Forelimb proportions and kinematics: how are small primates different from other small mammals?

A support that has a small diameter relative to the size of an animal places particular challenges on the locomotor performance and morphology of the musculoskeletal system. A small-diameter support is inherently unstable;twigs and branches may swing, yield or even break. An animal travelling on such a support has two major concerns – balance and compliance. Balance prevents the animal from falling down. Compliance reduces the branch oscillations, which would otherwise disturb cyclic locomotor performance and increase the energy costs of motion enormously. The distinctive characteristics of primate locomotion – powerful pedal grasping, hind limb dominance and diagonal sequence of footfalls(Martin, 1968; Martin, 1986) – have been interpreted as adaptive solutions to locomotion on terminal branches smaller in diameter than the animal(Cartmill, 1972; Rose, 1973; Cartmill, 1974; Sussman, 1991; Cartmill et al., 2002). Powerful prehensile feet enable primates to influence their substrate reaction forces via simultaneously transferred substrate reaction moments(Preuschoft, 2002; Witte et al., 2002). The counter-transfer of moments onto the trunk permits a dynamic weight shift from the forelimbs to the hindlimbs similar to the mechanism proposed by Reynolds(Reynolds, 1985). Combined with a diagonal footfall pattern – hindlimb contact prior to contralateral forelimb contact(Hildebrand, 1967) –this enables the hindlimbs to carry most of the body weight at the moment of forelimb touchdown (Reynolds,1985; Cartmill et al.,2002). Although the diagonal footfall pattern is less advantageous in terms of the static stability of locomotion relating the support polygon of the limbs to the location of the centre of body mass(Gray, 1944; Tomita, 1967; Shapiro and Raichlen, 2005; Wallace and Demes, 2007), it is superior to the lateral footfall pattern in terms of the dynamic stability of locomotion (control and transfer of moments imposed on the body axes). As the diagonally paired fore- and hindlimb make contact with the support concurrently, a dynamic weight shift from side to side (=balance) is possible at any moment of a stride cycle. At the same time, the other fore- and hindlimbs swing forward synchronously, thus counterbalancing the momentum on the transverse body axis. Compliance is basically provided by a crouched limb posture which extant arboreal primates certainly inherit from their non-primate ancestors.

Along with the locomotion-related primate features listed by Martin(Martin, 1968; Martin, 1986), various relative characters have been proposed to be unique to primates: larger limb excursion, greater step length, lower step frequency and longer limbs(Alexander et al., 1979; Alexander and Maloiy, 1984; Reynolds, 1987; Larson et al., 2001). The adaptive advantage of these features for locomotion on narrow branches is discussed in numerous recent publications. For example, lower step frequency means longer contact time for the limbs, which significantly reduces the peak forces the limbs are subjected to by gravity and, thus, further enhances the compliance of primate walking (Demes et al., 1990; Schmitt,1999). Although assessment of the polarity of these relative characters greatly depends on sample composition, phylogenetic hypotheses have often played a minor role in selecting species for comparison. Rather,comparative studies between `typical' primates belonging to Cebidae,Cercopithecidae, and even Hominoidea and `typical' members of the artificial taxon `non-primates' (e.g. cats, dogs, horses) form the majority of literature in this field of research. Furthermore, small sample size often weakens some of the most frequently cited references. For example, the notion that primates have longer limb bones and, thus, longer limbs than other mammals(Alexander et al., 1979) is based on data from six primate species. Reynolds' assumption(Reynolds, 1987) that primates display greater hindlimb angular excursion is based on a sample of four primates (chimpanzee, gibbon, spider monkey and brown lemur). Larson(Larson, 1998) and Larson et al. (Larson et al., 2000; Larson et al., 2001) went to great lengths to test the hypothesis proposed by Reynolds on the basis of a much larger sample (53 primates and 49 `non-primates' of several phylogenetic groups). Although this outstanding sample could potentially have allowed the ancestral pattern for each phylogenetic lineage to be derived, the authors compared the mean values of each group, making it impossible to estimate character polarity. The comparative evidence relating to whether limb lengths,angular excursion and step length in primates are uniquely large thus needs to be surveyed critically with regard to character polarity. In an earlier study,Schmidt (Schmidt, 2005a)compared the hindlimb kinematics of small arboreal quadruped primates with those of other non-cursorial mammals and suggested that the differences that occur with increasing body size result from the decreasing angular excursion in cursorial mammals, with larger primates merely retaining the primitive condition of large hindlimb excursion seen in the smaller primates,tree-shrews, rodents and marsupials.

Fischer and his team (Fischer et al.,2002) proposed kinematic principles for the locomotion of small mammals, which is suggested as being adaptive to postural stability in unanticipated situations within a disordered spatial arrangement of surfaces. These principles include a permanent crouched limb posture in which the most proximal element is predominant in the protraction and retraction of the limb. Intrinsic limb joints (shoulder, elbow, knee and ankle) mainly serve to provide limb compliance. It has further been suggested that some of these principles increase the self-stability of the limb and, thus, minimize neural control effort (Fischer and Blickhan,2006). These are the so-called `pantograph behaviour' (parallel motion of scapula and forearm and femur and tarsometatarsus, respectively) and the placement of the forelimb right below the eye. These features characterize the locomotion of small mammals regardless of their phylogeny. Their adaptive advantage for locomotion on irregular and uncertain substrates is further evident in the re-acquisition of a crouched posture in small-sized mammals that descent from larger-sized ancestors such as the hyraxes (Hyracoidea), the mouse deer (Tragulidae) or the ferrets (Mustelidae)(Jenkins, 1971; Fischer et al., 2002). It,therefore, seems reasonable to assume that small arboreal primates would benefit greatly from retaining these principles but it has been demonstrated that primates display a more extended and more protracted forelimb posture at the beginning of a step cycle than other mammals(Larson, 1998; Larson et al., 2000).

