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Primate long bone diaphyses show considerable morphological variation, reflecting a wide diversity of inter- and intraspecific modes of locomotion. Diaphyses serve as beams that must withstand the mechanical loads generated during locomotion, but how exactly diaphyseal form is related to locomotor function depends on a variety of factors. Relevant factors are gene-mediated developmental programs, long-term (evolutionary) adaptation as a response to selective pressures, and short-term (in vivo) modification as a response to mechanical loading patterns experienced during an individual's life. The relationship between these factors is complex, and the relative impact of each of them on long bone morphology is often difficult to assess (Pearson and Lieberman, 2004).
It is typically hypothesized that diaphyseal shape reflects locomotor behavior1 according to Wolff's Law (WL; Wolff, 1892, 1986), which posits that bones are remodeled in vivo to optimally resist mechanical loading patterns. WL has recently been restated in a more general form as “bone functional adaptation”2 (Ruff et al., 2006). WL is supported by various experimental studies that investigate the effects of mechanical loading in controlled settings (e.g., Lanyon and Baggott, 1976; Lanyon and Bourn, 1979; Lanyon, 1987; Turner et al., 1995; Robling et al., 2002; Warden et al., 2005). Another example is hypertrophy of the playing arm relative to the nonplaying arm in professional athletes (e.g., Jones et al., 1977; Bass et al., 2002). While WL still serves as a useful basic hypothesis of how diaphyseal form is related to function, it was challenged on several grounds. Due to difficulties in identifying direct effects of mechanical in vivo loading on diaphyseal shape, it was suggested that bone modification could be explained by factors other than mechanical loading such as bone inflammation and regeneration or bone fracture repair processes (Bertram and Swartz, 1991). Furthermore, various recent developmental studies (reviewed in Lovejoy et al., 2003) indicate that long bone shape largely reflects developmental programs. An additional level of complexity in diaphyseal form-function relationships was revealed by in vivo strain analyses, which showed that inferred biomechanical properties of long bones (e.g., inferred bending strength relative to the neutral axis) do not always coincide with biomechanical properties measured with strain gauges during locomotion (e.g., actual bending direction) (Demes et al., 2001; Lieberman et al., 2004).
Various research strategies are currently followed to gain new insights into form-function relationships in long bones. The first is to perform more detailed in vivo bone strain measurements to establish direct links between locomotor modes, spatiotemporal loading patterns, biomechanical properties, and diaphyseal morphology. Several studies showed, for example, that in vivo bone strain patterns change dynamically during locomotion, and that bone shape may be better correlated with peak loads than with average loading patterns (Szivek et al., 1992; Demes et al., 2001; Lieberman et al., 2004). The second strategy is an approach, which simulates the evolutionary process experimentally (Garland and Rose, 2009). A recent study showed that more robust diaphyses reflect the evolutionary history rather than in vivo activity levels of an individual, indicating a strong genetic influence on long bone diaphyseal development and morphology (Wallace et al., 2010).
The third strategy, which is adopted here, consists in analyzing patterns of variation of diaphyseal morphology. Data from different species, from ontogenetic series, and from individuals with known differences in in vivo loading histories help assess the respective roles of phylogenetic processes, developmental programs, and specific loading patterns on bone shape. Two approaches may be used to quantify diaphyseal morphology. The first evaluates biomechanical (i.e., functional) properties according to standard models of beam theory (Lovejoy et al., 1976; Ruff and Hayes, 1983; Ruff and Runestad, 1992). The second quantifies biologically homologous features and is known as Geometric Morphometrics (GM) (Bookstein, 1991). During the analysis of long bone diaphyseal morphologies, each approach has its specific potential and limitations.
Biomechanical properties of long bones such as resistance against axial loading or bending are typically quantified by cross-sectional properties, such as cortical bone area, second moments of area, and section modulus. Often, such data are acquired at the mid-shaft assuming that the mid-shaft represents a functionally equivalent region in different taxa. Various studies demonstrated a clear relationship between locomotor modes and cross-sectional properties of long bone diaphyses (Burr et al., 1989; Kimura, 1991; Ruff and Runestad, 1992; Demes and Jungers, 1993; Kimura, 1995; Ruff, 2002). For example, primates show greater cross-sectional strength than terrestrial mammals at similar body mass, which was interpreted as an adaptation to arboreal environments (Kimura, 1991, 1995). However, within primates and within rodents the relationship between cross-sectional strength and arboreality/terrestriality does not hold, indicating that other factors are relevant in determining diaphyseal shape (Polk et al., 2000). Also, it has been shown that specific locomotor modes are correlated with specific cross-sectional properties; for example, prosimian species specialized in leaping exhibit anteroposteriorly expanded femoral cross sections compared to nonleaping species of similar body mass (Demes and Jungers, 1993). Further, a comparative analysis of three Macaca species (Burr et al., 1989) demonstrated that humeral and femoral cross-sectional rigidity is higher in more terrestrial species than arboreal ones, and that relative strengths of fore- and hind limbs distinguish suspensory and leaping species in primates (Ruff, 2002).
Several studies compared cross-sectional properties of long bone diaphyses within species, be it between wild and captive individuals, or between individuals with known locomotor histories in the wild or in experimental setups. A comparative analysis of wild and captive Lemur catta did not find significant differences between groups in length, cross-sectional area and section modulus of the humerus and femur (Demes and Jungers, 1993). On the other hand, captive individuals of Macaca nemestrina showed greater second moments of area in humerus and femur relative to body mass than wild individuals in absolute value, but profiles of relative magnitude of second moments of area along femoral/humeral diaphyses did not differ between the two groups (Burr et al., 1989). Comparison of chimpanzees with known individual locomotor behaviors showed that femoral/humeral diaphyseal cross-sectional properties are only loosely correlated with the frequency of arboreal/quadrupedal locomotion (Carlson, 2005; Carlson et al., 2006), but well correlated with age (Carlson et al., 2008a). Differences were found between female chimpanzees from Taï versus Mahale/Gombe in the ratio of maximum to minimum bending rigidity (Imax/Imin) at the mid-proximal diaphysis of the humerus, and the mid-distal diaphysis of femur (Carlson et al., 2008a), but the question remains open whether such contrasts reflect differences between population-specific locomotor behaviors, or between population-specific developmental programs. Comparison of diaphyseal morphology between two groups of mice with different locomotor regimes (straight and curved-course running) showed that different activity patterns do not result in significant differences in various cross-sectional properties of cortical bone (cortical area, second moments of area in mediolateral and anteroposterior direction) nor in trabecular bone structure (Carlson and Judex, 2007; Carlson et al., 2008b). The ratio of mediolateral to anteroposterior bending rigidity was, however, found to be significantly different between groups (Carlson and Judex, 2007).
