Volume 304, Issue 9 p. 1833-1888
REVIEW
Free Access

A review and reappraisal of the specific gravities of present and past multicellular organisms, with an emphasis on tetrapods

Asier Larramendi

Corresponding Author

Asier Larramendi

Eofauna Scientific Research, Errondo 6, 10c, Donostia, Basque Country, 20010 Spain

Correspondence

Asier Larramendi, Eofauna Scientific Research, Errondo 6, 10c. 20010, Donostia, Basque Country, Spain.

Email: [email protected]

Contribution: Conceptualization, Data curation, Formal analysis, ​Investigation, Methodology, Resources, Supervision, Validation, Visualization, Writing - original draft, Writing - review & editing

Search for more papers by this author
Gregory S. Paul

Gregory S. Paul

N. Calvert St. Side, Baltimore, Maryland, 3109 USA

Contribution: Conceptualization, Data curation, Formal analysis, ​Investigation, Methodology, Resources, Supervision, Validation, Writing - original draft, Writing - review & editing

Search for more papers by this author
Shu-yu Hsu

Shu-yu Hsu

Eofauna Scientific Research, Errondo 6, 10c, Donostia, Basque Country, 20010 Spain

Contribution: Resources

Search for more papers by this author
First published: 01 December 2020
Citations: 12

[Correction added on 05 February 2021, after first online publication: Global corrections, Gallus domesticus should be update by Gallus gallus domesticus.]

[Correction added on 06 August 2021, after first online publication: The text and table errors were identified throughout the text and they have been corrected]

Abstract

The density, or specific gravity (SG), of organisms has numerous important implications for their form, function, ecology, and other facets of beings living and dead, and it is especially necessary to apply SG values that are as accurate as practical when estimating their masses which is itself a critical aspect of living things. Yet a comprehensive review and analysis of this notable subject of anatomy has never been conducted and published. This is such an effort, being as extensive as possible with the data on hand, bolstered by some additional observations, and new work focusing on extinct animals who densities are least unknown: pterosaurs and dinosaurs with extensive pneumatic complexes, including the most sophisticated effort to date for a sauropod. Often difficult to determine even via direct observation, techniques for obtaining the best possible SG data are explained and utilized, including observations of floating animals. Neutral specific gravity (NSG) is proposed as the most important value for tetrapods with respiratory tracts of fluctuating volume. SGs of organisms range from 0.08 to 2.6, plant tissues from 0.08 to 1.39, and vertebrates from about 0.75 (some giant pterosaurs) to 1.2 (those with heavy armor and/or skeletons). Tetrapod NSGs tend to be somewhat higher than widely thought, especially those theropod and sauropod dinosaurs and pterosaurs with air-sacs because respiratory system volume is usually measured at maximum inhalation in birds. Also discussed is evidence that the ratio of the mass of skeletons relative to total body mass has not been properly assayed in the past.

INSTITUTIONAL ABBREVIATIONS

  • AMNH
  • American Museum of Natural History, New York, United States
  • BSPG
  • Bayerische Staatssammlung für Paläontologie und historiche Geologie in Munich, Germany
  • CM
  • Carnegie Museum of Natural History, Pittsburgh, United States
  • NHMUK
  • Natural History, Museum, London, UK
  • TMP
  • Royal Tyrrell Museum of Palaeontology
  • NSM
  • National Museum of Science, Tokyo, Japan
  • UNSM
  • University of Nebraska State Museum, Lincoln, Nebraska, United States
  • USNM
  • Smithsonian National Museum of Natural History, Washington, United States
  • TECHNICAL ABBREVIATIONS

  • ASP
  • air space proportion
  • BM
  • body mass
  • BV
  • body volume
  • CT
  • computed tomography
  • FRC
  • functional residual capacity
  • GDI
  • graphic double integration
  • ITD
  • internal tracheal diameter
  • NSG
  • neutral specific gravity
  • SG
  • specific gravity
  • SM
  • skeletal mass
  • TLC
  • total lung capacity
  • TRSC
  • total respiratory system capacity
  • VT
  • tidal volume
  • WD
  • water displacement
  • 1 INTRODUCTION

