Hind limb proportions and kinematics: are small primates different from other small mammals?
Institut für Spezielle Zoologie und Evolutionsbiologie, Friedrich Schiller Universität Jena, Erbertstrasse 1, D-07743 Jena, Germany
e-mail: schmidt.manuela{at}uni-jena.de
Accepted 6 July 2005
![]() |
Summary |
---|
![]() ![]() ![]() ![]() ![]() ![]() ![]() |
---|
Hind limb kinematics of arboreal quadrupedal primates, ranging in size between 100 g and 3000 g, are size independent and resemble the hind limb kinematics of small non-cursorial mammals. A common feature seen in smaller mammals, in general, is the horizontal position of the thigh at touchdown and of the lower leg at lift-off. Thus, the maximum bone length is immediately transferred into the step length. The vertical position of the leg at the beginning of a step cycle and of the thigh at lift-off contributes the same distance to pivot height. Step length and pivot height increase proportionally with hind limb length, because intralimb proportions of the hind limb remain fairly constant. Therefore, the strong positive allometric scaling of the hind limb in arboreal quadrupedal primates affects neither the kinematics of hind limb segments nor the total angular excursion of the limb. The angular excursion of the hind limb in quadrupedal primates is equal to that of other non-cursorial mammals. Hence, hind limb excursion in larger cercopithecine primates differs from that of other large mammals due to the decreasing angular excursion as part of convergent cursorial adaptations in several phylogenetic lineages of mammals. Typical members of those phylogenetic groups are traditionally used in comparison with typical primates, and therefore the `uniqueness' of primate locomotor characteristics is often overrated.
Key words: joint kinematics, angular excursion, intralimb proportions, limb length scaling, Microcebus murinus, Eulemur fulvus, Saguinus oedipus, Saimiri sciureus
![]() |
Introduction |
---|
![]() ![]() ![]() ![]() ![]() ![]() ![]() |
---|
These characteristics are generally present in arboreal quadrupedal
primates and are absent even in the nearest relatives of primates as well as
in the majority of other placental mammals. Deviations occur only in primates
with more specialised locomotor habits such as slow climbing loris and pottos
(Ishida et al., 1990;
Schmitt and Lemelin, 2004
) and
terrestrial quadrupedal cercopithecines
(Vilensky and Larson, 1989
;
Demes et al., 1994
). Thus,
grasping hind feet, the diagonal-sequence gait, the posterior weight shift and
a large humeral protraction are hypothesised to be `unique' to the Order
Primates, representing a suite of derived characteristics. The convergent
evolution of such characteristics in several arboreal marsupials may imply
functional relationships between some or all of these characteristics
(Rasmussen, 1990
;
Schmitt and Lemelin, 2002
;
Lemelin et al., 2003
).
Other characteristics proposed as `unique' to primates are larger step
lengths (Alexander and Maloiy,
1984; Reynolds,
1987
), greater angular excursions of the fore and hind limbs
(Reynolds, 1987
; Larson et
al., 2000
,
2001
), greater long bone
lengths (Alexander et al.,
1979
) and a more compliant walk in comparison with other mammals
(Schmitt, 1999
). However,
based on a broad sample of mammalian species belonging to different
phylogenetic groups, Larney and Larson
(2004
) found that limb
compliance does not appear to be exclusive to primates. Obviously, whether
such relative features are hypothesised to be primate-specific characteristics
or not depends on the criteria for the sample selection and the extent to
which the comparative method is applied.
In most investigations of primate locomotor characteristics, special
emphasis is devoted to the differences between typical primates and typical
non-primates (Kimura et al.,
1979; Alexander and Maloiy,
1984
; Reynolds,
1987
; Schmitt,
1999
). Typical primates are mostly Old World cercopithecine
monkeys, apes and New World atelines. The artificial group `non-primate
mammals' is generally defined as domestic animals such as carnivores,
ungulates and rodents because kinematic data can be easily gathered for these
animals. The proposed uniqueness of primates with regard to step length, limb
angular excursion, and long bone lengths is therefore based on comparison
between such `typical' representatives of different phylogenetic groups. Only
Larson et al. (2000
,
2001
) support their
conclusions on a broad sample of mammalian species, but they concentrate their
attention on the pronounced differences between the larger animals of their
sample group, instead of examining the similarities among smaller species.
Primates and other mammalian groups diverge with increasing body size with
respect to hind limb excursion angle, whereas differences seem less pronounced
in small members (below 5 kg) of all groups
(Larson et al., 2001). Yet
Larson et al. (2001
) confirm
the previous findings of Reynolds
(1987
) that primates have a
greater hind limb angular excursion than other mammals. The question is: how
can one decide if hind limb excursion has increased during primate locomotor
evolution or if hind limb excursion has decreased in the other groups due to
convergent cursorial adaptations in those lineages? Observed differences among
primates and the phylogenetically distinct living carnivores, rodents,
artiodactyls and perissodactyls have amassed a host of evolutionary changes
along at least five phylogenetic lineages. The assertion that the primate
order is characterized by a derived limb excursion pattern requires a clearer
demonstration of character polarity for this feature in primates and their
sister taxa. Hence, smaller primates possessing postcranial character states
more similar to those preserved in the fossil record may offer better insights
about locomotor evolution than the typically studied, highly derived cursorial
forms.
Most extant orders of placental mammals appeared in the fossil record over
a relatively short period of time, ranging between 50 and 70 million years
ago, hence interordinal relationships are far from resolved. Nevertheless, the
adaptive nature of the last common ancestor of placental and marsupial mammals
appears to reflect a non-cursorial locomotor mode adapted for moving on
uneven, disordered substrates (Jenkins,
1971; Fischer,
1994
). Jenkins
(1974
), based on his study of
habitat-related behaviour and locomotor performance in tree-shrews, proposed
that the distinction between `arboreal' and `terrestrial' locomotion is
artificial for tiny forest-dwellers such as tree-shrews because most
substrates in the forest require the same basic locomotor repertoire. More
recently, Fischer et al.
(2002
) have demonstrated that
small mammals, independent of their phylogenetic position or natural habitat
type, generally display similar overall kinematic aspects of limb displacement
during locomotion.
The phylogenetic origin of the Order Primates within placental mammals is
still being discussed, and the sister-group of the Primates remains
contentious. Proposed extant sister groups of primates include the small
quadrupedal tree shrews (Wible and Covert,
1987) and the gliding Dermoptera
(Cronin and Sarich, 1980
;
Beard, 1993
). Despite the lack
of consensus on the actual sister taxon of primates, tree shrews have been
considered a reasonable morphological model for the last common ancestor of
primates and their closest relatives.
