3D quantitative comparative analysis of long bone diaphysis variations in microanatomy and cross‐sectional geometry

Abstract

Long bone inner structure and cross‐sectional geometry display a strong functional signal, leading to convergences, and are widely analyzed in comparative anatomy at small and large taxonomic scales. Long bone microanatomical studies have essentially been conducted on transverse sections but also on a few longitudinal ones. Recent studies highlighted the interest in analyzing variations of the inner structure along the diaphysis using a qualitative as well as a quantitative approach. With the development of microtomography, it has become possible to study three‐dimensional (3D) bone microanatomy and, in more detail, the form–function relationships of these features. This study focused on the selection of quantitative parameters to describe in detail the cross‐sectional shape changes and distribution of the osseous tissue along the diaphysis. Two‐dimensional (2D) virtual transverse sections were also performed in the two usual reference planes and results were compared with those obtained based on the whole diaphysis analysis. The sample consisted in 14 humeri and 14 femora of various mammalian taxa that are essentially terrestrial. Comparative quantitative analyses between different datasets made it possible to highlight the parameters that are strongly impacted by size and phylogeny and the redundant ones, and thus to estimate their relevance for use in form‐function analyses. The analysis illustrated that results based on 2D transverse sections are similar for both sectional planes; thus if a strong bias exists when mixing sections from the two reference planes in the same analysis, it would not problematic to use either one plane or the other in comparative studies. However, this may no longer hold for taxa showing a much stronger variation in bone microstructure along the diaphysis. Finally, the analysis demonstrated the significant contribution of the parameters describing variations along the diaphysis, and thus the interest in performing 3D analyses; this should be even more fruitful for heterogeneous diaphyses. In addition, covariation analyses showed that there is a strong interest in removing the size effect to access the differences in the microstructure of the humerus and femur. This methodological study provides a reference for future quantitative analyses on long bone inner structure and should make it possible, through a detailed knowledge of each descriptive parameter, to better interpret results from the multivariate analyses associated with these studies. This will have direct implications for studies in vertebrate anatomy, but also in paleontology and anthropology.

Introduction

Bones provide protection for vital organs and also rigid support for muscle attachments, consolidating the body and also enabling movement. As with any biological feature, bone structure is fashioned by phylogenetic, structural and functional constraints (Gould, 2002; Cubo, 2004). The long bones are naturally intensely involved in body support and propulsion. Beyond the phylogenetic history of the taxa, architectural properties and allometry, their shape reflects the biomechanical constraints they face. Their inner structure, i.e. the amount and distribution of the osseous tissue in the bone, and cross‐sectional geometry are known to respond to the constraints acting on the skeleton during body support and locomotion (Ruff & Hayes, 1983; Turner, 1998; Ruimerman et al. 2005; Habib & Ruff, 2008; Nikander et al. 2010). They thus display a strong functional signal, leading to convergences, and are widely analyzed in comparative anatomy at both small (Doube et al. 2009; Cosman et al. 2016) and large (Canoville & Laurin, 2010; Meier et al. 2013) taxonomic scales.

Comparative analyses on long bone inner structure enable us to understand better how the inner structure of these bones corresponds to the biomechanical constraints they are subject to, such as those from their habitat (Laurin et al. 2011; Quemeneur et al. 2013; Nakajima et al. 2014), locomotion (Ryan & Ketcham, 2002), posture and bodyweight (Houssaye et al. 2015) and behavior (Warden et al. 2007; Wilks et al. 2009). Beyond a better understanding of the bone form/function relationships, these types of studies have strong implications in vertebrate paleontology and paleoanthropology when inferring the lifestyle of fossil organisms (Ohman et al. 1997; Hayashi et al. 2013; Krahl et al. 2013; Amson et al. 2014).

Long bone microanatomical studies have been conducted on classical and virtual sections, essentially transverse ones (Klein, 2010; Laurin et al. 2011; Houssaye et al. 2015, b) but also, to a much smaller extent, on a few longitudinal ones (Nakajima et al. 2014; Houssaye et al. 2015). The latter highlighted in some taxa, strong variations in bone inner structure along the diaphysis. Thanks to the development of microtomography, the bone inner structure can now be accessed non‐destructively, which enables the development of virtual bone microanatomy, offering new types of investigations. It is now possible to analyze in detail the variations in bone inner structure along the entirety of a bone, which is of strong interest when trying to understand the biomechanical changes occurring in the skeleton through evolution. As the distribution of bone tissue is naturally linked to, for example, sites of muscle insertion, and constraint orientation and intensity on the bone, its analysis makes it possible to better characterize the biomechanical constraints on the bones (Currey, 2003; Petit et al. 2005; Nikander et al. 2006). Such analyses have been conducted on diaphyses of long bones of hominoids to estimate loading differences, assumed to reflect differences in posture and locomotion, between taxa (Puymerail et al. 2012; Puymerail et al. 2014; Puymerail, 2013; Ruff et al. 2015) but not on other groups.

