and Gankiewicz, 1986)
that because vervets have relatively longer
support lengths as well as stride lengths
compared with non-primates, the proposed
increase during galloping may not occur.
However, it also is reasonable that at higher
galloping speeds than used in this study,
greater flexion-extension movements of the
spine may increase support length in monkeys in the same manner as Grillner (1981)
hypothesized for cats. Accordingly, Hurov
(1985) noted that the range of back motion
in vervets increases with increases in speed
during galloping.
The apparent implication from the support length data (both absolute and relative)
is that increases in speed in quadrupeds occur primarily during a limb’s swing phase
(stride length - support length = distance
traveled during swing). However, it is also
clear that each limb‘s swing phase is usually
associated with some part of another limb’s
stance phase. Thus the meaning of the finding that increases in velocity occur primarily
during swing phase is probably not significant (cf. Grillner, 1981; Vilensky and Gankiewicz, 1986).More interesting would be an
analysis of the velocity of the animal’s center
476
J.A. VILENSKY ET AL
of gravity relative to limb support patterns.
This has not been done for any quadruped.
The reports detailing the relationships between speed and hindlimb angular excursion for quadrupeds are contradictory (cf.
Vilensky, 1987). Most reports suggest there
are no dramatic changes with speed, which
is in accord with the hindlimb excursion data
presented here. Reynolds (1987), however,
indicated that hindlimb excursion decreases
with speed in quadrupedal primates. Furthermore, Reynolds found that hindlimb excursion a t the run-gallop transition equals
approximately 85”.This is somewhat higher
than the angles we found for most of our
animals, but his animals were generally
substantially larger in body size, and his
measurements were taken in a slightly different manner.
According to McMahon’s (1975,1984) theory on the scaling of animals (elastic similarity), larger animals should have more
restricted joint motion. He specifically predicted that limb excursions a t the trotgallop transition should scale proportionally
to mass -O.lZ5. He empiricallyderived that hindlimb angular excursion at the trot-gallop
transition is equal to 74.4mass-0lo. Thus
larger animals should have smaller angular
excursions at this transition. If anything, our
data indicate the opposite (Table 4). However, the predicted values for the vervets using McMahon’s equation are not too far
removed from the actual values (predicted
rangeequaled65”-77”). Accordingly,for some
large primates (chimpanzees and spider
monkeys) Reynolds (1987) found notable differences between actual and predicted values, but for a 2.0-kg lemur Reynolds obtained
results that were compatible with those predicted.
Despite the theoretically and empirically
derived data relative to the effects of size on
hindlimb excursion, we found no consistent
differences between the large and small
monkeys at identical speeds. Similarly, in
comparisons of the angular excursions of human adults and children, reports have commented on the remarkable likeness in joint
angular movements (Foley et al., 1979;
Sutherland et al., 1980). However, Vilensky
et al. (1987) did find some consistent differences in joint postion, but not excursion, for
the hip and knee joints in a comparison of
different-sized children and adults locomoting at identical speeds. Finally, the larger
excursion angles found for No. 10’s gallops
(rotatory and left-lead transverse) at 2.58 m/
s, compared with the value for a right-lead
transverse gallop at the same speed, indicate that excursions may vary grossly across
different types of gallops.
Allomtry and similarity
To evaluate some of the predictions of the
effects of size on gait, based on McMahon’s
(1975, 1984) elastic similarity model (which
assumes that different-sized animals evolved
in a similar manner so as to resist buckling
under their own weight), we first determined the allometric exponents of the following linear measurements against body
mass: sitting height, trunk height, thigh
length, knee height, leg length, foot length,
arm length, forearm length, and hand length.
McMahon’s model would predict the exponent to be 0.25, while a geometric scaling
model would predict an exponent of 0.33.
Compared with other body segment lengths,
the exponents for hand and foot length were
both low, 0.26 and 0.23,respectively. Disregarding the hand and foot exponents, the
mean exponent for all the other length measurements was 0.38 (SD = 0.02; r values
ranged from 0.95 to 0.99, and %SEE values
were low), indicating that these measurement data are generally more in accord with
a geometric model, although neither model
is strongly supported.