Some analyses thus show that cross-sectional properties convey functionally relevant information, but others do not provide clear links between form and function. This might be due to limitations in the data rather than to actual absence of correlation. Cross-sectional data typically come from selected regions of the diaphysis (e.g. the midshaft), and biomechanical properties such as second moments of area are evaluated for a set of standard orientations around the diaphysis. Using such data, various studies showed that the midshaft is an adequate region to compare diaphyseal cross-sectional properties (e.g., Ruff et al., 1994; Ruff, 2002, 2009). Actual long bone loading patterns, however, may exhibit high spatial heterogeneity, as they result from a combination of bone geometry and the topography and activation patterns of the locomotor muscles acting on the bone. It was demonstrated that long bones experience dynamically changing patterns of strain during locomotion (Demes et al., 2001; Lieberman et al., 2004), and that they exhibit different remodeling patterns at different locations (Bass et al., 2002). Also, various muscles that are biomechanically relevant for quadrupedal versus bipedal locomotion attach to the proximal femoral diaphysis (Crass, 1952; Stern, 1972; Swindler and Wood, 1982; Lovejoy et al., 2002), such that one might expect different form-function relationships in proximal compared to middle and distal areas of the diaphysis. Accordingly, if we take into account that the second moment of area is a directional integral, tracking changes in its magnitude around and along the diaphysis may provide relevant additional data on bending resistance under complex in vivo loading conditions.
In studies analyzing form-function relationships, the femur has received special attention, because primate locomotion is typically hindlimb-dominated (Kimura et al., 1979; Reynolds, 1985; Demes et al., 1994; Schmitt and Lemelin, 2002), and because the transition from quadrupedal modes of locomotion (Lovejoy et al., 2009a, b, c) to obligate bipedalism in the hominins involved key changes in femoral biomechanics. How can structurally and functionally relevant quantitative information be gathered from the diaphysis as a whole, and in a comprehensive form? One possibility is to use landmark (or semilandmark)-based GM methods, which permit quantitative analyses of entire organismic forms in two or three spatial dimensions. GM methods use anatomical points of reference (so-called landmarks) to establish point-to-point homology between specimens of a sample. GM methods are thus optimized for the analysis of landmark-rich, modular biological structures such as the cranium of hominins and nonhuman primates (e.g., O'Higgins and Jones, 1998; Ponce de Leon and Zollikofer, 2001). Recently, GM has also been used to study long bone morphology, but while this set of methods is well applicable to epiphyses (Harmon, 2007, 2009; Holliday et al., 2010), it is less suited for diaphyses. Diaphyses consist of a single developmental module and exhibit only few clearly defined landmarks. In principle, ridge structures on the diaphyseal surface can be used to define semilandmarks, which quantify geometric (rather than biological) homology between specimens (Gunz et al., 2005), but most diaphyses exhibit relatively few such structures, which themselves tend to be highly variable.
Application of GM to long bone diaphyses also has technical and graphical limitations. In GM, size is normalized by centroid size (Bookstein, 1991) prior to analysis of shape variation. While this approach works well for landmark configurations with an approximately isotropic distribution in space, it is not suited for the cylindrical geometry of diaphyses, where most of size variation is due to differences in diaphyseal length. A straightforward workaround is to apply some form of affine normalization with different scaling factors along and across the diaphyseal geometry. However, the results of a semilandmark-based GM analysis of diaphyseal shape variation are difficult to visualize comprehensively, because our visual system is relatively inefficient in recognizing patterns of variation in a cylindrical geometry.
Measuring long bone structural and functional properties along the entire diaphysis, and visualizing and analyzing these data comprehensively thus represents a double challenge. GM methods must be expanded to permit shape analysis of the essentially landmark-free diaphysis, and the analysis of cross-sectional properties must be extended to comprise the entire diaphysis. Here we use morphometric mapping (MM) techniques to meet these challenges. The concept of MM was introduced by Amtmann and Schmitt (1968) to analyze patterns of cortical bone distribution and biomechanical properties along the femoral diaphysis (Amtmann and Schmitt, 1968). Later, MM was formalized and combined with 3D imaging to compare geometric and cross-sectional properties of human and great ape femora (Jungers and Minns, 1979; Zollikofer and Ponce de León, 2001). Recently, MM was re-applied to visualize femoral cortical bone thickness and canine dentine distribution (Bondioli et al., 2010). While MM has mainly been used as a visualization tool, we embed it here into the generalized framework of morphometric surface parameterization. Surface parameterization denotes the process of mapping the surfaces of biological structures onto Euclidean bodies. The latter can then be used as a frame of reference to compare the specimens of a sample. One example is spherical surface parameterization, which was introduced to map endocranial surfaces onto a sphere, and to analyze endocranial shape variation in terms of deformation of the sphere (Specht et al., 2007). In this article, we use cylindrical parameterization as a means to represent the distribution of data sampled on long bone diaphyses. These data represent geometric features of the diaphysis such as cross-sectional shape, surface curvature and cortical bone thickness, as well as biomechanical properties such as cross-sectional cortical bone area and second moments of area.
Aims and Hypotheses
This paper has two aims. The first is to introduce MM as a new analytical tool kit for long bone diaphyseal analysis and to compare its performance with traditional cross-sectional analysis and with GM methods. The second aim is to apply these methods to investigate patterns of femoral diaphyseal shape variation in an ontogenetic series of wild and captive common chimpanzees (Pan troglodytes troglodytes). This sample is used to address the question how developmental programs versus in vivo loading patterns influence femoral geometric and biomechanical properties. The captive chimpanzees used in this study were all held in traditional zoos (specimens were collected by A.H. Schultz between 1930 and 1950). This implies that these chimpanzees lived in spatially more confined and structurally less complex environments than their wild conspecifics, resulting in less overall locomotor activity and restricted/modified diversity of species-specific locomotor patterns (Jensvold et al., 2001).
Direct information about the locomotor behavior of the zoo individuals in our sample is not available, but clear differences between zoo and wild animals in locomotor behavior have been reported: Captive chimpanzees do not have the opportunity of long-distance traveling, as is typically observed in natural environments (Goodall, 1986; Jensvold et al., 2001). Chimpanzees held in traditional zoos exhibit a higher proportion of suspensory and climbing behaviors compared to wild chimpanzees, but no leaping behavior (Jensvold et al., 2001). When transferred from traditional to modern zoos offering large living areas and improved climbing structures, captive chimpanzees showed higher frequencies of bipedal, climbing, and leaping behaviors. Compared to wild-living individuals, they spent more time for standing bipedally/quadrupedally and lying (Jensvold et al., 2001), such that even in modern zoos locomotor behavior is constrained relative to free-range behavior. In summary, locomotor behavior of chimpanzees in captivity is constrained/modified compared with free-ranging chimpanzees in three respects: (a) in the diversity of the locomotor repertoire, (b) in the frequency of each locomotor mode, and (c) in activity levels. Comparing femoral morphology in wild and captive chimpanzees (all belonging to the same subspecies) thus provides an ideal test case to investigate the effects of locomotor differences in a sample with a common genetic and developmental background.
