Investigating the form-function interface in African apes Relationships between principal moments of area and positional behaviors in femoral and humeral diaphyses.код для вставкиСкачать
AMERICAN JOURNAL OF PHYSICAL ANTHROPOLOGY 127:312–334 (2005) Investigating the Form-Function Interface in African Apes: Relationships Between Principal Moments of Area and Positional Behaviors in Femoral and Humeral Diaphyses Kristian J. Carlson* Department of Anatomical Sciences, School of Medicine, Stony Brook University, Stony Brook, New York 11794-8081 KEY WORDS Gorilla cross-sectional geometry; principal moment of area; locomoter behavior; Pan; ABSTRACT Investigations of cross-sectional geometry in nonhuman primate limb bones typically attribute shape ratios to qualitative behavioral characterizations, e.g., leaper, slow climber, brachiator, or terrestrial vs. arboreal quadruped. Quantitative positional behavioral data, however, have yet to be used in a rigorous evaluation of such shape-behavior connections. African apes represent an ideal population for such an investigation because their relatedness minimizes phylogenetic inertia, they exhibit diverse behavioral repertoires, and their locomotor behaviors are known from multiple studies. Cross-sectional data from femoral and humeral diaphyses were collected for 222 wild-shot specimens, encompassing Pan paniscus and all commonly recognized African ape subspecies. Digital representations of diaphyseal cross sections were acquired via computed tomography at three locations per diaphysis. Locomotor behaviors were pooled broadly into arboreal and terrestrial categories, then partitioned into quadrupedal walking, quadrumanous climbing, scrambling, and suspensory categories. Sex-speciﬁc taxonomic differences in ratios of principal moments of area (PMA) were statistically signiﬁcant more often in the femoral diaphysis than the humeral diaphysis. While it appears difﬁcult to relate a measure of shape (e.g., PMA ratio) to individual locomotor modes, general locomotor differences (e.g., percentage arboreal vs. terrestrial locomotion) are discerned more easily. As percentage of arboreal locomotion for a group increases, average cross sections appear more circular. Associations between PMA ratio and speciﬁc locomotor behaviors are less straightforward. Individual behaviors that integrate eccentric limb positions (e.g., arboreal scrambling) may not engender more circular cross sections than behaviors that incorporate repetitive sagittal movements (e.g., quadrupedal walking) in a straightforward manner. Am J Phys Anthropol 127:312–334, 2005. © 2004 Wiley-Liss, Inc. Strain gauges applied to bone surfaces are the only direct means of measuring in vivo bone deformations during locomotion (e.g., axial compressive, axial tensile, or bending loads). Initial in vivo strain studies (Lanyon and Smith, 1969, 1970) and subsequent others (Biewener and Taylor, 1986; Biewener et al., 1983; Davies et al., 1993; Rubin and Lanyon, 1982) identiﬁed bending as the predominant deformation force that limbs experienced during locomotor activities. These studies addressed how size variation across taxa, as well as changes in speed and gait (e.g., walking and galloping), altered strain loads. However, the locomotor behaviors in these studies were limited to treadmill or runway locomotion, artiﬁcial settings in which limbs were restricted primarily to sagittal movements. Strain proﬁles (e.g., magnitude or orientation) appeared relatively consistent across behavioral changes in these studies. As a greater array of locomotor behaviors was investigated, the strain proﬁles became more variable. Burr et al. (1996) reported higher strain magnitudes in the human tibia during “zigzag” walking/ running on hillsides than during straight walking/ running on a hill or ﬂat surface. They speculated that a gait change created a new mechanical environment to which a bone would be less attuned, and that it would be difﬁcult to envision rapidly operating compensatory mechanisms responding to equally rapid alterations in strain patterns. It fol- © 2004 WILEY-LISS, INC. Grant sponsor: National Science Foundation; Grant number: Doctoral Dissertation Improvement Grant BCS-0002686; Grant sponsor: L.S.B. Leakey Foundation; Grant sponsor: Department of Anthropology, Indiana University; Grant sponsor: University Graduate School, Indiana University. *Correspondence to: Kristian J. Carlson, Department of Anatomical Sciences, Health Sciences Center, School of Medicine, Stony Brook University, Stony Brook, NY 11794-8081. E-mail: [email protected] Received 19 August 2003; accepted 15 June 2004. DOI 10.1002/ajpa.20124 Published online 6 December 2004 in Wiley InterScience (www. interscience.wiley.com). APE LONG BONE GEOMETRY AND LOCOMOTOR BEHAVIOR lows that a locomotor behavior incorporating frequent directional shifts in the velocity vector of an individual may promote the adaptation of a diaphysis to bending in multiple directions in order to reduce any deleterious consequences of a new mechanical environment. Nonhuman primates also demonstrated more variable in vivo strain proﬁles when a wider variety of locomotor behaviors was investigated. Gibbons encountered “considerable variability in strain pattern and peak magnitude among swings . . . contrasting with the stereotypic patterns recorded in walking and running animals” during brachiation (Swartz et al., 1989, p. 270). A macaque exhibited slightly higher average strain magnitudes in the tibia during climbing compared to stereotypical overground walking (Demes et al., 2001). Demes et al. (2001, p. 262) also observed that “the direction of bending [was] very consistent [during overground locomotion], and major variation [was] evident only for the few climbing cycles recorded for one animal.” Thus, it appears that some arboreal locomotor behaviors may be more strongly associated with generating multi-oriented bending loads in limb bones than some terrestrial locomotor behaviors. Substrates/superstrates are positioned erratically throughout three dimensions in arboreal settings, but in terrestrial settings they are relatively continuously distributed in two dimensions. Accordingly, it is reasonable to expect that limb position is variable during arboreal locomotion (i.e., limbs experience diverse movement planes), with limbs more often abducted while supporting body weight. During terrestrial locomotion, in contrast, limb movements are expected to be comparatively more repetitive and predictable (i.e., limbs move consistently in a narrow range of sagittal planes). These scenarios appear consistent with the strain data, since at least two arboreal behaviors (i.e., brachiation and climbing) exhibited greater variability in the direction of bending than terrestrial behaviors (i.e., quadrupedal walking and running). Substrate reaction forces (SRF) encountered by the forelimb of several monkeys, however, usually exhibited a more variably directed mediolateral (ML) component during terrestrial rather than arboreal locomotion (Schmitt, 2003). It is unclear how to resolve a possible contradiction between greater variation in the forelimb ML component of the SRF associated with terrestrial rather than arboreal quadrupedal walking, which presumably signals greater diversity in the direction of the forelimb SRF vector during terrestrial quadrupedal walking, yet greater forelimb and hindlimb variation in principal strain orientations during arboreal locomotor behaviors relative to terrestrial. Future studies that simultaneously collect strain and SRF data during arboreal and terrestrial quadrupedalism may shed light on this apparent disagreement. While cross-sectional geometry does not assess limb deformation loads directly, it is a useful means 313 of estimating bone adaptation to mechanical load history (Martin et al., 1998). Application of crosssectional geometry to long bone diaphyses assumes a relationship between bone organization and an engineering beam model. Compelling in vivo research by Lišková and Heřt (1971) and Heřt et al. (1969, 1971, 1972) provided experimental veriﬁcation for proposed relationships articulated in earlier work (Amtmann, 1971; Koch, 1917; Kummer, 1959; Meyer, 1867; Pauwels, 1968, 1980; Roux, 1881; Wolff, 1892). Subsequent experimental approaches (e.g., Biewener et al, 1983; Bouvier and Hylander, 1981; Burr et al., 1996, 2002; Churches et al., 1979; Goodship et al., 1979; Gross et al., 1992, 1997; Jones et al., 1977; King et al., 1969; Lanyon, 1980; Lanyon and Baggott, 1976; Lanyon et al., 1975, 1982; Loitz and Zernicke, 1992; Martin, 1991; O’Connor et al., 1982; Rubin and Lanyon, 1982, 1984b; Woo et al., 1981; Young et al., 1979; reviewed by Burr, 1980; Turner, 1998) have reﬁned this relationship even further. It is clear that long bone diaphyses adapt their shape in response to dynamic rather than static loads (Lanyon and Rubin, 1984). Dynamic loads evoke adaptive responses in diaphyses even when they are short in duration or infrequent (e.g., as few as ﬁve cycles per day) (Rubin and Lanyon, 1984a; Umemura et al., 1997). Though the current synthesis of the response of bone cross-sectional shape to mechanical loadings, historically known as “Wolff’s law,” may have various levels of interpretations, here it is understood as the guiding principle that cortical bone responds to stress created through mechanical load-induced strains by adapting a cross-sectional shape that minimizes stress, usually with an economical amount of material. Mathematical models for analyzing long bone diaphyses (Huiskes, 1982; Huiskes et al., 1981; Rybicki et al., 1972; Toridis, 1969; Valliappan et al., 1977) and the pioneering use of computed tomography (CT) by Jungers and Minns (1979) were a boon to cross-sectional geometry studies, which subsequently ﬂourished (e.g., Bridges, 1989; Burr et al., 1982, 1989; Carlson, 2002a,b; Churchill et al., 1996; Connour et al., 2000; Cubo and Casinos, 1998; Demes and Jungers, 1989, 1993; Demes et al., 1991; Heinrich and Biknevicius, 1998; Jungers and Burr, 1994; Kimura and Takahashi, 1992; Larsen and Ruff, 1991; Madar et al., 2002; Ohman, 1993; Polk et al., 2000; Robling, 1998; Ruff, 1989, 2002; Ruff and Hayes, 1983a,b; Ruff and Runestad, 1992; Runestad, 1994; Runestad et al., 1992; Selker and Carter, 1989; Stephenson and Seedhom, 1999; Terranova, 1995a,b; Trinkaus et al., 1994, 1999). Recent work, however, established that the relationships between cross-sectional shape and bone deformation were not as simplistic as often assumed (Bertram and Swartz, 1991; Daegling, 2002; Lieberman and Crompton, 1998; Lovejoy et al., 2003). For example, bone tissue in a given cross section was not always distributed economically, as assumed with a beam model, and the neutral axis of bending did not pass 314 K.J. CARLSON Fig. 1. CT images of transverse cross sections from two gorilla humeral midshafts. Gray lines represent principal centroidal axes. Black lines represent centroidal axes about x- and y-axes. Note in cross section on left that ratio of principal moments of area (PMAs) is about 1.75 times the ratio of second moments of area (SMAs) about mediolateral and anteroposterior axes. Compare this with a different cross section (right) in which ratios are relatively similar. While PMA ratio accurately portrays obvious shape (or circularity) differences of cross sections, Ix/Iy does not discriminate between their shapes (or degrees of circularity). through the centroid of a cross section when axial and bending loads were superimposed (Demes et al., 1998, 2001; Gross et al., 1997; Lieberman et al., 2004). Animals apparently encounter similar peak stresses during locomotion, regardless