The ultimate objective of the present study is to find out whether these changes in forelimb posture are related to changes in body size and/or to changes in the skeletal intra- and interlimb proportions. Considering the forelimb geometry of other small mammals on the one hand and the overall uniformity of hindlimb geometry in small mammals including primates on the other hand, it will be hypothesized that, in primates, changes in forelimb geometry are caused by constraints rather than by their increased adaptive value for arboreal locomotion on narrow supports. The present paper attempts to find out what kind of constraints act on forelimb geometry. The first part of the study investigates forelimb kinematics in four species of small arboreal quadruped primates (mouse lemur, brown lemur, cotton-top tamarin and squirrel monkey) with regard to the kinematic principles displayed by other small mammals: the predominance of scapula excursion in limb protraction and retraction, the parallel motion of scapula and forearm and the function of the intrinsic limb joints in providing limb compliance.

As the three-segmented fore- and hindlimbs of quadruped mammals are constrained to display the same pivot height and angular excursion, intralimb proportions and the length ratio between fore- and hindlimbs play a crucial role in adjusting limb kinematics to certain biomechanical demands such as postural stability and stress reduction. A crucial factor in the primate-specific diagonal sequence gait is the relationship between limb length and body size because long limbs increase the risk of interference between ipsilateral fore- and hindlimbs. It can be hypothesized that the relationship between limb length and body size and the ratio between fore- and hindlimb length act as constraints on limb geometry. Therefore, the second part of this study examines the scaling pattern of forelimb length, the length ratio between forelimbs and hind limbs and the intralimb proportions of the forelimb. Fischer and Blickhan demonstrated that the crouched forelimb posture of small mammals is combined with skeletal intralimb scapula, humerus and radius proportions of approximately 1:1:1(Fischer and Blickhan, 2006). A more extended limb posture requires asymmetrical proportions for self-stability (Seyfarth et al.,2001). In this morphometric part of the paper, a broader sample of quadrupeds is considered in an attempt to test whether primates in general differ from other mammals or whether previously suggested differences in limb bone lengths characterize only larger primates that display more derived locomotor behaviours such as terrestrial quadrupedalism.

Finally, the discussion section proposes a hypothesis about the hierarchical structure of dependencies in the character evolution of primate locomotion. This section explores the way in which concurrence between initial adaptations to walking on narrow supports (prehensile hindlimbs, diagonal footfall sequence and dynamic weight shift mechanism) and subsequent adaptations to other locomotor modes constrain the limb geometry in primates.

Forelimb kinematics were compared in four species of arboreal quadrupedal primates: the grey mouse lemur (Cheirogaleidae: Microcebus murinus J. F. Miller 1777), the brown lemur (Lemuridae: Eulemur fulvus E. Geoffroy St Hilaire 1796), the cotton-top tamarin (Callitrichidae: Saguinus oedipus Linnaeus 1758) and the squirrel monkey (Cebidae: Saimiri sciureus Linnaeus 1758). Motion analysis was conducted on two adult individuals of each species. Their body mass, sex and age are listed in Table 1. All animals were kept in accordance with German animal welfare regulations, and experiments were registered with the Committee for Animal Research of the Freistaat Thüringen, Germany.

Criteria for species selection were derived from the hypotheses placing the adaptive origin of primates in a small branch milieu(Napier, 1967; Cartmill, 1972; Rose, 1973; Sussman, 1991). Accordingly,the animals needed to be small in terms of body size but had to span a significant size range in order for the influence of size variation to be studied. Animals had to use arboreal quadrupedalism as their preferred locomotor mode. The four selected species fulfil these criteria. They prefer to run and walk on horizontal and oblique branches but are also capable of leaping. Grey mouse lemurs are the smallest primates in the world. Cotton-top tamarins and squirrel monkeys are small quadrupedal New World monkeys.

Animals were habituated 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 (Walker, 1979; Garber, 1980; Arms et al., 2002). The speed of the rope-mill was not fixed but was adjusted to obtain the animal's preferred walking velocity.

The walking velocity of each species varies moderately. Isolated very slow or very fast strides were excluded from the study. To compensate for differences in body mass across the sample, velocity was converted into Froude number using the Formula Fr=v²/gl(Alexander and Jayes, 1983),where v is raw speed, g is gravitational acceleration and l is a characteristic length of the animal. The cube root of body mass was used here as a characteristic length variable instead of hip height or hindlimb length because geometric similarity of hindlimb geometry is not present among the four primates.

Uniplanar cineradiographs were collected in lateral view at 150 frames per second. The methods of collecting and processing kinematic variables from cineradiographs have been described in detail elsewhere(Schmidt, 2005b) and will be summarized only briefly here. The X-ray equipment consists of an automatic Phillips® unit with one X-ray source which applies pulsed X-ray shots(Institut für den Wissenschaftlichen Film, Göttingen). The X-ray images were recorded from the image amplifier either onto 35 mm film(Arritechno R35-150 camera, Arnold & Richter Cine Technik, München,Germany) or using a high-speed CCD camera (Mikromak® Camsys; Mikromak Service K. Brinkmann, Berlin, Germany). X-ray films were then 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 the x and y coordinates of the landmarks, correcting the distortions of the X-ray maps automatically with reference to the x and ycoordinates of a recorded grid.

The complete dataset obtained for individuals of the four primate species in this study includes approximately 13,000 X-ray frames, with at least 25 steps analyzed for each species.