A growing number of investigations are being carried out on 3D virtual bone microanatomy, and the bones for which 3D microanatomical data are available. The possibility for comparative studies on the distribution of the bone tissue for a rather large number of specimens raises the issue of defining good quantitative criteria in order to describe quantitatively the pattern of distribution of the osseous tissue in the bone. Indeed, although a qualitative observation may appear sufficient for comparative studies on a limited sample size, it seems much more complex to perform a qualitative comparative analysis on hundreds of specimens. Our aim here is to establish appropriate quantitative criteria to describe bone diaphyseal microanatomical features, which will be analyzed in concert with cross‐sectional geometry parameters. The interactions of all these parameters, as well as their link with phylogeny and size, will be studied to estimate their relevance. This work aims to propose a reference for the quantitative description of long bone diaphysis microanatomical features in further comparative studies, notably in the fields of vertebrate anatomy, paleontology and anthropology.

Material and methods

Stylopod bones were chosen for this study since these bones are often analyzed in comparative studies (Meier et al. 2013; Nakajima et al. 2014; Houssaye et al. 2015, b). The bones sampled come from 15 mammalian species chosen with the aim of illustrating various ecologies (terrestrial, semi‐aquatic, fossorial, arboreal), morphologies and sizes, with a wide distribution across mammal phylogeny (Table 1). The material consists in 14 humeri and 14 femora of adult specimens (Table 1). This enabled us to analyze the signal of each parameter in two different contexts, a comparative analysis on humeri and one on femora, and to check the consistence between the results obtained.

Table 1.

List of the material analyzed

Taxon	Abbrev.	Coll. Nr.	Bone
Cavia porcellus	Cp	STIPB Unnumbered	F
Marmota marmota	Mma	STIPB Unnumbered	H, F
Tupaia belangeri	Tb	STIPB Unnumbered	H, F
Erinaceus europaeus	Ee	STIPB Unnumbered	H, F
Talpa europaea	Te	STIPB Unnumbered	H, F
Dama dama	Dd	STIPB M1	H
Rupicapra rupicapra	Rr	STIPB M1639	H, F
Rangifer tarandus	Rt	STIPB M47	H, F
Choeropsis liberiensis	Cl	ZFMK 65 570	H, F
Sus scrofa	Ss	STIPB M56	H, F
Felis silvestris	Fs	UFGK Unnumbered	H, F
Vulpes vulpes	Vv	STIPB M12	H, F
Mustela putorius	Mp	STIPB Unnumbered	H, F
Meles meles	Mme	STIPB M4002	H, F
Martes martes	Mm	STIPB Unnumbered	H, F

H, humerus; F, femur. Abbrev., Abbreviation of the taxon names used in the figures. Institutional abbreviations: STIPB, Steinmann‐Institut, Universität Bonn, Bonn, Germany; UFGK, Ur‐ und Frühgeschichte Köln, Cologne, Germany; ZFMK, Zoologisches Forschungsmuseum Alexander Koenig, Bonn, Germany. Coll. Nr.:Collection number.

Data acquisition

Bones were scanned using high‐resolution computed tomography (GE_phoenix∣X‐ray v∣tome∣xs 240) at the Steinmann‐Institut, University of Bonn (Germany), with reconstructions performed using datox/res software. Voxel size naturally varies between specimens depending on their size, from 22 μm (Talpa's humerus) to 246 μm (Rangifer's femur). Image segmentation and visualization were performed from the reconstructed image data using avizo 7.0 and 9.0 (VSG, Burlington, MA, USA).

The shape of these bones differs significantly between taxa. It was thus difficult to find a homologous criterion to delimit the diaphyseal region. To do so, images were first reoriented for some specimens not scanned ‘perfectly vertically’, in this case with an alignment in the three dimensions of the core of the metaphyses, so that each slide theoretically could correspond to a transverse section. Of course, many bones do not show a straight diaphysis but are bowed to various degrees; as a consequence, these sections do not always necessarily correspond to true transverse sections. Nevertheless, the bones from our sample have a nearly straight diaphysis, so that this was not an issue here. The perimeter of each cross‐section was then calculated along the bone, with the bonej plugin (plugin Slice Geometry; Doube et al. 2010) of imagej (Schindelin et al. 2015). The diaphysis was (distally and proximally) delimited from the epiphyses as the region from which a drastic decrease in this parameter had occurred (as indicated by a drop to a low‐value plateau in the plot of the perimeter values along the bone, the transition zone generally corresponding to the metaphysis). Observations of the inner structure were combined to validate the transition from epiphyses and metaphyses with a relatively (whatever the taxon) thinner cortex and a trabecular inner structure, and the diaphysis with a thicker cortex and a reduction or absence of trabeculae. The osseous tissue was segmented in the whole diaphysis.

To quantify the thickness of the layer of compact cortex, we isolated an outer surface (corresponding to the outer surface of the bone) and an inner surface (corresponding to the inner limit of the compact cortex) for each bone. This required us to remove the cavities located in the compact cortex and the trabeculae in the medullary space. The removal was performed on avizo 7.0. To be relatively objective and reproducible, a combination of the ‘remove islands’ and ‘smooth labels’ functions was added to manual segmentation. The conversion of these surfaces into an image stack enabled us to measure additional parameters on bonej linked to cortical bone thickness and the percentage of trabecular bone (see below).

