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Effects of size on vervet (Cercopithecus aethiops) gait parameters A longitudinal approach.

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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
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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.
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Hildebrand M (1966) Analysis of symmetrical gaits of
tetrapods. Folia Biotheor. 6:9-22.
Hildebrand M (1977) Analysis of asymmetrical gaits. J.
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McMahon TA (1984)Muscles, Reflexes and Locomotion.
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Neter J , and Wasserman W (1974) Applied Linear Statistical Models. Homewood, IL: Richard D. Irwin, Inc.
Schultz A (1929) The techniques of measuring the outer
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Smith RJ (1984) Allometric scaling in comparative biology. Am. J . Physiol. 15:R152-R160.
Stein PSG, Martin LI, and Robertson GA (1986) The
forms of a task and their blends. In S Grillner, PSG
Stein, DG Stuart, H Forssberg, and RM Herman (eds.):
Neurobiology of Vertebrate Locomotion. London: MacMillan, pp. 201-216.
Vilensky JA (1987) Locomotor behavior and control in
human and non-human primates: Comparisons with
cats and dogs. Neurosci. Biobehav. Rev. llt263-274.
Vilensky JA, and Gankiewicz E (1989) The effects of
growth and speed on hindlimb joint angular displacement patterns in vervet monkeys (Cercopithecus aethiops). Am. J. Phys. Anthropol. (This issue.)
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