of differences in their body size (e.g., Biewener, 1982; Lanyon et al., 1975). If an animal frequently travels in an arboreal setting, it should adapt sufﬁcient rigidity in multiple planes in order to prevent failure (e.g., fracture) in any one particular bending plane of a given diaphyseal cross section. An animal moving more frequently in a terrestrial setting, on the other hand, may adapt lower rigidity in particular planes from which bending loads presumably are less likely to be experienced. Maximum rigidity, which is expected to reﬂect the magnitude of peak loads and is approximated by Imax of a cross section, may vary less than minimum rigidity (approximated by Imin of a cross section) for animals of a given body mass. Schafﬂer et al. (1985) suggested that a ratio of principal moments of area (i.e., Imax/Imin) provided a good estimate of how a limb was used. While Ohman (1993, Tables 34 –36, 39 – 41) reported second moments of area about principal axes (PMAs), most studies emphasized ratios of second moments of area (SMAs) about alternative axes (e.g., Ix/Iy). The use of anteroposterior (AP) and mediolateral (ML) anatomical axes rather than principal axes was often necessary for methodological reasons (e.g., data were acquired via biplanar radiographs). Ratios of PMAs and other SMAs can depict similar shapes (e.g., similar degrees of circularity), but this is not always the case (Fig. 1). When principal angles (i.e., the angle between the maximum centroidal axis and the centroidal axis through the x-axis) approach 45°, discordance between these ratios increases. Given that principal angles of African apes vary within and between subspecies (Carlson, 2002b), principal axes rather than anatomical axes (e.g., AP and ML axes) provide a more accurate measure of cross section shape (e.g., circularity) in the limb diaphyses of African apes. Since Keith (1923, 1934) and others (Gregory, 1927, 1928; Hooton, 1942; Morton, 1922) ﬁrst employed ape models for understanding the evolution of the hominid postcranium, attributing unique characteristics of the ape postcranium to behaviors has become more focused both from a behavioral and a morphological standpoint (e.g., see Hunt, 1991b, and references therein). Suspensory locomotion or brachiation (sensu lato) (e.g., Ashton and Oxnard, 1963; Avis, 1962; Ellefson, 1974; Erickson, 1952; Grand, 1972; Gregory, 1916; Keith, 1891; Lewis, 1965; Napier, 1963; O’Connor, 1975; Ripley, 1970; Rose, 1974; Washburn, 1950), climbing (e.g., Cartmill and Milton, 1977; Fleagle et al., 1981; Jenkins and Fleagle, 1975; Washburn, 1973), and quadrumanous climbing (e.g., Fleagle, 1976; Kortlandt, 1975; Sarmiento, 1985; Stern et al., 1977; Tuttle, 1975; Tuttle et al., 1979) have been identiﬁed at one time or another as a unique evolutionary pressure facing apes. Once behavioral repertoires of African apes in their natural habitats were characterized (e.g., Doran, 1989; Hunt, 1989; Remis, 1994), it became possible to more clearly identify which positional behaviors were potentially relevant for understanding ape morphology. Apes, especially chimpanzees, demonstrated morphological adaptations to a variety of positional behaviors, including postural behaviors such as arm-hanging (Hunt, 1991a, 1992, 1994, 1996). These behavioral studies also documented not only species-speciﬁc patterns, but intraspeciﬁc differences as well: Gombe chimpanzees were more terrestrial than Mahale chimpanzees (Hunt, 1989, p. 160); Gorilla gorilla gorilla was more arboreal than G. g. beringei (Remis, 1995). Positional behavior data (Doran, 1989, 1993, 1996; Doran and Hunt, 1994; Hunt, 1989, 1991a,b, 1992; Remis, 1994, 1995, 1998; Susman, 1984; Tuttle and Watts, 1985) are currently available for all three species of African ape (i.e., Pan paniscus, Pan troglodytes, and G. gorilla). Yet another crucial revelation sprouting from the behavioral studies was that a variety of behaviors with potentially disparate functional implications quadrupedal walking on inclined branches, such as (e.g., Fleagle, 1976), vertical climbing (e.g., Fleagle et al., 1981), and scrambling (e.g., Doran, 1996) often were pooled in a single quadrumanous climbing category. Hunt et al. (1996) deﬁned scrambling as “upward (ⱖ45°) progression on multiple often oddly angled supports, typically without a discernible gait pattern.” Scrambling behaviors (i.e., vertical scramble (L8: c) in Hunt et al., 1996) incorporated more 315 APE LONG BONE GEOMETRY AND LOCOMOTOR BEHAVIOR eccentric, erratic limb positions than other behaviors grouped in the quadrumanous climbing behavior category (i.e., inclined quadrupedal walking and vertical climbing). Such qualitative differences, with potentially relevant functional consequences, between scrambling, quadrupedal walking, and vertical climbing suggest that scrambling should be treated as a separate behavior in locomotor proﬁles. Differentiation between cross-sectional properties of fore and hind-limbs has been observed to varying degrees among leapers, brachiators, arboreal quadrupeds, and terrestrial quadrupeds (Burr et al., 1989; Demes et al., 1991, 1994; Ruff, 2002; Runestad et al., 1992; Schafﬂer et al., 1985). These studies, however, typically used qualitative characterizations of locomotor behaviors. Ruff (1987) and Ohman (1993) provided the initial data on cross-sectional properties of African ape limb bones, but their results reﬂected relatively small or homogenous samples of apes, respectively. The potential consequences of this limitation were articulated by Carlson (2002a,b) and recently voiced by Ruff (2002, p. 307), who “recogniz[ed] that some variability in locomotor/positional behavior exist[ed] within . . . African ape genera, where locomotor behavior can vary signiﬁcantly depending on the particular species/subspecies.” No study has combined a large sample of all African ape taxa with quantitative positional behavior data. The present study serves two primary functions: ﬁrst, it expands the sample of African ape crosssectional properties from femoral and humeral diaphyses to a sufﬁciently large size that incorporates existing taxonomic diversity; and second, it uses quantitative positional behavior data rather than qualitative descriptions for investigating form-function relationships. In pursuit of these goals, four speciﬁc questions are addressed: 1) Does the summed percentage of all arboreal locomotor behavior correlate negatively with the ratio of PMAs (Imax/ Imin) in femoral and humeral diaphyses? In other words, as the summed percentage of all arboreal locomotion increases, irrespective of changes in the frequency of speciﬁc arboreal behaviors, does the ratio of PMAs decrease (i.e., Imin approaches Imax, and circularity increases)? In order to discern whether speciﬁc arboreal locomotor behaviors are differentially associated with PMA ratios, or whether summing them into total arboreal locomotion and comparing this to total terrestrial locomotion is more insightful, three additional questions are investigated: 2) Do PMA ratios correlate negatively with the percentage of an arboreal behavior that presumably incorporates more varied limb positions during movements (e.g., scrambling)? 3) Do PMA ratios correlate positively with the percentage of an arboreal behavior that presumably induces more repetitive sagittal limb positions during movements (e.g. arboreal quadrupedal walking)? 4) Does bone shape (i.e., circularity) potentially reﬂect the percentage of scrambling more than other arboreal behaviors? TABLE 1. Taxonomic distribution of sample (n ⫽ 222)1 Gorilla Pan n ⫽ 102 F M G. g. beringei G. g. gorilla G. g. graueri 13 22 8 17 32 10 n ⫽ 120 P. P. P. P. t. schweinfurthii t. troglodytes t. verus paniscus F M 13 26 9 10 27 27 3 5 1 Powell-Cotton Museum, Birchington, Kent, UK (14 individuals); Museum für Naturkunde der Humboldt Universität, Berlin, Germany (21 individuals); Musée Royal de l’ Afrique Centrale, Tervuren, Belgium (69 individuals); Anthropologisches Institut und Museum der Universität Zürich-Irchel, Zürich, Switzerland (23 individuals); American Museum of Natural History, New York, NY (44 individuals); British Museum of Natural History, London, UK (15 individuals); National Museum of Natural History, Washington, DC (36 individuals). MATERIALS AND METHODS Sample composition Data were acquired from femora and humeri of 222 G. gorilla, P. paniscus, and P. troglodytes specimens. The sample encompassed the six commonly recognized subspecies of African pongids beringei, gorilla, graueri, schweinfurthii, troglodytes, and verus (Table 1; background information for individual specimens listed in Carlson, 2002b, Appendix A). All specimens were relatively complete (i.e., few missing elements), skeletally mature, apparently healthy (as assessed skeletally), and unaffected by catastrophic injury (i.e., no visible evidence of healed or unhealed fractures in any long bones). Among smaller groups, the completeness criterion (i.e., number of missing long bones) occasionally was relaxed to ensure sufﬁcient sample sizes, despite the possibility that locomotor performance-altering fractures in the appendicular skeleton would have been missed in such specimens. When sex was not indicated in museum records (n ⫽ 53), it was predicted via a discriminant analysis using orbital, articular, and diaphyseal metric measurements (Carlson, 2002b). The sample incorporated an approximately equal number of left and right bones, with a femur and humerus measured from the same side in each individual. In a few instances (i.e., less than ﬁve), a femur and contralateral humerus were matched in order to bolster sample size. Single slice scans were made at 35%, 50%, and 65% length for each pair of bones (see below for deﬁnitions of length). CT scan parameters Critical user-selected CT parameters, such as ﬁeld of view (FOV), matrix size, and slice thickness, were standardized to the extent possible (see values reported in Carlson, 2002b). Remaining user-selected parameters (e.g., kV, mA, mAs, and scanning time), while also standardized, varied more, since settings often were speciﬁc to the CT manufacturer. All images were reconstructed using a bone algorithm, since this facilitated edge-detection better than other commercially available options (Ohman, 1993; 316 K.J. CARLSON Ruff and Leo, 1986; C. Zollikofer, personal communication, 1999). Since CT images are digital representations of the scan ﬁeld divided into a ﬁnite number of pixels, maintaining a constant pixel size is necessary for standardizing the resolution of images. Pixel length in a CT digital image is calculated as the matrix size (held constant as 512 ⫻ 512 pixels) divided into the FOV (200 mm at all facilities save one, which used 180 mm). Digital image data acquired from 6 of the 7 CT facilities had equivalent pixel areas (approximately 0.39 ⫻ 0.39 mm ⫽ 0.15 mm2), while pixel area from the seventh location differed by approximately 0.03 mm2. Voxels, pixel area multiplied by slice thickness (2.0 mm at ﬁve facilities, 1.5 mm at one facility, and 1.0 mm at one facility), represent three-dimensional units of space in digital image data. A voxel is assigned a CT number that represents the average of all CT numbers for objects occupying that discrete unit of space (e.g., bone, air, and soft tissue). Each CT number corresponds to a linear attenuation coefﬁcient, which is a measure of apparent density in Hounsﬁeld units (HUs). The CT number for water is conventionally 0 HUs, while air is calibrated to ⫺1,000 HUs (Hendee, 1983). The CT number for cortical bone is typically around 2,000 HUs (Ohman, 1993). Since all bones were scanned in air, the only objects that