First, we ask whether differences in locomotor behavior between subsamples manifest themselves as differences in morphological and biomechanical properties of the femoral diaphysis. We hypothesize that ontogenetic trajectories between wild and captive chimpanzees diverge as an effect of in vivo bone modification [WL, or functional bone adaptation sensu Ruff et al. (2006)]. Accordingly, we expect femoral diaphyseal shape variation in the pooled sample to be larger in adult than in immature specimens. Second, we ask whether cross-sectional measurements taken at the femoral midshaft optimally capture differences between subsamples. To test this hypothesis, we perform separate MM analyses of the proximal, middle, and distal thirds of the femoral diaphysis, and analyze which region, and which morphometric and biomechanical features, discriminate best between wild and captive chimpanzees. Third, we compare the outcomes of MM, GM, and midshaft cross-sectional analyses to assess the potential and limitations of each method.
morphometric map, morphometric mapping
MATERIALS AND METHODS
Wild (N = 22) and captive (N = 26) chimpanzees (Pan troglodytes troglodytes) from infant to adult stages (pooled sex; femoral diaphyseal length: 79 to 212 mm) were obtained from the collection of the Anthropological Institute and Museum of the University of Zurich. To facilitate visualization of age-related trends, the sample is divided into three developmental categories according to femoral diaphyseal length (I: ≤120 mm; II: >120–≤180 mm; III: >180 mm). These categories largely correspond to the following dental eruption stages: I: second deciduous molar erupted (infant); II: M1-M2 erupted (juvenile); III: M2-M3 erupted (adult) (see Fig. S1 for details). As mentioned, all captive individuals are from “traditional” zoos, i.e., where chimpanzees were held in small living areas and could not engage in long-range locomotion.
Volumetric and Cross-Sectional Data Acquisition
Femora of all specimens were scanned using a Siemens 64-detector-array CT device with the following data acquisition and image reconstruction parameters: beam collimation: 1.0 mm; pitch: 0.5–0.75; image reconstruction kernel: standard/sharp (B30s/B70s); slice increment: 0.3 to 0.5 mm. This resulted in volume data sets with isotropic spatial resolution in the range of 0.3 to 0.5 mm. Small specimens (femoral length <150 mm) were scanned using a micro-CT scanner (μCT80, Scanco Medical, Switzerland), and volume data were reconstructed at an isotropic voxel resolution of 75 μm.
Using the software package Amira 4.1 (Mercury Systems), each original CT data set was resampled along the principal axis of the femoral diaphysis in order to obtain K = 300 equally spaced cross-sectional images along the entire diaphysis (Fig. 1A). These standardized data sets served as a basis for all further calculations. Biomechanical properties (such as second moments of area, see below) were calculated directly from the cross-sectional image data. Endosteal (internal, Lint) and subperiosteal (external, Lext) outlines were extracted from each cross section (Fig. 1B), and each outline was submitted to Elliptic Fourier analysis (EFA; Kuhl and Giardina (1982); see Appendix A for details). EFA was used to represent each outline by a parametric function, which represents the position of consecutive points on the outline as a function of the distance traveled along the outline. EFA provides a convenient means to control the level of detail of an outline representation (which is useful for noise reduction), to calculate standard geometric descriptors such as normal/tangent vectors, and to evaluate various morphometric variables (see below).
Morphometric Data Acquisition
Figure 1A–C provides a scheme of morphometric data acquisition. Various structural and functional variables can be defined on diaphyseal cross sections, such as external/internal radius, external/internal curvature, cortical bone thickness, and second moments of area. These variables depend on each other to some extent. For example, cortical bone thickness is derived from external and internal radius; curvature is a function of the first and second derivatives of the outline; second moments of area are area integrals related to radius and thickness. According to the question asked [structural (geometric) and/or functional (biomechanical)] it is convenient to visualize, explore and analyze various combinations of variables. In this study, we focus on external radius, external surface curvature, cortical bone thickness and second moments of area to investigate overall shape, surface topography, cortical bone distribution patterns, and biomechanical properties of the femoral diaphysis.
Radii rext and rint were calculated as the distance from the center of mass to the periosteal and endosteal outlines respectively (Fig. 1B). Surface curvature kext was calculated analytically using the parametric function of the external outline (Fig. 1B; see Appendix A for details). Cortical bone thickness h was measured as the distance from a point Pint on the endosteal outline to the periosteal outline, measured along the surface normal vector at Pint (Fig. 1B). This definition of cortical bone thickness provides locally unbiased measurements even when cross-sectional shape deviates significantly from circularity.
To estimate resistance against bending, second moments of area, Iθ, were evaluated (Fig. 1C). Iθ represents the variance (spatial distribution) of cortical bone distribution orthogonal to the bending plane with normal vector θ (see Appendix B for details). Iθ is typically calculated at a single location of the diaphysis (midshaft) and along selected directions θ (e.g. anteroposteriorly/mediolaterally, and along directions of maximum/minimum rigidity). Here, we evaluate the spatial distribution of Iθ along and around the entire diaphysis. Section modulus Z was calculated using Iθ and local maxima of rext (Fig. 1C). Since the in vivo neutral axis may deviate significantly from the centroid axis (Demes et al., 2001; Lieberman et al., 2004; Demes, 2007), these variables should be considered as proxies of bending resistance.
Longitudinal features such as diaphyseal bending (which is a measure of longitudinal curvature) (Yamanaka et al., 2005; Groote et al., 2010), or general spatial features such as 3D-surface curvature can, in principle, also be analyzed with MM methods. One longitudinal feature that is considered here is diaphyseal torsion. Long bone torsion is typically measured as the difference in orientation of proximal and distal joint axes (e.g., Elftman, 1945; Aiello and Dean, 1990; Cowgill, 2007). Here diaphyseal torsion is measured by changes in the orientation of the cross-sectional principal axis along the diaphysis (Fig. 1B).
Figure 1D–F shows the principle of cylindrical projection and MM. For each specimen, measurements of r, k, h and Iθ were sampled in each cross section, and along the entire diaphysis. These data were normalized to their respective median values, and mapped onto a cylindrical coordinate system (ρ, θ, z), where ρ = 1/(2π) = const. denotes the radius of the cylinder, angle θ denotes the anatomical direction (θ=0°→360°: lateral → anterior → medial → posterior → lateral; note the periodicity around θ), and z denotes the normalized position along the diaphysis (z = 0 → 1: distal → proximal) (Zollikofer and Ponce de León, 2001) (Fig. 1E, F). The orientation of the diaphysis in anatomical space was determined by calculating its three principal axes of cortical bone distribution: While the first axis represents the proximodistal direction, the second and third axes were used to define the mediolateral and anteroposterior directions, respectively (as will be described below, further fine-adjustment was performed for quantitative comparative analyses). Since the radius ρ = 1/(2π) = const., data can be visualized as two-dimensional morphometric maps M(θ, z), and distributions of r(θ, z), k(θ, z), h(θ, z) and I(θ, z) can be represented as K × L matrices where K and L denote the number of elements along θ and z respectively (K = L = 300) (Fig. 1B, C, Fig. 2). In formal terms, these procedures carry out a cylindrical surface parameterization (Fig. 1E). In practical terms, MMs are similar to topographic maps: the “longitude” (θ) of these maps corresponds to the anatomical orientation around the diaphysis, the “latitude” (z) to the position along the diaphysis (“north” =proximal; “south” =distal), and the “altitude” represents local values of morphometric variables (r, k, h, I).