Various microanatomical and cross‐sectional geometry quantitative parameters were calculated using bonej for each transverse section: CSAb (cross‐sectional area of bone), representing the surface occupied by bony tissue (CSA value in bonej when only bone tissue is in black); CSAt (total cross‐sectional area), as the surface of the whole transverse section (CSA value in bonej when the whole section is in black); C (Compactness), as the ratio of CSAb over CSAt; R, as the radius of the section if approximated as a disk, and used as a size‐estimate; CSS (cross‐sectional shape), as the ratio between the maximal and minimal second moment of area (Imax/Imin); Zpol (polar section modulus) representing the resistance of a section to torsion and bending (see Ruff, 2002; Kespka et al. 2015); MaxT, representing the maximum thickness of cortical bone, comprising two components: an absolute value AMaxT and a relative value RMaxT, calculated as AMaxT/R; MeanT, as the mean thickness of cortical bone, similarly comprising AMeanT and RMeanT; SDT, as the standard deviation of the cortical thickness among the section, also comprising ASDT and RSDT. C, R, MaxT, MeanT and SDT were averaged for the whole diaphysis. Because CSS and Zpol essentially express and rely on the shape of the diaphysis, and not that much on the inner structure, these were only calculated for the mid‐diaphysis, based on the 20% centralmost sections of each bone (taking 100% as the whole diaphyseal length). In addition, the standard deviation of some of these parameters (SD_C, SD_AMaxT, SD_AMeanT, SD_RMaxT, SD_RMeanT, SD_ASDT, SD_RSDT) was calculated to characterize variations along the diaphysis. Two additional parameters were calculated using the Volume Calculator plugin of imagej [measuring the volume in black when bone tissue alone is in black and dividing it by the volume obtained when the whole bone (bone tissue + cavities) is in black] and avizo, respectively: 3DC (3D Compactness), as the volume occupied by bone (cortex and spongious bone) divided by the whole diaphyseal volume; and %Trab (Trabecular ratio), as the surface occupied by the trabecular bone in 3D [obtained by removing the secondarily segmented area of the compact cortex (see above) to the volume occupied by bone], over the total surface of osseous tissue in 3D.

Two virtual thin sections were also made for each bone to compare data based on 2D sections with those obtained based on 3D quantifications. Since previous studies analyzed 2D transverse sections, the aim was to estimate whether the 2D and 3D approaches (and the two sectional planes) are comparable, and to evaluate the benefit of the 3D approach. The sections were taken at the mid‐diaphysis (generally chosen as the reference plane in previous studies, see Ksepka et al. 2015; Canoville & Laurin, 2010; Quemeneur et al. 2013), and at the plane crossing (internally) the nutrient foramen, assumed to correspond to the plane where growth originated (which can be located proximal or distal to the mid‐diaphysis depending on the bones because of different proportions between the speed of proximal and distal growth in the various taxa analyzed; see Nakajima et al. 2014; Houssaye et al. 2015). The parameters used to describe these sections are: C, R, CSS, Zpol, AMaxT, AMeanT, ASDT, RMaxT, RMeanT and RSDT. Additionally, parameters generally used for 2D sections, obtained with the software bone profiler (Girondot & Laurin, 2003), were added: P = the extent of the medullary cavity as measured by the relative distance from the center of the section to the point where the most abrupt change in compactness occurs; S = the width of the transitional zone between the compact cortex and the medullary cavity as measured by the reciprocal of the slope of the compactness profile at the inflection point; R/t = the outside radius of the bone divided by the thickness of the cortex (cf. Currey & Alexander, 1985). Both sets of (2D) sections were analyzed independently.

Quantitative analyses

We thus obtained three datasets based on (i) mid‐shaft sections (MSS), (ii) sections at the growth center (GCS) and (iii) whole diaphysis analysis (WD).

We estimated the amount of phylogenetic signal for each parameter, on raw data, for each dataset. This was done through randomization tests and the calculation of the K‐statistic (library ‘picante’), following Blomberg et al. (2003). The K‐statistic makes it possible to compare the observed phylogenetic signal in a dataset to the signal under a Brownian motion model of trait evolution along a given tree (K > 1 implies more similarity between relatives than expected under Brownian motion, and K < 1 highlights convergences). The phylogeny used, derives from Meredith et al. (2011) based on a mammal molecular supermatrix.

We performed linear regressions of each parameter to R, on raw data, in order to estimate the possible impact of size on the data. We also analyzed it for the two first axes of the PCAs (see below).

We then conducted normalized PCAs for all datasets. Since the various parameters have different units and scales, they differ widely in their variance, which can be homogenized thanks to normalized PCAs (David & Jacobs, 2014). The aim of these PCAs was not only to explore the distribution of the different taxa in morphospace, but mainly to analyze the contribution of the different variables and to make comparisons between results obtained based on the different datasets, analyzing which dataset was the most compatible with qualitative observation. To remove size (with only allometry remaining), we, before the PCA, calculated a size index as the average of all parameters (except R) for a given specimen and subtracted this value from all parameter values for this same specimen. We removed R from the PCAs because we wanted to analyze microanatomical and cross‐sectional geometry parameters and not size.

We then performed normalized PCAs on new datasets corresponding to the previous ones with the parameters correlated with size removed, in order to estimate the impact of the use of these specific parameters. Removing the value of the size index for all parameters makes it possible to remove size from the whole dataset. Here an additional aim was to identify clearly the impact of the specific parameters which display a proper correlation with size (and so bear a strong allometry).

We also conducted different RV tests (library ‘ade4’; Heo & Ruben Gabriel, 1998), which test the covariation between the different datasets, for all specimens for which both a humerus and a femur were available. The aim was to estimate the covariation between the three datasets for each bone and also between the humerus and the femur for each dataset.

All statistical analyses were performed using statistical software r (R Core Team 2014).