The following kinematic variables were measured or calculated: (1) segment angles – calculated relative to the horizontal plane (the term`protraction' is used for the cranial displacement of the distal end of each segment, `retraction' describes its caudal displacement)(Fig. 1B). (2) Limb joint angles – defined anatomically and measured at the flexor side of each joint (Fig. 1B). (3) Maximum amplitudes of joint excursions during the support phase – difference between maximum extension angle and maximum flexion angle. (4) Total angular excursions of the forelimb – measured as the angle between the lines connecting the point of contact with the ground and the proximal pivot at touchdown and lift-off (Fig. 1C). The proximal pivot of the forelimb is the instantaneous centre of scapular rotation, held and guided by muscles. The pivot corresponds to the point of zero velocity and is usually marked by the intersection of the two overlaying scapular spines near the vertebral border. The forelimb pivot can thus generally be estimated to be the proximal end of the scapular spine.(5) Protraction angle and retraction angle of the forelimb – total angular excursion was divided into an anterior and a posterior angle by drawing a vertical line through the point of ground contact(Fig. 1C). (6) The relationship between anatomical limb length and the shortest functional limb length –distance between the proximal pivot and the point of ground contact – at mid-support, which, here, is used as a kinematic key point, namely the vertical alignment of ground contact point and the proximal pivot of the limb. The term `mid-support' is normally defined as the instant of the peak vertical substrate reaction force, which nearly coincides with the instant at which the shoulder joint passes the wrist joint.

Skeletal specimens (N=222) of 110 mammalian species were examined at the Phylogenetisches Museum Jena, Germany, at the Museum für Naturkunde Berlin, Germany and at the Naturhistorisches Museum Bern,Switzerland. Over 50% of the sample was composed of specimens collected in the wild (N=113), nine specimens were captured wild and then kept in a zoo. The remaining specimens died in a zoo and were probably born in captivity. The adult status of the specimens was judged on the basis of the fusion of the epiphyses of the long bones. In those species for which more than one specimen was available, the largest specimen in terms of total fore-and hindlimb length was chosen. It was decided not to calculate mean values for each species because the intraspecific and interspecific allometry of limb bones can be different (e.g. Steudel,1982). While static intraspecific allometry between different sized adults of a species is determined by ontogenetic development(Wayne, 1986; Lammers and German, 2002; Schilling and Petrovitch,2005), interspecific allometry reflects size-related mechanical adaptations. Accordingly, the limb proportions of different sized conspecifics do not scale isometrically and can be very different. The taxa included and the sample representing each taxon can be seen in Table 2, along with the corresponding body mass values and the measured lengths of scapula, humerus and radius. Those specimens labelled with an asterisk denote specimens for which body masses were compiled from the literature. The available head–trunk length in those specimens was used to decide whether the mean or the maximum body mass values were more appropriate in estimating the unknown mass (Grzimek, 1987; Rowe, 1996; Garbutt, 1999; Nowak, 1999). All other body mass values relate to the skeletal specimens.

The majority of taxa included in the primate sample consist of arboreal quadrupedal primates. The members of the Cheirogaleidae, Lemuridae,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 taxa exhibits distinct specializations for leaping(e.g. extremely elongated hind limbs)(Rowe, 1996; Fleagle, 1999). Included Galagonidae are mostly such species that prefer to walk and run quadrupedally but do not show the morphological specializations of vertical clingers and leapers with the exception of the Northern lesser bush baby. Loridae walk and climb with large limb excursions but none of these primates has been observed to leap (Walker, 1979; Demes et al., 1990; Schmitt and Lemelin, 2004). Quadruped climbing is – along with walking and leaping – a preferred mode of locomotion in Colobinae(Napier, 1963; Morbeck, 1979; Isler and Grüter, 2005). Cercopithecine Old World monkeys (baboons, macaques, patas monkeys, guenons)are primarily adapted to semi-terrestrial and terrestrial quadrupedalism(Napier, 1967; Rollinson and Martin, 1981; McCrossin et al., 1998). Still, most guenons and some macaques have returned to arboreality. Re-adaptations to arboreality in guenons have been observed to affect the morphology of the autopodia more than that of proximal limb elements(Meldrum, 1991; Schmitt and Larson, 1995). The marsupial, rodent and carnivore samples mostly include small arboreal and terrestrial species. The majority of these mammals tend to move in a roughly similar fashion characterized by a crouched limb posture(Jenkins, 1971; Fischer et al., 2002). Cursorial specializations were attributed to the larger carnivores (racoon,cats and viverrids) (Jenkins and Camazine,1977; Nowak,1999).

In order to evaluate the proportions of a three-segmented limb structure,intralimb proportions in this study are expressed as the percentage each segment length represents of the sum of the lengths of the segments. The hand is omitted due to its negligible quantitative contribution to forelimb protraction and retraction in palmigrade mammals(Fischer et al., 2002; Schmidt, 2005b). Only a few species in the sample use their hands in a digitigrade posture (some terrestrial cercopithecines and some carnivores) but for comparative reasons their hand proportions were not considered in this study.

Interlimb ratio is calculated for the three-segmented limbs using the following formula: scapula+humerus+radius/femur+tibia+ tarsometatarsus in percent. The morphometric data of the hindlimb for this sample were taken from a previous publication (Schmidt,2005a). Original data on hindlimb length for the new specimens in the sample (Loridae, Galagonidae, Daubentoniidae and Colobinae) can be provided on request.

A one-way fixed-factor analysis of variance (ANOVA) was used to determine the degree of variance of forelimb proportions. Comparison took place on the lowest taxonomic level of families, among primates at least. The lower sample size of tree-shrews, marsupials, rodents and carnivores made a further subdivision into families less appropriate. Because sample sizes are unequal across the taxa, the GT2 method was employed(Hochberg, 1974; Sokal and Rohlf, 1995) to compare group means and to calculate lower and upper comparison limits for each sample mean. Means are significantly different if their comparison intervals do not overlap (Hochberg,1974; Sokal and Rohlf,1995). The comparison interval is different from the confidence interval because its computation uses the critical values of the studentized maximum modulus distribution for the comparison of multiple means instead of the Student's t-distribution used to calculate confidence intervals.

It was investigated whether the allometric scaling of the relative segment lengths is a significant source of their variation. Relative segment lengths and body mass values were log-transformed (ln) to produce log shape variables. Bivariate regressions were derived using the reduced major axis (RMA)line-fitting technique. The coefficient of determination r² was calculated in order to estimate the portion of variation in relative segment length that can be explained by the variation of body mass (Sokal and Rohlf,1995).