MMs are visualized using false-color mapping schemes, which render relative values of morphometric variables according to a predefined color scale (Fig. 1G). The resulting “topographies” provide a comprehensive overview over the spatial distribution of variables r, k, h, and I around and along the diaphysis. As an additional feature, the orientations of cross-sectional major and minor axes along the diaphysis are visualized as lines (Fig. 1E, F).
To go beyond visual comparisons of MMs (Fig. 2), methods for quantitative comparative analysis of entire morphometric maps of multiple specimens are required. Here we propose a combination of standard methods of image analysis and multivariate analysis. MMs have the same structure as images (K × L matrices), whose spatial properties are conveniently quantified by the 2D-Fourier transform (FT, see Appendix C for details). The FT is especially appropriate here for the following reasons: (a) MMs have a natural periodicity in θ (i.e., around the shaft), which is optimally represented by the periodic basis functions used in FT; (b) the FT provides a quantitative method to compare nonlandmark structures; (c) the FT can be extended to the third dimension (K × L × J), where J morphometric maps representing different aspects of long bone morphology and/or biomechanics (variables r, k, h, I) are analyzed together, as described below.
MM-based Shape Analysis
In analogy to standard GM procedures, MM-based analyses require that specimens be superimposed according to a best-fit criterion prior to shape analysis. While GM superposition involves size normalization, translation and rotation via Generalized Procrustes Analysis (Rohlf, 1990), MM superposition is performed by rotation around θ, which represents the only degree of freedom remaining after cylindrical projection. The method described above to evaluate mediolateral and anteroposterior directions of the diaphysis was used as a first step to orient all specimens in a similar direction. In a second step, optimal alignment was achieved by iteratively minimizing inter-specimen distances in Fourier space through appropriate rotation of each specimen around θ. This procedure performs small rotations around θ until differences between specimens are minimized. Together, the superposition procedures yield a set [M] of aligned MMs of all specimens (see Appendix C for details).
2D-FTs F(M) are then calculated for each M, resulting in K×L Fourier coefficient sets. To identify principal patterns of shape variability in the sample, Fourier coefficient sets are submitted to Principal Components Analysis (PCA). In analogy to GM, the mean (consensus) map <M> can be used as a reference shape, and specimens can be expressed by their deviation from the consensus map: M′=M-<M>. Nevertheless, PCA of F(M-<M>) is mathematically equivalent to PCA of F(M), such that both methods produce identical results. Here we use the latter method to reduce computing time. The Fourier Transform represents MMs as a set of spatial frequencies with associated amplitudes. Accordingly, a basic property of the FT is that the low-frequency domain captures global features (i.e., large-scale variation), while the high frequency domain captures local features (i.e., small-scale variation). Low-pass filtering in Fourier space (i.e., removal of the high-frequency domain) thus allows to capture variation in global features. As will be shown below, the statistically most relevant information about shape variation in the sample is typically contained in the low frequency domain.
To facilitate visual inspection of the results of PCA, MMs are reconstructed by transforming a given point P* in PC space into its corresponding set of Fourier coefficients F(M*), and applying an inverse Fourier transform to obtain a morphometric map M*.
The principal goal of PCA is to reduce the high dimensionality (K × L or K × L × J [analysis of J features]) of MM-based shape analyses. Graphing the first few PCs is a convenient means to explore statistically relevant patterns of shape variability in the sample; however, variation along a given PC does not typically represent variation caused by a single biological factor. It is thus more adequate to visualize patterns of shape variation and shape difference as a function of specific factors, such as body size, age, sex, and zoo/wild condition. Overall, it should be reiterated that, unlike GM, the proposed method of MM-based shape analysis does not presume point-to-point homology between specimens; rather, it analyzes variation of morphometric patterns along and around the entire long bone diaphysis.
Comparison of Ontogenetic Trajectories
When group-specific ontogenetic trajectories through PC space (shape space) are approximately linear, they can be characterized by their position and direction in shape space. Accordingly, they can be compared by measuring between-trajectory distance and divergence. Trajectory position was measured by the group mean position in shape space. Trajectory direction was quantified with two methods: (a) the principal direction of the group-specific distribution in shape space (first principal axis), and (b) the ontogenetic allometric vector (multivariate regression of shape against diaphyseal length) (Penin et al., 2002; Zollikofer and Ponce de León, 2006). As an additional method to compare group-specific distribution patterns in shape space, the distance between group-specific variance-covariance matrices was calculated following a method proposed by Mitteroecker and Bookstein (2009) (see Appendix D for details). Statistical tests on differences between groups were performed with bootstrapping (1,000 resamplings). All calculations were performed in MATLAB 7.7 (MathWorks).
MMs as a Tool for Visualizing Patterns of Diaphyseal Shape Variation
Figure 2 provides an MM-based visual comparison of femoral diaphyseal morphology in two adult captive chimpanzees, who represent extremes of the shape variation contained in the sample (these specimens are represented by vertical and horizontal rectangles in graphs of Figs. 3, 4, 8, 9). The MM of the external radius (Fig. 2B) visualizes diaphyseal surface morphology in terms of how cross-sectional shape deviates from a circle, thus permitting identification of regions of platymery. The MM of surface curvature (Fig. 2C) permits identification of ridges (crests) and grooves (fossae), and of their relative location and orientation along the diaphysis. Surface curvature reveals anatomically well-defined but often highly variable features, such as the linea aspera (la), the lateral spiral pilaster (lsp) (Lovejoy et al., 2002), the lateral supracondylar line (lsl), medial ridge (mr), and the pectineal line (pl). The MM of cortical bone thickness (Fig. 2D) gives a comprehensive view of cortical bone distribution along and around the diaphysis. The MMs of second moments of area (Fig. 2E) and section modulus (Fig. 2F) visualize the distribution of diaphyseal rigidity against bending, revealing changes in the magnitude of bending rigidity along and around the diaphysis.
Table 1. Comparison of ontogenetic trajectories of wild and captive chimpanzees
Relative magnitude of variation = (variation across ontogeny)/(variation along ontogeny). The first four columns represent p-values for differences between captive and wild chimps.