Results

Phylogenetic signal

A significant phylogenetic signal was detected in AmaxT, AMean and R in all datasets, and in Zpol for all except the MSS of the femur (Table 2). In addition, the phylogenetic signal was significant for ASDT for the humerus GCS, SD_AmaxT, SD_AMeanT, ASDT and SD_ASDT for the 3D parameters of the humerus (Table 2).

Table 2.

Values obtained for the tests of a phylogenetic and size effect in the various parameters used in the analyses

	C	CSS	Zpol	AmaxT	AMeanT	ASDT	S	P	R/t	RMaxT	RMeanT	RSDT	R
H MSS
PS
K	0.45	0.44	0.63	1.15	1.33	0.65	0.35	0.41	0.41	0.43	0.35	0.46	1.17
P	0.17	0.17	0.01	0.01	< 0.01	0.07	0.60	0.32	0.32	0.29	0.60	0.28	< 0.01
LR
P	0.39	0.58	< 0.01	< 0.01	< 0.01	< 0.01	0.93	0.16	0.21	0.02	0.10	0.38
r	−0.25	−0.16	0.91	0.94	0.93	0.92	0.03	0.40	0.35	−0.63	−0.46	−0.25
Hum GCS
PS
K	0.41	0.39	0.83	1.14	1.26	0.76	0.33	0.38	0.40	0.32	0.35	0.34	1.36
P	0.39	0.42	< 0.01	< 0.01	< 0.01	0.04	0.78	0.55	0.45	0.82	0.64	0.69	< 0.01
LR
P	0.92	0.69	< 0.01	< 0.01	< 0.01	< 0.01	0.51	0.69	0.84	0.53	0.25	0.77
r	−0.03	−0.12	0.93	0.98	0.99	0.89	0.19	0.12	0.06	−0.18	−0.33	0.08
Fem MSS
PS
K	0.51	0.36	0.70	0.96	0.97	0.64	0.45	0.46	0.44	0.51	0.55	0.46	1.22
P	0.18	0.88	0.06	< 0.01	< 0.01	0.141	0.65	0.28	0.35	0.16	0.09	0.31	< 0.01
LR
P	0.23	0.22	< 0.01	< 0.01	< 0.01	< 0.01	0.96	0.30	0.27	0.06	0.15	0.06
r	−0.35	−0.35	0.93	0.88	0.89	0.74	−0.02	0.30	0.31	−0.51	−0.41	−0.51
Fem GCS
PS
K	0.38	0.40	0.64	1.05	1.08	0.65	0.50	0.38	0.38	0.31	0.43	0.32	1.25
P	0.59	0.80	0.03	< 0.01	< 0.01	0.11	0.19	0.58	0.56	0.97	0.40	0.93	< 0.01
LR
P	0.74	0.27	< 0.01	< 0.01	< 0.01	< 0.01	0.72	0.61	0.76	0.91	0.98	0.72
r	0.10	−0.32	0.89	0.99	0.99	0.90	−0.10	−0.15	−0.09	−0.03	−0.01	−0.10

	3DC	C	%Trab	SD_C	CSS	Zpol	AMaxT	SD_AMaxT	AMeanT	SD_AMeanT	ASDT	SD_ASDT	RMaxT	SD_RMaxT	RMeanT	SD_RMeanT	RSDT	SD_RSDT	R
Hum WD
PS
K	0.43	0.45	0.37	0.31	0.39	0.79	1.10	0.86	1.18	0.97	0.79	0.74	0.31	0.36	0.35	0.43	0.33	0.34	1.34
P	0.28	0.23	0.73	0.94	0.59	0.02	< 0.01	< 0.01	< 0.01	< 0.01	0.02	0.03	0.87	0.73	0.56	0.22	0.89	0.91	< 0.01
LR
P	0.68	0.70	0.21	0.72	0.56	< 0.01	< 0.01	< 0.01	< 0.01	< 0.01	< 0.01	< 0.01	0.25	0.34	0.22	0.15	0.77	0.90
r	−0.12	−0.11	0.36	0.11	−0.17	0.91	0.99	0.96	0.99	0.97	0.95	0.91	−0.33	0.28	−0.35	0.41	−0.09	0.04
Fem WD
PS
K	0.42	0.42	0.42	0.32	0.39	0.64	1.03	0.63	1.06	0.60	0.81	0.70	0.35	0.40	0.44	0.40	0.34	0.41	1.20
P	0.45	0.41	0.85	0.92	0.88	0.03	< 0.01	0.10	< 0.01	0.13	0.05	0.06	0.74	0.62	0.33	0.63	0.82	0.53	< 0.01
LR
P	0.35	0.46	0.31	0.36	0.28	< 0.01	< 0.01	< 0.01	< 0.01	< 0.01	< 0.01	< 0.01	1.00	0.77	0.85	0.91	0.78	0.71
r	0.27	0.21	0.30	−0.26	−0.31	0.88	0.99	0.80	0.99	0.79	0.96	0.83	0.00	−0.09	0.06	−0.03	−0.08	0.11

F, femur; GCS, growth center section; H, humerus; LR, linear regression (P value and correlation coefficient r); MSS, mid‐sagittal section; PS, phylogenetic signal (K and P value); WD, whole diaphysis.

The abbreviations of the various parameters are listed in Material and Methods. Significant P‐values are shown in bold.