    Specific gravity (SG), the density ratio between mass versus volume relative to freshwater, is an important property of organisms living in 1G on land or in the air, and 0G when buoyed by total immersion in water. The importance of SG is especially true for semi and fully aquatic creatures in which buoyancy and control has a direct impact in energetics, physiology, survival and behavior (Cantrell, Dong, Hill, & Warren, 2014; Gee & Waldick, 1995; Tu, Chu, & Lue, 1999). SGs can also of special importance in flying animals that make their way through an atmosphere hundreds of times less dense than water. For those examining paleobiology, a correct as possible understanding of SGs is a significant factor in estimating the masses of extant and extinct organisms when using volumetric methods (Bates, Falkinghorn, Maccaulay, Brasseu, & Maidment, 2015; Brassey, Maidment, & Barrett, 2015; Hurlburt, 1999; Ibrahim, Sereno, et al., 2020; Larramendi, 2016; Paul, 1988a, 1988b, 1997, 2002, 2019) and is correspondingly relevant for brain-body scaling, encephalization quotient, and brain evolution studies (Font, García-Roa, Pincheira-Donoso, & Carazo, 2019). SG is important among plants because wood density has direct impacts on functional traits, ecology and evolution (Bastin et al., 2015; Muller-Landau, 2004; Swenson & Enquist, 2007), as well as in the estimation of the biomass and carbon sequestration (Keeling & Phillips, 2007; Nogueira, Nelson, & Fearnside, 2005; Roxburgh et al.,  2006; Vieilledent et al., 2012).

    A number of studies have focused on measuring or calculating the SGs of extant animals including invertebrates (Blake, 1985; Bucher, Harriott, & Roberts, 1998; Carta and Carta, 2000 and references therein; Hughes, 1987; Lowndes, 1938; Lowndes, 1942; Lowndes, 1943; Oliver, Chalker, & Dunlap, 1983; Shapiro, 1980; Tunnicliffe, 1983) fish (Baldridge Jr, 1970; Davenport, 1999; Davison, 2011; Lowndes, 1942, 1943; Parker, McElderry, Rankin, & Hannah, 2006; Stewart & Hughes, 2014; Taylor, 1922), mammals (Buchner, Savelberg, Schamhardtt, & Barneveld, 1997; Crompton, Li, Alexander, Wang, & Gunther, 1996; Dempster, 1955; Garrett, 1967; Kodama, 1971; Larramendi, 2015, 2016; Luque & Aurioles-Gamboa, 2002; Miller et al., 2016; Narazaki et al., 2018; Pearson, Purchas, & Reineke, 1968; Shafer, Siders, Johnson, & Lukaski, 2010; Watanabe, Baranov, Sato, Naito, & Miyazaki, 2006), birds (Alexander, 1983; Allen, Paxton, & Hutchinson, 2009; Hamershock, Seamans, & Bernhard, 1993; Hazlehurst & Rayner, 1992; Hutchinson, Ng-Thow-Hing, & Anderson, 2007; Tserveni & Yannakopoulos, 1988; Welty, 1962; Welty & Baptista, 1988; Wilson et al., 1992), and reptiles (Cantrell et al., 2014; Colbert, 1962; Cott, 1961; Jackson, 1969; Jackson, 2011; Patterson, 1973; Peterson & Gomez, 2008; Tu et al., 1999; Williams & Han, 1964; Zug, 1971). In addition to the above, several attempts have been made to estimate the SG of extinct animals, with particular emphasis on dinosaurs (Alexander, 1985; Brassey et al., 2015; Colbert, 1962; Gregory, 1905; Henderson, 1999, 2018; Henderson, 2004; Mallon, Henderson, McDonough, & Loughry, 2018; Molina-Pérez & Larramendi, 2019; Paul, 1988a, 1988b, 1997, 2002, 2016, 2019; Wedel, 2005) as well as pterosaurs (Bramwell & Whitfield, 1974; Henderson, 2010; Paul, 1991; Paul, 2002), and giant mammals (Larramendi, 2015, 2016). For practical purposes a number of studies have focused on plants (wood, vegetables, and fruits: Kumar, Ezekiel, Singh, & Ahmed, 2005; Ting & Blair, 1965; Yıldız, İzli, Ünal, & Uylaşer, 2015 and references therein; Zanne et al., 2009 and references therein).