Although not all living primates are tree-dwellers, they all appear to
derive from arboreal small-bodied ancestors
(Cartmill, 1972;
Gebo, 2004
). Unlike
tree-shrews, primates possess an opposable nailed hallux responsible for the
grasping capabilities of the hind feet. The hallux of tree-shrews is able to
abduct but not to oppose against the other digits
(Jenkins, 1974
). Supported by
the coincidence of small body size and grasping hind feet, small terminal
branches in the top of the trees are suggested to be the locomotor habitat of
the last common ancestor of living primates (Cartmill,
1972
,
1974
).
The aim of this study is to compare the hind limb kinematics of a selection of small arboreal quadrupedal primates with those of tree-shrews and other small mammals that exhibit an unspecialised locomotor behaviour comparable with the ancestral mode of mammalian locomotion. In this way, ancestral and derived primate-specific characteristics of hind limb kinematics can be differentiated. Scaling of hind limb length to body size and the intralimb proportions of the three-segmented hind limb are also considered in relation to the similarities and differences in hind limb kinematics.
![]() |
Materials and methods |
---|
![]() ![]() ![]() ![]() ![]() ![]() ![]() |
---|
|
Mouse lemurs are the smallest primates in the world. They are found only in
Madagascar and inhabit the dense leafy areas of the secondary forest with
tangles of fine branches and lianas
(Martin, 1973). Mouse lemurs
are agile and active at night, usually travelling along branches on all four
legs.
The family Lemuridae is also confined to Madagascar. Members of the genus
Eulemur are arboreal forest-dwellers. The brown lemur is by far the
most widespread of the `typical' lemurs and is divided into no less than six
subspecies. Lemurs are active, quadrupedal animals that run and walk on
horizontal and oblique branches and are capable of leaping to and from
vertical and horizontal supports (Garbutt,
1999).
Members of the family Callitrichidae are among the smallest of primates.
They are found in the tropical forests of Central and South America, mainly in
the Amazon region. The thumb of tamarins and marmosets is not opposable, and
all the digits bear pointed, sickle-shaped nails, except the great toe, which
has a flat nail. Callitrichids are sometimes considered primitive,
squirrel-like primates. Most tamarins (Saguinus, Leontopithecus,
Callimico) are active arborealists that move by running quadrupedally
along thin horizontal branches and leaping between terminal supports
(Fleagle and Mittermeier,
1980; Garber,
1980
; Sussmann and Kinzey, 1984). Unlike tamarins, marmosets
(Callithrix) forage on large vertical supports rather than on small
flexible branches (Cartmill,
1974
; Hershkovitz,
1977
).
Squirrel monkeys are among the small members of the family Cebidae.
Squirrel monkeys are found in primary and secondary forests of Central and
South America, where they are commonly found in the lower levels. They are
arboreal quadrupeds that frequently leap
(Thorington, 1968).
Motion analysis
Each of the individuals was trained to walk on a raised pole or on a
horizontal motor-driven rope-mill, an arboreal analogue of a treadmill. The
diameter of the support was adapted to the preferred natural substrate of the
species (mouse lemur, 10 mm; cotton-top tamarin, 25 mm; squirrel monkey, 30
mm; brown lemur, 50 mm). Data on substrate preferences were obtained from
several sources (Tattersall,
1977; Walker,
1974
; Garber,
1980
; Gebo, 1987
;
Arms et al., 2002
). Rope-mill
speed was not fixed but adjusted to obtain the animal's preferred walking
speed.
Uniplanar cineradiographs were collected in lateral view at 150 frames
s1, in order to visualize joints and obtain angular
excursions of limb segments. Segment abduction angles were approximated from
the foreshortening of the bones in the parasagittal projection. The methods of
collecting and processing kinematic variables from cineradiographs have been
described elsewhere in detail (Schmidt and
Fischer, 2000; Schmidt,
2005
) and will be summarised only briefly here. The x-ray
equipment consists of an automatic Phillips® unit with one
x-ray source that applies pulsed x-ray shots (Institut für den
Wissenschaftlichen Film, Göttingen, Germany). Distortions of the x-ray
maps were corrected by reference to an orthogonal grid of steel balls
(diameter 1.0 mm, with a mesh width of 10.0 mm), filmed before and after each
experimental session. The x-ray images were recorded from the image amplifier
either onto 35 mm film (Arritechno R35-150 camera) or using a high-speed CCD
camera (Mikromak® Camsys; Mikromak Service K. Brinkmann,
Berlin, Germany). X-ray films were then copied onto video tapes and
A/D-converted using a video processing board. Afterwards, these films were
analyzed frame-by-frame to identify previously defined skeletal landmarks
(software `Unimark' by R. Voss, Tübingen, Germany;
Fig. 1A). The software Unimark
calculates angles and distances based on x- and
y-coordinates of the landmarks, correcting the distortions of the
x-ray maps automatically with reference to the x- and
y-coordinates of the grid.
|
The following kinematic variables were measured or calculated.
Morphometry
Skeletal specimens (N=118) belonging to 58 mammalian species were
examined at the Phylogenetisches Museum, Jena and at the Museum für
Naturkunde, Berlin, Germany. Adult status of the specimens was judged by
fusion of the epiphyses of the long bones.
Table 2 lists the different
specimens analyzed in this study and indicates the body mass values. Those
specimens labelled with an asterisk denote specimens for which body masses
were compiled from the literature
(Grzimek, 1987;
Rowe, 1996
;
Nowak, 1999
). All other body
mass values were associated with actual specimens.
|
The majority of taxa included in the primate sample consist of arboreal
quadrupedal primates. Included members of the Cheirogaleidae, Lemuridae,
Galagonidae, Callitrichidae and Cebidae prefer to walk and run quadrupedally
along narrow branches but also use other modes of progression such as climbing
and leaping. However, none of these named taxa shows distinct specialisations
for climbing or leaping (e.g. extremely elongated hind limbs;
Grzimek, 1987;
Rowe, 1996
;
Fleagle, 1999
;
Nowak, 1999
). Only
cercopithecine Old World monkeys (baboons, macaques, patas monkeys, guenons)
are basically adapted to terrestrial quadrupedalism
(McCrossin et al., 1998
;
Fleagle, 1999
). Still, most
guenons and some macaques have returned to arboreality. Hence, re-adaptations
to arboreality in these animals were observed to affect the kinematics and
morphology of the autopodia rather than that of proximal limb joints
(Meldrum, 1991
;
Schmitt and Larson, 1995
).