Size effect

For the MSS and GCS datasets, a size effect (allometry) was significant both for the humerus and the femur in Zpol, AMaxT, AmeanT and ASDT; it was also significant for RMaxT, but only for the humerus MSS data (not even for the GCS) (Table 2). Similarly, for the 3D parameters, a phylogenetic signal was detected in both humerus and femur for the same four parameters and the corresponding standard deviations (SD_AMaxT, SD_AMeanT, SD_ASDT; Table 2).

Principal component analyses

The aim of the PCAs was to estimate the contribution of the different variables in the distinction between the different specimens, and to make comparisons between the various analyses. We present the results obtained for each bone separately and, for each bone, distinguishing the results obtained based on the different datasets.

Humerus

The two first axes of the PCA including all parameters for the mid‐shaft sections (MSS) and for the sections crossing the growth center (GCS), represent 73.8 and 77.9% of the variance, respectively (Fig. 1). There are similarities in the relative weights of the various parameters. In both cases, P and R/t, Zpol and ASDT, and AMeanT and AMaxT strongly co‐vary; however, the last four variables co‐vary in GCS, not in MSS (Fig. 1A,C). CSS and S strongly covary in MSS, but they are oriented at about 90° to each other in GCS (Fig. 1A,C). Except for CSS and S, the orientation of the different variables is consistent between the two sectional planes. In MSS, most of the combined variation observed along the two first axes is explained by P, R/t, RMeanT, RMaxT and C; in GCS, it is essentially explained by P and R/t. Conversely, ASDT and Zpol contribute poorly to MSS, which is also the case for S, RSDT and ASDT for GCS (Fig. 1A). The variables contributing the most for PCA1 for MSS are P and R/t (negatively) and RMaxT, C, RMeanT and RSDT (positively). The variables contributing the most to PCA2 for MSS are CSS and S (positively), and RMeanT, AMeanT and AMaxT (negatively). PCA1 is correlated with size, whereas PCA2 is not (Table 3). Nevertheless, although the larger specimens are on the negative side of PCA1 (for MSS), Erinaceus and Tupaia, which are the smallest specimens, occupy a central position along PCA1 (Fig. 1B).

Figure 1.

Contribution of the different parameters (A, C) and distribution of the specimens in the morphospace (B, D) along the two first axes of the humerus PCA for the mid‐shaft sections (MSS; A, B) and for the sections crossing the growth center (GCS; C, D). Colors indicate the intensity of the relative contribution for each parameter. Abbreviations as listed in Table 1.

Table 3.

P‐values of the regressions of the two first axes of the various PCAs performed on size (estimated by R) and associated correlation coefficient (r)

	PCA1	PCA2	PCA1a	PCA2a
H MSS	P  < 0.01 r = −0.71	P = 0.32 r = −0.28	P = 0.15 r = −0.41	P = 0.47 r = 0.21
H GCS	P = 0.37 r = −0.26	P  < 0.01 r = −0.94	P = 0.78 r = −0.08	P = 0.95 r = 0.02
H WD	P  < 0.01 r = 0.83	P = 0.16 r = −0.40	P = 0.6966 r = −0.11	P = 0.38 r = 0.25
F MSS	P  = 0.01 r = −0.65	P  = 0.01 r = 0.65	P = 0.13 r = −0.42	P = 0.68 r = −0.12
F GCS	P = 0.18 r = 0.38	P  < 0.01 r = −0.86	P = 0.86 r = 0.05	P = 0.55 r = −0.17
F WD	P  < 0.01 r = 0.84	P = 0.51 r = 0.19	P = 0.96 r = −0.02	P = 0.30 r = 0.30

Significant P‐values are shown in bold. Other abbreviations as in Table 2.

^aWhen the parameters correlated with size are removed.

The variables contributing the most to the PCA1 for GCS are the same as for MSS (Fig. 1C). The ones contributing the most to PCA2 for GCS are AMeanT, AMaxT (negatively), CSS (positively), ASDT and Zpol (negatively). This time, PCA2, and not PCA1, is correlated with size (Table 3).

Although the distribution of the sections in the morphospace appears consistent with the (qualitative) observations, some sections are very close despite clearly distinct microanatomical features. This is notably the case for Choeropsis and Rupicapra for MSS (Fig. 1B).

The two first axes of the PCA for the whole diaphysis (WD) express 70.0% of the variance (47.2 and 22.8%, respectively; Fig. 2). The parameters explaining most of the distribution of the specimens are CSS, SD_C, RMaxT, RMeanT, 3DC and C. All thickness parameters in absolute value, group with Zpol. C and 3DC group together, as do RMaxT and RMeanT. The first axis is essentially controlled by RMeanT, RMaxT, 3DC and C (negatively), but also by absolute cortical thickness indices and Zpol (positively) and RSDT (negatively). The second axis is essentially controlled by CSS and SD_C (positively). The first axis is correlated with size, whereas the second is not (Table 3).

Figure 2.

Contribution of the different parameters (A) and distribution of the specimens in the morphospace (B) along the two first axes of the humerus PCA for the whole diaphysis (WD). Colors indicate the intensity of the relative contribution for each parameter. Abbreviations as listed in Table 1.

On both MSS and WD analyses, absolute and relative thickness values vary antagonistically along the first axis, whereas the reverse is true for the second axis for GCS. These parameters thus appear to vary antagonistically relative to size. Considering the apparent importance of size in this distribution, we performed another analysis removing the variables strongly correlated with size.