The first part of this section describes forelimb kinematics in four small arboreal quadruped primates (the grey mouse lemur, the brown lemur, the cotton-top tamarin and the squirrel monkey) with regard to the kinematic principles displayed by other small mammals: the predominance of scapula excursion in limb protraction and retraction, the parallel motion of scapula and forearm and the function of the intrinsic limb joints in providing limb compliance. The body mass of the animals ranges from 100 to 3000 g, thus allowing some conclusions to be drawn regarding the influence of size on forelimb kinematics. Walking speed varies considerably in all four species(grey mouse lemur, 0.39–0.89 m s^–1; brown lemur,0.56–1.45 m s^–1; cotton-top tamarin, 0.40–0.87 m s^–1; squirrel monkey, 0.39–1.00 m s^–1)but its influence of limb kinematics is lower than one might expect. Like various other small non-cursorial mammals(Fischer et al., 2002; Schilling and Fischer, 1999),the primates modify their walking speed mainly by changing temporal gait parameters. Contact phase duration decreases with increasing speed and thereby step frequency increases. Spatial gait parameters like step length and body progression during the contact phase were not or only to a minor degree modified to increase velocity. Only the cotton-top tamarin increases its walking speed by increasing both step frequency and step length. Fig. 2 shows the variation of step duration and step length over the range of dimensionless speed. The majority of steps of the grey mouse lemur, the brown lemur and the tamarin overlap with respect to Froude numbers but the squirrel monkeys moved somewhat slower. At Froude numbers equal to those of the other primates, squirrel monkeys preferred to run. Although kinematic parameters vary considerably in all species, on average less than 20% of this variation results from variation in speed. Speed-dependence is, therefore, considered in the description only for those kinematic parameters that consistently and to a higher percentage change with increasing walking velocity. r² values are given to characterize the strength of the relationship between walking speed and the respective parameter.

The second part of this section focuses on intra- and interlimb proportions in primates and other mammals. In the primate-specific diagonal footfall sequence, the relationship between limb length and body size and the ratio between fore- and hindlimb length can act as constraints on limb kinematics. Therefore, the scaling pattern of forelimb length, the length ratio between fore- and hindlimbs and the intralimb proportions of the forelimb are examined. In this morphometric section of the paper, a broader sample of quadrupeds is considered in an attempt to test whether primates in general differ from other mammals.

The proximal pivot of the forelimb is the instantaneous centre of scapular rotation, held and guided by muscles. This point is on the same height level as the ipsilateral hip joint providing fore- and hindlimbs the same functional length. Lemurs, however, seem to have unequal functional limb lengths, judging by the strong downward incline of their trunks when they walk, meaning that their proximal scapular border is lower than their hip joint. The scapula excursions of the brown lemur are very large and the two spines hardly overlap at touchdown or lift-off indicating that the point of zero velocity is situated outside the body (Fig. 3). The measured angle of total forelimb excursion in the brown lemur (86±3 deg.), therefore, is not only significantly larger than that of the other primates but is also larger than its hindlimb excursion angle (74 deg.) (Schmidt,2005a). With the exception of the brown lemur, total forelimb excursion is fairly similar among the primates(Table 3). Angular excursion hardly changes with increasing speed. Variations in step length are often accompanied by variations of limb stiffness and functional limb length. Therefore, angular excursion does not necessarily increase with increasing step length.

By drawing a vertical line through the point of ground contact, the total angular excursion of the forelimb can be split into a retraction angle and a protraction angle. The protraction angle of the forelimb is always larger than the retraction angle. The retraction angle is fairly constant in the grey mouse lemur, the cotton-top tamarin and the squirrel monkey but larger in the brown lemur (Table 3). Accordingly, protraction is more variable. The forelimb of the brown lemur is the most protracted; the forelimb of the squirrel monkey is the least protracted. Obviously, body size has no significant effect on angular excursion in the three smaller primates but the brown lemur exhibits a higher degree of forelimb protraction.

As previously shown for the hindlimbs in these species(Schmidt, 2005a), highly uniform limb excursion can be the result of quite different segment and joint kinematics. This is also the case for the forelimb. Fig. 4 shows the typical excursion of scapula, humerus, radius and hand during the support phase of a step cycle. Table 4 lists mean values, standard deviations and the overall range of the touchdown and lift-off angles, as well as the amplitude of excursion during the stance phase.

The movement of the scapula is the most similar factor among the species(Fig. 4). Mean angles at touchdown and lift-off and the mean amplitude of scapula retraction hardly differ among the species (Table 4). Scapula retraction starts at an angle of approximately 45 deg., continues more or less regularly throughout the support phase and ends at an angle of approximately 90 deg. No yield has been observed in the scapulo–thoracic `joint', and in this respect the most proximal forelimb joint is comparable with the hip joint of the hindlimb.

Humeral excursion differs much more among the species and in such a way that body size seems to influence the degree of humeral protraction. The brown lemur exhibits the greatest humeral protraction and the largest amplitude of humeral excursion. The lowest mean touchdown angle was measured in the grey mouse lemur at less than 90 deg. Cotton-top tamarins and squirrel monkeys protract their humeri to a similarly larger degree. The average touchdown angle is approximately 100 deg. but increases with increasing walking velocity in both species (Saguinus, r²=0.245; Saimiri,r²=0.516). It should be noted, however, that despite the lower degree of humeral protraction, the forelimb in the mouse lemur exhibits the same degree of protraction as in the cotton-top tamarin and the squirrel monkey. In all four species, the angular velocity of humeral protraction is higher in the first half of the support phase and slows down to near zero during the last 10% of the stance phase when the humerus reaches a more or less horizontal position. This positioning is influenced by walking speed in the brown lemur (r²=0.241). At higher speeds, the distal end of the humerus is raised upon the level of the shoulder. It might be affected by the overall slower walking speed that the humerus of the squirrel monkey is markedly less retracted and seldom, if ever, reaches a horizontal position.