Unlike strepsirhine and platyrrhine arboreal quadrupeds, the limbs of
tree-dwelling cercopithecines are rather extended and adducted, moving
primarily in a parasagittal plane
(Meldrum, 1991
;
Schmitt, 1999
). The samples of
rodents, carnivores and marsupials include both arboreal and terrestrial
quadrupeds. Still, cursorial adaptations to terrestrial running occur only in
some of the Carnivora (grey wolf, red fox, domestic cat;
Jenkins and Camazine, 1977
;
Nowak, 1999
).
Table 2 also contains the
measured values of the lengths of the three functional hind limb segments
(femur, tibia and tarsometatarsus) for each specimen. The calculation of
average values for each species was rejected because there is no evidence that
bone length scales isometrically with body size among different sized
conspecifics. Rather, an intraspecific allometric scaling is more likely
because long bones scale differentially with body size ontogenetically
(Jungers and Fleagle, 1980;
Roth, 1984
;
Turnquist and Wells, 1994
;
Lammers and German, 2002
; N.
Schilling and A. Petrovitch, manuscript submitted) and across taxa
(Aiello, 1981
;
Jungers, 1985
;
Bertram and Biewener, 1990
;
Christiansen, 1999
;
Lilje et al., 2003
). Hind limb
length is calculated as the sum of the lengths of the three segments. Body
mass is employed as the most appropriate and meaningful size variable for the
scaling analysis of hind limb length
(Aiello, 1981
;
Jungers, 1985
).
The data were transformed to logarithms to normalize the distribution of
the dependent variable Y, and linear regression lines were fitted to
the data by means of the reduced major axis model (model II). The reduced
major axis model was used rather than least-square regression because the
latter assumes that there is no error term associated with the X
variable (body mass) (Sokal and Rohlf,
1995). As the body mass of most specimens included here was taken
as an average from the literature, it can hardly be considered free of
statistical error. Furthermore, the use of least-square regression can lead to
biased results if loglog bivariate regressions are used
(Zar, 1968
). Pearson's
product-moment correlation coefficient was computed for each taxonomic group,
and the 95% confidence interval surrounding the allometry coefficients (slope)
of each sample was calculated. If the confidence interval of a slope does not
include the value for geometric similarity (0.33), the slope is said to
describe significant allometry.
Standard anthropometric indices, traditionally constructed to assess relative limb proportions in mammals, consider the two long bones of the limbs only (crural index = tibia length/femur lengthx100). Therefore, they are insufficient to assess intralimb proportions of a three-segmented limb. Thus, intralimb proportions in this study are expressed as percentages of each segment length to the sum of the lengths of the three segments.
![]() |
Results |
---|
![]() ![]() ![]() ![]() ![]() ![]() ![]() |
---|
For descriptive and comparative convenience, the analysis of limb kinematics focuses on limb configurations at the instant of touchdown and lift-off during a step cycle. Touchdown and lift-off mark the natural subdivision of a step cycle into a support phase and a swing phase. These points can be compared among quadrupedal animals independent of their limb proportions and other peculiarities of their locomotor apparatus.
When interpreting the similarities and differences in hind limb kinematics within primates and between primates and other mammals, it is necessary to consider the influence of body mass and phylogeny upon hind limb length and intralimb proportions. Therefore, a morphometric analysis of these characteristics in a broader sample of quadrupedal primate and non-primate species is included.
Comparison of hind limb kinematics
Angular excursion of the hind limb
Total angular excursion was measured as the angle between the lines
connecting the point of ground contact and the proximal pivot at touchdown and
lift-off. By drawing a vertical line through the point of ground contact, the
total angular excursion can be split into a retraction angle and a protraction
angle.
Total angular excursion of the hind limb varies little among the four primate species. It ranges from 74° in the brown lemur to 77° in the cotton-top tamarin at the preferred moderate walking speeds of the animals. Hind limb angular excursion is greater at a slow walking speed. The maximum values at slow steps are 88° in the mouse lemur, 86° in the brown lemur, 87° in the tamarin and 80° in the squirrel monkey.
The protraction angle and retraction angle of the hind limb are nearly
equal in the mouse lemur and the squirrel monkey, where the protraction angle
exceeds the retraction angle by a maximum of 3°. In the brown lemur and
the cotton-top tamarin, the retraction angle is distinctly greater than the
protraction angle. Maximum differences of 8° were observed in the
brown lemur.
Kinematics of hind limb segments
The kinematic behaviour of the hind limb segments varies more strongly
among the four species than might be expected from their similarity in total
limb angular excursion (Fig.
2).
|
|
The lesser protracted thigh in the squirrel monkey is compensated for by a greater protraction of the leg at touchdown. The touchdown angle of the leg exceeds 90°, and the ankle is consistently placed in front of the knee joint. Due to this compensation, the protraction angle of the hind limb is as great as that of the mouse lemur and even greater than those of the cotton top tamarin and the brown lemur. The leg is vertically positioned at the beginning of a step cycle in the mouse lemur, the brown lemur and the tamarin.
|
At the end of the stance phase, the femoral shaft is either vertically positioned (mouse lemur, squirrel monkey) or has moved beyond the vertical position (brown lemur, cotton-top tamarin), so that the knee joint is behind the hip joint. The extensive thigh retraction in the brown lemur and the cotton-top tamarin is the main reason for the great retraction angle of the hind limb measured in these two species.
At lift-off, the leg of the lemurs and the tamarin is horizontally positioned or nearly so. In the squirrel monkey, it is rather inclined (Fig. 2). Despite this reduced segment retraction angle, the total excursion angle of the leg is the greatest in the squirrel monkey due to the greater degree of protraction (Table 3). Lower leg kinematics are fairly uniform in the mouse lemur and the brown lemur as well as in the cotton-top tamarin.
Mouse lemurs and brown lemurs retract their tarsometatarsus to a greater degree than do the two New World primates. The segment moves beyond the vertical position in the prosimian species, whereas its retraction ends in a vertical position in the tamarin and the squirrel monkey.
Hind limb excursions outside a parasagittal plane are restricted to the initial phase of propulsion, when the femur is abducted, and adduction of the lower leg brings the foot below the animal's trunk to grasp the pole. Femoral abduction varies between 10° in the squirrel monkey, 22° in the cotton-top tamarin and 38° in the mouse lemur and the brown lemur. Leg adduction is due to thigh rotation about its longitudinal axis.
Kinematics of hind limb joints
The extent of overall limb flexion can be expressed as the percentage of
functional limb length from the anatomical limb length. The hind limbs of the
mouse lemur are most flexed relative to the other species. The functional hind
limb length at touchdown is 66% and at lift-off 71% of the anatomical hind
limb length. The most extended limbs were observed in the squirrel monkey.
Both at touchdown and lift-off, functional hind limb lengths were 80% of the
anatomical hind limb length. Hind limbs are normally more flexed at touchdown
than at lift-off in the other three primate species.