factored into voxel CT numbers were bone, air, and the rare desiccated soft-tissue. Additional discussions of technical issues relevant to using CT in research appear elsewhere (Hendee, 1983; Newton and Potts, 1981; Ruff and Leo, 1986; Sumner et al., 1985, 1989; Spoor et al., 2000). Given time and resource constraints, spatial resolution of each CT scanner could not be determined precisely for a given set of parameters (e.g., line pairs per centimeter; cf. Ohman, 1993). Equivalency of CT numbers and object cross-sectional properties at different CT facilities was assessed by scanning two standard objects (a water-ﬁlled container and a segment of a machined aluminum pipe) at each facility. Cross-sectional geometric properties for a reference object (i.e., the pipe) did not differ between facilities by more than 5% (Table 3.2 in Carlson, 2002b). Thus, potential variation due to CT facility, including a difference in pixel area or voxel volume, was considered trivial. Scanning preparations Positioning and scanning required approximately 5 min per bone pair. Scan times were 2.0 sec or less per slice. The majority of time required for generating CT digital image data was spent aligning specimens, as opposed to actual image acquisition and reconstruction. Guide devices (e.g., lasers or lights integrated into the scanner), which permit precise alignment of bones, were available at all CT facilities. By positioning predeﬁned reference axes of specimens (i.e., AP, ML, and longitudinal) parallel to these guide devices, second moments of area (SMAs) about anatomical axes (e.g., Ix, Iy) could be measured. Femoral and humeral reference axes were deﬁned previously (Carlson, 2002b; Ruff, 1981, 2002). Scan locations on a diaphysis were selected by identifying 35%, 50%, and 65% femoral mechanical length (Carlson, 2002b; Ruff, 1981, 2002) or humeral maximum length (Carlson, 2002b; Ruff, 2002). A femur and humerus from a single individual were scanned simultaneously. Aligning and scanning a minimum number of bones (e.g., a pair) ensured that they could be placed as near to the center of the gantry opening as possible. Center positioning is important because objects positioned near the edge of the scan ﬁeld are more distorted than objects positioned near the center (Newton and Potts, 1981; Ruff and Leo, 1986). While scanning single elements rather than pairs would have facilitated even greater center positioning, and further reduced potential beam hardening artifacts, these concerns were outweighed by practical issues (e.g., ﬁnite scanning opportunities). The humerus was adjusted between scans so that the humeral region of interest (ROI) matched the femoral ROI in a CT digital image (i.e., 35%, 50%, or 65%). This facilitated image analysis and archiving. A sturdy styrofoam square (⬇ 2.25 cm thick) was afﬁxed to the scanner bed in order to create a ﬂat surface that could be moved with CT table controls. An ordinary carpenter’s level was placed on the styrofoam surface, but out of ROI scan planes, to allow continual assessment of the horizontal level of the surface. The styrofoam platform was covered with parallel lines for relatively quick, accurate positioning of a bone along its longitudinal axis. For larger bones, a second piece of styrofoam was inserted under the original lined piece in order to avoid its deformation. Styrofoam is more appropriate than wood, metal, or plastic because it introduces fewer “streaks,” e.g., clip artifacts, in an image (C. Zollikofer, personal communication, 1999). Once reference axes of a bone were aligned to CT guide devices, proximal and distal reference points of a bone were leveled in the ML plane (Ruff, 1981). Proximal and distal reference points (Fig. 2; also see Ruff, 2002) could be leveled to within 0.8 mm or less, using a series of premeasured wooden blocks. Careful leveling prevented distortion in cross sections due to AP curvature (Fig. 3). Humeri and femora were leveled in the ML plane following the same protocol, although humeral adjustments were less frequently necessary since they exhibited less AP curvature. Three locations (35%, 50%, and 65% lengths; Fig. 2) per diaphysis were chosen for analysis. Comparable data were available from the same ROIs in ape femora and humeri (Ohman, 1993; Ruff, 1987, 2002). The midshaft diaphysis (50% length) is theoretically the location of the highest bending strains according to a beam model (Biewener and Taylor, 1986; Mott, 1996). Neighboring areas of the diaphysis (e.g., 35% and 65% lengths) may exhibit rela- APE LONG BONE GEOMETRY AND LOCOMOTOR BEHAVIOR Fig. 2. Approximate location of femoral and humeral regions of interest (ROIs). For femur (a) and humerus (b) in lateral view, longitudinal axis is level in ML plane when difference between distances h1 and h2 is 0.8 mm or less. Approximate locations of ROIs (35% (mid-distal), 50% (midshaft), and 65% (midproximal) diaphyseal lengths) are displayed for femur and humerus. Approximate locations of proximal and distal AP/ML reference points are depicted. *Deepest portion of patellar notch, which is distal reference point of longitudinal axis in femur. tively high bending strains as well. These locations also were selected since they avoided areas of the diaphysis that were likely to contain substantial trabecular bone. When occasional trabecular bone was observed, particularly in the mid-distal diaphysis of gorilla femora, this had negligible effects on rigidity even if it could not be removed manually from images (see Burr and Piotrowski, 1982; Ruff, 1983). Image analysis Compared to standard radiography, CT exhibited greater accuracy and precision in reproducing geometric properties of a bone cross section (Ohman, 1993; Ruff, 1989). While potential sources of error existed during image acquisition (e.g., beam hardening, Gibbs phenomenon, and “partial volume” artifacts) and image analysis (e.g., choice of image display parameters, particularly window settings), reasonable solutions have been proposed (Carlson, 2002b; Ohman, 1993; Ruff and Leo, 1986). CT raw data were reconstructed into DICOM image ﬁles at each CT facility with the assistance of a technician. Files were imported into two image analysis programs, Osiris 3.1 (Unité d’ Imageri Numerique, 1995) and Scion Image (release Beta 4.0.2), each available as a free download on the worldwide web. Scion Image is posted from NIH Image for the 317 Fig. 3. Effects of leveling vs. not leveling bones exhibiting AP diaphyseal curvature. Solid lines represent periosteal envelope. Dashed lines represent endosteal envelope. Dotted/dashed lines represent region of interest from which data are acquired. Both hypothetical long bones have the same dimensions, but differ in orientation. a: Hypothetical bone is leveled by orienting its ML plane (e.g., a coronal plane through proximal and distal diaphyseal midpoints of AP shaft diameter parallel to underlying surface), resulting in cross section to its left. b: Hypothetical bone is not level on ML plane, resulting in cross section to its left. Comparing cross sections, width (e.g., intracortical envelope) at anterior and posterior regions is slightly expanded in b relative to in a. Thus, more bone in anterior and posterior regions of cross section b relative to a is an artifact of their different alignments. Macintosh by Scion Corporation and available on the Internet at http://www.scioncorp.com. Following a recommendation to alter the traditional fullwidth-half-maximum (FWHM) threshold for determining the bone/air boundary (Ohman, 1993, p. 42– 45), a custom Scion Image macro was written to calculate the mean FWHM (mFWHM) of a cross section (see Carlson, 2002b, Appendix B). Replacing the standard FWHM protocol with the mFWHM protocol added approximately 30 sec to the time required to complete the analysis of an image. Brieﬂy, the mFWHM threshold considers variation within the CT numbers of a cross section, while the FWHM threshold relies only on the single densest voxel in an image (i.e., one CT number). The mFWHM threshold tailors the actual bone/air threshold to an individual cross section by embracing variation in optical density of that cross section rather than ignoring it as the FWHM threshold does. This is particularly relevant when multiple objects (e.g., bones) are scanned simultaneously. If 318 K.J. CARLSON TABLE 2. Locomotor behavior percentages Locomotor Taxon (Total) 1 G. g. beringei (10.71) (9.77) G. g. gorilla (15.73) (8.53) P. paniscus5 P. t. schweinfurthii (15.75) (15.97) P. t. verus (13.59) (14.57) 2 Combined locomotor3 Arboreal4 Sex Arb Terr Q walk Q climb Q scramble Suspend Bipedal SU B Q QS QC F M 8.15 2.32 91.85 97.68 90.02 94.30 2.65 0.63 0.20 0.21 0.20 0.00 6.31 4.22 2.50 0.00 7.50 18.18 52.50 45.45 2.50 9.09 32.50 27.27 F M 9.13 2.03 90.87 97.97 ⫺ ⫺ ⫺ ⫺ ⫺ ⫺ ⫺ ⫺ ⫺ ⫺ 10.99 3.80 4.40 1.27 14.29 21.52 30.76 25.31 39.56 48.10 F M ⫺ ⫺ ⫺ ⫺ ⫺ ⫺ ⫺ ⫺ ⫺ ⫺ ⫺ ⫺ ⫺ ⫺ 18.20 15.31 1.30 1.41 25.51 17.72 25.33 25.78 23.84 30.51 F M 12.02 8.20 87.98 91.80 91.49 93.85 5.96 4.27 1.23 0.26 0.95 0.60 0.28 0.26 7.87 7.29 2.36 2.08 30.71 33.33 10.24 3.13 48.82 52.08 F M 18.20 14.70 81.80 85.30 85.63 86.61 9.29 8.33 1.89 1.37 1.45 1.09 1.16 1.23 7.44 5.83 0.83 5.83 30.58 11.65 8.26 7.77 51.24 59.22 1 All locomotor behavior as a percentage (multiplied by 100) of total positional behavior repertoire. Percentages (multiplied by 100) of arboreal (Arb) and terrestrial (Terr) locomotion. 3 Percentages of locomotor behaviors in pooled arboreal and terrestrial substrates/superstrates. 4 Percentage (multiplied by 100) of SU ⫽ suspend (includes brachiate, arm swing, and drop), B ⫽ bipedal (includes bipedal walk, run, and stand), Q ⫽ quadrupedal walk (includes quadrupedal walk and run, tripedal walk and run, and knuckle-walking or palmigrade quadrupedalism), QS ⫽ quadrupedal scrambling (includes scramble, bridge, ﬁreslide, tree sway, and leap), and QC ⫽ quadrupedal climbing (on vertical or inclined substrates) within arboreal locomotor behaviors only. 5 Bout sampling data. 2 the FWHM threshold is used when multiple objects are scanned, one bone (i.e., the one containing the voxel with the highest CT number) conceivably could set the threshold for the other bone. Since apparent density of bone (e.g., measured by CT numbers) varies due to biological (Martin et al., 1998) or diagenetic processes (e.g., curation techniques), even within a single cross section (Burr, 1979a,b; Ruff and Leo, 1986), an mFWHM threshold is preferable to a FWHM threshold. On occasion, preprocessing of cross sections was necessary. For example, some cross sections contained trabecular bone, a nutrient foramen, or longitudinal cracks as a result of postmortem events. Obvious trabecular bone was “erased” to the level of the neighboring endosteal envelope, using pencil and brush tools in Scion Image. If a nutrient foramen appeared in a cross section (e.g., at the humeral midshaft), the image was adjusted (i.e., in less than 10 of the approximately 1,300 cross sections), depending on how much of the total area of the nutrient foramen was in the cortical wall (i.e., area relative to a line running through the foramen and connecting the neighboring endosteal borders). If more than 50% of the foramen lay within the cortical wall, bone tissue separating the foramen from the medullary space was considered cortical bone, and no modiﬁcation was made. If less than 50% of the foramen lay within the cortical wall, bone tissue separating the foramen from the medullary space was considered trabecular bone and it was removed. In the rare instance (i.e., in less than 5 of the approximately 1,300 cross sections) when cortical bone in a cross section was interrupted by a