    Accurately determining SGs can be difficult for a number of reasons. To start with, direct measurements of SGs of extant animals are fairly scarce. Nor is there a common standard when estimating animal SGs. The methodologies and procedures applied have been varied, and are often conducted in a manner that produces errant results; in particular, maximal inflation of respiratory tracts will produce SG values lower than the normal average for an animal. As a result, studies carried out to estimate animals SGs differ significantly even when examining very closely related animals or even individuals within the same species.

    We also realized that to date there has not been a comprehensive review of the specific gravities of organisms. For certain groups, major questions remain. This unprecedented review and analysis correspondingly aims to do the following. Review the available data for multicellular organisms with a particular emphasis on tetrapods, specifically those the masses of extinct examples of which can be estimated via volumetric modeling. Expand as much as possible within the scope of this study the data base on extant and extinct organism using methodologies that appropriate for a given case. Needing the most attention are extinct groups the body form of which does not have close living analogs—for example, the SG of a Miocene horse can be assumed to be the same as for a living horse, but the SG of a sauropod dinosaur cannot be based directly on any living similar creature. In general, SGs appear to be somewhat higher than have been used for estimating dinosaur masses via volumetric modeling (contra Alexander, 1985; Bates et al., 2015; Bates et al., 2016; Colbert, 1962; Henderson, 1999; Henderson, 2018; Mallon et al., 2018; Paul, 1988a, 1988b, 1997, 2002, 2016, 2019; Sellers et al., 2012; Wedel, 2005). The result of this study is the most extensive examination of the SGs of multicellular organisms to date, along with notes on the ratio of the mass of the skeleton to total mass, which may be useful in future investigations dealing with buoyancy, biomechanics, body mass (BM) estimations of extant and extinct taxa, and other factors.

    2 METHODOLOGICAL CONSIDERATIONS

    2.1 Water and air

    The SG of 1.0 is applicable to freshwater, salty ocean water is 1.025. Because the density of air at sea level at average barometric pressure is exceptionally low (SG = 0.0012 [Chen, Liu, Li, & Yang, 2015]), over eight hundred times less than water, its SG was placed at zero in the present contribution.

    2.2 Neutral specific gravity

    The SG of any given air breathing tetrapod is normally variable on the short term depending on the amount air within the respiratory system at a particular moment as it inhales and exhales. The fluctuation can occur over a few seconds as a land animal naturally breathes, or markedly longer when an aquatic animal holds its breath while submerged. It is logical to estimate the SG based on what is expected in a living animal in a relaxed position during normal breathing, this being the most common state during the animal's daily life (walking, feeding, etc.). The SG value for a given tetrapod is therefore herein set as being the density when it is at respiratory neutral, with the volume of the respiratory tract being about intermediate to inhalation maximum and exhalation minimum (Gillespie, 1983; O'Neil & Raub, 1984, Paul, 2002, 2019; York et al., 2018). It is concluded that neutral specific gravity (NSG) should be the standard for future work with organisms the volumes of which can fluctuate over the short term.

    Meanwhile, general or adjusted SG values can be used for other situations, such as a swimming animal keeping its lungs as inflated as much as practical to float, or the opposite to sink, or the density of a floating waterbird that uses its water resistant feather shell to achieve extra high buoyancy, or the density of a dried out or of a waterlogged tree trunk. That previously published SGs measured and calculated for extant and extinct animals are often set at respiratory maximum is one reason mass values are often somewhat reduced. BV is usually that contained within the skin, but the BV of some birds also includes their feather shells under certain circumstances. Also involved in the NSG are gut contents in terms of ingested foodstuffs that are normally undergoing digestive processes, gut flora, and gastroliths, the first two factors are particularly likely to be most significant among herbivores. Inclusion of gut contents is important when examining certain aspects of biology such as buoyancy, and the mass induced stress loads during locomotion, as well as internal heat production including fermentation processes relative to BM and surface area.