Relative to locomotion, McMahon’s model
makes a number of predictions that he tests
at the trot-gallop transition speed for a variety of animals. As noted previously,
McMahon assumes that this speed is “physiologically similar” across animals and occurs a t close to the animal’s maximum stride
frequency. We have already demonstrated
that this transition in the vervets did not
occur at maxiumum stride frequency and that
the stride frequency at which it did occur
was not strongly dependent on body size, that
is, the correlation coefficient for body mass
vs. stride frequency at the run-gallop transition was very low. Thus, at least for these
monkeys, the run-gallop transition speed is
probably not “physiologically similar” and we
did not test McMahon’s predictions a t these
speeds. Rather, we believe the “best”’speed
to test McMahon’s predictions in our study
is the highest speed for which we obtained
data (2.81 d s ; n = 8, as animal Nos. 2 and
3 did not locomote at this speed). It is clear
from Figure 2 that each animal’s cycle duration at this speed is close to its mini-
EFFECTS OF SIZE ON VERVET GAIT
477
mum value (assuming the curves may be ex- at similar Froude numbers, should be using
trapolated). According to McMahon (1975), similar gaits. They found that at Froude
minimum cycle duration (maximum stride numbers below 2,mammals tend to use symfrequency) should be proportional to masso.125, metrical gaits and at numbers above 3,
while according to the geometric scaling asymmetrical gaits are used. For the vermodel, it should be proprotional to ma~sO.~~.
vets, galloping began a t Froude numbers
The transformed data in Table 3 indicate an rangingfrom 0.87to 2.6,with a mean of 1.43.
exponent of 0.21,which is between the two. Thus the monkeys tended to switch to asymTherefore, it is not evident as to which model metrical gaits at rather low Froude numbers
is appropriate in this case. Additionally, a and perhaps, more important, were not conmajor disagreement between our data and sistent in the number at which they switched.
McMahon’s hypothesis exists relative to hind- Accordingly, Alexander and Maloiy (1984)
limb angular excursions. In the vervets these reported that a chimpanzee switched to galexcursions were not correlated with body size loping at low Froude numbers and that they
at the run-gallop transition speeds (Table could not generalize regarding the speed at
4).This is consistent with geometric scaling which primates change gaits.
(excursions are proportional to masso).
A second prediction based on dynamic
Alexander (1976)and Alexander and Jayes similarity is that animals will use equal stride
(1983)developed a principle relating the length + hip height ratios when locomoting
concept of geometric scaling to movement. at similar Froude numbers. Figure 4A deAlexander and Jayew called this principle picts a log-log plot of Froude number vs.
dynamic similarity. Two movements are dy- stride length + hip height. As evident from
namically similar if the motion of one can the figure, the fit is remarkably good. The
be made identical to that of the other by coeffkients for the regression line depicted
multiplying all linear dimensions of the first in the figure are presented in Table 5, along
by one constant, all temporal components by with similar values from other studies. Ina second constant, and all forces by a third terestingly, although primates, in general,
constant. Dynamic similarity is only possi- appear to increase their stride length a t a
ble when animals run with equal Froude rate comparable to other cursorial mamnumbers (calculated as: velocity* t [gravity mals, the intraspecific rate for vervets is less
x hip weight], where hip height is the “char- than the interspecific rate for primates and
acteristic length” used by Alexander and other mammals. This is similar to other reJayes, but any comparable length measure- lationships, that is, intraspecific scaling of
ment can be used). Alexander and Jayes gen- brain weight + body weight values is less
erated and tested several predictions relative than interspecific scaling (Gould, 1975).
to different-sized animals locomoting at simA third prediction of the dynamic simiilar Froude numbers. In many cases they larity hypothesis is that at similar Froude
found good agreement between predictions numbers, different-sized animals will have
and empiricallyderived data.4We tested some the same duty factor. Figure 4B depicts a
of their predictions using the vervet data. It log-log plot of Froude number vs. duty factor
should be noted that precise dynamic simi- for the vervets. Again, the fit is very good
larity is only possible if animals are geo- although there is notably more spread than
metrically similar and each body segment for the stride length fit. From the data precomprises the same proportion of total body sented in Table 5, it is clear that vervets do
mass.
not differ markedly in slope or intercept from
Alexander and Jayes (1983) proposed that other cursorial mammals with regard to duty
animals of different sizes, when locomoting factor. Furthermore, inter- and intraspecific
scaling are not differentiated.
Obviously, from the above discussion, data
from the current study appear to lend more
4We considered hip height for this study to be the same as
support to the dynamic similarity hypothehindlimblength (thigh length plus knee height),while Alexander
sis than to the elastic similarity model. Reand Jayes (1983) defined it as the height of the hip joint in
“normal standing.” We chose to use our definition because we
cently,
Alexander (1985) criticized the elastic
had exact body measurements on our animals. During “normal”
scaling model and concluded by questioning
standing primates have bent knees; from this standpoint, our
measurement overestimates hip height relative to Alexanderand
the value of using any similarity principle
Jayes. On the other hand, for some mammals the metatarsals,
to understand the effects of size on locomotor
tarsals, and phalanges substantially contribute to hip height;
this is obviously not the case for primates.
behavior. Rather, he suggested that evolu-
478
J.A. VILENSKY ET AL.