longitudinal crack in the diaphysis, the resulting gap in a cross section prevented calculation of cross-sectional properties. In each case, it was clear that the crack was a postmortem event. Crack openings at the perios- teal and endosteal envelopes (⬇ 1 mm or less in width) were bridged with minimal “bone,” using the pencil tool in Scion Image. After continuous surfaces were restored, the remaining intracortical portion of the crack was left unﬁlled to minimize distorting cortical area, SMAs, and PMAs. Following thresholding and preprocessing adjustments, Scion Image macros modeled after the SLICE program (Nagurka and Hayes, 1980) were used to calculate standard cross-sectional properties. Behavioral data Percentages of locomotor behaviors occurring within terrestrial and arboreal settings are derived and discussed in depth elsewhere (Carlson et al., unpublished ﬁndings). Brieﬂy, these data were calculated from Doran (1989, original data), Doran and Hunt (1994, Tables 16.3, 16.4, and 16.5), Hunt (1989, 1992, original data), and Remis (1994, Tables 4.4, 4.20, 4.21, and 4.22, 1995, 1998) (Table 2). Doran (1989) and Remis (1994) used instantaneous focal sampling with 1-min intervals, while Hunt (1989) used 2-min intervals with instantaneous focal sampling. Given large sample sizes, rare behaviors should be represented equally, regardless of whether 1- or 2-min intervals are used (K. Hunt, personal communication, 2002). The G. g. gorilla data were pooled wet and dry season data, and pooled lone and group male data (Remis, 1994, Tables 4.4, 4.20, 4.21, and 4.22). Percentages of arboreal locomotion for G. g. gorilla females and males were calculated by multiplying sex-speciﬁc values for total locomotion (i.e., travel in Remis, 1994, Table 4.4) and percentages of ﬁrst contacts in which gorillas were arboreal. Data on positional behavior repertoires for G. g. graueri and P. t. troglodytes are unavailable. To the extent possible, methodological differences between behavioral studies were compensated by 319 APE LONG BONE GEOMETRY AND LOCOMOTOR BEHAVIOR TABLE 3. Group means for principal moment of area ratios1 G. g. beringei G. g. gorilla G. g. graueri Bonobo P. t. schweinfurthii P. t. troglodytes P. t. verus 1 2 Sex n F 35 F 50 F 65 n H 35 H 50 H 65 F M F M F M F M F M F M2 F M 11 15 22 30 8 10 10 5 13 26 26 26 9 2 1.82 1.99 2.05 2.33 1.85 2.18 1.16 1.17 1.29 1.33 1.37 1.37 1.59 1.25 1.61 1.68 1.74 2.04 1.60 1.68 1.14 1.18 1.28 1.31 1.35 1.37 1.52 1.36 1.17 1.25 1.34 1.52 1.34 1.33 1.29 1.40 1.35 1.39 1.40 1.41 1.41 1.25 13 17 22 32 8 9 9 4 13 26 26 26 9 3 1.27 1.51 1.29 1.49 1.22 1.46 1.13 1.23 1.23 1.39 1.21 1.34 1.23 1.45 1.30 1.43 1.21 1.42 1.20 1.22 1.32 1.24 1.29 1.21 1.24 1.19 1.38 1.32 1.17 1.18 1.17 1.14 1.14 1.19 1.17 1.22 1.24 1.20 1.21 1.14 1.32 1.20 F, femur; H, Humerus; 35, mid-distal diaphysis; 50, midshaft diaphysis; 65, mid-proximal diaphysis. Mid-proximal locations were sampled from only 25 individuals due to a scanning error. collapsing or expanding behavioral categories, following suggestions of Hunt et al. (1996). It was not possible to separate the frequency of individual acrobatic behaviors used by Remis (1994), so all acrobatic behaviors were pooled as scrambling behaviors. The scrambling category combined vertical scrambling, bridging, leaping, tree sway, and ﬁrepole slide. Among the acrobatic behaviors, leaping, tree sway, and ﬁrepole slide were comparatively rare in chimpanzees and mountain gorillas. Quadrupedal walking combined tripedal or quadrupedal walking/running, knuckle-walking, and palmigrade quadrupedalism. The bipedal category pooled bipedal walking/running and assisted/unassisted bipedal standing. A majority of these observations were likely bipedal standing, since most bipedalism in African apes occurs posturally rather than during locomotion (Hunt, 1994). The suspensory category combined brachiation, arm swing, and drop. Statistical analyses Distributions of data were assessed with Kolmogorov-Smirnov normality tests. Sex-speciﬁc subspecies distributions of PMA ratios did not depart signiﬁcantly from normal distributions. The Levene test for homogeneity of variances assessed equal variances. Since data did not depart signiﬁcantly from normal distributions, parametric statistical tests were chosen. Analysis of variance (ANOVA) was selected as the statistical test to assess group differences in PMA ratios. A signiﬁcant ANOVA result was explored further with a Bonferroni (equal variances) or Tamhane’s T2 (unequal variances) post hoc test. The Bonferroni method was preferable for its conservative nature (e.g., accounted for multiple comparisons). Pearson correlations were used to examine associations between PMA ratios and locomotor behavior percentages. Statistical signiﬁcance was assigned when P ⬍ 0.05. Statistical tests were performed with SPSS software, version 11.0.1 (SPSS, Inc., Chicago, IL). RESULTS One-way ANOVA results and descriptive statistics for group mean PMA ratios at genus- and spe- Fig. 4. Line plot of principal moments of area (PMAs) ratio for sex-speciﬁc group means reported in Table 5. Ratios, along y-axis, plotted against femoral (F) and humeral (H) regions of interest (ROIs) at 35%, 50%, and 65% diaphyseal lengths, along x-axis. For each group, a line connects points from corresponding ROIs in order to visualize diaphyseal trends, as well as to contrast femoral and humeral trends. cies-level comparisons are reported elsewhere (Carlson, 2002b, Tables 7.1–7.4, summarized in Table 7.5). Sex exhibits a signiﬁcant interaction with taxon, hence sexes are treated individually within taxa. In the absence of bilateral data from individuals, side differences are not emphasized (i.e., sides are pooled). Group differences in mean PMA ratios Subspeciﬁc means for femoral and humeral ratios are reported in Table 3 and are plotted by ROI in Figure 4. Group mean PMA ratios are more variable in the femoral than the humeral diaphysis (Fig. 4). Variation between groups is lower in more proximal ROIs of both diaphyses. Among female Pan groups, the largest humeral ratios (i.e., least circular cross sections) are observed at the midshaft. No taxon consistently exhibits smaller or larger ratios (i.e., lesser or 320 K.J. CARLSON TABLE 4. One-way ANOVA results for comprehensive sample1 1 Location F 35 F 50 F 65 H 35 H 50 H 65 Between groups Within groups Between groups Within groups Between groups Within groups Between groups Within groups Between groups Within groups Between groups Within groups Females Males SS df MS F P SS df MS F P 10.014 3.950 3.928 3.479 0.483 2.309 0.210 1.206 0.287 1.332 0.228 1.093 6 92 6 92 6 92 6 93 6 93 6 93 1.669 0.043 0.655 0.038 0.080 0.025 0.035 0.013 0.048 0.014 0.038 0.012 38.877 0.000** 42.185 0.000** 3.206 0.007** 4.681 0.000** 2.700 0.018* 3.324 0.005** 3.337 0.005** 12.067 0.000** 3.237 0.006** 3.882 0.052 1.766 0.042 0.146 0.031 0.101 0.030 0.219 0.018 0.015 0.008 0.000** 0.000** 6 107 6 107 6 106 6 110 6 110 6 109 74.293 17.313 23.294 5.591 10.594 4.478 0.875 3.304 0.606 3.342 1.312 1.993 0.091 0.887 1.858 0.095 1 F, femur; H, humerus; 35, mid-distal diaphysis; 50, midshaft diaphysis; 65, midproximal diaphysis. * P ⬍ 0.05. ** P ⬍ 0.01. SS, sum of squares; MS, mean squares. TABLE 5. Summary of post hoc ANOVA results1 G. g. beringei Fe G. g. beringei G. g. gorilla G. g. graueri F65*2 F65**2 G. g. gorilla G. g. graueri M Bonobo H35**3 P. t. schweinfurthii P. t. troglodytes P. t. verus H50**2 F35**2 F50**3 F65**3 G. g. beringei G. g. gorilla G. g. graueri H50*2 H50*2 Bonobo P. t. schweinfurthii P. t. troglodytes H50*2 H50**2 H35*2 H50**2 H50**2 H50**2 H35*2 H50**2 F50**3 P. t. schweinfurthii P. t. troglodytes F35**2 F50**2 F35**2 F50**2 F35**2 F50**2 F65**2 F35**2 F50**2 F35**2 F50*2 F35**2 F50**2 F65**2 F35**2 F50**2 F35**2 F35**2 F50**3 F35**2 F50**3 F35**2 F50**3 F35**2 F50**3 F35**2 F50**3 F35**2 F50**3 F35**2 F50**3 F35**2 F50**3 F35**2 F50**3 Bonobo F35**2 F50**2 F35**2 F50**2 P. t. verus F35**2 F35**2 F50*2 F35*2 F50**3 P. t. verus 1 Fe, female; M, male; F, femur; H, humerus; 35, mid-distal diaphysis; 50, midshaft diaphysis; 65, mid-proximal diaphysis. Unequal variances post hoc test (Tamhane’s T2) was used when groups failed Levene test for homogeneity of variances. 3 Equal variances post hoc test (Bonferroni method) was used when groups passed Levene test for homogeneity of variances. * P ⬍ 0.05. ** P ⬍ 0.01. 2 greater circularity of cross sections) throughout both diaphyses when groups are compared. Less generalized trends, however, are apparent. Within the femoral diaphysis, gorilla subspecies typically exhibit smaller ratios proximally (i.e., more circular cross sections), while Pan groups (except P. t. verus) exhibit larger ratios proximally (i.e., less circular) (Fig. 4). Bonobos usually exhibit the smallest femoral ratios (i.e., most circular cross sections), while western lowland gorillas exhibit the largest (i.e., least circular). One-way ANOVAs examining sex-speciﬁc taxonomic differences in group mean ratios are reported in Table 4. At each ROI, females differ signiﬁcantly in group mean ratios, as do males (excluding the mid-proximal humeral ROI). Post hoc analyses demonstrate signiﬁcant differences between sex-speciﬁc groups (Table 5). For females and males, a majority of these differences occur between a gorilla and a Pan group (see Table 5, upper right and lower left quadrants for female and male sections). In order to address the possibility that a difference in body size between gorilla and Pan groups may be obscuring variation within groups, a second set of one-way ANOVAs is reported, in which Gorilla and Pan are analyzed separately (Table 6). Gorilla subspecies differ signiﬁcantly at the mid-distal and 321 APE LONG BONE GEOMETRY AND LOCOMOTOR BEHAVIOR TABLE 6. One-way ANOVA results for Gorilla and Pan samples analyzed separately1 Females Genus Location Gorilla F 35 F 50 F 65 H 35 H 50 H 65 Pan F 35 F 50 F 65 H 35 H 50 H 65 Males Variance SS df MS F P Between groups Within groups Between groups Within groups Between groups Within groups Between groups Within groups Between groups Within groups Between groups Within groups Between groups Within groups Between groups Within groups Between groups Within groups Between groups Within groups Between groups Within groups Between groups Within groups 0.484 2.334 0.187 1.514 0.229 0.840 0.031 0.528 0.072 0.370 0.005 0.277 0.945 1.616 0.742 1.965 0.109 1.468 0.067 0.678 0.142 0.963 0.120 0.817 2 38 2 38 2 38 2 40 2 40 2 40 3 54 3 54 3 54 3 53 3 53 3 53 0.242 0.061 0.094 0.040 0.115 0.022 0.016 0.013 0.036 0.009 0.002 0.007 0.315 0.030 0.247 0.036 0.036 0.027 0.022 0.013 0.047 0.018 0.040 0.015 3.942 0.028* 2.348 0.109 5.187 0.010* 1.176 0.319 3.893 0.029* 0.353 0.705 10.529 0.000** 6.796 0.001** 1.337 0.272 1.743 0.169 2.609 0.061 2.602 0.062 SS df MS F P 1.129 4.379 1.793 3.091 0.814 1.718 0.013 1.341 0.311 1.323 0.031 0.372 0.184 1.213 0.174 1.388 0.049 1.586 0.121 2.001 0.050 0.670 0.050 0.514 2 52 2 52 2 52 2 55 2 55 2 55 3 55 3 55 3 54 3 55 3 55 3 54 0.564 0.084 0.897 0.059 0.407 0.033 0.007 0.024 0.155 0.024 0.016 0.007 0.061 0.022 0.058 0.025 0.016 0.029 0.040 0.036 0.017 0.012 0.017 0.010 6.704 0.003** 15.083 0.000** 12.328 0.000** 0.271 0.763 6.464 0.003** 2.321 0.108 2.779 0.050* 2.293 0.088 0.552 0.649 1.108 0.354 1.376 0.260 1.752 0.167 1 F, femur; H, humerus; 35, mid-distal diaphysis; 50, midshaft diaphysis; 65, mid-proximal diaphysis. * P ⬍ 0.05. ** P ⬍ 0.01. SS, sum of squares; MS, mean squares. mid-proximal femoral diaphysis (females and males), femoral midshaft (males only), and humeral midshaft (females and males). Pan groups, in contrast, differ signiﬁcantly only at the