Humeral diaphysis structure across mammals

Long bones comprise articular ends (epiphyses) joined by transitional metaphyses and a diaphysis (shaft). The structure of the latter is often viewed as regularly tubular across tetrapods (limbed vertebrates). However, assessments of the bone structure along the whole diaphysis are rare. Here, I assess whole‐diaphysis profiles of global compactness (bone fraction) of 164 species of extant and extinct therian mammals (marsupials + placentals) in a phylogenetically informed context. Generally terrestrial, mammals have acquired multiple times the highly specialized aerial, fully aquatic, and subterranean lifestyles, allowing to potentially associate specific traits with these lifestyles. I show that there is a consistent increase in global compactness along the diaphysis in most mammals. This pattern is modified in a limited number of specialized species: all aerial clades (gliders and bats) have rather uniform and low values, while cetaceans’ humeral diaphysis is marked by a slightly more compact mid‐diaphyseal region. Among subterranean clades, structure alterations are most obvious in fossorial talpids (true moles) and their highly modified humerus. These results call for the investigation of bone structure in whole skeletal elements of key fossils in order to reconstruct the patterns of evolutionary modifications associated with lifestyle transitions.

The diaphysis (shaft) of long bones in many tetrapods is often assimilated to a simple tubular structure, with an open medullary cavity surrounded by a compact cortex. Metrics such as the relative cortical thickness were hence used to assess the robusticity of the bone under consideration (Currey & Alexander 1985;Ruff et al. 1993). However, the long bones of some species depart from that simple structure (in featuring a medullary cavity filled by spongy bone for instance ;Wall 1983). It is therefore in comparative analyses including such species that the need for a more widely usable parameter arose. Bone compactness, measured on a section as the area occupied by mineralized tissue against total cross-sectional area, stems from the standard histomorphometric assessment of bone volume (Parfitt et al. 1987;Hua & Buffrénil 1996). Subsequently referred to as global compactness (Cg; Girondot and Laurin 2003), this parameter revealed clear lifestyle adaptations, in particular to the aquatic environment (Canoville & Laurin 2010). While bone microanatomy in amniotes is assumed to usually be rather uniform along the diaph-ysis of long bones (Houssaye et al. 2015;Amson & Kolb 2016), Cg is generally acquired at mid-diaphysis or at the growth centre of long bones.
Here I test whether Cg shows proximodistal trends along the diaphysis of long bones, using the humerus of therian mammals. I also endeavour to test whether these trends (if any) relate to the species' lifestyle and body size. During the evolution of therian mammals, some linages acquired adaptions to highly specialised lifestyles. The aerial, fully aquatic, and subterranean lifestyles, in particular, were acquired by clades with extant representatives seven times (among which three in the Petauroidea), two times, and 13 times, respectively (Amson & Bibi 2020). I sampled several extant representatives of each of these clades, along with terrestrial species spread across the tree of therian mammals, using high resolution micro-Computed Tomography (μCT). A few extinct species were sampled as well, demonstrating that the method can be applied to fossil specimens. Figure 1. Timetree of the extant species sampled. Colors correspond to the specialized lifestyles, that is, aerial, aquatic, and subterranean; grey corresponds to the terrestrial lifestyle. Each silhouette represents an independent acquisition of one of the three specialized lifestyle.

BONE COMPACTNESS DATA
Whole humeri were μCT-scanned (Phoenix nanotom, General Electric; FF35-CT-System, YXLON; HMX ST 225, Nikon Metrology) at resolutions ranging from 0.003 to 0.077 mm (depending on the bone's size and geometry). Humeral global compactness (Cg) and total cross-sectional area (Tt.Ar) were quantified along the diaphysis using a slice-by-slice, ImageJ/Fiji (Schindelin et al. 2012) based approach (Amson 2019). Measurements were restricted to a region spanning the middle 40% of the humerus' functional length (for only the diaphysis to be sampled across all studied taxa). Sedimentary matrix had to be deleted manually from some of the fossil scans. Raw data are provided in the Supporting Information S1 (available online).

ANALYSES
All analyses were performed with R version 4.0.2 (R Core Team 2020). Proximodistal profiles were scaled relative to one another by sampling proportionally 100 slices for each specimen. Proximodistal Cg trends were assessed for each specimen by fitting a linear model (lm function) to the Cg values against the relative position of the slice in the diaphysis, and extracting the slope (unit: % per %) and associated p-value and R 2 (Table S1, available online). I used the extant species timetree from TimeTree.org (Kumar et al. 2017), modifying it according to the sampled species as detailed in Amson and Bibi (2020) (provided in the File S1, available online). When several specimens of the same species were sampled, their slopes were averaged. The model based on Pagel's lambda (λ = 0.83) was found as the one explaining the best the evolution of the slope (Fig. S1, available online; Monte Carlo approach, pmc package and function, 1000 simulations per comparison; Boettiger et al. 2012). The corresponding trait evolution was mapped on the timetree with the contmap function (phytools package; Revell 2012). The effects of body size and lifestyle on Cg slopes were assessed using ANCOVAs phylogenetically informed with Pagel's lambda (gls function, nlme package (Pinheiro et al. 2016); corPagel function, APE package (Paradis et al. 2004)), and posthoc pairwise comparisons (glht and mcp functions, Tukey's multiple comparisons, multcomp package (Hothorn et al. 2008)). Size was included as a covariate using species body mass (from the AnAge ( Tacutu  databases) for one ANCOVA. This analysis was repeated using the specimen-specific mean Tt.Ar (see above). Both body size proxies were natural log-transformed before the analyses.