In addition to the overall flexion of the hind limb, the limb undergoes a more or less deep flexion and a subsequent re-extension in the course of the support phase. This change of the functional limb length is called limb yield. This means that the hind limb bears weight and yields to hold the hip joint at an almost constant level. The extent of this yield can be expressed as the percentage of the shortest functional limb length at mid-support from the functional limb length at the beginning of a step cycle. Mid-support is defined as the moment when the point of ground contact passes underneath the hip joint. The yield of the hind limb is similar in the four species and independent of overall limb flexion and body weight. The percentage of functional hind limb length at mid-support from the functional limb length at touchdown is 84% in the mouse lemur and the squirrel monkey, 86% in the brown lemur and 90% in the cotton-top tamarin.
Protraction and retraction of the hind limb are mainly executed by femoral displacement in the hip joint. The hip joint is the only limb joint with a monophasic angular excursion during the step cycle, whereas knee and ankle joints display a biphasic angular excursion (Fig. 3). Thus, the hip joint is exclusively propulsive and does not assist in the compensation of vertical oscillations of the trunk. Hip joint extension starts immediately before touchdown and lasts until the end of the support phase. Thus, the difference between the touchdown angle and the lift-off angle of the hip joint corresponds to the joint amplitude, calculated as the difference between maximum and minimum joint angle (Table 4).
|
In the case of the knee and ankle joints, the difference between the
touchdown angle and the lift-off angle (= effective joint movement;
Fischer, 1994) is rather low
compared with the joint amplitude, the difference between maximum and minimum
angle during the support phase. In all four primate species, the knee joint is
strongly flexed during the first half of the support phase and is afterwards
re-extended until the end of the support phase
(Fig. 3). Maximum knee joint
flexion coincides with the point of mid-support in the cotton-top tamarin and
the squirrel monkey, when the ankle joint passes underneath the hip. It occurs
early in the two prosimians, at the moment when the tip of the foot passes
underneath the knee joint. The knee joint angle of the squirrel monkey is
always greater than that of the other primates due to the more extended hind
limbs at the beginning of the step cycle.
The angular excursion of the ankle joint during the support phase shows stronger variation between the species. The ankle joint of the cotton-top tamarin is much more flexed than that of the lemurs, but no flexion occurs in the ankle joint of the squirrel monkey. Angular excursion of the ankle joint is nearly identical in the two prosimian primates.
Pelvic movements and hip joint translation
The hip joint is the proximal pivot of the hind limb during walking. The
pivot is not fixed in height. Extensive lateral bending and twisting movements
of the lumbar spine change the pelvic position. Pelvic tilting about an
anteroposterior axis alternately moves one hip joint below the other. Maximum
downward tilt occurs towards the side that begins the support phase; the
contralateral side, completing the support phase, is correspondingly tilted
upwards. The second component of pelvic movement is a rotation about a
vertical axis due to lateral bending of the lumbar spine. This rotation moves
one hip joint ahead of the other. In summary, the hip joint of the hind limb
at touchdown lies ahead of and below the hip joint of the contralateral hind
limb that is beginning to take off. Sagittal bending of the lumbar spine,
which moves the whole pelvis up and down, is less pronounced.
The prosimian primates studied here make extensive use of pelvic tilting
and pelvic rotation to gain additional step length from horizontal hip
translation (Table 5). These
findings confirm previous observations by Shapiro et al.
(2001) that lateral spine
bending has an important functional role for gaining step length in walking
primates. In the brown lemur, for example, a total horizontal translation of
the hip joint of
19 mm contributes 5% to the step length of the hind
limb. The angle of the longitudinal pelvic axis to the horizontal plane as
well as to the sacrum is more inclined in the primate species compared with
other small mammals (Fischer et al.,
2002
). Mean touchdown angle of the pelvis relative to the
horizontal plane ranges between 38° in the squirrel monkey and 59° in
the tamarin (Table 5). For
comparison, the respective value in tree-shrews is 19°
(Schilling and Fischer, 1999
).
Further personal observations have shown that in mammals that utilize
synchronous gaits with extensive sagittal spine movements, the angle between
the pelvis and the sacrum is rather flat. Thus, the pelvis is aligned with the
line of action of the lumbar spine. The inclined pelvis in primates has a
positive influence on gain step length in symmetrical rather than in
synchronous gaits.
|
Hind limb proportions in quadrupedal primates and non-primate mammals
Scaling of hind limb length to body size
Fig. 4 shows the
log-transformed scaling pattern of the hind limb length to body size in a
sample of quadrupedal primates in comparison with other groups of mammals.
Intensified sampling effort was made for small-sized taxa to permit
comparisons of similarly sized animals across mammalian orders. Regression
equations, confidence intervals for the allometry coefficients and correlation
coefficients are noted under the graph
(Fig. 4). Hind limb length is
calculated as the sum of the lengths of the three functional hind limb
segments: femur, tibia and tarsometatarsus.
|
Obviously, small mammals exhibit consistent relationships between hind limb
length and body size that do not appear to be influenced by locomotor mode or
phylogeny. Hence, small primates, tree-shrews, small rodents and small
marsupials all have similar size-related hind limb lengths, a pattern highly
suggestive of functional constraint. Yet it is likely to represent a similar
functional constraint experienced by the early members of their respective
orders, as all are postulated to derive from small-bodied ancestral forms
(Jenkins and Parrington, 1976;
Luckett and Jacobs, 1980
;
Carroll, 1988
;
Gingerich et al., 1991
;
Dawson, 2003
;
Gebo, 2004
).
Intralimb proportions of the hind limb
The limbs of quadrupedal mammals consist of three functional segments
the thigh, the lower leg and the foot. But, anthropomorphic indices,
traditionally used to assess intralimb proportions in mammals, take only two
limb segments into consideration. In the case of the hind limb, the crural
index is normally used to calculate the proportional relationship between the
thigh and the leg. In the following description, intralimb proportions are
expressed as a percentage value of each segment length over the sum of the
lengths of the three segments.