Entire diaphysis analyses
MM (radius ext)
MM (radius + curvature + thickness)
MM (second moments of area)
GM (radius ext)
The MMs of Fig. 2 reveal considerable inter-individual variation in diaphyseal morphology and biomechanical properties. Basic anatomical features can be identified in MMs of both individuals, but these features differ in location, orientation and prominence. Overall, the diaphysis of individual 1 is rounder than that of individual 2 (Fig. 2B). At the same time, it exhibits a more prominent linea aspera (Fig. 2C). Diaphyseal torsion (lines in Fig. 2D) is more expressed, and cortical bone thickness is increased in the posterior diaphysis (Fig. 2D-1). Comparison of Figs. 2D and E shows that areas of increased cortical bone thickness coincide with the orientation of the principal cross-sectional axes (Fig. 2D) and with some, but not all, features on the external surface (Fig. 2B). MMs of biomechanical properties (Figs. 2E, F) indicate differences between individuals in absolute and relative values of bending rigidity. Individual 1 shows higher second moments of area in anteroposterior direction than in mediolateral direction (Fig. 2E-1), while the situation is reverse in individual 2 (Fig. 2E-2). MMs of section modulus (Fig. 2F) are largely similar to those of second moments of area (Fig. 2E). Overall, compared with direct inspection of femoral diaphyseal anatomy (Fig. 2A), MMs provide a comprehensive visualization of the spatial distribution of morphological and biomechanical features, which facilitates explorative studies of diaphyseal shape variation.
MM-based Shape Analysis
MM-based shape analyses of the entire sample (pooled wild and captive specimens) were performed for external diaphyseal radius (Fig. 3A), external surface curvature (Fig. 3B), and cortical bone thickness (Fig. 3C), respectively, as well as for these variables together (Fig. 3D). Results are presented as PC plots (Figs. 3, 6) and MM visualizations (Figs. 4–7). Statistical tests for differences between captive and wild animals were performed for the following measurements:
agroup-specific means (H0: zero distance between group centroids in PC space)
bgroup-specific principal directions in PC space (H0: directions are identical)
cgroup-specific ontogenetic allometric trajectories (H0: trajectories are parallel)
dgroup-specific modes of variation (H0: zero distance between variance-covariance matrices).
None of these tests yielded significant results that would permit rejection of the respective null hypotheses (Table 1). Also, both groups show similar common ontogenetic allometric shapes at a given femoral diaphyseal length and cross-sectional area (Fig. 3E,F; slope: p = 0.66 and 0.73, intercept: p = 0.25 and 0.17, respectively).
Wild and captive chimpanzees thus exhibit statistically indistinguishable femoral diaphyseal shapes and patterns of diaphyseal ontogeny. Variation along and across the ontogenetic trajectory was calculated as the variance of the data scatter along the ontogenetic trajectory vector, and as the maximum variance perpendicular to it, respectively. Diaphyseal shape variation across the trajectory is similar in magnitude to the variation along the ontogenetic trajectory (Table 1), and already present at early developmental stages.
Since ontogenetic trajectories do not differ statistically between the two groups, common ontogenetic patterns are visualized as MMs (Fig. 4). Figure 4A shows that proximal and distal ends of the diaphysis are mediolaterally more extended (relative to the mid-shaft) in immature individuals. Figure 4B (surface curvature) shows development of the pectineal line, lateral spiral pilaster, linea aspera and medial ridge. The linea aspera is more laterally located in early ontogenetic stages and shifts to a more posterior location during ontogeny. Figure 4C (cortical bone thickness) shows that cortical bone is more evenly distributed in young individuals, and becomes proximally concentrated in adult individuals.
Figure 5 visualizes femoral diaphyseal shape variation independent of the ontogenetic stage (i.e., across the ontogenetic trajectory) with two MMs corresponding to the positions of the two diamonds in Fig. 3D. While overall diaphyseal topography is similar in both instances, differences can be observed in prominence and orientation of the linea aspera, in the degree of platymery (mediolateral relative to anteroposterior expansion) of the diaphysis (Fig. 5A), in prominence and position of the lateral spiral pilaster and pectineal line (Fig. 5B), and in the proximodistal distribution of cortical bone (Fig. 5C).
Figure 6 visualizes patterns of variation in biomechanical properties (second moments of cross-sectional cortical area). No statistical differences could be found between wild and captive chimpanzees (Fig. 6A, Table 1), such that patterns of variation are visualized along and across a common ontogenetic trajectory. In infant chimpanzees, diaphyseal bending rigidity exhibits strong mediolateral to anteroposterior polarity especially toward the distal end of the shaft. During ontogeny, this pattern becomes more homogeneous along the shaft. Intraspecific variation independent of ontogeny (i.e., across the ontogenetic trajectory; Fig. 6C) is largely similar to the pattern visualized for the two examples in Fig. 2F, exhibiting a continuum between diaphyses exhibiting mediolaterally versus anteroposteriorly increased bending rigidity.
Femoral length, median external radius and median cortical bone thickness are plotted against each other in Fig. 7. None of these graphs shows statistical differences between wild and captive groups (length-radius, slope: p = 0.08, intercept: p = 0.16; length-thickness, slope: p = 0.46, intercept: p = 0.79; radius-thickness, slope: p = 0.12, intercept: p = 0.45). Independent of ontogenetic stage, some captive individuals exhibit slightly thicker cortical bone (Fig. 7B). However, captive and wild subsamples do not differ significantly in adult mean values (p = 0.41, t-test). External radius and thickness shows negative and positive allometry against femoral diaphyseal length (exponents: 0.94 and 1.37, respectively), and thickness shows positive allometry against external radius (exponent: 1.38).
MM-BASED ANALYSIS OF DIAPHYSEAL SUBREGIONS
MM analyses were also performed for the proximal, middle and distal thirds of the diaphysis separately (Fig. 8A, B, C-1). Analyzing surface curvature and cortical bone distribution in each of these subregions separately permits comparisons with earlier studies, which typically focus on the midshaft, and can be expected to reveal localized differences between captive and wild subsamples. Results are represented as PC plots (Fig. 8) and MMs (Fig. 9), and statistics are summarized in Table 1.
Significant differences between wild and captive chimpanzees could be identified in only one region: Cortical bone distribution in the distal diaphysis exhibits distinct patterns (Fig. 8C-2, Table 1), while the surface topography is indistinguishable between the two groups (Fig. 8C-3). Also, the captive group shows significantly greater variance in cortical bone distribution (Fig. 8C) (p < 0.01, F-test). Corresponding MMs and cross-sectional representations of cortical bone distribution are visualized in Fig. 9A, B. While wild individuals show increased cortical bone thickness on medial and lateral sides of the distal femoral diaphysis, captive individuals show thicker anterior and posterior sides.
Comparison of MM Methods with Geometric Morphometric and Cross-sectional Methods
To compare the new MM methods proposed here with earlier methods, long bone diaphyseal morphology was also analyzed using geometric morphometric (GM) methods, and traditional cross-sectional analysis. A semilandmark-based GM approach was used to represent internal and external diaphyseal surfaces (internal surface: 60 × 25 3D coordinates; external surface: 60 × 50 3D coordinates). To control for the predominant effects of variation in diaphyseal length, specimens were normalized to unit diaphyseal length and unit median radius respectively, then submitted to standard semilandmark-based PCA of shape (Gunz et al., 2005). GM analyses were performed for the entire diaphysis (Fig. 10) and for the three subregions (Fig. S2). Similar statistical analyses were performed to permit comparison with MM methods (Table 1). PC scores of MM and GM analyses were compared using least-squares fitting, and the results showed that PCs of GM and MM analyses are largely similar (Table 2). MM and GM methods thus capture similar patterns of diaphyseal shape variation, and GM-based visualization (Fig. 10B) shows patterns of ontogenetic shape change, which largely correspond to the MMs in Fig. 4. However, characteristic features observed in MMs (Figs. 4, 5, 6, 9) such as changes in cortical bone distribution and in prominence of surface features cannot be visualized with GM methods, despite the large number of semilandmarks (Fig. 10).