Throughout most of the support phase, the forearm moves exactly in parallel to the scapula (Fig. 4). This matched-motion pattern of the first and the third segment is said to be typical of a three-segmented leg and can also be seen in the hindlimb between thigh and foot (Fischer and Witte,1998; Fischer et al.,2002). The matched-motion pattern is only broken at the beginning and end of the support phase, when forearm excursions exceed scapula excursions. The variability of forearm excursion among the four species does not appear to be related to size. In the cotton-top tamarin, the degree of forearm retraction is influenced by speed (r²=0.274) in such a way that step length increases by an increasing lift-off angle of the forearm.

While the upper arm and forearm undergo large angular excursions and the scapula dominates limb retraction due to its high pivot, the hand plays a minor role in forelimb excursion. All four species place their hands in a palmigrade posture. The touchdown angle deviates from zero only because of the thickness of the palmar patches. Carpus and metacarpus are lifted from the support during the second half of the stance phase. The angles at lift-off vary widely in each species but their mean values are similar(Table 4).

Almost all quadrupedal mammals flex their limbs to a certain degree during the support phase. This means that the anatomical limb length, i.e. the sum of the lengths of limb segments, does not correspond to the functional limb length, i.e. the distance between the point of ground contact and the proximal pivot of a limb. The ratio between functional limb length and anatomical limb length expresses the degree of overall limb flexion and normally varies throughout the support phase. Functional limb length is at its minimum when the hand passes under the scapula pivot. Several authors term this posture`mid-stance' or `mid-support' regardless of its timing relative to stance duration because it marks the transition from the braking phase to the propulsive phase in limb retraction. Table 5 gives the mean angles at mid-stance of the limb joint illustrating how each joint contributes to overall limb flexion and, thus, to the compliance of the limb. Of the four primates in this study, the forelimb of the grey mouse lemur is the most flexed throughout the support phase. At touchdown, it forms 82% of the anatomical limb length and at lift-off, 74%. In the most flexed posture, functional forelimb length is 62% of the anatomical length. The most extended forelimbs are exhibited by the squirrel monkey(ratio: touchdown 96%, lift-off 91%). Although the ratio between functional and anatomical limb length is very similar to that in the brown lemur(touchdown 95%, lift-off 94%), limb flexion at mid-stance is less pronounced in the squirrel monkey (77%) than in the brown lemur (73%). Generally, the forelimb is most extended at the beginning of the step cycle. The grey mouse lemur and the brown lemur significantly decrease limb compliance with increasing speed. In the grey mouse lemur, the amount of shoulder flexion(r²=0.338) and elbow flexion(r²=0.327) during the contact phase decreases. Limb compliance in the brown lemur is reduced due to a decrease of elbow flexion(r²=0.429).

Fig. 4 depicts the joint excursions for the shoulder, elbow and wrist joint of the four species during the support phase of a step cycle. Maximum shoulder joint extension occurs at the beginning of the cycle. The shoulder joint is almost fully extended in the brown lemur but only moderately extended in the grey mouse lemur. A significant yield followed by a re-extension phase was observed only in the squirrel monkey. In the other three species, shoulder flexion lasts until mid-stance, from whence on the shoulder joint seems to be frozen at a constant angle and the humerus is further displaced only by scapular retraction.

The flexion and re-extension pattern of the elbow joint reveals the prominent role it plays in yielding (Fig. 4; Table 5). With the exception of in the grey mouse lemur, the elbow joint is at its most extended at touchdown. Maximum flexion occurs at mid-stance.

While the hand is resting on the support, the wrist joint extends continuously (dorsiflexion) as a result of the retraction of the forearm during the first half of the stance phase. Maximum extension occurs when the hand passes under the elbow joint. Then, the hand is subsequently lifted from the ground by the flexion of the wrist. This motion can be fairly rapid, as observed in the grey mouse lemur and the squirrel monkey.

The evaluation of limb proportions focuses on the basic difference between primates and other mammals of small body size. Greater effort was, therefore,made to obtain large samples of small-sized taxa, in order to permit comparison between those animals thought to be closest to the presumed ancestral morphometric pattern of each phylogenetic lineage.

Biewener emphasizes that scaling analyses in a large and phylogenetically diverse sample are often marred by the fact that body size-related effects cannot accurately be distinguished from phylogenetic signals and other functional determinants of skeletal form (evolutionary ancestry, life style,locomotor behaviour) (Biewener,2005). Therefore, morphometry in this study focuses on comparison at the family level within primates. Differences in forelimb length and proportion can be expected to reflect size-related effects much more accurately on this lower taxonomic level due to the greater similarity of locomotor behaviours. The cercopithecid Old World monkeys were divided into the two subfamilies Cercopithecinae and Colobinae because the colobus monkeys and leaf monkeys generally use more quadrupedal climbing, suspensory behaviour and leaping in progression than the macaques, baboons and guenons. The lower sample size of tree-shrews, marsupials, rodents and carnivores made a further subdivision into families less appropriate.

Fig. 5 shows the scaling pattern of forelimb length to body mass for the entire sample of quadrupedal mammals included in this study. Body mass ranges between 15 g (dormouse Muscardinus avellanarius) and 23.5 kg (baboon Papio hamadryas). Because subdivision of the primate sample into the eight families would be less illustrative, primates were subdivided into Strepsirhini, Platyrrhini and Catarrhini for graphical reasons. Allometry coefficients are shown in Table 6 along with the corresponding confidence intervals at the various taxonomic levels, which indicate that the scaling pattern strongly depends on the degrees of relationship between the taxa considered. Slopes were considered to deviate significantly from isometry if the 95% confidence interval did not include the isometric expectation (0.33). The F-value indicates that body mass influences forelimb length significantly in all groups but the Galagonidae and Colobinae.