Fig. 5 shows that intralimb proportions of the hind limbs in quadrupedal mammals are fairly uniform. Intralimb proportions vary more among members of the same phylogenetic group than between different phylogenetic groups. Marsupials are distinct in that they possess relatively shorter feet in combination with longer lower legs. Observed divergence from the common pattern within a phylogenetic group is not generally related to size or to locomotor behaviour. The allometric relationship of the hind limb with respect to body size has no distinct effects on the proportional relationship of hind limb segments. The size-related increase of hind limb length in arboreal strepsirhines and platyrrhines does influence all three segments in the same fashion, or nearly so. No significant difference in intralimb proportions between the arboreal strepsirhines and platyrrhines and the terrestrial cercopithecines could be found. In the majority of primates, the percentage of the thigh length over the hind limb length ranges between 38% and 42%, and the percentage of the lower leg varies between 37% and 39%. The thigh is normally longer than the leg. Only the smallest primate included in the sample, the pygmy mouse lemur (31 g), has exceptionally long legs (44%) and short thighs (34%). Still, the best evidence that intralimb proportions of quadrupedal primates are size independent is that the hind limb of a mouse lemur, Microcebus rufus (70 g), is similar in proportions to the hind limb of the large gelada, Theropithecus gelada (20.5 kg). In tree-shrews, the relative length of the lower leg is the same as in primates, although the thigh is somewhat shorter (37%), and the foot is relatively longer (26%).
|
![]() |
Discussion |
---|
![]() ![]() ![]() ![]() ![]() ![]() ![]() |
---|
Primates, like other mammals, change step length and frequency to change
their walking speed. Consequently, limb kinematics are also speed dependent.
The preferred walking speed of each animal was used to define equivalent
mechanical and physiological situations so that comparison between different
sized animals running at different speed was possible (Hildebrand,
1966,
1985
;
Hoyt and Taylor, 1981
;
Perry et al., 1988
;
Larson et al., 2001
).
Hind limb kinematics in primates and other mammals
Fig. 6 combines hind limb
touchdown and lift-off postures of the four primates analyzed in this study
with data from other primates, including the slender loris, two larger Old
World monkeys, and a sample of other mammals (references given in the figure
legend).
|
This principle is equivalent at lift-off, when the thigh is positioned vertically and the leg is horizontal. In this case, the increased length of the long bones would contribute the same degree to step length as to pivot height, and the total angular excursion of the limb would remain the same. Still, the lift-off position of the hind limb is obviously more variable than the touchdown position, perhaps relating to differences in thigh and leg length among taxa.
Only a few exceptions from this generalised pattern occur among smaller
taxa (below 3.0 kg): in the tree-shrew, the hind limb is more strongly flexed
at touchdown due to knee and ankle joint angles below 90°
(Schilling and Fischer, 1999).
Hind limb protraction angle is thus very low (less than 30°), compensated
for by the enormous retraction of the thigh and foot at the end of the support
phase. In the laboratory rat, the thigh is less retracted, resulting in a more
flexed lift-off position of the limb relative to the other mammals. Jenkins
(1971
) observed a similar
crouched lift-off position in the Virginian opossum. Among primates, the
squirrel monkey exhibits a more extended hind limb posture at touchdown than
do other similarly sized primates and non-primates. It is quite similar to
larger cercopithecine primates. Another similarity to the cercopithecine
monkeys is the nearly parasagittal displacement of the hind limbs in squirrel
monkeys, whereas most other arboreal primates as well as non-cursorial
non-primates abduct their thighs in the first half of the support phase. The
peculiar hind limb kinematics of squirrel monkeys among small arboreal
quadrupedal primates cannot be explained by the peculiarities of their
skeletal locomotor apparatus regarding intra- and interlimb proportions, or
allometric scaling of limb length or limb bone length. Even the load that the
hind limb must bear is not much more than that of other arboreal primates
(Schmidt, 2005
). For the
moment, the question of why hind limb kinematics in squirrel monkeys differ
from those of other arboreal primates remains open.
Fig. 6 includes the hind
limb posture of two Old World cercopithecine monkeys in comparison with larger
carnivore species (Muybridge,
1957; Jenkins and Camazine,
1977
; Goslow et al.,
1981
; Meldrum,
1991
; Kuhtz-Buschbeck et al.,
1994
). The hind limbs of these larger mammals are generally more
extended than in the smaller species, mainly due to a more inclined thigh
position at touchdown (3540° to the horizontal) and a more inclined
position of the leg at lift-off. Additionally, the hind limbs of these five
species move almost exclusively in a parasagittal plane. The guenon and the
baboon protract their lower legs like the racoon but to a greater degree than
the cat and the dog at the beginning of a step cycle, and therefore their hind
limbs have a greater protraction angle. The vertical position of the thigh at
the end of the support phase is a kinematic feature of arboreal primates that
appears to be retained in terrestrial Old World monkeys. Jenkins and Camazine
(1977
) reported a similar
thigh excursion for the cat and the red fox. Racoons exhibit greater
retraction of the thigh. Such extended limb postures are usually said to be a
biomechanical consequence of cursorial specialisation
(Hildebrand, 1985
;
Stein and Casinos, 1997
).
Primates and cursoriality
Cursoriality is a specific morpho-functional complex of features related to
the specialization of the locomotor apparatus of animals for high-speed and
long-lasting locomotion on the ground. Parasagittal limb excursions and more
extended limb joints align the limb axis of cursorial mammals with the vector
of the gravitational force and reduce the moment arms of the ground force
vector acting on the limb joints (Biewener,
1983). Thus, bending stress acting upon the limb bones decreases
with the adoption of an extended limb posture. Morphological traits usually
associated with cursoriality include relatively long limbs, lengthened
metapodials, shortened humeri/femora and a reduction in the number of distal
limb bone elements (Steudel and Beattie,
1993
; Lilje et al.,
2003
). Such cursorial adaptations evolved convergently with
increasing body size in several lineages of mammals (rodents, carnivores,
artiodactyls, perissodactyls). Terrestrial quadrupedal cercopithecine primates
show cursorial-like limb kinematics, combined with other morphological
adaptations. Hind limb length scales isometric to body size in order to have
an equivalent limb length to the forelimbs. If limbs are extended, functional
limb length approaches the anatomical limb length. In this case, limb flexion
cannot be used to adopt an equivalent functional length of the fore and hind
limb if limbs differ in their anatomical length. Unlike `true' cursorial
mammals, intralimb proportions of the hind limb do not change with changing
limb kinematics in quadrupedal primates. Thus, length and excursion of the
distal limb elements are not as important as they are in cursorial mammals for
gaining pendular length and step length. Secondarily arboreal cercopithecine
monkeys maintain most of these terrestrial adaptations. While travelling on
arboreal substrates, the limbs of these monkeys are more flexed relative to
ground walking (Schmitt, 1999
)
but they never attain the crouched posture exhibited by dedicated primate
arborealists (Meldrum,
1991
).
Angular excursion of the hind limb in primates and other mammals
Different kinematics of hind limb segments in quadrupedal primates and
other mammals do not inevitably affect the total angular excursion of the hind
limb. Table 6 shows hind limb
excursion angles in quadrupedal primates in comparison with a sample of
quadrupedal non-primate mammals. Total angular excursion is size independent
in quadrupedal primates, varying between 73° (squirrel monkey) and 81°
(slender loris). Larson et al.