Table 2. Coefficients of least square fitting
For comparison, standard cross-sectional analyses were performed for the proximal, middle and distal shaft (Fig. S3). None of these analyses reveals statistically significant differences between femoral diaphyseal biomechanical properties of wild and captive chimpanzees.
Summary of Results and Comparison with Earlier Studies
The main results of this study can be summarized as follows:
aThe MM methods proposed here provide an efficient tool kit to analyze cross-sectional geometric and biomechanical properties of entire long bone diaphyses, to visualize the results comprehensively, and to identify group-specific features and modes of variation.
bAverage modes of femoral diaphyseal ontogeny and shape variation are largely similar in wild and zoo chimpanzees. During ontogeny, the relative diameter of the proximal and distal ends of the diaphysis decreases, and the linea aspera, lateral spiral pilaster and medial ridge become more prominent. Cortical bone is more evenly distributed along the shaft in early stages of ontogeny and becomes more concentrated proximally in adults. A large proportion of variation in femoral diaphyseal shape is not related to ontogenetic change.
cMM reveals subtle differences between wild and zoo chimpanzees in femoral diaphyseal ontogeny and patterns of shape variation. Overall, femoral shape variation in the zoo sample is larger than in the wild sample, especially with regard to variability in patterns of cortical bone distribution. Differences between groups have been identified in the distal third of the shaft. In captive animals, cortical bone deposition on the anterior and posterior endosteal surfaces is more intense. Midshaft morphology, which is the subject of many studies, does not exhibit significant differences between groups.
dTraditional GM-based analyses yield largely similar results in PC space, but visualization and interpretation of patterns of shape change and shape variation is less effective than with MM methods. Cross-section-based analysis cannot detect the differences found with MM methods between wild and zoo animals.
The result that average femoral morphology does not differ between wild and captive chimpanzees (P. t. troglodytes) is consistent with earlier studies: Wild and captive Lemur catta do not differ significantly in diaphyseal biomechanical properties (Demes and Jungers, 1993), nor do wild and captive Macaca nemestrina in relative magnitudes of second moments of area (Burr et al., 1989). The present study further showed that wild and captive groups did not differ in femoral morphology along the course of ontogeny. Convergent results from three different primate species with different locomotor modes indicate that captivity does not have a major impact on average diaphyseal morphology. The results of our study are also in congruence with earlier studies of chimpanzee long bone cross-sectional properties (Carlson, 2005; Carlson et al., 2006, 2008a), which showed that differences between individuals in locomotor behavior are not paralleled by significant differences in cross-sectional biomechanical properties of the femoral diaphysis.
The MM-based comparative analyses performed in this study revealed subtle differences between wild and captive chimpanzees in the internal morphology of the distal femoral diaphysis. Such differences have not been found in earlier studies analyzing cross-sectional properties at predefined locations along the diaphysis. This demonstrates that MM methods, which use comprehensive diaphyseal cross-sectional data, are highly sensitive tools to detect inter-group differences in diaphyseal morphology and biomechanical properties. The results described here are best compared with those of a study reporting differences between two chimpanzee communities (8 Mahale vs. 4 Taï female chimpanzees) in biomechanical properties (Imax/Imin) of the mid-distal femoral diaphysis (Carlson et al., 2008a). Such differences between wild-living groups may indeed reflect population-specific differences in locomotor behavior. However, Mahale and Taï populations represent evolutionary divergence at the subspecies level (P. t. troglodytes, and P. t. verus), such that it remains to be clarified whether the reported differences reflect taxon-specific diaphyseal morphologies unrelated to in vivo locomotor loading history.
Overall, the findings of this study, and of the studies of Carlson and colleagues (Carlson, 2005; Carlson et al., 2006, 2008a) imply that differences in locomotor behavior have comparatively little impact on femoral diaphyseal morphology and development. One possible explanation for this lack of correlation is that long bone diaphyseal shape is mainly controlled by genes and the developmental program. Another possible explanation is that even notable differences in locomotor behaviors may result in only minor differences in actual diaphyseal loading patterns. This second possibility would imply that the musculoskeletal system tends to maintain biomechanical homeostasis: different locomotor modes elicit different force patterns, but these differences are buffered through differential muscular activity, resulting in largely similar loading patterns on long bone diaphyses.
In any case, our findings have several implications for the interpretation of the femoral diaphyseal morphology of fossil hominins. Reconstruction of the locomotor behavior of fossil hominins has often been based on Wolff's Law, that is, the assumption that diaphyseal cross-sectional properties reflect the mechanical loading history and the locomotor behavior of the specimen under study. For example, long bone diaphyses of early Homo typically exhibit higher degrees of robusticity (i.e., larger cortical cross-sectional area and different shapes) than those of modern humans, and this condition is thought to be associated with higher levels of mechanical loading during lifetime (Ruff et al., 1993, 1994). Actualistic support for this hypothesis comes from various studies analyzing changes in long bone cross-sectional geometry during human ontogeny. It has been reported that increased rigidity of long bones reflects increased mechanical loading during lifetime (Ruff et al., 1994; Sumner and Andriacchi, 1996), specifically at the onset of bipedal locomotion (Ruff, 2003a, b). Likewise, increased diaphyseal cross-sectional robusticity of the humerus relative to femur of early hominins is thought to be indicative of higher proportions of arboreal locomotion in early Homo compared to H. erectus and modern humans (Ruff, 2009).
Our data, however, indicate that differences between locomotor behaviors do not necessarily result in distinct morphologies or different degrees of robusticity of the femoral diaphysis. Caution is thus warranted when interpreting fossil diaphyseal cross-sectional data in terms of individual locomotor behavior, and the following range of possible alternative explanations must be considered:
differences between diaphyseal morphologies in fact reflect in vivo functional adaptation to different locomotor behaviors
differences between diaphyseal morphologies reflect evolutionary adaptation to taxon-specific locomotor behaviors, i.e. taxon-specific developmental programs (Wallace et al., 2010)
differences between diaphyseal morphologies reflect differences in taxon-specific developmental programs not related to actual locomotor adaptations (Wallace et al., 2010).