Forelimb length tends to scale with positive allometry in most primate families, tree-shrews, rodents and carnivores but only in primates does the confidence interval of the allometry coefficient fail to overlap with the isometric expectation of 0.33. However, this is not the case for primate families. The y-intercept and its 95% confidence interval indicate that primates as a group do not have significantly longer forelimbs than the other mammals. Adaptive differences among primates are reflected by the huge variation in y-intercepts but the confidence intervals do widely overlap (Table 6). Among the smallest species of all groups, where body mass is below 150 g, forelimb lengths are equal (Fig. 5). A clear distinction between primates and other mammals appears if body mass exceeds 200 g. The forelimbs of primates, then, are relatively longer than those of other mammals, regardless of the locomotor habitat or phylogenetic position of the latter.

Almost all species considered here have shorter forelimbs than hindlimbs(Fig. 6). Interlimb ratio is calculated for the three-segmented limbs using the following formula: scapula+humerus+radius/femur+tibia+tarsometatarsus in percent. The majority of specimens up to a body size of about 5 kg have interlimb ratios below 90,except in the case of marsupials. No distinction can be made between rodents,carnivores, primates and tree-shrews. Scaling effects emerge if body mass exceeds 2.5 kg but they are significant only for the Cebidae and Cercopithecinae, in which the interlimb ratio increases with increasing body size. The four primates investigated in the kinematic study exhibit the following interlimb ratios: grey mouse lemur 75, brown lemur 73, cotton-top tamarin 70 and squirrel monkey 77.

Fig. 7 shows the mean values of the relative segment lengths and their associated comparison intervals at the taxonomic level of families (primates) or higher phylogenetic levels in the other mammals. Primates differ significantly from other mammals in the relative lengths of their scapula and radius, with Cheirogaleidae being intermediate. Scapula proportion in primates has reduced to approximately 20%of forelimb length whereas radius proportion has increased to approximately 38–40%. The relative length of the middle segment, however, is fairly constant. In most cases, the comparison intervals of the humerus mutually overlap among the groups. Changes in forelimb proportion are, thus, mainly brought about by alterations in the relative lengths of the outer segments.

The intermediate position of the Cheirogaleidae results from size-related differences between the grey mouse lemurs and the dwarf lemur. The genus Microcebus differs from Cheirogaleus and all other primates in having forelimb proportions of nearly 1:1:1, fairly similar to other small mammals. The forelimb proportions of Cheirogaleus tend to approximate proportions of 1:2:2, the pattern found in most other primates.

Although group-specific differences occur to some degree in primates, the general pattern is less dependent on body size, phylogeny and locomotor habitat than one might expect. The significant exceptions of Loridae and Colobinae may be related to the two groups' preference for quadruped climbing. A relatively short scapula probably facilitates forelimb excursions outside the parasagittal plane (e.g. reaching above the head). The secondarily dwarfed Callitrichidae have relatively longer shoulder blades and shorter forearms than other arboreal quadruped primates but don't revert to the forelimb proportions of the primarily small grey mouse lemurs.

A scaling analysis of the relative segment lengths was carried out to test the influence of body mass variation on forelimb proportions. The overall scaling pattern of the relative segment lengths is shown in Fig. 8. Body mass values are log-transformed (ln) but to make it easier to distinguish between the groups the relative segment lengths were not log-transformed here. Regression was, of course, computed from bivariate log-transformed data. It turns out that body mass has almost no influence on forelimb proportions in most of the groups, as is indicated by the F-values and the coefficients of determination(Table 7). Proportions are size-independent in Marsupialia, Carnivora, Scandentia and most primate families except Cheirogaleidae and Lemuridae. Body mass affects the relative length of the humerus in Rodentia, Cheirogaleidae and Lemuridae, in which humerus proportion increases with increasing size. Size seems to influence radius proportions in primates as a whole but this effect is not visible at the family level, indicating again that the taxonomic level chosen for analysis affects the interpretation of the results.

Like many other mammalian lineages, primates descended from ancestors whose body size was small (Jenkins,1974; Gebo, 2004; Soligo and Martin, 2006). Several authors have, therefore, emphasised the importance of studying the behaviour and ecology of small arboreal mammals in reconstructing the early evolution of primates and understanding the functional significance of special morphological adaptations (LeGros Clark,1959; Cartmill,1972; Martin,1972; Cartmill,1974; Jenkins,1974; Rasmussen,1990; Gebo, 2004; Sargis et al., 2007). Various locomotor studies have shown that small mammals display a high level of similarity in their locomotor kinematics and limb proportions independent of phylogeny and locomotor habitat (Jenkins,1971; Fischer et al.,2002). These common kinematic principles (crouched limb posture,operational division between propulsive proximal elements and limb joints that serve for compliance) have been proposed to be adaptive to postural stability in unanticipated situations within a disordered spatial arrangement of surfaces (Fischer, 1994). This section of the paper will, thus, investigate why primate forelimb geometry differs in some regards from that of other small mammals by combining the present results on forelimb geometry with the author's previous study of hindlimb geometry (Schmidt,2005a). Links will be made to other distinctive characters of primate locomotion such as the preference for a specific footfall sequence,the particular weight distribution pattern between fore- and hindlimbs, and subsequent adaptations to other locomotor modes. It will be discussed how this set of factors generated a frame of constraints within which limb geometry evolved. A hierarchical structure of dependencies between the individual characters can, thus, be proposed which will assist in differentiating between true adaptations (to the small-branch locomotor habitat) and constrained character transformations. The latter are better regarded as evolutionary by-products [`spandrels' according to Gould and Lewontin(Gould and Lewontin, 1979)] as recently proposed by Raichlen and Shapiro(Raichlen and Shapiro,2007).