(2001) also report for their
much broader sample of primates that hind limb excursion angles are fairly
uniform within the order. Angular excursion of the hind limbs in the
small-sized sample of other mammals is also independent of body size and may
vary more in relation to data collection methodologies, as noted in
Table 6. Comparisons among
primates and other quadrupedal mammals in the size range between 50 g (spiny
mouse) and 3.0 kg (Virginian opossum, brown lemur) show no definitive
differences or similarities. The hind limb angular excursion of arboreal
quadrupedal primates resembles that of tree-shrews and other non-cursorial
primates and is far from being uniquely large, as proposed by Reynolds
(1987
) and Larson et al.
(2001
).
|
Interestingly, the contrasting interpretations of Reynolds
(1987) and Larson et al.
(2001
) and those presented
here are based upon similar observations, but the conclusion is different due
to different comparative methods and different strategies in sample selection.
Both Reynolds (1987
) and
Larson et al. (2001
) paid more
attention to the differences between typical primates and typical non-primate
mammals. They are right that typical primates have larger hind limb angular
excursions relative to typical non-primate species. But, these differences
occur through the decrease of hind limb angular excursion as a part of
convergent cursorial adaptations in the larger species of their sample of
non-primate mammals, whereas larger quadrupedal primates maintain the hind
limb angular excursion of their smaller ancestors. Hence primates as a clade
do not exhibit uniquely large hind limb angular excursions; indeed, small
primates exhibit angular excursions quite similar to those observed in other
small mammals. Hind limb angular excursion would be uniquely large in primates
only if ancestral primates exhibited significantly larger angular excursions
than did their non-primate sister taxa. In an evolutionary sense, it would
seem that the derived limb excursions actually belong to the non-primate
cursors that have exchanged larger angular excursions for enhanced stability
of longer limbs.
Conclusions
The specific characteristics of primate locomotion evolved in small
arboreal quadrupedal mammals with a body mass of less than 100 g. Therefore,
some living small arboreal primates can serve as reliable models to study the
basic characteristics of primate locomotion. The comparison of such species
with tree-shrews and other non-cursorial small mammals thought to possess the
ancestral pattern of mammalian locomotion enables the differentiation between
derived, primate-specific locomotor characteristics and functional or
ancestral traits common to small mammals in general.
Hind limb kinematics of arboreal quadrupedal prosimians are size
independent and resemble those of small non-cursorial mammals. Plesiomorphic
characteristics include the horizontal position of the thigh and the vertical
position of the lower leg at touchdown. At lift-off, the thigh is vertically
oriented and the leg is nearly horizontal. This initial pattern is independent
of the actual anatomical length of the hind limb. In arboreal primates, hind
limb length scales with strong positive allometry to body size, but intralimb
proportions do not change with increasing size. Step length and pivot height
increase to the same degree by the proportional lengthening of limb bones.
Thus, total angular excursion of the hind limb in arboreal primates remains
equal to other non-cursorial mammals and is far from being uniquely large in
primates, as previously proposed by Reynolds
(1987) and Larson et al.
(2001
). Terrestrial primates
alter hind limb kinematics through the adoption of more extended joint
postures, whereas intralimb proportions and total angular excursions remain
equal to small arboreal ancestors. The observed difference in angular
excursion between large primate and non-primate mammals probably stems from
the decreasing excursion angle of the limbs as part of cursorial adaptations
in several phylogenetic lineages of mammals.
![]() |
Acknowledgments |
---|
![]() |
References |
---|
![]() ![]() ![]() ![]() ![]() ![]() ![]() |
---|
Aiello, L. C. (1981). The allometry of primate body proportions. Symp. Zool. Soc. Lond. 48,331 -358.
Alexander, R. McN. and Maloiy, G. M. O. (1984). Stride length and stride frequencies of primates. J. Zool. Lond. 29,577 -582.
Alexander, R. McN., Jayes, A. S., Maloiy, G. M. O. and Wathuta, E. M. (1979). Allometry of the limb bones of mammals from shrews (Sorex) to elephant (Loxodonta). J. Zool. Lond. 189,305 -314.
Arms, A., Voges, V., Fischer, M. S. and Preuschoft, H. (2002). Arboreal locomotion in small New-World monkeys. Z. Morph. Anthropol. 83,243 -263.
Beard, K. C. (1993). Phylogenetic systematics of the Primatomorpha, with special reference to Dermoptera. In Mammal Phylogeny: Placentals (ed. F. S. Szalay, M. J. Novacek and M. C. McKenna), pp. 129-150. New York: Springer Verlag.
Bertram, J. E. A. and Biewener, A. A. (1990). Differential scaling of the long bones in the terrestrial Carnivora and other mammals. J. Morph. 204,157 -169.[CrossRef][Medline]
Biewener, A. A. (1983). Locomotory stresses in the limb bones of two small mammals: the ground squirrel and chipmunk. J. Exp. Biol. 103,131 -154.[Abstract]
Carroll, R. L. (1988). Vertebrate Paleontology and Evolution. New York: W. H. Freeman and Company.
Cartmill, M. (1972). Arboreal adaptations and the origin of the order Primates. In Functional and Evolutionary Biology of Primates (ed. R. Tuttle), pp.97 -122. Chicago: Aldine Atherton.
Cartmill, M. (1974). Pads and claws in arboreal locomotion. In Primate Locomotion (ed. F. A. Jenkins, Jr), pp. 45-83. New York: Academic Press.
Cartmill, M., Lemelin, P. and Schmitt, D. (2002). Support polygons and symmetrical gaits in mammals. Zool. J. Linn. Soc. 136,401 -420.[CrossRef]
Christiansen, P. (1999). Scaling of mammalian long bones: small and large mammals compared. J. Zool. Lond. 247,333 -348.
Cronin, J. E. and Sarich, V. M. (1980). Tupaiid and Archonta phylogeny: the macromolecular evidence. In Comparative Biology and Evolutionary Relationships of Tree Shrews (ed. W. P. Luckett), pp. 293-312. New York: Plenum Press.
Dawson, M. R. (2003). Paleogene rodents of Eurasia. Deinsea 10,97 -126.
Demes, B., Jungers, W. L. and Nieschalk, U. (1990). Size- and speed-related aspects of quadrupedal walking in slender and slow lorises. In Gravity, Posture and Locomotion in Primates (ed. F. K. Jouffroy, M. H. Stack and C. Niemitz), pp.175 -197. Florence: Il Sedicesimo.