    Attempting to directly measure the NSGs of air breathing tetrapod bodies whether living or dead can be problematic (Sato et al., 2002; Stephenson, 1995), it often being difficult to assess whether or not the respiratory complex is at neutral inflation. The SGs obtained for crocodilians by Cott (1961) and Colbert (1962) differed by about 20% for reasons discussed below. Regarding insects there is the potential issue of flooding of the trachea, or of air trapped with wing shells or on body fuzz.

    An important means of approximating the NSG of living tetrapods is to observe how their bodies perform when floating, swimming or sinking in water via photographs and motion videos a large sample of which are available on the web and print publications, and personal observation. Such real world examples of actual animal density act as a check on experimental measurements of less certain reality. If the subject sinks then its NSG must be over 1.0. If an animal barely floats, its body awash and only the head at least partly out of water and perhaps a small portion of the neck, that means that the portion of the animal above the waterline is roughly countered by the swimming action that slightly propels the body upward, so its SG is very close to or at 1.0. The role that swimming can play in keeping a small part of an animal above the waterline is supported by how many animals –humans included– if they tire to the degree that they can no longer vigorously swim are at risk of not being able to keep their head high enough to avoid drowning. The more of the volume of the organism that is above the waterline the lower the SG. Extremes of this spectrum include hippos that cannot float on buoyancy alone at the high density end, and water resistant feather shelled anatids, waterfowl whose freeboard (the height from the waterline to the top of the body) is very high. Further useful is if the fur or feather coat of given animals that have them are fluffy and air filled versus waterlogged, the latter being closer to representing the NSG of the body contained within the creature's skin. Assessing the SG of very small organisms subject to water surface tension effects such as insects requires entirely submerging the organism to observe whether it remains under the surface, or floats. Further pinning down NSG can require approximations of bone density, including surface armor. NSGs thus determined from extant examples can then be extrapolated via comparative and functional anatomy to extinct forms of similar biodesigns, with adjustments to morphological differences as needed.

    2.3 Respiratory system capacities in relaxed tetrapods

    When land mammals are in a relaxed state their lungs are only filled by about a 40–50% their total lung capacity (TLC), which corresponds to the functional residual capacity (FRC) (Ganong, 2003; Gillespie, 1983; Prange, 1996), although there can be few exceptions (Gillespie, 1983; O'Neil & Raub, 1984; Table 1). Tidal volume (VT), the amount of air displaced between normal inhalation and exhalation, corresponds to about 1% of the total body volume (BV) in mammals and birds (Stahl, 1967; Table 1), and therefore has a very low impact in the animals' SGs (Table 1), and this only happens during inhalation. In reptiles, the resting lung volume (comparable to FRC, and used as synonym herein) (see Perry & Duncker, 1978) is considerably smaller than mammals being generally, about 20–30% of the TLC (Table 1).