A condition of symmetrical tetrapod locomotion is that the proximal pivots of fore- and hindlimbs are on the same level(Kuznetsov, 1985; Fischer and Witte, 1998). This is also the case for the majority of quadruped mammals. Exceptions occur, for example in chimpanzees, giraffes and hyenas, in which adaptations to other locomotor modes or to non-locomotor activities are predominant. In mammals,the level of the proximal limb pivots is not necessarily constant during the support phase but can raise and fall synchronously in a pair of fore- and hind limbs (Fig. 9), thus permitting vertical oscillations of the centre of body mass that are essential for whole-body mechanics (Cavagna et al.,1977; Biewener,2006; Biknevicius and Reilly,2006). Fore- and hindlimbs, thus, have the same functional length regardless of differences in anatomical length. This guarantees that the limbs move with the same step frequency and that the same step length is brought about by the same angular excursion. As a result, it largely determines the relationship between functional and anatomical limb length and, thus, the adaptability of limb geometry to biomechanical demands through the adjustment of limb segmentation and angulation. For primates displaying a specific diagonal sequence gait, another crucial factor is the relationship between limb length and body size because long limbs increase the risk of interference between ipsilateral fore- and hindlimbs. Most primates have significantly longer limbs relative to their body size than other mammals, except in the case of the very small species which weigh less than 200 g. The anatomical length differences between fore- and hindlimbs, however, remain similar to those in other mammals, with an interlimb ratio of between 70 and 85 being typical for smaller mammals in general. Hindlimbs, then, are always more flexed than forelimbs. Interestingly, hindlimb lengthening in primates affects neither intralimb proportions nor limb kinematics in the four species studied here (Schmidt, 2005a). Hindlimb elongation is simply achieved through the proportional lengthening of all three limb segments. Thus, limb lengthening has no effect on intralimb proportions, limb excursion angle or limb kinematics. Fig. 9 shows that the prosimian primates and the small callitrichid New World monkeys share a similar hindlimb posture with other mammals of their body size. In Cebidae (e.g. Saimiri sciureus) and Cercopithecidae, hindlimb kinematics have changed in the direction of a more erect limb posture. As a result of this very conservative hindlimb geometry, the point of touchdown of the hind limb is shifted cranially – and, thus, into the excursion sphere of the forelimb.

In the diagonal footfall sequence of primates, hindlimb touchdown is followed by the touchdown of the contralateral forelimb(Hildebrand, 1967; Tomita, 1967). Moreover, the ipsilateral forelimb is still on the ground when the hindfoot is positioned. Primates can avoid interference between the ipsilateral limbs by overstriding(Hildebrand, 1967; Larson and Stern, 1987; Demes et al., 1994; Wallace and Demes, 2007). This is very typical for many species when walking on the ground but it has been less frequently observed during arboreal locomotion(Wallace and Demes, 2007). Obviously, many primates avoid overstriding on arboreal substrates. Therefore,limb interference has to be avoided by means of another strategy.

Arboreal primates avoid limb interference by a cranial shift of the forelimb step (Fig. 10). They display much greater asymmetry between the angles of protraction and retraction. As the protraction angle increases, retraction decreases, with the forelimb thus sacrificing part of its caudal excursion sphere to avoid interference with the hindlimb. Total forelimb excursion, however, can thus remain equal to hind limb excursion (Fig. 10). Larson (Larson,1998) has already proposed that forelimb protraction could be a strategy to avoid limb interference – an assumption supported by the present survey of both limb kinematics and limb proportions. A significantly higher degree of forelimb protraction has been observed in those primates with very long hindlimbs (e.g. Lemuridae). Species with short limbs (e.g. grey mouse lemurs) do not display greater forelimb protraction than other small mammals. This also applies to those arboreal marsupials that show certain locomotor characteristics, which are convergent with primates. Although Schmitt and Lemelin (Schmitt and Lemelin,2002) argued that the touchdown position of the forelimb of the woolly opossum Caluromys philander is primate-like, the photographs in their study and in Lemelin et al.(Lemelin et al., 2003) show that it is quite similar to the forelimb position of tree-shrews(Schilling and Fischer, 1999),with the hand placed right below the eye and the touchdown angle of the humerus almost vertical. The majority of quadruped mammals place their forefeet right below the eye, not for visual control but as a fixed point to control the geometry of the touchdown position(Fischer et al., 2002). This strategy makes the angle of attack of the centre of body mass very constant. Some authors have explained this invariant angle as a mechanical parameter to control limb stability (Fischer and Blickhan, 2006; Hackert et al., 2006).

From this comparative perspective, the question of why primates have abandoned this strategy deserves attention and further discussion. Is the`new' forelimb posture at touchdown really better adapted to the specific demands of primate locomotion than the `old' one? One argument against this assumption is that the extended and protracted forelimb of primates is more susceptible to gravitational loading than the crouched posture of other mammals as the substrate reaction force vector is far removed from the limb joints (Biewener, 1983; Schmitt, 1999; Larney and Larson, 2004; Schmidt, 2005b). Only the ability of many primates to reduce the weight borne by the forelimb may help to overcome this problem (Reynolds,1985). Those primate species that do not reduce forelimb loading– Loridae (Ishida et al.,1990; Demes et al.,1994; Schmitt and Lemelin,2004) and Callitrichidae(Schmitt, 2003) –display significant changes in the contractile properties of their forelimb muscles (Schmidt and Leuchtweis,2007; Schmidt and Schilling,2007).

As some strategies of stabilizing the forelimb posture mechanically (e.g. through an invariant touch down angle) have given way to a restrictive footfall sequence combined with limb elongation, it might well be that the observed changes in forelimb proportions reflect advanced mechanical strategies to deal with the problem of limb instability. As a result of the shift towards a (relatively speaking) shorter scapula and longer forearm,forelimb proportions go from being symmetrical to being asymmetrical. Based on numerical simulations, Seyfarth et al. suggested that the asymmetric structuring of a three-segmented limb enhances the self-stability of movement(Seyfarth et al., 2001). The hindlimb of mammals generally corroborates this hypothesis(Seyfarth et al., 2001; Schmidt and Fischer, 2008). Whether the basic change in forelimb proportions in primates really enhances limb stability, however, remains to be proven using mathematical simulations.