This leads to the question as to which mechanisms – if not in vivo functional adaptation sensu Ruff et al. (2006)—govern ontogenetic changes of the chimpanzee femoral diaphysis (Fig. 4). As stated in the above list, one hypothesis is that the underlying developmental program reflects evolutionary adaptation, such that changes in femoral diaphyseal morphology are in concert with changes in locomotor modes during a typical chimpanzee's ontogeny: During early stages of ontogeny, chimpanzees exhibit hand-assisted or short bouts of free bipedalism, as well as climbing and suspensory behavior more frequently than during later stages, while knuckle-walking frequency increases toward adulthood (Doran, 1992, 1997). These changes are paralleled by ontogenetic changes of diaphyseal features: Cortical bone thickness and second moments of area exhibit a more homogeneous distribution around and along the femoral diaphysis in infants than in juveniles and adults (Fig. 4B, 6B). A homogeneous distribution might represent an optimum biomechanical design for the wide variability of loading patterns occurring in mixed terrestrial/arboreal activities of young chimpanzees (Demes and Carlson, 2009). Cortical bone becomes concentrated proximally, and the distal diaphysis becomes relatively smaller in diameter during later development toward adulthood. Concentration of mass toward the proximal femur might contribute to reduce the energy needed to swing the hind-limb during locomotion. A higher degree of platymery (Fig. 4A, 6B) and a more slender shape (Fig. 7A) of the femoral diaphysis might be favorable during terrestrial locomotion, because increased platymery could be consistent with a more stable loading pattern in terrestrial locomotion (Demes and Carlson, 2009), and longer limbs permit energetically more efficient locomotion (Pontzer et al., 2009).
While this set of hypotheses postulates direct links between developmental programs and stage-specific locomotor repertoires, it remains to be tested whether the developmental pattern of the femoral diaphysis of chimpanzees (Fig. 4) in fact closely reflects chimpanzee-specific locomotor behavior. An alternative hypothesis is that it reflects general developmental processes and associated biomechanical constraints experienced by any developing hominoid primate, such as increase in body size, neurological maturation, and changes in social behavior (Doran, 1992, 1997). Also, evolutionary developmental inertia needs to be considered, implying that the diaphyseal development in extant chimpanzees reflects adaptation to an ancestral form of locomotion. Clearly, additional empirical evidence from a wider range of hominoid species and from other long bones (especially the humerus) is required to resolve these issues, and to investigate how long bone development is related to the development of locomotor behavior.
Chimpanzee Femoral Ontogeny and Wolff's Law
WL predicts that wild and captive groups of chimpanzees show different ontogenetic patterns in femoral diaphyseal morphology reflecting their different locomotor modes. However, average developmental patterns of femoral diaphysis of wild and captive chimpanzees are indistinguishable with regard to both morphology and biomechanical properties (Figs. 3, 6, 7, 10). Moreover, the range of variation across ontogenetic trajectories does not increase during ontogeny but is already high at early stages. A constant amount of variation throughout ontogeny could indicate that morphological variation is not primarily due to in vivo differences in mechanical loading but has a strong genetic component. Alternatively, one could argue that variation in fact reflects in vivo differences between individuals, but that the factors causing these differences are largely unknown.
While wild and zoo animals are similar in average femoral diaphyseal morphology and ontogeny, it appears that femoral diaphyseal shape variation is constrained to a narrower range in wild compared with captive chimpanzees (Fig. 8C-2). Apparently, the large inter-individual variation in zoo animals is canceled out, and the average ontogenetic trajectory tends to reflect “WL-free” developmental programs. Overall, the fact that wild and captive chimps exhibit the same average trajectory of diaphyseal ontogeny is relevant, because it indicates that there is no systematic “bias” due to WL. We may thus infer that the basic developmental program of the diaphysis is not affected by differences in locomotor modes, but that in vivo modification (WL) acts as a powerful modulator of femoral morphological variation: natural locomotor modes and loading patterns clearly constrain variation, while locomotion in a zoo environment permits a wide range of morphological variation.
This finding seems paradoxical at first sight, because a natural environment permits a more diverse locomotor repertoire than a zoo environment. However, locomotion under natural conditions is biomechanically and metabolically more demanding, such that actual loading patterns are expected to exert a stronger influence on diaphyseal shape than under the less constrained conditions of a zoo environment. These findings may explain why comparative studies of wild individuals did not reveal significant correlations between locomotor habits and diaphyseal morphology (Carlson et al., 2006): even if differences between individual locomotor behaviors are significant, overall constraints (probably due to high levels of physical activity) are predominant in shaping diaphyseal morphology. This finding is relevant for practical work too, as it demonstrates that MM methods permit to retrieve basic ontogenetic patterns despite large interindividual variation. Also, our data indicate that wild and captive samples can be pooled in studies focusing on average modes of morphological change. This might be especially valuable in developmental studies, where sample sizes of wild immature specimens are typically small. Applying MM methods to compare diaphyseal developmental modes in various hominoid taxa can thus be expected to yield new insights into the evolution of long bone development and of locomotor behaviors (Shea, 1981; Ruff, 2003a, b).
Collectively, the hypothesis that WL predominantly governs long bone morphology (i.e., that long bone morphology reflects in vivo mechanical loading of locomotion) can be rejected. As shown in the analyses of diaphyseal subregions (Figs. 8 and 9), bone functional modification tends to occur locally, on specific features in a specific region of the diaphysis, and probably of a specific individual, rather than on the average morphology and developmental pattern. We conclude that femoral diaphyseal morphology is largely determined by genetically defined developmental modes, while in vivo modification only partly reflects in vivo mechanical loading conditions.
Diaphyseal ontogeny proceeds via external (subperiosteal) bone deposition and internal (endosteal) bone resorption (modeling), while in vivo modification (remodeling) is achieved via internal deposition/resorption in adults (Carter, 1990; Standring, 2004). Accordingly, ontogenetic changes in the external surface (MMs of external radius and curvature) indicate differential external (re-)modeling processes, while ontogenetic changes in cortical bone distribution (MMs of bone thickness) indicate differential internal (re-)modeling. Our data provide evidence for both processes (Fig. 4): endosteal remodeling yields a thickness gradient in proximodistal direction, while subperiosteal surface remodeling yields more prominent ridge structures. The first process might reflect changes in diaphyseal loading patters with increasing body mass (Moro et al., 1996; vanderMeulen et al., 1996), while the second process might reflect changes in muscle strength (Benjamin et al., 2002 and references therein; Weiss, 2004; Drapeau, 2008).
While MMs represent relative values of morphometric variables, absolute values of external radius, cortical bone thickness and femoral diaphyseal length are informative regarding actual rates of external versus internal bone deposition/resorption: If thickness remains constant, this indicates equal rates of external deposition and internal resorption. If thickness grows faster than external radius, this indicates higher deposition than resorption rates, and if external radius grows faster than thickness, this indicates higher internal resorption rate than external deposition rate. Our results (Fig. 7) show that, relative to its length, the chimpanzee femoral diaphysis becomes thin in diameter and strong in cortical bone thickness during ontogeny. Rates of endosteal bone resorption are thus smaller than rates of subperiosteal bone apposition, and the latter are smaller than rates of diaphyseal proximodistal extension.