mid-distal femoral diaphysis (females and males) and femoral midshaft (females only). In four other diaphyseal locations (three among females, one among males), differences between group mean ratios approach statistical signiﬁcance (e.g., P ⬍ 0.11). Post hoc analyses of separated genera indicate signiﬁcant differences between subspecies (Table 7). Those subspeciﬁc differences that are signiﬁcant only after separating genera in analyses include: female mountain and western lowland gorillas at mid-distal femoral and midshaft humeral diaphyses, male lowland gorilla subspecies at the mid-proximal femoral diaphysis, female western and central chimpanzees at the mid-distal femoral diaphysis, and male bonobos and central chimpanzees at the mid-distal femoral diaphysis (compare Tables 5 and 7). Variability in group PMA ratios Since ANOVA between-groups vs. within-groups variance ultimately determines statistical signiﬁcance, a signiﬁcant result may be attributed to either remarkably high variation between group means, or remarkably low variation between individuals within groups. Similarly, nonsigniﬁcant results may be attributable to the converse relationships. There is biological meaning in either scenario, in that whether one of the two sources of variance drives signiﬁcance or nonsigniﬁcance is potentially useful information. Whether considering between-groups or withingroups variance (average square difference from the mean), each is generally higher in the femoral than the humeral diaphysis of Pan groups (Table 6). Nonsigniﬁcant ANOVA results of Pan mid-distal and midshaft humeral diaphyses, in comparison to signiﬁcant results for analogous femoral ROIs, exhibit much lower humeral (e.g., factor of 5–10) betweengroups variance (sum of squares: for H35, 0.067 [F35 ⫽ 0.945]; for H50, 0.142 [F50 ⫽ 0.742]) and only slightly lower humeral (e.g., factor of 2–3) within-groups variance (sum of squares: for H35, 0.678 [F35 ⫽ 1.616]; for H50, 0.963 [F50 ⫽ 1.965]). In other words, group mean ratios from both the middistal and midshaft diaphyses are more similar in the humerus than the femur, since variation between groups is lower in the humerus (see also, Fig. 4). Nonsigniﬁcant ANOVA results for Pan humeral ROIs, when juxtaposed with signiﬁcant ANOVA results for analogous femoral ROIs, appear related to less divergence within the range of group mean PMA ratios (i.e., individuals may vary in humeral PMA ratios, but little of this is explained by group). Pan groups exhibit a pattern in mid-proximal diaphyses (greater similarity in femoral and humeral between-groups variance than within-groups variance) that is opposite the pattern in more distal locations of diaphyses. While occasionally the magnitude of humeral between-groups or within-groups variance exceeds analogous femoral variances in the Pan sample, gorilla humeral variances never exceed femoral variances (Table 6). Gorilla sexes exhibit predom- 322 K.J. CARLSON P. t. troglodytes P. t. schweinfurthii 2 F35**3 F50**2 F35**3 F35*3 F35**3 F50**2 M H50**3 P. t. verus P. t. troglodytes P. t. schweinfurthii P. t. schweinfurthii P. t. troglodytes P. t. verus Bonobo G. g. graueri G. g. gorilla H50*3 Bonobo Fe 1 F35** F50**3 F65**3 M F65** F35* F65**2 G. g. beringei Fe Fe, female; M, male; F, femur; H, humerus; 35, mid-distal diaphysis; 50, midshaft diaphysis; 65, mid-proximal diaphysis. Unequal variances post hoc test (Tamhane’s T2) was used when groups failed the Levene test for homogeneity of variances. 3 Equal variances post hoc test (Bonferroni method) was used when groups passed Levene test for homogeneity of variances. * P ⬍ 0.05. ** P ⬍ 0.01. Do summed arboreal locomotor behaviors correlate negatively with PMA ratios? H50**3 Bonobo F50**3 F65*3 G. g. graueri 3 G. g. gorilla G. g. beringei G. g. graueri 2 3 G. g. gorilla G. g. beringei TABLE 7. Summary of post hoc ANOVA results for Gorilla and Pan samples analyzed separately1 F35*3 P. t. verus inantly the same variance patterns as Pan sexes: humeral variances are absolutely lower than femoral variances, and between-groups variance is usually much lower than within-groups variance in the humerus, but this difference is less in analogous femoral variances. Female gorillas exhibit much lower humeral between-groups variance at the mid-distal and midproximal humeral diaphysis, rather than at the mid-distal and midshaft diaphysis as do female Pan. Gorilla males, unlike Pan males, have consistently much lower between-groups variance than within-groups variance in each of the humeral ROIs when comparing analogous femoral and humeral variances (i.e., gorilla males vary little by group). Correlations between group mean PMA ratios and locomotor behaviors are reported in Table 8 (femoral) and Table 9 (humeral). A negative correlation between group mean ratios and percentages of total arboreal locomotion is observed at each ROI, except at the midproximal humerus. Two of the ﬁve negative correlations (i.e., mid-distal femur and humerus) exhibit statistical signiﬁcance, while a third (i.e., midshaft femur) exhibits borderline statistical signiﬁcance. Analyzing Gorilla and Pan separately provides a means of reducing potential confounding effects of their body size differences. In gorillas, 5 of 6 correlations between PMA ratio and the percentage of total arboreal locomotion remain negative, while the mid-proximal humerus maintains a positive correlation (Tables 10 and 11). Negative correlations are signiﬁcant at the mid-distal and midshaft humerus. In Pan groups, however, only 2 of 6 correlations are negative (i.e., mid-proximal femur and mid-distal humerus). Neither negative correlation is signiﬁcant. Does PMA ratio correlate negatively with scrambling percentage? Among femoral ROIs, correlations between arboreal scrambling and group mean PMA ratio are positive (Table 8). In contrast, humeral ROIs exhibit a negative correlation with arboreal scrambling, although coefﬁcients are nonsigniﬁcant and relatively low in strength (i.e., ⱕ0.3) (Table 9). Gorillas exhibit negative correlations at 2 of 6 ROIs (midshaft and midproximal humerus) when analyzed separately from Pan (Tables 10 and 11). Neither correlation is signiﬁcant. Pan, on the other hand, exhibits negative correlations at all ROIs when analyzed separately. The correlation for the femoral midshaft, however, is the only signiﬁcant one. Does PMA ratio correlate positively with arboreal quadrupedal walking percentage? Mid-distal and midshaft diaphyses exhibit positive correlations between group mean PMA ratios and percentages of arboreal quadrupedal walking, while mid-proximal diaphyses exhibit negative cor- 323 APE LONG BONE GEOMETRY AND LOCOMOTOR BEHAVIOR TABLE 8. Pearson correlations between femoral PMA ratios and locomotor behaviors (comprehensive sample)1 F 35 Imax/Imin r n Sign as predicted Correlation rank2 F 50 Imax/Imin r n Sign as predicted Correlation rank F 65 Imax/Imin r n Sign as predicted Correlation rank % total quad walk % total quad climb % total quad scramble % total suspensory % overall arboreal locomotion % arboreal quad walk % arboreal quad climb % arboreal quad scramble % arboreal suspensory 0.270 6 Yes ⫺0.675 6 No ⫺0.476 6 Yes ⫺0.672 6 Yes ⫺0.690* 8 Yes 0.205 10 Yes ⫺0.053 10 No 0.187 10 No ⫺0.596* 10 Yes 4 1 3 2 2 4 3 1 0.040 6 Yes ⫺0.507 6 No ⫺0.325 6 Yes ⫺0.534 6 Yes 0.116 10 Yes 0.114 10 Yes 0.144 10 No ⫺0.635* 10 Yes 4 2 3 1 3 4 2 1 ⫺0.072 6 No 0.516 6 Yes 0.504 6 No 0.641 6 No ⫺0.450 10 No 0.356 10 Yes 0.425 10 No 0.176 10 No 4 2 3 1 1 3 2 4 ⫺0.6213 8 Yes ⫺0.082 8 Yes 1 F, femur; 35, mid-distal diaphysis; 50, midshaft diaphysis; 65, mid-proximal diaphysis; quad, quadrupedal. 1, highest; 4, lowest. 3 P approaches 0.05. * P ⬍ 0.05 (one-tailed). 2 TABLE 9. Pearson correlations between humeral PMA ratios and locomotor behaviors (comprehensive sample)1 H 35 Imax/Imin r n Sign as predicted Correlation rank2 H 50 Imax/Imin r n Sign as predicted Correlation rank H 65 Imax/Imin r n Sign as predicted Correlation rank % total quad walk % total quad climb % total quad scramble 0.390 6 Yes ⫺0.423 6 No ⫺0.447 6 Yes ⫺0.481 6 Yes 4 3 2 1 ⫺0.193 6 No ⫺0.082 6 No 0.230 6 No ⫺0.067 6 Yes 2 3 1 4 ⫺0.586 6 No 0.745* 6 Yes 0.848* 6 No 0.828* 6 No 4 3 1 2 % total suspensory % overall arboreal locomotion ⫺0.644* 8 Yes ⫺0.248 8 Yes 0.819** 8 No % arboreal quad walk % arboreal quad climb % arboreal quad scramble % arboreal suspensory 0.042 10 Yes 0.337 10 Yes ⫺0.237 10 Yes ⫺0.757** 10 Yes 4 2 3 1 0.276 10 Yes ⫺0.038 10 No ⫺0.131 10 Yes ⫺0.507 10 Yes 2 4 3 1 ⫺0.025 10 No 0.323 10 Yes ⫺0.300 10 Yes 0.145 10 No 4 1 2 3 1 H, humerus; 35, mid-distal diaphysis; 50, midshaft diaphysis; 65, mid-proximal diaphysis; quad, quadrupedal. 1, highest; 4, lowest. * P ⬍ 0.05 (one-tailed). ** P ⬍ 0.01 (one-tailed). 2 relations (Tables 8 and 9). No correlations are signiﬁcant. Separating genera illustrates different patterns of associations between PMA ratios and behaviors (Ta- bles 10 and 11). Only 2 of 6 ROIs (i.e., midshaft and midproximal humerus) exhibit positive correlations among gorillas. Neither coefﬁcient is signiﬁcant. Four of 6 ROIs exhibit positive correlations among Pan, but 324 K.J. CARLSON TABLE 10. Pearson correlations between femoral PMA ratios and locomotor behaviors (separated Gorilla and Pan groups)1 % total quad walk F 35 Imax/Imin r n Sign as predicted Correlation rank2 F 50 Imax/Imin r n Sign as predicted Correlation rank F 65 Imax/Imin r n Sign as predicted Correlation rank % total quad climb % total quad scramble % total suspensory % overall arboreal locomotion % arboreal quad walk % arboreal quad climb % arboreal quad scramble % arboreal suspensory Gorilla (Pan) G (P) G (P) G (P) G (P) G (P) G (P) G (P) G (P) ⫹(⫺0.479) 2 (4) Yes (no) ⫺(0.525) 2 (4) No (yes) ⫹(0.545) 2 (4) No (no) ⫺(0.684) 2 (4) Yes (no) ⫺0.586 (0.638) 4 (4) Yes (no) ⫺0.722 (0.491) 4 (6) No (yes) 0.817 (0.568) 4 (6) Yes (yes) 0.726 (⫺0.629) 4 (6) No (yes) 0.176 (⫺0.611) 4 (6) No (yes) (4) (3) (2) (1) 3 (4) 1 (3) 2 (1) 4 (2) ⫹(⫺0.800) ⫺(0.815) ⫹(0.724) ⫺(0.854) ⫺0.549 (0.852) ⫺0.647 (0.193) 0.885 (0.732*) 2 (4) Yes (no) 2 (4) No (yes) 2 (4) No (no) 2 (4) Yes (no) 4 (4) Yes (no) 4 (6) No (yes) 4 (6) Yes (yes) 0.642 (⫺0.771*) 4 (6) No (yes) 0.129 (⫺0.782*) 4 (6) No (yes) (3) (2) (4) (1) 2 (4) 1 (3) 3 (2) 4 (1) ⫹(0.258) 2 (4) Yes (yes) ⫺(⫺0.195) 2 (4) No (no) ⫹(⫺0.060) 2 (4) No (yes) ⫺(0.053) 2 (4) Yes (no) ⫺0.775 (0.568) 4 (6) No (yes) 0.889 (⫺0.037) 4 (6) Yes (no) 0.774 (⫺0.084) 4 (6) No (yes) 0.278 (⫺0.055) 4 (6) No (yes) (1) (2) (3) (4) 2 (1) 1 (4) 3 (2) 4 (3) ⫺0.476 (⫺0.031) 4 (4) Yes (yes) 1 F, femur; 35, mid-distal diaphysis; 50, midshaft diaphysis; 65, mid-proximal diaphysis; quad, quadrupedal. Numbers in parentheses are for Pan (P); otherwise, they are for Gorilla, G. 2 1, highest; 4, lowest. Gorilla coefﬁcient signs, but not magnitudes reported when n ⫽ 2. * P ⬍ 0.05 (one-tailed). TABLE 11. Pearson correlations between humeral PMA ratios and locomotor behaviors (separated Gorilla and Pan groups)1 % total quad walk H 35 Imax/Imin r n Sign as predicted Correlation rank2 H 50 Imax/Imin r n Sign as predicted Correlation rank H 65 Imax/Imin r n Sign as predicted Correlation rank % total quad climb % total quad scramble % total suspensory % overall arboreal locomotion % arboreal quad walk % arboreal quad climb % arboreal quad scramble % arboreal suspensory Gorilla (Pan) G (P) G (P) G (P) G (P) G (P) G (P) G (P) G (P) ⫹(0.074) ⫺(⫺0.167) ⫹(⫺0.469) ⫺(⫺0.443) 2 (4) No (yes) 2 (4) Yes (yes) 0.060 (⫺0.796*) 4 (6) Yes (no) ⫺0.572 (⫺0.742) 2 (4) No (no) ⫺0.009 (⫺0.323) 4 (6) No (no) 0.040 (⫺0.706) 2 (4) Yes (yes) ⫺0.982** (⫺0.349) 4 (4) Yes (yes) 4 (6) No (yes) 4 (6) Yes (yes) (4) (3) (1) (2) 4 (4) 2 (1) 3 (3) 1 (2) ⫹(⫺0.932*) 2 (4) Yes (no) ⫺(0.962*) 2 (4) No (yes) ⫹(0.991**) 2 (4) No (no) ⫺(0.996**) 2 (4) Yes (no) 0.314 (⫺0.044) 4 (6) Yes (no) ⫺0.050 (0.137) 4 (6) No (yes) ⫺0.293 (⫺0.047) 4 (6) Yes (yes) ⫺0.821 (⫺0.119) 4 (6) Yes (yes) (4) (3) (2) (1) 2 (4) 4 (1) 3 (3) 1 (2) ⫹(⫺0.564) 2 (4) Yes (no) ⫺(0.630) 2 (4) No (yes) ⫹(0.755) 2 (4) No (no) ⫺(0.819) 2 (4) Yes (no) 0.372 (0.324) 4 (6) Yes (yes) ⫺0.865 (0.319) 4 (6) No (yes) ⫺0.348 (⫺0.281) 4 (6) Yes (yes) 0.003 (⫺0.380) 4 (6) No (yes) (4) (3) (2) (1) 2 (2) 1 (3) 3 (4) 4 (1) ⫺0.968* (0.993**) 4 (4) Yes (no) 0.388 (0.762) 4 (4) No (no) 1 H, humerus; 35, mid-distal diaphysis; 50, midshaft diaphysis; 65, mid-proximal diaphysis; quad, quadrupedal. Numbers in parentheses are for Pan (P); otherwise, they are for Gorilla (G). 