For MSS, the two first axes express 90.5% of the variance (63.7 and 26.8%, respectively; Fig. 3A,B). For GCS, they express 81.1% (68.2 and 12.9%, respectively; Fig. 3C,D) of the variance. In both cases, the distribution of the variables remains similar to that in the previous studies, but there is no longer a correlation with size (Table 3). The distribution of the specimens, with the removal of the variables strongly correlated with size, is slightly different (Fig. 3B,D) and appears more consistent with the qualitative observations, notably for the relative distribution of the largest and smallest taxa: Choeropsis (both MSS and GCS) and Tupaia (GCS), respectively.

Figure 3.

Contribution of the different parameters, except those strongly correlated with size (A, C) and distribution of the specimens in the morphospace (B, D) along the two first axes of the humerus PCA for the mid‐shaft sections (MSS; A, B) and for the sections crossing the growth center (GCS; C, D). Colors indicate the intensity of the relative contribution for each parameter. Abbreviations as listed in Table 1.

For the WD analysis, the two first axes of the PCA, which express 69.2% of the total variance (42.3 and 26.9%, respectively; Fig. 4) are not correlated with size (Table 3). The relationships between the different parameters is similar, except for %Trab, which remains poorly involved in the differentiation between the specimens. However, the impact of SD_RMeanT and SD_RMaxT is much greater and the distribution of the taxa are more compatible with the observations describing the whole diaphyseal microstructure.

Figure 4.

Contribution of the different parameters, except those strongly correlated with size (A) and distribution of the specimens in the morphospace (B) along the two first axes of the humerus PCA for the whole diaphysis (WD). Colors indicate the intensity of the relative contribution for each parameter. Abbreviations as listed in Table 1.

Femora

The two first axes of the PCA for the MSS and for the GCS represent 81.9 and 69.9% of the variance, respectively (Fig. 5). The variables contributing the most to the distribution along the two first axes are P and R/t and then (for MSS) RMaxT, RMeanT, C, RSDT, AMaxT, AMeanT, and (for GCS) AMeanT, AMaxT, C, Zpol and RmeanT; S always contributes the least. The relationships between the different variables are similar in both cases (Fig. 5A,C). For MSS, both axes correlate with size, whereas only PCA2 is correlated for GCS (Table 3). For MSS, the distribution along the first axis (52.4% of the variance) is essentially driven by P and R/t (negatively) and RMaxT, RMeanT, C and RSDT (positively). The variables contributing the most to the second axis (29.5%) are CSS (negatively), AMaxT, AMeanT and ASDT (positively), but also P and R/t (negatively) (Fig. 5A). The variables contributing the most to the first axis (40.7% of the variance) for GCS are P, R/t (negatively), C and RMeanT (positively), and to the second axis (29.2%) AMaxT, AMeanT, Zpol (negatively) and CSS (positively) (Fig. 5C). The relative position of the various specimens is rather similar in both cases, though there are of course slight differences, notably for Martes (Fig. 5B,D). The impact of allometry on the distribution of the data is observable with, for example, Erinaceus, Talpa and Marmota at one extreme and Choeropsis at the other, but with exceptions, such as Rangifer, closer to much smaller taxa, and Mustela closer to much larger taxa (for GCS).

Figure 5.

Contribution of the different parameters (A, C) and distribution of the specimens in the morphospace (B, D) along the two first axes of the femur PCA for the mid‐shaft sections (MSS; A, B) and for the sections crossing the growth center (GCS; C, D). Colors indicate the intensity of the relative contribution for each parameter. Abbreviations as listed in Table 1.

The two first axes of PCA for the WD express 68.6% of the variance (41.9 and 26.7%, respectively; Fig. 6). The relationships between the different variables are similar to those observed for the humerus. The variables contributing the most are essentially C, 3DC and SD_C, with CSS and %Trab contributing the least. Only the first axis correlates with size. The variables contributing the most to the latter are SD_C (negatively), AMeanT, AMaxT, Zpol and ASDT (positively). For the second axis, C and 3DC contribute the most (negatively). The distribution along the first axis is correlated with size (Table 3). Although it is not along the second axis, the high position of Rangifer along this axis is probably affected by the parameters correlated with size.

Figure 6.

Contribution of the different parameters (A) and distribution of the specimens in the morphospace (B) along the two first axes of the femur PCA for the whole diaphysis (WD). Colors indicate the intensity of the relative contribution for each parameter. Abbreviations as listed in Table 1.

With the exclusion of the parameters correlated with size, PCAs for MSS and GCS express 90.7% (69.5 and 21.2%) and 76.4% (52.7 and 23.7%) of the variance, respectively (Fig. 7). The contribution of the different variables is similar in both studies, except that RMaxT contributes more in MSS than in GCS. The variables contributing the most to the first axis are P, R/t (negatively), C, RMeanT, and also RMaxT (positively) for MSS. The variables contributing the most to the second axis are S and CSS (positively). The distribution of the various specimens is similar, despite some differences, e.g. for Martes and Tupaia (Fig. 7B,D). Similarly as for the humerus, the distribution appears more consistent with the qualitative observation of the sections than when parameters correlated with size are included.

Figure 7.

Contribution of the different parameters, except those strongly correlated with size (A, C) and distribution of the specimens in the morphospace (B, D) along the two first axes of the femur PCA for the mid‐shaft sections (MSS; A, B) and for the sections crossing the growth center (GCS; C, D). Colors indicate the intensity of the relative contribution for each parameter. Abbreviations as listed in Table 1.