    TABLE 1. Estimated NSGs of extant vertebrates species based on multiple measurements and parameters exlapined in Methodological Considerations.
    Neutral specific gravities (NSG) of different extant vertebrates
    Species N BM (g) BM without plumage (g) SG of the body without air Max. air volume in lungs (ml) Max. air volume in air sacs (ml) Air volume in bones (ml) Air volume in trachea (ml) TRSC (ml) FRC (ml) VT (ml) BV without air (ml) BV with air at resting (ml) NSG NSG with inhalated VT Body mass and air volumes references
    Birds
    Gallus gallus domesticus 10 3,756 3,531 1.044 70 425 7 502 254.5 3,382 3,636 0.971 (King, 1966; King & Payne, 1962)
    Gallus gallus domesticus 10 2,905 2,731 1.044 35 259 4 298 151 2,616 2,767 0.987 (King, 1966)
    Gallus gallus domesticusa 1 1,944 1,827 1.044 206 3 209 106 1,750 1,856 0.984 (Lasiewski & Calder, 1971)
    Columbia liviab 382 359 1.000 8 66 6 80 43 4.6 359 402 0.893 0.883 (Hart & Roy, 1966; King, 1966)
    Columbia liviac 1 328 308 1.000 49.5 5 54.5 29.8 4.6 308 338 0.912 0.900 (Hart & Roy, 1966; Lasiewski & Calder, 1971)
    Struthio camelusd 1 88,000 85,360 1.000 3,000 10,000 400 13,400 6,900 1,200 85,360 92,260 0.925 0.913 (Schmidt-Nielsen, Kanwisher, Lasiewski, Cohn, & Bretz, 1969)
    Passer domesticus 16 27.33 25.69 1.050 0.8 5.76 0.08 0.08 6.72 3.44 24.47 27.9 0.921 (Dubach, 1981)
    Melopsittacus undulatus 12 39.8 37.4 1.000 1.11 5 0.17 0.1 6.38 3.325 37.41 40.7 0.918 (Dubach, 1981)
    Colibri coruscans 13 7.3 6.9 1.000 0.27 1.59 0.08 0.05 1.99 1.06 6.86 7.9 0.866 (Dubach, 1981)
    Amazona and Psittacusc 8 453 425.8 1.000 14.23 65.63 1.2 81.06 41.13 425.82 467.0 0.912 (Krautwald-Junghanns, Valerius, Duncker, & Sohn, 1998)
    Anser indicuse 2 2,620 2,462.8 1.000 65.2 674 16 9.6 764.8 408 45 2,462.80 2,870.8 0.858 0.845 (York, Scadeng, McCracken, & Milsom, 2018)
    Chloephaga melanopterae 2 2,400 2,256.0 1.000 100.5 661 28 6.8 796.3 430 33 2,256.00 2,686.0 0.840 0.830 (York et al., 2018)
    Branta leucopsise 2 2,120 1,992.8 1.000 39.3 473 9.2 6.4 527.9 227 25 1,992.80 2,219.8 0.898 0.888 (York et al., 2018
    Mammals
    Homo sapiensf 162 77,300 1.050 6,783 150 6,933 3,327 502 73,619 77,096 1.003 0.996 (Intagliata, Rizzo, & Gossman, 2019; Withers, Bourdon, & Crockett, 1988)
    Macaca radiata 22 5,870 1.050 468 468 310 5,590 5,900 0.995 (Kosch et al., 1979)
    Macaca mullata 12 7,770 1.050 673 673 333 7,400 7,733 1.005 (Kosch et al., 1979)
    Canis lupus familiaris 6 18,600 1.050 997 309 17,714 18,711 0.994 0.978 (Gillespie & Hyatt, 1974)
    Bos taurus 7 517,000 1.050 20,370 4,136 492,381 512,751 1.008 1.000 (Gallivan, 1989)
    Equus ferus 6 402,000 1.050 20,623 4,985 382,857 403,480 0.996 0.984 (Gallivan, 1989)
    Giraffa camelopardalis 1 1,440,000 1.050 69,300 4,200 73,500 51,700 15,000 137,1429 1,423,129 1.012 1.001 (Mitchell & Skinner, 2011)
    Giraffa camelopardalis 1 775,000 1.050 36,300 2,240 38,540 28,400 8,180 738,095 766,495 1.011 1.000 (Mitchell & Skinner, 2011)
    Mesocricetus auratus 23 122.3 1.050 7.2 7.2 2.4 116.5 118.9 1.029 (Koo et al., 1976)
    Rattus norvegicus 15 279 1.050 5.37 265.7 271.1 1.029 (Tajiri et al., 2006)
    Spermophilus lateralis 172 1.050 12.66 12.66 2.81 1.42 163.8 166.6 1.032 1.024 (Milsom & Reid, 1995)
    Reptiles
    Tupinambis nigropunctatus 3 701 1.050 105.3 105.3 30.7 668 698.3 1.004 (Perry & Duncker, 1978)
    Lacerta viridis 6 28 1.050 5.3 5.3 1.3 26.7 28.0 1.001 (Perry & Duncker, 1978)
    Gekko gecko 4 108 1.050 33.2 33.2 7 102.9 109.9 0.983 (Perry & Duncker, 1978)
    Chamaeleo chamaeleon 3 19 1.050 22 22 4.4 18.1 22.5 0.845 (Perry & Duncker, 1978)
    Varanus exanthematicus 3 249 1.050 126.6 126.6 30.3 237 267.4 0.931 (Perry & Duncker, 1978)
    Igauna iguana 652 1.050 125 125 29.3 621 650 1.003 (Perry, 1983; Pinacho et al., 2010)
    Caiman yacare 2 27,900 1.080 3,984 3,984 499 25,833 26,332 1.060 (Reichert et al., 2019)
    Crocodylus niloticus 1 5,680 1.080 558 558 102 5,259 5,361 1.059 (Perry, 1988)
    Trachemys scripta elegans (on land) 8 500 1.140 147 147 11.9 439 450 1.110 Jackson, 1969; Patterson, 1973
    Natrix rhombifera 350 1.100 119.4 3.9 123.3 26.3 318 344 1.016 (Gratz, 1978)
    Hydrophis platurus (resting on surface of water) 1 120.7 1.130 15.65 107 122 0.986 (Graham et al., 1975)
    Hydrophis platurus (diving) 1 120.7 1.130 10.65 107 117 1.028 (Graham et al., 1975)
    Hydrophis platurus (resting bottom) 1 120.7 1.130 8.74 107 116 1.045 (Graham et al., 1975)
    • a Inferred air within pneumatic bones from the preceding two samples of Gallus gallus domesticus.
    • b Body mass from Hart and Roy (1966).
    • c Inferred air within pneumatic bones from the above Columbia livia.
    • d Inferred air within pneumatic bones based on Rhea Americana, which skeletal pneumaticity is twice greater than in Galliformes (Canoville, Schweitzer, & Zanno, 2019).
    • e Lung volumes includes the air volumes of dorsobronchi and ventrobronchi.
    • f VT calculated from Myrianthefs and Baltopoulos (2013); the trachea volume includes the air in nose and bronchi.