TABU 4. Hindlimb excursion values (degrees) for each animal at each speed and mean values'
Speed ( d s )
Animal No.
1
0.62
70
2
3
4
84
5
6
0.89
75
1.17
78
1.44
70
-
1.72
77
78
85
89
64
85
73
70
79
84
78
75
74
82
65
75
70
75
70
79
83
85
83
63
67
1.99
-
79
73
80
78
83
2.28
-
2.58
89
87
2.81
87
-
-
78
72
78
80
72
83
81
85
78
-
-
75
79
76
83
82
80
84
88
81
101
101
63
85
78.8
85.4
105
104
98
94
90
84
78
82
102
~~
7
71
82
-
83
88
81
80
78
78
77
91
93
67
83
73.8
83.2
69
83
76.5
83.2
8
67
9
78
85
88
79
75
91
10
81
82
89
86
x
71.5
78.9
81.0
67.5
82.6
67
83.3
80
'Italicized numbers indicate values during galloping.
TABU 5. Log-log regression coefficients of Fmude No. us. stride length + hip height,' and Froude No.
us. hindlimb duty factor
Parameter
Froude No. vs. stride length + hip height
Cursorial mammals, walking
Cursorial mammals, faster gaib
Primates (seven species
including C. aethiops)
Vervets
Froude No. vs. hindlimb duty factor
Cursorial mammals, waking
Cursorial mammals, faster gaits
Vervets
m
Y
0.34
0.40
0.33
0.38
0.28
0.54
Alexander and Jayes, 1983'
Alexander and Jayes, 1983
Alexander and Maloiy, 1984'
0.25
0.47
This study
- 0.18
- 0.28
- 0.29
- 0.28
- 0.30
- 0.21
Source
Alexander and Jayes, 1983
Alexander and Jayes, 1983
This studv
m = slope; y = y intercept
'cf. Footnote 4 of text.
'Alexander and Jayes (1983) and Alexander and Maloiy (1984) computed their regression coeffcients using a model I1
method, while we used a model I (cf. Footnote 2 of text). As is apparent, Alexander and Jayes (1983) found it necessary
to divide their data into walking and non-walking gaits. This was not necessary for the primates.
tion acts by seeking optimality. Since Alexander had previously suggested that
dynamic similiarity is applicable because
animals seek to minimize their energy utilization at a particular speed (Alexander and
Jayes, 1983;Alexander, 19841,we are somewhat surprised by his recent statement. It
seems reasonable to assume that if, in fact,
some optimalization principle is applicable
among a related group of animals, then there
should be some "rules" that predict how the
group will respond in its locomotor behavior
to differences in body size.
CONCLUSIONS
This study has demonstrated that, intraspecifically,body size is undoubtedly the most
important variable in determining a specific
vervet's cycle and stance durations at a specific speed. Swing duration is also dependent
on body size but does not vary consistently
across speed. Obviously, a goal of future
studies is to determine if body size per se
can be further differentiated, that is, does
the mass or length of certain segments have
greater influence on these parameters than
EFFECTS OF SIZE ON VERVET GAIT
other segments. We hope that the forthcoming longitudinal study may contribute to this
goal. Additionally,that study should also give
an indication of the degree to which individual animals may differ from the average in
their relationships between body size and
various locomotor parameters.
Although the present paper has demonstrated excellent relationships between body
size and certain locomotor parameters, it is
equally important to emphasize that some
other parameters, previously thought to be
strongly dependent on body size (based primarily on interspecific studies), were not dependent on it. Most important, the latter
group includes the run(trot)-gallop transition speed. Although, clearly, there are physiological mechanisms that affect gait
transitions, other factors are probably also
important. Thus the idea of the trot-gallop
transition speed being physiologically similar among animals, at least intraspecifically,
is questionable. Again, we suggest that Stein
et al.’s (1986) view of a transition zone be
considered, rather than the idea of a specific
transition speed for every individual.
In addition to the above, it is important to
emphasize that our results demonstrate the
importance of speed in any consideration of
the effects of body size on locomotor parameters. Velocity is the single most important
element of an animal’s locomotor behavior,
and the influence of size on locomotor behavior changes with changes in speed.
Finally, the data presented here are generally consistent with the view that younger
and older animals of the same species will
locomote in dynamically similar fashion at
identical Froude numbers.
ACKNOWLEDGMENTS
We are grateful to Mr. G. Duncan and Ms.
P. Wilson for assistance during filming, to
Ms. E. Wilson and Ms. C. Oliver for typing
the many drafts of this manuscript, and to
Ms. R. Shadle for making illustrations. We
also very much appreciate the in depth comments made on the original manuscript by
three anonymous reviewers.
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