2 1, highest; 4, lowest. Gorilla coefﬁcient signs, but not magnitude reported when n ⫽ 2. * P ⬍ 0.05 (one-tailed). ** P ⬍ 0.01 (one-tailed). none are signiﬁcant. Only their mid-distal and midshaft humeral ROIs exhibit negative correlations. Does bone shape (e.g., circularity) potentially reflect scrambling more than other arboreal behaviors? Scrambling exhibits the second or third strongest correlation with PMA ratio among four locomotor behaviors (Tables 8 and 9). When compiling the average relative strength of all six correlation coefﬁcients for each locomotor behavior (i.e., 1, strongest correlation; 4, weakest correlation), scrambling is surpassed in relative strength only by suspensory behavior. The strength of correlations between the percentage of scrambling and PMA ratios, however, is generally low (r ⫽ 0.131– 0.425) APE LONG BONE GEOMETRY AND LOCOMOTOR BEHAVIOR In analyses of separate genera, the relative pattern of correlation coefﬁcient strengths differs between groups (Tables 10 and 11). Among gorillas, quadrumanous climbing is followed in strength of association by quadrupedal walking. Both surpass scrambling in average strength of correlation coefﬁcients. In Pan, scrambling has the same relative position across the six ROIs as quadrumanous climbing. Both locomotor behaviors are surpassed in average position only by suspensory behavior. DISCUSSION Diaphyseal shape differences using PMA ratios It is clear that Gorilla and Pan exhibited variable shapes (e.g., different circularity as measured by PMA ratio) in their femoral cross sections, particularly when viewing mid-distal and midshaft ROIs. In the humeral diaphysis, signiﬁcant shape differences between subspecies were observed only at the midshaft, and only among gorillas. The midshaft of a diaphysis theoretically encounters the highest bending loads. Thus, maximum femoral and humeral bending loads presumably differ in orientation between African ape subspecies. Whether both genera were included, or whether they were separated in ANOVAs (compare Tables 5 and 7), several trends in PMA ratios emerged (see below). Western lowland gorillas and western chimpanzees (particularly females) exhibited the most distinct PMA ratios among their respective genera. Humeral PMA ratios exhibited substantially less intergroup variability (between-groups variance) than femoral PMA ratios when genera were analyzed separately. Femoral PMA ratios discriminated between taxa more successfully than humeral ratios, for which between-groups and within-groups variance diverged more, proportionately speaking, throughout the diaphysis. This result appears counterintuitive, since the forelimb would seem a more likely candidate to differentiate groups during arboreal locomotor behaviors than the hindlimb. If primate hindlimb peak vertical forces usually exceed forelimb peak vertical forces (i.e., more weight is carried on the hindlimbs than the forelimbs) during various arboreal forms of locomotion, as they regularly do in primates during terrestrial quadrupedal locomotion (Demes et al., 1994; Kimura, 1985; Kimura et al., 1979; Reynolds, 1985), then the hindlimb could experience a greater range of forces over the full complement of locomotor behaviors. This may contribute to the hindlimb apparently being a better reﬂection of group differences in locomotor behaviors than the forelimb. Studies of other primates may offer a glimpse of the SRFs encountered by African apes during locomotion. Old World monkeys remained hindlimbdominant during arboreal quadrupedalism, even after reducing the magnitude of SRF components experienced by all limbs (Schmitt, 1998). Less reduction was observed in the hindlimbs than the fore- 325 limbs, but all forces were reduced below those encountered during terrestrial quadrupedalism. Nonstrepsirhine primates experienced a larger vertical force component of the SRF in the hind limbs than the forelimbs during vertical climbing (Hirasaki et al., 1992). This distinction between hind limbs and forelimbs, while less obvious, was also observed in the horizontal force component (i.e., pushing or pulling against the vertical substrate). If African apes are like other primates in this regard, they also may experience greater SRF components in their hind limbs than forelimbs during arboreal locomotor behaviors (e.g., vertical climbing and scrambling). The humeral diaphysis apparently provides a signal that transcends group-speciﬁc behavioral patterns (i.e., much lower humeral between-groups variance than within-groups variance when compared to the analogous femoral variances). This could be related to greater individual-based than group-based variation in forelimb segment conﬁgurations during locomotor behaviors of African apes. Carlson et al. (2000) reported that both G. g. gorilla and P. paniscus exhibited modal forelimb and hind limb conﬁgurations during some positional behaviors, but not during others. Larger mammals exhibit lower limb angles relative to SRFs during quadrupedal locomotion than smaller mammals, thus avoiding excessively high bending moments generated by ﬂexed limb postures (Biewener, 1983). It is unclear, however, whether intrinsic variation within a behavioral category (e.g., different limb segment conﬁgurations within a locomotor mode) has an important effect on the associations between humeral PMA ratios and percentages of locomotor behavior. Forelimb cross-sectional properties in modern and fossil human populations have been portrayed as reﬂecting tool-use activities (e.g., Churchill, 1994; Churchill et al., 1996; Trinkaus and Churchill, 1999; Trinkaus et al., 1994). Humeral PMA ratios of apes could also reﬂect the involvement of the forelimb in nonlocomotor activities (e.g., tool use, and feeding or postural behaviors). African apes, however, do not exhibit tool manufacture or use activities to the same extent as humans. Bending loads associated with tool-making and tool use are almost certainly less likely to impact the shape of a cross section in the ape humeral diaphysis than bending loads arising during locomotor activities. Feeding or postural behaviors in general, as typical “static” behaviors, are also less likely to induce large bending loads in the limbs than dynamic behaviors (e.g., locomotor behaviors). Group PMA ratios from midshaft ROIs that are reported in the present study were broadly equivalent (i.e., similarly circular) to comparable data reported elsewhere. Previous studies of cross-sectional properties in African apes were restricted to one humeral ROI (Ohman, 1993) and one femoral ROI (Ohman, 1993; Ruff and Runestad, 1992, ML/AP ratios). While Ohman (1993) separated G. gorilla 326 K.J. CARLSON sexes, he pooled P. troglodytes sexes, reporting only a mid sex average. His African ape samples primarily represented P. t. troglodytes and G. g. gorilla. The mid sex mean of the chimpanzee femoral PMA ratio of 1.28 reported by Ohman (1993, Table 39) was slightly lower (i.e., more circular) than a P. t. troglodytes mid-sex average (1.36) calculated from Table 3. Gorilla female (1.70) and male (1.80) femoral PMA ratios reported by Ohman (1993) were also lower (i.e., more circular) than comparable PMA ratios reported in the present study (1.74 and 2.04, respectively). Humeral midshaft data reported by Ohman (1993), on the other hand, exhibited more similarity to data in the present study. Ohman (1993, Table 34) reported a mid-sex average for the humeral PMA ratio of chimpanzees (1.24) that was close (i.e., equally circular) to the mid-sex average of female and male P. t. troglodytes PMA ratios (1.22) calculated from Table 3. Mean female (1.23) and male (1.37) gorilla PMA ratios reported by Ohman (1993) were close (i.e., equally circular) to those reported in the present study (1.21 and 1.42; Table 3). The low femoral PMA ratios reported by Ohman (1993), relative to those presented here, could have reﬂected idiosyncratic behavioral differences inherent to one or both samples of G. g. gorilla. Ohman (1993) also pooled sexes in his human sample, reporting a higher average PMA ratio for the humeral midshaft than the femoral midshaft (i.e., a less circular humeral cross section). It is interesting to note that Gorilla and P. troglodytes in the present study exhibited the opposite pattern: a higher PMA ratio for the femoral midshaft than the humeral midshaft (i.e., less circular femoral cross section), with one exception (P. t. schweinfurthii exhibited a greater humeral ratio, but by 0.01). Bonobo females and males, however, were unique among African apes in exhibiting the same pattern as H. sapiens (i.e., humeral midshaft ratio ⬎ femoral midshaft ratio). A behavioral explanation for the similarity between humans and bonobos, to the exclusion of other African apes, is unclear. A strong positive association at the femoral midshaft (r ⫽ 0.940) was reported between ML/AP bending rigidity ratios and body mass for a diverse range of primates, including hominoids (Ruff and Runestad, 1992, their Fig. 5). An ML/AP ratio, however, does not necessarily measure the same characteristic of a cross section as the PMA ratio. Figure 1 demonstrates that PMA ratios can provide a more accurate assessment of cross section shape (e.g., circularity). Twenty of the 222 specimens (but only 18 of the 20 contributed humeral data) had associated body mass data, most of which were chimpanzees. In 3 of 6 ROIs (F35: rs ⫽ 0.539, P ⬍ 0.05; F50: rs ⫽ 0.647, P ⬍ 0.01; and H35: rs ⫽ 0.503, P ⬍ 0.05), PMA ratio exhibited a signiﬁcant correlation with body mass. The other three ROIs exhibited weaker, nonsigniﬁcant correlations (F65: rs ⫽ 0.397; H50: rs ⫽ ⫺0.292; and H65: rs ⫽ ⫺0.176). In the same 20 specimens (again, 18 for the humerus), ML/AP bend- ing rigidity ratios usually exhibited a stronger correlation to body mass than PMA ratios. Correlations between ML/AP ratios and body mass were signiﬁcant at 4 of 6 ROIs (F35: rs ⫽ 0.605, P ⬍ 0.01; F50: rs ⫽ 0.615, P ⬍ 0.01; H35: rs ⫽ 0.849, P ⬍ 0.01; and H50: rs ⫽ 0.496, P ⬍ 0.05), while only two ROIs exhibited nonsigniﬁcant correlation coefﬁcients (F65: rs ⫽ 0.235; and H65: rs ⫽ 0.135). Humeral midshaft (H50) and midproximal (H65) ROIs exhibited negative (nonsigniﬁcant) correlations between PMA ratio and body mass, but positive correlations between ML/AP ratio and body mass (H50 was signiﬁcant). Ratios of PMAs rather than ML/AP ratios apparently reveal differences in locomotor repertoires more readily, apart from body mass differences, since ML/AP ratios appear more confounded by differences in body mass. It was not possible to determine the extent to which body mass and PMA ratio were directly correlated in African apes independently of arboreal locomotor behavior, or the extent to which they covaried due to a strong correlation between body mass and arboreal locomotor behavior. It remains unknown how much PMA ratio estimates arboreal locomotion percentages vs. how much it