    Avian ventilation is different because along with lungs they possess a system of air sacs and diverticula, plus some pneumatic bones that could include some air inside them. At this point two different concepts need to be clarified regarding the air system capacity of birds. The total volume of the lung and air sacs should not be confused with the volume of the air they contain, because the tissues of the lungs and air sacs have their own volume (parabronchi, fluids, blood, epithelium, etc.). However, these two concepts are sometimes mixed up in the literature and can cause confusion. It should be noted that the soft tissues in the lungs of birds can represent a very high percent of the lung volume (Duncker, 1972; Maina, 2000; see below). Although relatively similar in mass, bird lungs have proportionately smaller air space than those of their mammalian counterparts because avian lungs are rigid and can expand only a small amount (Jones, Effmann, & Schmidt-Nielsen, 1985; Lasiewski & Calder Jr, 1971; York et al., 2018). The respiratory system capacities of birds were taken from the literature (see Table 1). A recent study made on high and low altitude geese has shown that the amount of air in their respiratory systems in resting or neutral state (comparable to FRC) with respect to the total respiratory system capacity (TRSC, TLC in mammals and reptiles) varies from 43 to 54% in different species, which is comparable to what is observed in mammals (calculated from York et al., 2018: table 1). The FRC of birds was, therefore, set in 50% of the TRSC, which correspond closely to the upper value found in different geese species (York et al., 2018). To our knowledge, no pneumatic diverticula volumes of birds have been published in the literature, however, their impact in NSG of birds presumably would have been very low, probably below 2% (see below). Also, York et al. (table 1 in 2018) listed the volumes of the different respiratory system components. However, these also include the soft tissues. For this article, in order to get a more precise amount of air of the respiratory system of the geese (Table 1), the following three considerations have been taking into account: (a) since epithelium of the air sacs is extremely thin, a factor of 0.99 was applied to air sacs volumes to obtain the air amount in them; (b) trachea walls are considerably thicker, Clench (1978) found that the outer tracheal diameter of adult Phonygammus is about a quarter greater than lumen diameter, so a factor of 0.8 was applied; (c) lungs on the other hand, are configured by large amounts of soft tissue: parenchyma, the principal lung composition among others, on average constitutes about 45% of the lung volume in birds (Maina, 2000). So, a factor of 0.5 was applied in this case.

    For this article, FRC is considered the amount of air within the respiratory system at resting position, on the other hand TRSC and FRC sometimes includes the air in the bones (Table 1).