For WD, the two first axes express 71.5% of the variance (45.2 and 26.3%, respectively; Fig. 8). Numerous variables contribute approximately equally to the distribution of the specimens, whereas the contribution of CSS was rather poor (Fig. 8A). When the variables correlated with size are removed, all parameters contribute positively to the first axis, with a maximum contribution from the parameters linked to the thickness of the cortex (except RMeanT) and SD_C. The variables contributing the most to the second axis are 3DC and C, and to a lesser extent %Trab (positively). The distribution of the various taxa appears much more compatible with the observations of the diaphyseal microstructure. The removal of the parameters strongly correlated with size on the femur analyses makes it possible to better determine the shape specificity of the Erinaceus sections.

Figure 8.

Contribution of the different parameters, except those strongly correlated with size (A) and distribution of the specimens in the morphospace (B) along the two first axes of the femur PCA for the whole diaphysis (WD). Colors indicate the intensity of the relative contribution for each parameter. Abbreviations as listed in Table 1.

Tests of covariation

All tests show that the two 2D section analyses and the whole diaphysis analysis are always consistent for the humerus and for the femur, respectively, with or without the inclusion of parameters strongly correlated with size (Table 4). However, although the femur data covary with those of the humerus when the parameters strongly correlated with size are included, this is no longer the case when these parameters are removed.

Table 4.

Results of the covariation tests with indication of the P‐value and of the covariation coefficient (r)

	H MSS	H GCS	H WD	H MSSa	H GCSa	H WDa	F MSS	F GCS	F WD	F MSSa	F GCSa	F WDa
H MSS	–
H GCS	P  < 0.01 r = 0.59	–
H WD	P  < 0.01 r = 0.73	P  < 0.01 r = 0.75	–
H MSSa	–	–	–	–
H GCSa	–	–	–	P  = 0.01 r = 0.43	–
H WDa	–	–	–	P  < 0.01 r = 0.57	P  < 0.01 r = 0.69	–
F MSS	P  = 0.046 r = 0.40	–	–	–	–	–	–
F GCS	–	P  < 0.01 r = 0.38	–	–	–	–	P  < 0.01 r = 0.71	–
F WD	–	–	P  = 0.01 r = 0.51	–	–	–	P  < 0.01 r = 0.72	P  < 0.01 r = 0.62	–
F MSSa	–	–	–	P = 0.54 r = 0.14	–	–	–	–	–	–
F GCSa	–	–	–	–	P = 0.36 r = 0.19	–	–	–	–	P  < 0.01 r = 0.56	–
F WDa	–	–	–	–	–	P = 0.81 r = 0.21	–	–	–	P  < 0.01 r = 0.49	P  < 0.01 r = 0.52	–

Significant P‐values are shown in bold.. Other abbreviations as in Table 2.

^aWhen the parameters correlated with size are removed.

Discussion

Phylogenetic and size signals

A significant phylogenetic signal was detected only in parameters that are also correlated with size. Size (here represented by R) in our dataset shows a phylogenetic signal. Although this is often the case (Blomberg et al. 2003; Kamilar & Cooper, 2013; Thiagavel et al. 2017), a test of phylogenetic signal in these parameters in a sample with no phylogenetic signal in size would be interesting. The occurrence of a phylogenetic signal is highly sample‐dependent. That is why, although it was not significant here for most parameters, we recommend always testing the occurrence of a phylogenetic signal in such a dataset to see whether phylogenetically informed statistical analyses are required.

Some parameters showed a strong correlation with size and thus showed a strong allometry. In this study, the aim was to define new parameters and to discuss how well they could describe microanatomical features. We used two sets of variables to describe cortical bone thickness, i.e. in absolute and relative values. Considering the strong allometry in the absolute parameters, the relative parameters appear more adequate for describing microanatomical features with as little noise as possible. The various thickness parameters in relative value should thus be preferred to the ones in absolute value. The strong link with size for Zpol was already highlighted in previous studies (Houssaye et al. 2016b; the other parameters that correlate with size were not measured in previous studies). The removal of these variables showed a relatively similar impact and relationships of and between all other parameters, but this time with no strong allometry (as highlighted by a nonsignificant correlation of the axes with size) on the two first axes of PCAs, which express a very high percentage of the total variance. Moreover, as previously noted, removing these parameters enables a better fit between the quantitative description and the qualitative observation of the microanatomical features, which supports the removal of these parameters in further microanatomical analyses.

Choice of variables

For 2D sections, the variables contributing the most are always P and R/t. These variables strongly covary. Since both express the general relative thickness of the medullary cavity, this covariation is logical. It is also consistent that they vary antagonistically with the indices related to the relative thickness of the cortex: RMaxT and RMeanT. However, it is interesting to note the following. The latter can but do not generally vary antagonistically with P and R/t; they thus provide data that is different from that for P and R/t. RMaxT and RMeanT do not always strongly covary, and indeed provide different information. This demonstrates the advantage of using RMaxT, RMeanT and one variable between P and R/t; the last two variables display redundant information and there is no need to use both. RSDT, which expresses the variation in cortical bone compactness in the whole section, shows a specific signal and its use appears well justified. If CSS and S sometimes strongly covary, this is not a general trend. S expresses variation in the transition zone, between the cortex and the medullary area; in fact, it provides some, but not all, of the information present in RSDT, as it also encounters the trabecular bone between the cortex and the open medullary cavity. C is naturally often associated with indices linked to cortical bone thickness, but covariation is not at all automatic and is not strong enough to prevent the use of this parameter. AMaxT and AMeanT always strongly covary and thus display similar information. They often but not necessarily strongly covary with ASDT and Zpol. If the three of these four variables thus appear as distinct (though close) variables, their strong correlation with size suggests that it would be better not to use these parameters (see above), all the more as the information in AMaxT and RMaxT is the same (as between AMeanT and RMeanT, ASDT and RSDT) and thus a set of these variables should be preferred to another.