estimates body mass. A sample of individuals with associated body mass, associated locomotor behavior, and associated cross-sectional properties is required before these relationships can begin to be unraveled. Such a sample could also ultimately prove more insightful regarding within-groups variance and demonstrate more clearly how strongly femoral or humeral diaphyseal PMA ratios are correlated with locomotor behaviors. In the present sample, group PMA ratios were correlated to group percentages of total arboreal locomotion in the proposed direction more often than not, but this was less often the case when speciﬁc arboreal locomotor behaviors were investigated. Correlations between body mass and PMA ratio, or ML/AP ratio for that matter, may be inﬂuenced by correlations between body mass and arboreal locomotor behaviors. Group percentages of total arboreal locomotion exhibited a body mass trend, since chimpanzee subspecies, for which behavioral data exist, exhibited higher percentages of total arboreal locomotion than gorilla subspecies with associated behavioral data (Table 2). Mass-related trends among speciﬁc arboreal locomotor behaviors may have been muddled by potential bias reﬂected in P. paniscus and G. g. gorilla behavior percentages. Field studies that were the basis for these behavioral data reported that focal groups were not habituated fully at time of study (respectively, Doran, 1989, p. 194; Remis, 1994, p. 149). This was most evident in an absence of terrestrial locomotor data for both groups (but see Materials and Methods for a description of how G. g. gorilla arboreal locomotion percentage was estimated). However, these studies minimized potential bias by discounting observa- APE LONG BONE GEOMETRY AND LOCOMOTOR BEHAVIOR tions in which an individual was startled into ﬂeeing upon recognizing the presence of the observer. PMA ratio and percentage of a locomotor behavior The ﬁrst question posed (do PMA ratios correlate negatively with arboreal locomotion?) is answered with a tentative yes. Generally lower mean ratios (i.e., a circular cross section) were associated with higher percentages of total arboreal locomotion in the combined genera comparisons. This trend remained visible when gorillas were analyzed separately, but was not particularly obvious when Pan groups were analyzed separately. In fact, Pan exhibited negative correlations at only 2 of 6 ROIs (middistal femur and mid-proximal humerus). The PMA ratio apparently responded differently to an increased percentage of total arboreal locomotion among gorillas (decreased) and Pan (increased). The second (are PMA ratios and scrambling negatively correlated?) and third (are PMA ratios and arboreal quadrupedal walking positively correlated?) questions were answered more equivocally. Inspecting the combined-genera sample, as well as the separate analysis of gorillas, PMA ratios and scrambling were seldom negatively correlated. Arboreal quadrupedal walking and PMA ratios frequently were correlated positively in the combined sample, or when Pan was analyzed separately. However, when gorillas were analyzed separately, the correlation between PMA ratios and arboreal quadrupedal walking often was not positive. This may indicate that African ape arboreal quadrupedal walking does not involve stereotypical limb movements as much as originally assumed. The fourth question (is scrambling correlated to PMA ratio more strongly than other arboreal locomotor behaviors?) was answered with a deﬁnitive no. Gorillas, except at their humeral midshaft, exhibited the strongest correlations between group PMA ratios and a behavior other than scrambling (i.e., arboreal quadrupedal climbing). This underscores the importance of distinguishing scrambling from quadrupedal climbing in behavioral studies. No single arboreal locomotor behavior consistently exhibited the highest correlation with PMA ratio in Pan. While scrambling correlation coefﬁcients exhibited a higher average position (1, highest; 4, lowest) in Pan (2.5) than in gorillas (2.8), suspensory behaviors usually exhibited the strongest correlations in Pan. Arboreal scrambling and suspensory behaviors often exhibited the highest positions in Pan femoral ROIs, while arboreal quadrupedal climbing and suspensory behaviors were regularly the highest in their humeral ROIs. Quadrupedal walking frequently exhibited low positions in both genera, especially in Pan. The lack of a single clearcut behavioral correlate with PMA ratios in Pan, as demonstrated by quadrupedal climbing in Gorilla, could indicate that bending load orientations were relatively similar (or similarly variable) during each 327 of their arboreal locomotor behaviors (i.e., each promotes a circular cross section to a similar degree), or at least more similar than those encountered by gorillas during the same arboreal locomotor behaviors. This speculation, however, must be veriﬁed experimentally. To the extent that group mean PMA ratios reﬂect locomotor behaviors, the locomotor repertoires of G. g. graueri and P. t. troglodytes may be estimated in lieu of absent positional behavior data. These estimates do not reﬂect the amount of time spent in arboreal vs. terrestrial settings (e.g., classiﬁcation as arboreal or terrestrial primates). Rather, they correspond to the percentage of locomotion that occurred in each setting (e.g., travel). Femoral diaphyses of G. g. graueri exhibited a pattern in PMA ratios that was more similar to gorilla subspecies than Pan, but they exhibited magnitudes of PMA ratios that were intermediate (i.e., between Pan and other gorilla subspecies). Humeral PMA ratios of G. g. graueri typically were lower than those of the other gorilla subspecies. At the humeral midshaft, G. g. graueri displayed the least sexual dimorphism of all gorilla subspecies. Femoral and humeral bending load orientations in G. g. graueri were apparently the most variable of all gorilla subspecies (i.e., they usually exhibited the most circular cross sections). Gorilla g. graueri appears to have exhibited less total arboreal locomotor behavior than G. g. gorilla, but more total arboreal locomotor behavior than G. g. beringei. To the extent that PMA ratios reﬂected locomotor behavior proﬁles, sex-speciﬁc characterizations of P. t. troglodytes generally were most comparable to P. t. schweinfurthii. Female femoral PMA ratios were intermediate to those of P. t. verus and P. t. schweinfurthii females, and higher than P. paniscus females. Male P. t. troglodytes exhibited the highest femoral PMA ratios of all Pan males. In the humerus, P. t. troglodytes sexes exhibited lower ratios than sexes of other subspecies, but higher ratios than P. paniscus sexes. Femoral PMA ratios of P. t. troglodytes might indicate a lower amount of variability in femoral bending regime orientations than experienced by most chimpanzees, while humeral PMA ratios might indicate a higher amount of variability in humeral bending regime orientations. Ruff (2002) was among the ﬁrst to incorporate positional behavior data in a study of cross-sectional geometry of limb bones. The effects locomotor behavior repertoire may have had on long bone articular dimensions and cross-sectional properties were discussed, but links to shape differences in cross sections were not explored. Ruff (2002, Table 2, p. 328, 331) characterized locomotor behavior in Pan as “knuckle-walking, climbing, and some suspension” and in Gorilla as “knuckle-walking, some climbing, and infrequent suspension.” Such a generalized approach in partitioning behavioral repertoires (e.g., qualitative behavioral comparisons) masked important distinctions in the locomotor behavior proﬁles 328 K.J. CARLSON of African apes that could be useful to interpretations of cross-sectional properties. For example, G. g. gorilla females, but not males, apparently engage in at least as much arboreal suspensory and arboreal climbing behaviors as Pan females (Table 2 in the present study; Remis, 1998, p. 102). Also, chimpanzees exhibit signiﬁcantly more knuckle-walking than climbing when comparing total locomotion percentages, but this pattern is reversed if only arboreal locomotor behaviors are considered (Table 2). Knuckle-walking or, more generally speaking, quadrupedal walking is less frequently observed in arboreal settings than terrestrial settings. While a generalized description of locomotor repertoires may be sufﬁcient depending on the question of interest, such as a broad-ranging taxonomic comparison (e.g., Ruff, 2002), functionally relevant similarities and distinctions are more readily available when behavioral comparisons use quantitative behavioral data. There are several possible explanations for the lack of consistent close correspondence between group PMA ratios and group percentages of locomotor behaviors. The PMA ratio quantiﬁes the amount of uniformity between the maximum and minimum bending rigidity for a diaphyseal cross section. When femoral or humeral bending loads are experienced from multiple orientations, it is proposed that PMAs should be more similar in magnitude than when bending loads are more uniform in orientation (e.g., Fig. 1). A relatively circular cross section, in this sense, would be a preventative response that may minimize failure (i.e., fracture) from large bending loads oriented in any one of many directions. When bending load orientations are relatively stereotypical in the limb of an individual, it is suggested that PMA magnitudes may diverge as minimum rigidity declines relative to maximum rigidity. A relatively noncircular cross section, in this sense, would be a preventative response to failure (i.e., fracture) from large bending loads that are oriented over a relatively select range of directions. Studies combining in vivo strain data and cross-sectional geometric properties purported that PMAs assessed relative to centroidal axes, as used in the present analysis, may not have reﬂected maximum bending loads accurately in ulnae and tibiae (Demes et al., 1998, 2001; Lieberman et al., 2004). Lieberman et al. (2004) reported that the experimental neutral axis (NA) of a sheep tibia cross section diverged from the centroidal axis (CA) to a variable degree during treadmill walking. They suggested that cross-sectional properties (e.g., PMAs) calculated with respect to the CA in the sheep tibiae were less accurate than cross-sectional properties calculated with respect to the NA. They recommended caution when comparing properties calculated about CAs, and endorsed a more conservative approach, such as the comparison of patterns rather than magnitudes. Perhaps correlations between speciﬁc locomotor modes and PMA ratios calculated about NA axes would provide a clearer pattern of form-function relationships. The femoral or humeral diaphysis of any African ape did not exhibit a uniform pattern in response to bending load regimes engendered during locomotor behaviors (i.e., intradiaphyseal variation in correlation strengths was common). Whether bending regimes were in fact uniform along the diaphysis cannot be ascertained with the indirect evidence presented here (i.e., in vivo strain data are necessary). The lack of uniform correlation coefﬁcients in a diaphysis could be indicative of bending load orientations being inﬂuenced by localized phenomenon (e.g., muscle-bone interaction), as opposed to the direction of SRF vectors. It is suspicious that where bending load regimes theoretically should be the highest, namely at midshaft diaphyses (e.g., Biewener and Taylor, 1986), behavioral correlations were inconsistently the strongest. This was most evident in the gorilla sample, especially in the humeral diaphysis. Weiss (2003) reported that cross-sectional geometric properties were correlated signiﬁcantly to humeral muscle attachments in a large sample of prehistoric Amerindians. Of all six ROIs in the combined African ape sample, only the mid-proximal humerus displayed a positive (signiﬁcant) correlation. The humeral midshaft, although displaying a negative correlation, exhibited a relatively weak correlation. These two ROIs were located within or near the insertion of the deltoid (Gregory, 1950; Swindler and Wood, 1973). As the percentage of arboreal locomotion increased, more frequent forelimb abduction could be reasonably anticipated due to engaging in scrambling and suspensory behaviors, among other arboreal locomotor behaviors. Greater use of the deltoid may have elevated its impact on bending regimes speciﬁcally at these ROIs, relative to the local impact of other muscles at other ROIs. While it is conceivable that the contribution of a muscle to a local bending regime (e.g., ROIs) may vary in magnitude depending on how many muscle ﬁbers are recruited simultaneously, the orientation of the muscle force is assumed to be stereotypical (i.e., muscle attachments are assumed to be statically positioned on a diaphysis). Thus, the humeral midshaft and mid-proximal PMA ratios, if primarily reﬂecting deltoid-generated bending loads, may have increased (counter the original proposition) as the percentage of arboreal locomotion rose. This could partially explain why these two ROIs often did not exhibit the proposed relationships with locomotor behaviors. Local bending regimes at femoral ROIs could be affected by muscle attachment sites as well. Insertions of several small muscles (e.g., pectineus or adductor brevis) intersected only the midproximal femoral ROI, while larger muscles with more expansive origins (e.g., vastus intermedius or biceps femoris caput breve) or insertions (e.g., adductor magnus, adductor longus, or gluteus maximus) either APE LONG BONE GEOMETRY AND LOCOMOTOR BEHAVIOR intersected all three femoral ROIs, or only the two more distal ROIs (Gregory, 1950; Swindler and Wood, 1973). The relevance of muscle forces to local bending regimes would seem considerably more complex when multiple muscles were involved. Whether muscle function (e.g., measured by electromyography or architectural properties) exerted substantive inﬂuence on local bending regimes in diaphyses, and if so, how they may inﬂuence crosssectional properties, are critical questions that warrant investigation. Since Lanyon et al. (1975, p. 267) initially issued the challenge to identify “the mechanisms by which continued intermittent deformation inﬂuences bone structure . . . so the relative importance of large or small deformation cycles and the signiﬁcance of their alignment [could be made less] speculative,” our understanding of the response of bone to mechanical stimuli has deepened (Burr et al., 2002; Martin et al., 1998). Considerably less attention, however, has been devoted to documenting and understanding the variability in bending regimes that arises during various modes of locomotion. In primate studies that used indirect assessments of bending forces, such as SRFs and kinematic analyses, primarily quadrupedal or bipedal walking and running were emphasized (D’Août et al., 2001, 2002; Demes et al., 1994; Ishida et al., 1990; Kimura, 1985; Kimura et al., 1979; Reynolds, 1985; Schmitt, 1994, 1995, 1998, 2003). Among nonhuman primates, direct measurements of variability in the orientation of bending regimes (i.e., in vivo limb bone strains) were characterized only in gibbons during brachiation (Swartz et al., 1989), and in macaques during overground quadrupedal walking and galloping, with some anecdotal climbing data reported (Demes et al., 1998, 2001). The degree to which additional locomotor behaviors, most notably many arboreal behaviors, engender strains within limb bones is largely unknown. The relationship between bending strains generated during arboreal locomotion compared to those generated during terrestrial locomotion also has not been addressed. For example, does arboreal quadrupedal walking engender more variability in the orientation of bending strains than terrestrial quadrupedal walking? A more variably oriented ML component of the SRF vector experienced by the forelimb during terrestrial quadrupedal walking compared to arboreal quadrupedal walking may suggest that the forelimb ML bending regime could be comparatively less variable during arboreal quadrupedal walking as well (Schmitt, 2003). If arboreal quadrupedal walking were to elicit a narrower range of bending orientations in the forelimb (e.g., the humeral diaphysis), this would lend support to the positive correlations between PMA ratio and the percent arboreal quadrupedal walking for all three femoral ROIs and one humeral ROI in the separate analysis of Pan. However, negative correlations 329 for all three femoral ROIs and one humeral ROI in the separate analysis of gorillas would not be explained. The absence of a consistent association between PMA ratios and speciﬁc arboreal locomotor behaviors (e.g., arboreal quadrupedalism, quadrumanous climbing, or suspensory behaviors) highlights the need for additional experimental data from more diverse ranges of locomotor behaviors and animals. A growing body of literature supports the notion that the distribution of cortical bone in a diaphyseal cross section may not reﬂect the strain history of long bones in a simple and straightforward manner. Alternative views of results for many of the early studies that provided experimental support for bone adaptation to mechanical stimuli have been articulated (Bertram and Swartz, 1991). Recent in vivo analyses (e.g., Demes et al., 1998, 2001; Lieberman et al., 2004), along with the demonstration of strain gradients in long bone diaphyseal cross sections (e.g., Gross et al., 1997; Judex et al., 1997), present persuasive evidence that the location of maximum strain in a cross section does not always correspond to the maximum PMA. The assumption of tissue efﬁciency in “Wolff’s law” (see working deﬁnition in the introduction) apparently may not always be the case. An alternative nonmechanical explanation for the shape of long bone diaphyses (developmental determination) has been summarized recently by Lovejoy et al. (2003). CONCLUSIONS Patterns in group PMA ratios were rarely consistent throughout femoral and humeral diaphyses. Variability in bending load orientation, as assessed by the circularity of cross sections, apparently was not consistent throughout either diaphysis of African apes. Humeral ratios varied between groups (e.g., subspecies) or within groups less than femoral ratio, exhibiting less between-groups variance (e.g., differences between subspecies) than within-groups variance (e.g., differences between individuals) when femoral and humeral PMA ratio variances were compared. Humeral PMA ratios presumably reﬂected individual-based behavioral differences (i.e., idiosyncratic behaviors) that transcended taxonomic boundaries. Femoral PMA ratios, on the other hand, reﬂected group-based behavioral differences more readily. The expression of limb differentiation in humeral and femoral PMA ratios could be related to greater group-speciﬁc functioning of the hind limbs during locomotion, possibly inﬂuenced by hind limb drive, that does not apply in the forelimb where idiosyncrasies in limb segment positions may arise more frequently. Despite ﬁnding a nonuniform pattern in ROIs (i.e., variation within a diaphysis was observed), a few general observations can be made from correlations between PMA ratios and locomotor behaviors. A negative association between mean PMA ratios and percentages of total arboreal locomotion was 330 K.J. CARLSON observed frequently, although less so in Pan when African ape genera were analyzed separately. Group mean PMA ratios provided a moderately reasonable substitute for the degree of total arboreal locomotion when comparing genera (e.g., gorillas and chimpanzees) or even subspecies (e.g., mountain gorillas and western lowland gorillas). Thus, PMA ratios may provide reasonable estimates for the degree of arboreal locomotion in ape taxa, extant or extinct, for which locomotor behavior data are unavailable. No single behavior (e.g., arboreal scrambling) consistently demonstrated the highest correlations with femoral and humeral ratios. However, when analyzed separately, gorillas frequently exhibited the strongest correlations between PMA ratios and quadrupedal climbing. Pan PMA ratios usually exhibited the strongest correlations with suspensory behavior, followed by scrambling and quadrupedal climbing. Quadrupedal walking consistently exhibited some of the weakest correlations with PMA ratios (i.e., diaphyseal circularity), whether genera were combined or separated in analyses. Additional direct (e.g., in vivo strain) or indirect (e.g., substrate reaction force) primate data, particularly for arboreal locomotor behaviors, are needed. Such investigations would provide critical data for addressing whether the hypothesized relationships between group mean PMA ratios and locomotor behaviors were accurate in assumptions regarding variable bending load orientations engendered during arboreal locomotor behaviors. These data could also address whether subspecies exhibited differences in locomotor behavior repertoires that could not be observed with PMA ratios. For example, did overlapping ranges of behavioral modes (i.e., all groups used the same suite of behaviors) drown quantitative behavioral differences (e.g., groups used different percentages of behaviors within the suite)? ACKNOWLEDGMENTS I acknowledge the extraordinary cooperation of several museums, hospitals, and their staffs that made this research possible. For granting access to their collections and arranging specimen loans for CT scanning, I express my gratitude to the American Museum of Natural History, New York, NY; the Musée Royal de l’Afrique Centrale, Tervuren, Belgium; das Anthropologisches Institut und Museum der Universität Zürich-Irchel, Zürich, Switzerland; the National Museum of Natural History, Washington, DC; the Powell-Cotton Museum, Birchington, Kent, UK; the Natural History Museum, London, UK; and das Museum für Naturkunde der Humboldt Universität, Berlin, Germany. For granting access to their CT facilities, I acknowledge Hammersmith Hospital, London, UK; QEQM Hospital, Margate, Kent, UK; Charité Hospital, Berlin, Germany; Mount Sinai Hospital, New York, NY; Universitaire Ziekenhuizen, Leuven, Belgium; Kantonsspital, Institut für Radiologie, Winterthur, Switzerland; and the Department of Anthropology, Smithsonian Institution, Washington, DC. For their personal cooperation, I offer my sincerest gratitude to the numerous CT technicians who assisted me: Stuart Daws, CT Superintendent; Anja Boldt, M.T.A.R.; Justine DePonte, B.Sc. (Hons.), Diagnostic Radiography; Sandra Jones Dillard, R.T., CT; Marc Verburgh; and Isuf Hoxha. Without their cooperation, this research would not have been possible. I am also deeply grateful to Kevin Hunt, David Burr, Brigitte Demes, Della Cook, Jeanne Sept, Diane Doran, Christoph Zollikofer, Marcia Ponce de León, and Jessica Satkoski for discussions, guidance, and support during the course of this research. I thank Kevin Hunt for help in drawing Figure 2, and Luci Betti-Nash for her expert help in generating Figure 4. Brigitte Demes, Jack Stern, Clark Larsen, and two anonymous reviewers provided insightful comments from which the quality of this manuscript beneﬁted tremendously. LITERATURE CITED Amtmann E. 1971. 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