Demes, B., Larson, S. G., Stern, J. T., Jr, Jungers, W. L., Biknevicius, A. R. and Schmitt, D. (1994). The kinetics of primate quadrupedalism: "hindlimb drive" reconsidered. J. Hum. Evol. 26,353 -374.[CrossRef]
Fischer, M. S. (1994). Crouched posture and high fulcrum. A principle in the locomotion of small mammals: the example of the rock hyrax (Procavia capensis) (Mammalia: Hyracoidea). J. Hum. Evol. 26,501 -524.[CrossRef]
Fischer, M. S., Schilling, N., Schmidt, M., Haarhaus, D. and
Witte, H. (2002). Basic limb kinematics of small therian
mammals. J. Exp. Biol.
205,1315
-1338.
Fleagle, J. G. (1999). Primate Adaptation and Evolution. San Diego, CA: Academic Press.
Fleagle, J. G. and Mittermeier, R. (1980). Locomotor behavior, body size, and comparative ecology of seven Surinam monkeys. Am. J. Phys. Anthropol. 52,301 -314.[CrossRef]
Franz, T. M., Demes, B. and Carlson, K. J. (2005). Gait mechanics of lemurid primates on terrestrial and arboreal substrates. J. Hum. Evol. 48,199 -217.[CrossRef][Medline]
Garber, P. A. (1980). Locomotor behavior and feeding ecology of the Panamanian tamarin (Saguinus oedipus geoffroyi, Callitrichidae, Primates). Int. J. Primatol. 1,185 -201.
Garbutt, N. (1999). Mammals of Madagascar. New Haven, London: Yale University Press.
Gebo, D. J. (1987). Locomotor diversity in Prosimian Primates. Am. J. Primat. 13,271 -281.[CrossRef]
Gebo, D. L. (2004). A shrew-sized origin for primates. Yrbk. Phys. Anthropol. 47, 40-62.
Gingerich, P. D., Dashzeveg, D. and Russell, D. E. (1991). Dentition and systematic relationships of Altanius orlovi (Mammalia, Primates) from the early Eocene of Mongolia. Geobios 24,637 -646.
Goslow, G. E., Jr, Seeherman, H. J., Taylor, C. R., McCutchin, M. N. and Heglund, N. C. (1981). Electrical activity and relative length changes of dog limb muscles as a function of speed and gait. J. Exp. Biol. 94,15 -42.[Abstract]
Grzimek, B. (1987). Enzyklopädie der Säugetiere (ed. R. Kleienburg). München: Kindler Verlag.
Hershkovitz, P. (1977). Living New World Monkeys (Platyrrhini) With an Introduction To Primates, vol. 1. Chicago: University of Chicago Press.
Hildebrand, M. (1966). Analysis of the symmetrical gaits of tetrapods. Folia Biotheor. 6, 9-22.
Hildebrand, M. (1967). Symmetrical gaits of primates. Amer. J. Phys. Anthropol. 26,119 -130.[CrossRef]
Hildebrand, M. (1985). Walking and running. In Functional Vertebrate Morphology (ed. M. Hildebrand, D. M. Bramble, K. F. Liem and D. B. Wake), pp. 38-57. Cambridge, MA, London: The Belknap Press of Harvard University Press.
Hoyt, D. F. and Taylor, C. R. (1981). Gait and energetics of locomotion in horses. Nature 292,239 -240.[CrossRef]
Ishida, H., Jouffroy, F. K. and Nakano, Y. (1990). Comparative dynamics of pronograde and upside down horizontal quadrupedalism in the slow loris (Nycticebus coucang). In Gravity, Posture and Locomotion in Primates (ed. F. K. Jouffroy, M. H. Stack and C. Niemitz), pp. 209-220. Florence: Il Sedicesimo.
Jenkins, F. A., Jr (1971). Limb posture and locomotion in the Virginia opossum (Didelphis marsupialis) and in other non-cursorial mammals. J. Zool. Lond. 165,303 -315.
Jenkins, F. A., Jr (1974). Tree shrew locomotion and the origins of primate arborealism. In Primate Locomotion (ed. F. A. Jenkins, Jr), pp.85 -115. New York: Academic Press.
Jenkins, F. A., Jr and Camazine, S. M. (1977). Hip structure and locomotion in ambulatory and cursorial carnivores. J. Zool. Lond. 181,351 -370.
Jenkins, F. A., Jr and Parrington, F. R. (1976). The postcranial skeletons of the triassic mammals Eozostrodon, Megazostrodon and Erythrotherium. Phil. Trans. Roy. Soc. Lond. 273,387 -431.
Jungers, W. L. (1985). Body size and scaling of limb proportions in primates. In Size and Scaling in Primate Biology (ed. W. L. Jungers), pp.345 -381. New York: Plenum Press.
Jungers, W. L. and Fleagle, J. G. (1980). Postnatal growth allometry of the extremities in Cebus albifrons and Cebus apella: a longitudinal and comparative study. Am. J. Phys. Anthropol. 53,471 -478.[Medline]
Kimura, T., Okada, M. and Ishida, H. (1979). Kinesiological characteristics of primate walking: its significance in human walking. In Environment, Behavior, and Morphology: Dynamic Interactions in Primates (ed. M. E. Morbeck, H. Preuschoft and N. Gomberg), pp. 297-311. New York: Gustav Fischer.
Kuhtz-Buschbeck, J. P., Boczek-Funke, A., Illert, M. and Weinhardt, G. (1994). X-ray study of the cat hindlimb during treadmill locomotion. Eur. J. Neurosci. 6,1187 -1198.[Medline]
Lammers, A. R. and German, R. Z. (2002). Ontogenetic allometry in the locomotor skeleton of specialized half-bounding mammals. J. Zool. Lond. 258,485 -495.
Larney, E. and Larson, S. G. (2004). Compliant walking in primates: elbow and knee yield in primates compared to other mammals. Am. J. Phys. Anthropol. 125, 42-50.[CrossRef][Medline]
Larson, S. G., Schmitt, D., Lemelin, P. and Hamrick, M. (2000). Uniqueness of primate forelimb posture during quadrupedal locomotion. Am. J. Phys. Anthropol. 112,87 -101.[CrossRef][Medline]
Larson, S. G., Schmitt, D., Lemelin, P. and Hamrick, M. (2001). Limb excursion during quadrupedal walking: how do primates compare to other mammals? J. Zool. Lond. 255,353 -365.
Lemelin, P., Schmitt, D. and Cartmill, M. (2003). Footfall patterns and interlimb co-ordination in opossums (Family Didelphidae): evidence for the evolution of diagonal-sequence walking gaits in primates. J. Zool. Lond. 260,423 -429.