As the smallest living primates, grey mouse lemurs have often been suggested to be reliable models of the last common ancestor of primates(Martin, 1972; Gebo, 2004). In the present study, it has been shown that grey mouse lemurs display exactly the same limb geometries as other small mammals. Limbs are not elongated and move in a crouched posture during the entire step cycle. However, grey mouse lemurs differ from other small mammals in having powerful prehensile hindfeet. They walk in a diagonal-sequence gait and they are able to shift weight dynamically from the forelimbs to the hindlimbs (M.S., unpublished observations). As the set of these three characters evolved convergently in arboreal mammals three times at least, namely in primates(Hildebrand, 1967; Martin, 1968; Kimura et al., 1979; Reynolds, 1985), in some marsupials (Goldfinch and Molnar,1978; Cartmill et al.,2002; Schmitt and Lemelin,2002; Cartmill et al.,2008) and in some carnivores(Rollinson and Martin, 1981; Cartmill et al., 2007), it is plausible to assume that the characters not only coincide but are mutually interdependent, as already suggested by several authors(Rollinson and Martin, 1981; Cartmill et al., 2002; Schmitt and Lemelin, 2002; Lemelin et al., 2003). The reasons for these interdependencies have been discussed for many years but are not yet completely understood.

Grasping feet have the unique capacity to produce moments about the substrate axes, which can, in turn, be transmitted to the body, thus allowing a dynamic weight shift from side to side(Cartmill, 1985; Preuschoft, 2002) or from the forequarter to the rear (Witte et al.,2002; Schmidt,2005b). A consistent posterior weight shift does not occur if forelimbs are equipped with the same capacity for powerful grasping and weight shifts in any direction, as seems to be the case in Loridae(Ishida et al., 1990; Schmitt and Lemelin, 2004). The production of moments requires forces to be exerted from more than one point of the plantar surface onto the substrate. Moments can also be produced on flat ground but the substrate reaction moments will be lower under these conditions. Once powerful pedal grasping had evolved in primates, it could be used to actively regulate the weight distribution between the limbs regardless of the position of the centre of body mass(Witte et al., 2002). Only under these circumstances was a change in the footfall sequence to hindlimb contact prior to forelimb contact meaningful because it could reduce the impact of touchdown of the forelimb. The moment the forelimb contacts the support is perhaps one of the most critical phases in quadruped locomotion. The forelimb normally carries the greatest part of the body mass because of its closer proximity to the centre of body mass (e.g. Demes et al., 1994). As a result, it is mainly the forelimb that has to redirect the body's vertical velocity component from down to up. As the quality of the support cannot be anticipated, however, secure contact cannot be guaranteed, especially in smaller mammals. The adjustment of limb geometry to an obstacle or unstable support is only possible after contact, not prior to it. Small mammals deal easily with unexpected irregularities in the support and are highly adapted to compensate for any disturbance in the trajectory of the centre of body mass because of their permanent crouched limb posture(Jenkins, 1974; Fischer et al., 2002). However, the dynamic weight shift mechanism of primates and some marsupials allows them not only to react to but also avoid undesirable disturbances by reducing the load carried by the forelimb.

Limb elongation relative to body size, one of the major adaptations to leaping, appeared later in primate evolution(Gebo, 2004), at a time when the trinity of grasping limbs, weight shift mechanism and diagonal sequence gait was already established. Assuming that a diagonal footfall sequence makes the posterior weight shift mechanism most effective and is therefore indispensable, a change in limb geometry is, then, essential to avoid interference between ipsilateral fore- and hindlimbs. The fact that only the forelimb was affected by this change might be explained by the dominant role of the hindlimb as the propulsive organ (e.g. Demes et al., 1994). Hindlimb geometry seems to be optimized to fulfil this function and is, therefore, much more conservative across mammals in general(Schmidt and Fischer,2008).

Finally, it is important to emphasize that the proposed hierarchical structure of dependencies in character evolution is assumed to be valid for the evolutionary processes that produce these characters. The sometimes weaker relationship between these characters in several primate taxa reflects the multiple strategies `invented' by primates to overcome the problems and constraints connected with the competition between initial walking adaptations on terminal branches and successive adaptations to other locomotor modes such as leaping in lemurs or acrobatic climbing in lorises. These constraints and their solutions were the driving force behind primate locomotor evolution. Once the transfer of moments by prehensile feet was part of the standard locomotor repertoire, a gradual caudalization of the centre of body mass from its anterior position in quadrupeds to a more posterior location, for example in hominoids (Stern, 1976; Reynolds, 1985; Raichlen et al., 2007), was possible without any mechanical constraints. Once primates had learned to stabilize the protracted and extended forelimb against disruptive forces, they were able to use the forelimb to reach out and test the support, to increase gait compliance and, of course, in many other locomotory and non-locomotory functions as suggested by Larson (Larson,1998).

This research was supported by the Deutsche Forschungsgemeinschaft(Innovationskolleg `Bewegungssysteme', INK 22/B1-1). I wish to thank Dieter Haarhaus (Institut für den Wissenschaftlichen Film, Göttingen) and his team for their patience and competence in cineradiography. Danja Voges kindly provided the X-ray films of the cotton-top tamarins. Thanks also to the German Primate Research Centre (Göttingen), Gettdorf Zoo and the Institute of Zoology at the Veterinary University Hannover for kindly providing our institute with animals. I am also grateful to the curators of the Phylogenetisches Museum Jena, Museum für Naturkunde Berlin, Bayrische Staatssammlung München and Naturhistorisches Museum Bern for access to skeletal material in their care. I'm grateful to Martin S. Fischer, Hartmut Witte, and Nadja Schilling for insightful discussions during the stages of this project. I thank the anonymous reviewers for providing many constructive comments and useful advice on the previous draft of the manuscript and Lucy Cathrow for thoroughly editing the language of the manuscript.