APPENDIX 1
Dry bone tissue water loss and its specific gravity
Bone tissue (including cortical or compact bone) in both terrestrial and aquatic mammals typically consists of approximately 25.5% water, 4.5% volatile inorganic material, 35% organic material, and 35% inorganic (ash), and each of these components has an approximate specific gravity (SG) as follows: 1.0 for water, 1.7 for volatile inorganic material, 1.45 for organic material, and 3.15 for ash (Gong et al., 1964a; Tont et al., 1977; O'Flaherty, 1991). This indicates that the specific gravity of fresh or wet bone tissue is approximately 1.94 (Table 1), which is commonly observed in compact bone in living vertebrates (Gong et al., 1964a; Tont et al., 1977; Larramendi et al., 2021). However, when a bone is completely dried, it will lose both water and inorganic volatile material, causing the SG of dry bone tissue to increase to 2.3 (Table 2; Gong et al., 1964a; O'Flaherty, 1991; ICRP, 1995). For example, the dry and free fat skeleton of an adult male humans (~173 cm tall and ~70 kg) weighs around 4,500 ± 500 grams (see Trotter, 1954; Baker, 1957; Baker and Schraer, 1958), while the fresh skeleton of an adult male (176 cm tall and 73 kg) weighs around 10,500 grams, with 5,500 grams comprising bone tissue, plus 50 grams including teeth (ICRP, 1995). Such reduction in skeletal tissue weight (~23%) is only possible if virtually all the moisture in the skeleton has been removed. In this scenario, when the water and volatile inorganic material are extracted from the human example bone tissue, a skeletal weight of 4,611 grams (4,561 + 50 grams of teeth) is obtained, or 4,828 grams and a bone tissue SG of 2.26 if only water is excluded (Table 2), closely aligning with findings from empirical studies (Trotter, 1954; Baker and Newman, 1957; Baker and Schraer, 1958). It is noteworthy that since water and inorganic material together constitute approximately 30% of bone tissue volume, the removal of these components would theoretically lead to a reduction in the bone's linear dimensions. Surprisingly, to our knowledge, no studies have explored whether there is a shrinkage in the linear dimensions of dehydrated bones, although since the water is in the bone inorganic matrix, any shrinkage would be minimal (Wescott, personal commun., 2023). However, this does not appear to be the case with fossilized bones. The fossilization process seems to prevent such potential reduction due to the deposition of minerals in the bony spaces, which acts to maintain the bone's structural integrity, and the saturation of the bones with ground water especially in aquatic environs, nor is there evidence for a reduction in bone volume, which would likely be evident in microstructural analyses (Schweitzer, personal commun., 2023). Hence, the tissue of fossilized bones very likely does not reflect a dehydrated volume bone state.
Despite Bianucci et al. (2023) did acknowledge some water loss in dried skeletons, albeit insufficiently, this factor was not considered in their calculations for the dry skeletal mass of Perucetus colossus. Accounting for this water loss is essential for a meaningful comparison of the dry skeletal mass of P. colossus with data from dried skeletons of extant aquatic mammals gathered from the literature.
Inorganic volatile material typically requires very high temperatures for disintegration (see Gong et al., 1964b). Therefore, in the case of museum specimens, which are typically dried out at room temperature -and which normally have been previously macerated- (see Hendry, 1999), it is unlikely that a significant amount of inorganic volatile material would evaporate. Consequently, for the calculations in this study, only the water content was subtracted from the Perucetus colossus skeleton, and therefore, a SG of 2.26 was applied to calculate the bone tissue mass.
Steller's sea cow skeletal fraction
The composite Steller’s sea cow (Hydrodamalis gigas) skeletons do not provide consistent dimensions, as shown by NHMW 614 and NMKK 7628 with their apparently oversized manatee like broad ribcages versus the MNHN 14516 and USNM 21966 mounts with their narrow dugong style trunk. The subarctic sea cow was probably a relative of the dugong (Springer et al., 2015) sharing its more whale-like form including Y-shaped flukes, and the more complete UZMH 710 specimen and contemporary illustrations indicate it shared the latter’s subcircular cross section. Our mean k value for H. gigas, indicates that the mass-to-length ratio presented here aligns well with the findings of Scheffer (1972). It is estimated that fully grown individuals of this species on Bering Island likely reached lengths of around 8 m (Domning, 1978), suggesting a body mass around 10 tonnes. However, fossil evidence from farther south indicates that maximum body lengths may have reached 9-10 m (Anderson and Domning, 2009), suggesting a potential body mass of up to 19 tonnes.
On the other hand, Domning and Buffrénil (1991) found that the skeletal mass of the Florida manatee, Trichechus manatus, scales with strong positive allometry (slope = 1.13). However, this may be a result of their sample, which includes individuals of all ages, from very young individuals weighing 21 kg to fully grown ones weighing up to 1,057 kg. Therefore, ontogeny may play a major role in this allometry. For instance, when specifically examining adult individuals over 3 meters in length (as per Bianucci et al., 2023, supplementary data 2), this positive allometry is not observed; rather, a negative trend emerged, contradicting the findings of Motani and Pyenson (2024) for their truncated manatee sample. In fact, the SFs of the largest individuals (USNM 551,672 and USNM 530,299) are among the lowest in the sample, while the highest SFs are found in the smallest individuals (USNM 550,321 and USNM 527,901) (see Motani and Pyenson 2024, supplementary information). Motani and Pyenson (2024) also identified strong positive allometry in manatees in a larger sample, but included very young individuals (starting with individuals 1.5 m in length), suggesting that ontogeny likely played a significant role in their results. Nevertheless, at a length of 5.74 meters, the skeleton MNHN 14516 of the extinct Steller’s sea cow sirenian, Hydrodamalis gigas (accessed on Sketchfab.com), has a skeletal volume of 259 liters, suggesting a dry skeletal mass of about 365 kg when applying an SG of 1.41 for the overall skeleton density (see Bianucci et al., 2023, supplementary table 11) They calculated an overall skeleton SG of 1.57 for sirenians, but based on their data, it should be 1.41. It appears they multiplied the SG of each skeletal body part by its mass rather than dividing them. However, it is possible that the composite nature of MNHN 14516 (Mattoli and Domming, 2006) effects these calculations in uncertain regards.
Assuming as reasonable the aforementioned skeletal mass, in our H. gigas volumetric model (Figures 1H, 2H; Table 1, in the main text), at a skeletal length of 5.74 m (5.95 m in the flesh) yields a mean body mass of 4,065 kg, implying a SF of 9%. This SF is 2.75 percentage points higher than the average found in adults of the much smaller Trichechus manatus (Bianucci et al., 2023), suggesting that skeletal mass in sirenians might scale with strong positive allometry, at least inter-specifically -and probably in other pachyosteosclerotic clades as well.
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