In the analyses of the whole diaphysis, C and 3DC strongly covary, which is logical considering that they aim to express similar information, although C is a mean of the compactness values obtained for each diaphyseal section, whereas 3DC corresponds to the true compactness index of the diaphysis calculated in three dimensions. These results suggest that it is not justified to use both C and 3DC. In that case, we would suggest using 3DC instead, which truly expresses diaphyseal whole compactness. %Trab shows a distinct signal but does not generally contribute greatly to the distribution of the specimens. This parameter expresses the amount of trabecular bone occurring in the diaphysis. In our sample the contribution was rather slight (Supporting Information Fig. S1A,C), except for a few taxa (Choeropsis, Meles; Fig. S1B,D). However, the impact of this parameter might be stronger in analyses including various taxa showing trabecular bone in their medullary area, such as graviportal (Houssaye et al. 2016b) or aquatic (Houssaye et al. 2016a) taxa. Nevertheless, the contribution of this parameter is greater when the variables correlated with size (and thus bearing allometry) are removed. SD_C provides its own unique information. It can be pointed out that although this standard deviation parameter has a strong impact for the humerus WD, in the analysis without the parameters correlated with size, the other standard deviation parameters also strongly contribute. For the same reason as above, the parameters in absolute value linked to cortical bone thickness and Zpol should thus be removed in analyses that aim to describe microanatomical features in detail. SD_RMeanT and SD_RMaxT always strongly covary. As a consequence, only one of these should be used. Considering that RmeanT describes a more ‘general’ pattern than RMaxT, we prefer the latter. However, SD_RSDT provides its own unique information, as does CSS. This work thus enabled us to select seven parameters for 2D section analyses and nine for 3D whole diaphysis analyses. Of course, the impact of parameters can vary depending on the sample. This study makes it possible to estimate the pros and cons of each of the previously used parameters and of the above newly defined parameters. It will thus enable the direct performance of multivariate analyses in the future with a better knowledge of these parameters and thus with better means to interpret the results.

Comparisons between the datasets

For all analyses, i.e. humeral and femoral ones with or without the inclusion of parameters correlated with size, there is a strong covariation of the different datasets (MSS, GCS and WD). This result shows, at least in these taxa, that the 2D transverse sections, rather at mid‐shaft or along the sectional plane crossing the growth center, provide a good description of the general organization of the whole diaphysis. If care is taken not to mix MSS and GCS in the same analysis, results based on either one or the other type of section appear consistent. Again, this result is based on our sample, which illustrates a wide range of morphologies and ecologies in mammals, although in terrestrial forms displaying essentially a tubular inner organization. This may no longer hold for taxa showing a much stronger variation in bone microstructure along the diaphysis; nevertheless, it seems to represent a much more limited percentage of the tetrapod species diversity. Considering the significant contribution of the parameters describing variations along the diaphysis, it appears of interest to perform this type of analysis when possible in order to obtain a more precise description of the diaphyseal inner structure; that is, to express in detail quantitatively what is observed qualitatively. In addition, if these parameters are already of interest, as in the case of rather tubular organizations, resorting to a 3D analysis of the whole diaphysis should be of great interest in the case of bones showing a high variability of microstructure along the diaphysis.

Some limited differences between the results obtained from the different datasets can nevertheless be pointed out. S and CSS always covary, except for humerus GCS. CSS has a weaker impact on the femur than on the humerus WD, but not in 2D sections. These observations are compatible with a greater change in shape along the diaphysis in the humerus than in the femur, which appears notably linked with the deltoid tuberosity shape.

Covariation tests are significant between the humerus and femur datasets for the first analyses. However, when the variables strongly correlated with size are removed, this is no longer the case. This result shows that allometry impacted the results and that the taxa analyzed do not show similar distributions of the osseous tissue in the bone of the humerus and the femur. These bones thus do not show a similar evolution in their structure through their evolutionary history, which is in accordance with the idea that the forelimb and hindlimb bones are subject to different functional constraints. It thus indicates the strong interest in removing parameters bearing a strong allometry, in order to highlight the differences in the microstructure of the bones between the forelimb and the hindlimb.

Author contributions

A.H. designed the study, with significant input from R.C. A.H. did the data acquisition. A.H. and M.T. conducted the segmentation and analyses. A.H. drafted the manuscript, and all authors contributed to the final manuscript, read it and approved it.

Supporting information

Fig. S1. Longitudinal sagittal (left) and coronal (right) sections of the humeri (A, B) and femora (C, D) of Felis silvestris UFGK Unnumbered (A, C) and Meles meles STIPB M4002 (B, D) showing strong differences in microanatomical organization between a tubular structure in Felis and a medullary area partially filled by a spongiosa in Meles. Not to scale.