Lilje, K. E., Tardieu, C. and Fischer, M. S. (2003). Scaling of long bones in ruminants with respect to the scapula. J. Zool. Syst. Evol. Res. 41,118 -126.[CrossRef]
Luckett, W. P. and Jacobs, L. L. (1980). Proposed fossil tree shrew genus Palaeotupaia. Nature 288, 104.
Martin, R. D. (1973). A review of the behaviour and ecology of the lesser mouse lemur (Microcebus murinus J. F. Miller, 1777). In Comparative Ecology and Behaviour of Primates (ed. R. P. Michael and J. H. Crook), pp.1 -68. London: Academic Press.
McCrossin, M. L., Benefit, B. R., Gitau, S. N., Palmer, A. K. and Blue, K. T. (1998). Fossil evidence for the origin of terrestriality among Old World higher primates. In Primate Locomotion. Recent Advances (ed. E. Strasser, J. G. Fleagle, A. Rosenberger and H. McHenry), pp. 353-395. New York: Plenum Press.
Meldrum, D. J. (1991). Kinematics of the cercopithecine foot on arboreal and terrestrial substrates with implications for the interpretation of hominid terrestrial adaptations. Am. J. Phys. Anthropol. 84,273 -289.[CrossRef][Medline]
Muybridge, E. (1957). Animals in Motion (ed. L. S. Brown), pp. 1-75. New York: Dover. (Originally published by Chapman and Hall, London, 1899.)
Nowak, R. M. (1999). Walker's Mammals of the World. Sixth edition. Baltimore, London: The Johns Hopkins University Press.
Perry, A. K., Blickhan, R., Biewener, A. A., Heglund, N. C. and Taylor, C. R. (1988). Preferred speeds in terrestrial vertebrates: are they equivalent? J. Exp. Biol. 137,207 -219.[Abstract]
Rasmussen, D. T. (1990). Primate origins: lessons from a Neotropical marsupial. Am. J. Primatol. 22,263 -277.[CrossRef]
Reynolds, T. R. (1985). Mechanics of increased support of weight by the hindlimbs in primates. Am. J. Phys. Anthropol. 67,335 -349.[Medline]
Reynolds, T. R. (1987). Stride length and its determinants in humans, early hominids, primates, and mammals. In Primate locomotion (ed. F. A. Jenkins, Jr), pp.171 -200. New York: Academic Press.
Roth, V. L. (1984). How elephants grow: heterochrony and the calibration of developmental stages in some living and fossil species. J. Vertebrate Palaeontol. 4, 126-145.
Rowe, N. (1996). The Pictorial Guide to the Living Primates. Charlestown, RI: Pogonias Press.
Schilling, N. and Fischer, M. S. (1999). Kinematic analysis of treadmill locomotion of tree shrews, Tupaia glis (Scandentia: Tupaiidae). Z. Säugetierk. 64,129 -153.
Schmidt, M. (2005). Quadrupedal locomotion in squirrel monkeys (Cebidae: Saimiri sciureus) a cineradiographic study of limb kinematics and related substrate reaction forces. Am. J. Phys. Anthropol. doi:10.1002/ajpa/20089[CrossRef]
Schmidt, M. and Fischer, M. S. (2000). Cineradiographic study of forelimb movements during quadrupedal walking in the brown lemur (Eulemur fulvus, Primates: Lemuridae). Am. J. Phys. Anthropol. 111,245 -262.[CrossRef][Medline]
Schmitt, D. (1999). Compliant walking in primates. J. Zool. Lond. 248,149 -160.
Schmitt, D. (2003). Evolutionary implications of the unusual walking mechanics of the common marmoset (C. jacchus). Am. J. Phys. Anthropol. 122, 28-37.[CrossRef][Medline]
Schmitt, D. and Larson, S. G. (1995). Heel contact as a function of substrate type and speed in primates. Am. J. Phys. Anthropol. 96,39 -50.[CrossRef][Medline]
Schmitt, D. and Lemelin, P. (2002). Origins of primate locomotion: gait mechanics of the woolly opossum. Am. J. Phys. Anthropol. 118,231 -238.[CrossRef][Medline]
Schmitt, D. and Lemelin, P. (2004). Locomotor mechanics of the slender loris (Loris tardigradus). J. Hum. Evol. 47,85 -94.[CrossRef][Medline]
Shapiro, L. J., Demes, B. and Cooper, J. (2001). Lateral bending of the lumbar spine during quadrupedalism in strepsirhines. J. Hum. Evol. 40,231 -259.[CrossRef][Medline]
Sokal, R. R. and Rohlf, F. J. (1995). Biometry: The Principles and Practice of Statistics in Biological Research. Third edition. San Francisco: W. H. Freeman and Company.
Stein, B. R. and Casinos, A. (1997). What is a cursorial mammal? J. Zool. Lond. 242,185 -192.
Steudel, K. and Beattie, J. (1993). Scaling of cursoriality in mammals. J. Morph. 217, 55-63.[CrossRef][Medline]
Sussman, R. W. and Kinzey, W. G. (1984). The ecological role of the Callitrichidae: a review. Am. J. Phys. Anthropol. 64,419 -449.[Medline]
Tattersall, I. (1977). Ecology and behavior of Lemur fulvus mayottensis. Anthropol. Papers Am. Mus. Nat. Hist. 54,421 -482.
Thorington, R. W., Jr (1968). Observations of squirrel monkeys in a Colombian forest. In The Squirrel Monkey (ed. L. A. Rosenblum and R. W. Cooper), pp.69 -85. New York: Academic Press.
Turnquist, J. E. and Wells, J. P. (1994). Ontogeny of locomotion in rhesus macaques (Macaca mulatta): I. Early postnatal ontogeny of the musculoskeletal system. J. Hum. Evol. 26,487 -499.[CrossRef]
Vilensky, J. A. and Larson, S. G. (1989). Primate locomotion: utilization and control of symmetrical gaits. Annu. Rev. Anthropol. 18, 17-35.[CrossRef]
Vilensky, J. A., Gankiewicz, E. and Townsend, D. W. (1988). Effect of size on vervet (Cercopithecus aethiops) gait parameters: A cross-sectional approach. Am. J. Phys. Anthropol. 76,463 -480.
Walker, A. C. (1974). Locomotor adaptations in the past and present prosimian primates. In Primate locomotion (ed. F. A. Jenkins, Jr), pp.349 -382. New York: Academic Press.
Wible, J. R. and Covert, H. H. (1987). Primates: cladistic diagnosis and relationships. J. Hum. Evol. 16,1 -22.[CrossRef]
Zar, J. H. (1968). Calculation and miscalculation of the allometric equation as a model in biological data. BioScience 18,1118 -1120.