Some, but not all, captive chimpanzees exhibit thicker cortical bone than wild chimpanzees (Fig. 7). Because external morphology showed smaller variation than cortical bone thickness, and external morphology was indistinguishable between wild and captive groups, this likely reflects differences in endosteal bone deposition (Ruff et al., 1994; Pearson and Lieberman, 2004). This is also supported by the analyses of diaphyseal subregions in which wild and captive groups exhibited indistinguishable external morphology but different distribution patterns of cortical bone. Different bone deposition patterns could reflect different loading conditions, but also result from dietary differences relative to activity levels (Bass et al., 2005). In any case, increasing cortical bone thickness alone (without increasing the external diaphyseal radius) does not substantially increase biomechanical rigidity (Sparacello and Pearson, 2010), because biomechanical rigidity is primarily defined by the external radius (note that second moment of area is proportional to fourth power of radius).
Locomotor Modes and Femoral Diaphyseal Morphology
MM analyses of subregions of femoral diaphysis showed that it is not the mid-shaft but the distal diaphysis that exhibits significant differences between zoo and wild chimpanzees. The second hypothesis that the femoral mid-shaft optimally reflects differences in locomotor modes is not supported by this study. The “captive” pattern is characterized by anteroposteriorly increased cortical bone thickness whereas the “wild” pattern is characterized by mediolaterally increased cortical bone thickness (Fig. 9). Because the external morphology of the distal diaphysis is similar in the two groups (Fig. 8A-3,B-3,C-3), differences in cortical bone distribution most likely are due to differences in endosteal bone deposition/resorption. These might reflect different mechanical loading conditions. Currently we cannot associate these patterns with specific inter-individual differences in locomotor modes. However, our data indicate that differences in activity patterns/locomotor modes could be best revealed in the distal femur, while the mid-shaft might be sub-optimal for such comparisons.
Comparison of MM Methods with Landmark-based GM Methods
A comparison of semilandmark-based and MM-based PCAs shows that these methods yield largely convergent results (Figs. 3, 10; Table 2). Both methods are thus equally efficient in detecting patterns of variation of long bone diaphyseal morphology. However, MM methods are advantageous in various respects. MM methods are especially suitable for the analysis of the “featureless” morphologies of long bone diaphyses, since these methods do not require a priori definition of landmarks and/or semilandmarks (e.g., on ridge lines). MM methods clearly facilitate visual inspection and exploration of morphometric data. MM-guided feature detection may ultimately lead to a posteriori definition of features such as “ridge lines” along the diaphyseal surface, which can be used as biologically and/or geometrically homologous structures in subsequent landmark-based analyses. An additional benefit of MM methods is that they permit to investigate external and internal morphologies, as well as biomechanical properties. Accordingly, while GM is restricted to the analysis of 3D point coordinates on surfaces, MM also permits analysis of higher-order geometric and biomechanical properties of the 3D data volume representing the diaphysis. MM methods provide a means to effectively visualize such higher-order anatomical/biomechanical features (Figs. 2, 4, 5, 6) which are hardly recognizable in GM-based visualizations (Fig. 10). However, MMs also have several limitations. Since MM methods do not assume point-to-point or line-to-line homologies, feature similarity (e.g. ridges at corresponding locations in MMs) does not imply functional or developmental homology between individuals or groups. While MM analysis is a powerful tool to reveal previously “unseen” morphological features and modes of diaphyseal shape variation, direct inspection of the original morphologies is indispensable to check the results of MM analyses and to obtain developmentally and functionally significant insights into diaphyseal shape variation.
In this study, we used new methods of MM for a comprehensive analysis of the spatial distribution of geometric and biomechanical features around and along the femoral diaphysis. We demonstrated that MM methods provide new insights into diaphyseal form variability that cannot be gained with traditional cross-sectional analyses nor with geometric-morphometric analyses. We used these methods to compare femoral diaphyseal ontogeny in captive and wild common chimpanzees (Pan troglodytes troglodytes), and to test Wolff's Law, which predicts that differences in locomotor behavior between these groups result in different diaphyseal ontogenies and morphologies. Our data indicate that the hypothesis underlying WL must be rejected: in vivo functional bone modification only accounts for a minor part of the observed morphological variability, and it appears that femoral diaphyseal shape is mainly mediated by taxon-specific developmental programs. While these results put a caveat on inferring locomotor behavior from fossil hominin long bone morphology, the visual and analytical methods proposed here should encourage further exploration and morphometric mapping of the terra incognita of long bone diaphyses in terms of evolution, development and function.
We thank P. Jans for help with sample preparation and CT scanning. We are also grateful to the three anonymous reviewers for valuable comments and suggestions.
In this study, locomotor behavior is defined as the relative frequencies of locomotor modes (e.g., climbing, terrestrial bipedal walking, etc.) displayed by an individual over a given time span (e.g., as an infant or adult).
In this study, modification is used as a more general term in place of functional adaptation (Ruff et al. 2006) to discern between adaptation as a long-term evolutionary process and modification as a process occurring during an individual's lifetime.
Elliptic Fourier Analysis
be a parametric representation of a closed line L in the xy-plane, where the x and y coordinates of line points are expressed as functions of path length t along L. EFA is based on the respective Fourier decompositions of the independent functions x(t) and y(t):
Using these parametric functions, surface curvature k is analytically calculated as
where positive/negative values of k represent convex/concave regions of the outline.
Second Moments of Area
Second moments of area Iθ are calculated for each diaphyseal cross section as
where θ is the direction of the normal vector of the bending plane (B-B; see Fig. 1C), i and j are coordinates across/perpendicular to the bending plane (coordinate origin is at the center of mass), Aij is the area of cortical bone at pixel location (i,j), and dj is the distance of that pixel from the bending plane (Fig. 1C).
Two-dimensional Fourier Transform
A morphometric map with its coordinate system (θ, z) represents a 2-dimensional image, which is periodic in θ. The two-dimensional Fourier Transform (FT) of an image of size of K × L is defined as
A K × L image yields an K × L set of Fourier coefficients (complex numbers). The inverse FT is defined as
and used here to calculate a K × L MM from a K × L set of Fourier coefficients.
Optimal Superposition (alignment) of Morphometric Maps
MMs are optimally superimposed by rotating diaphyses around their long axes until a predefined morphometric distance metric is minimized. MM superposition is performed by minimizing the distance DF in Fourier space between each MM's FT F(Mn) (n=1, 2, …, N) and the FT of the consensus map F(<M>)
Rotating a diaphysis around its longitudinal axis corresponds to a horizontal shift of its MM. According to the Fourier shift theorem, a horizontal shift of MM(θ, z) by A can be expressed as
When each MM is aligned to the reference map, the reference should be a biologically relevant consensus. Therefore, when there are several groups for comparison, it is recommended to first calculate a consensus map for each group separately, and align each MM to this group-specific consensus. One can minimize the distance among group-specific consensus maps to avoid a “biased” reference due to different numbers of specimens in each group (i.e., calculating mean of mean).
Comparison of Ontogenetic Trajectories
Trajectory divergence Vij was calculated as
where ai and aj are normalized trajectory direction vectors. Larger value of Vij means larger divergence between two vectors. The difference between group-specific modes of variation is measured as the variance-covariance matrix distance
where λk are the relative eigenvalues of group-specific covariance matrices Si and Sj as defined in (Mitteroecker and Bookstein, 2009).