Results
The general condition for mammals, found in virtually all terrestrial species, is to increase diaphysis compactness proceeding distally ( Fig. 2A). Mean Cg values in terrestrial mammals increase from ca. 50% proximally to 69% distally (Table 1). A similar pattern is found in most subterranean species, with the notable exception of subterranean talpids (true moles), whose humeral structure tends to be more uniform proximodistally (Fig. 2B). Aerial mammals depart from the general condition in featuring uniform and low Cg values (ca. 48-57%). Aquatic species show two distinct patterns: sirenians have extremely high values, that nevertheless increase proceeding distally; cetaceans have Cg values falling among those of terrestrial species, but differ in featuring a mid-diaphyseal region of higher compactness. The sampled extinct species (subterranean and aerial) fall close to their extant kin (Fig. 2B, D). The slope of the Cg profiles is on average of 0.22 for terrestrial mammals (Fig. 3A). Similar slopes are observed in subterranean species, while aerial and aquatic species differ in showing more moderate slopes (0.10-0.12). The difference is most pronounced for the aerial versus subterranean and aerial versus terrestrial comparisons (phylANCOVA, corrected P-values < 0.044; Supporting Information S2). Size (either body mass or mean Tt.Ar) correlates with the slopes (phylANCOVA, P-values < 0.034), although the effect is not strong (figure 3b).
A decrease of the Cg profile slope is associated with each of the five independent acquisitions of an aerial lifestyle (the petauroid marsupials are here represented by a single acquisition; figures 3c). The same is true for sirenians, and only trivially so for cetaceans. Among the 13 clades of subterranean mammals, it is mostly the talpid radiation that is associated with the acquisition of a weaker slope. This is also found, to a lower extent, in chrysochlorids (golden moles), Spalacopus (coruro), Ctenomys (tuco-tuco), and Notoryctes (marsupial mole).  Among the 10 specimens for which the Cg regression's R 2 is the lowest (<0.25) are all five sampled subterranean talpids, along with another subterranean species (Amblysomus iris), three aerial taxa (Pipistrellus pipistrellus, Petaurus norfolcensis, Idiurus zenkeri), and one terrestrial species (Chaetodipus formosus). All profiles show a positive slope, except for three specimens, for which the regression fit is poor (the talpids Euroscaptor mizura and Parascaptor leucura and the pocket mouse Chaetodipus formosus; P-values > 0.19; R 2 < 0.02).

Discussion
Nuancing with the preconception that the diaphysis of long bones is uniformly tubular, I showed that the general condition for the humeral diaphysis of terrestrial mammals is to show an increase in bone fraction proceeding distally. For terrestrial taxa, mid-diaphysis is where maximum strains are generally expected during loading. To the best of my knowledge, this assumption is based on in vivo strain recording made with gauges placed at mid-diaphysis and in its close vicinity (Biewener & Taylor 1986). While further biomechanical investigations should probably be dedicated to the understanding of strain distribution along the diaphysis during terrestrial locomotion, a finite element analysis (FEA) of the cow's humerus suggests that the distal diaphysis undergoes greater stresses under various loading regimes (Bouza-Rodríguez & Miramontes-Sequeiros 2014). The present results might imply that this holds true for terrestrial mammals in general. But this should be tempered by the results of previous examinations of cross-sectional properties along the humeral diaphysis: cross-sectional area, second moment of area, and/or section modulus were found to be rather uniform in felids (Doube et al. 2009), mustelids (Kilbourne & Hutchinson 2019), macropods and artiodactyls (Doube et al. 2018), and hominines (Mongle et al. 2015) (though profile slopes were not computed as in the present study).
The aerial lifestyle (gliding + volant species) seems to be the lifestyle associated with the clearest modification of diaphysis organization, with all species showing low Cg values and a diaphysis truly approaching a uniformly tubular structure. Indeed, the evolution of each aerial clade is associated with a reduction of the Cg regression slope (Fig. 3c). This is evidently a modification that has to be associated with diaphysis elongation, which is indeed found in all aerial mammals (Amson & Bibi 2020), even though their convergence was found as "incomplete" (Grossnickle et al. 2020). The earliest bats with known postcranium (Onychonycteris finneyi, Early Eocene), already show anatomical features of modern chiropterans, including an elongate humerus (Amador et al. 2019). Unsurprisingly, all the bats sampled here (from the late Eocene on, who all show a specialized and elongate gross morphology), also feature a uniformly tubular structure. Concerning subterranean species, the present results showcase the relatively intense humeral modifications in the subterranean talpids, with fairly high and uniform values of compactness along the diaphysis (either the Cg profile regression fit is poor or the associated slope is low). An examination of humeral microanatomy at mid-diaphysis of this family found no clear lifestyle specialization involving Cg (Meier et al. 2013), which demonstrates that whole diaphysis analysis can reveal novel patterns of structural modifications. Furthermore, the Cg profile of Urotrichus giganteus, a co-generic of the Japanese shrew mole who is regarded as being semi-fossorial (Ellerman 1956;Sansalone et al. 2020) and who shows a more conservative gross morphology, features high and uniform values. Structural modifications of the humeral diaphysis related to fossoriality hence seem to affect this genus as well, consistent with the fact that they were found as intermediate between fully fossorial and nonfossorial species regarding the distribution and magnitude of von Mises stress recovered from FEA (Sansalone et al. 2020). Both Notoryctes and chrysochlorids also show relatively uniform Cg values when compared to their close relatives. But at least for the latter that should be tempered by the fact that the most closely related terrestrial taxa, the tenrecs (which are quite distant phylogenetically), feature exceptionally high slope values. Intermediate stress values have also been found for Notoryctes and chrysochlorids (Sansalone et al. 2020). The humeri of the early Miocene notoryctid Naraboryctes philcreaseri (Archer et al. 2011;Beck et al. 2016) and of the early Pliocene chrysochlorid Chrysochloris arenosa (Asher & Margaret Avery 2010) are characterized by an intermediate gross morphology (relative to their most specialized extant kin). An examination of their diaphyseal structure would enable to confront the evolution of humeral gross anatomy and structure in relation to transitions to a subterranean lifestyle.
The Cg profiles of fully aquatic mammals reflect the two well-known microstructural adaptations found in extant sirenians and cetaceans, the non-pathological osteosclerotic and osteoporotic-like patterns, respectively (Buffrénil et al. 2010). Even though in terms of absolute Cg values, the sirenian modifications appear as the most extreme, they preserve the proximosdistal Cg increase found in terrestrial taxa (the mean slope of their Cg is however particularly low; Fig. 3c). Cetacean modifications differ in that regard, with Cg profiles showing a central region with slightly raised values (Fig. 2c). The overall humeral structure in extant representatives of this clade approaches the structure of 'short bones' such as carpals for instance (Francillon-Vieillot et al. 1990). A noteworthy condition is documented in the middle Eocene protocetid Qaisracetus: its humeral diaphysis compactness peaks at mid-diaphysis (with a Cg value of ca. 92%; Houssaye et al. 2015). This is hence both reminiscent of sirenian osteosclerosis in terms of absolute Cg values (Fig. 2c) and extant cetaceans in terms of the proximodistal Cg distribution pattern. A pattern involving a more compact region at mid-diaphysis was also described in the femur of the sea otter (Enhydra), which was found as reminiscent to that of some early "archaeocetes" such as Ambulocetus (Madar 1998). The humerus of the sea otter, however, seems to show the pattern here identified in terrestrial mammals, with a thickening of the cortex proceeding distally (Houssaye & Botton-Divet 2018).

Conclusion
Bone fraction within mammalian long bones vary considerably from one species to another. Some of this variation can be related to functional adaptations, such as the sirenian bone mass increase and its purported hydrostatic role (Buffrénil et al. 2010). However, I found that there is a rather consistent increase in global compactness along the diaphysis of therian mammals. This pattern is modified in a limited number of species, in particu-lar those who acquired an aerial lifestyle (gliders and bats), the subterranean talpids, as well as fully aquatic, active swimmers (cetaceans). Further whole-diaphysis investigations of exceptionally preserved fossils should aim at deciphering the patterns of bone structure alterations associated with lifestyle transitions.

Supporting Information
Additional supporting information may be found online in the Supporting Information section at the end of the article.
File S1. Archive with raw data acquisition for both extant and extinct species, as well as timetree used for phylogenetically informed tests. File S2. Detailed output of the phylogenetically informed ANCOVAs. Figure S1. Monte Carlo based continuous model choice to reconstruct the evolution of the slope of the global compactness (Cg) profiles. Pairwise comparisons (null model_test model): BM_lambda, Brownian motion vs. Lambda, OU_lambda, Ornstein-Uhlenbeck (one central tendency) vs. Lambda; OU_EB, OU vs. Early burst; EB_white, EB vs white noise (non-phylogenetic model). AICc list: Lambda, -249.795166;OU, -243.253293;BM, -225.393118;EB,-223.310270;white, -211.932044 .  Table S1. Data table comprising the raw data file names for each extant species (LabelHum), species name, lifestyle, body mass (BM), catalogue number (CNum), mean total cross-sectional area (MeanTotArea), and p-value associated to the slope of each Cg profile regression (slopeP) as well as its slope and R 2 .