    2.4 Procedures in general

    Based on a set of variables, this article utilizes a new methodology to arrive at tetrapod NSGs. This requires to having the following data for each specimen taxon under study: BM, the SG of the body without air, and the FRC, which can be estimated from TLC/TRSC if necessary. If tracheal internal air volume is not available, it does not matter because this dead space corresponds to well below 1% of the total BV in vertebrates (calculated from Table 1), and thus, it has no significant impact in these living organisms NSG. To be as exhaustive as possible, we have reviewed and estimated the SG of different body tissues and the whole bodies of vertebrates, sans air. Then we used these data to estimate NSG in different extant and extinct taxa. The densities of a large number of invertebrates have appeared in previous studies, these were presented along with new data in order to produce the first extensive reference work while giving a broad perspective on this group. Any other considerations specific to given taxa are further explained in their corresponding sections below.

    For practical proposes, neutral BV—the BV of any tetrapod at resting stage—measure was utilized in several particular cases. For example, it is a useful reference for making calculations on the ratio between this volume and TRSC for estimating the last in volumetric models. However, to avoid misinterpretations, when a living animal has its TRSC is fully filled the BV also increases accordingly exceeding BV of a neutral state. So neutral BV is only applicable for calculations purposes. When necessary, areas were calculated using the SketchAndCalc and imageJ software.

    2.5 Tissues SGs

    Because keratin can account for a significant percent of the BM in some animals, it is important to ascertain its density. The SG of it was found to be around 1.3 in a cow horn and in an echidna quill tip (Mason, 1963), 1.28–1.4 in human hair (Leider & Buncke, 1954) and a mean value of 1.26 was obtained in the anterior horn tips of white rhinoceros (Pienaar & Hall-Martin, 1993). These range values indicate that the mean keratin SG is around 1.33, and this was utilized in the present study.

    In order to calculate the SG of bones and flesh the ICRP (1995) and McIntosh and Anderson (2010) data was followed. Bones can be mainly divided in the next different tissues: compact or cortical bone, trabecular or cancellous bone, red marrow, yellow or fatty marrow, periosteum, cartilage, and blood vessels (ICRP, 1995). Cartilage, periosteum, and blood vessels were excluded from below Diplodocus analysis because first, cartilage and periosteum are not preserved in fossil skeletons—and thus are not necessary to calculate the SG of different skeletal parts restored herein—and blood vessels mass, including periosteum, are residual compared to the skeleton mass, (e.g., <2% in the human skeleton e.g., [ICRP, 1995]). Compact bone, trabecular bone, red marrow and yellow marrow possess different SGs. The compact bone SG has been measured up to 2.1 (Brassey et al., 2015; McIntosh & Anderson, 2010; Mallon et al., 2018; McGowan, 1991). However, in living animals the bones are hydrated so that the average SG of compact bone does not reach the maximal value of 2.1. In general the compact bone SG can be averaged to 1.9 (ICRP, 1995), and therefore, this value was used herein. The SG of red marrow is 1.03 and that of trabecular bone (which contains soft tissue, namely bone marrow) is about 1.21 (McIntosh & Anderson, 2010). Finally, yellow marrow SG is 0.98 (McIntosh & Anderson, 2010). According to Robinson (1960) the SG of the human whole fresh skeleton is around 1.3, and as reported by ICRP (1995), a healthy male human of 73 kg has on average a skeleton of 10.5 kg, in which 5.5 kg corresponds to the bone, 2.48 kg to yellow marrow, 1.17 kg to red marrow, 1.1 kg to cartilage (SG 1.1: McIntosh & Anderson, 2010), and a residual 0.25 kg to miscellaneous components (teeth, periosteum, and blood vessels). Applying the here defined SG values for different components and excluding residual miscellaneous, an average SG of 1.356 (1.395 excluding cartilage) is obtained for the human skeleton, in accordance with Robinson (1960), which supports the values applied herein. Subtracting the SM (9.15 kg excluding cartilage) from the 73 kg human body, 63.85 kg of flesh is obtained. On the other hand, the FRC of 73 kg man should be very close to 3.15 l (Table 1). So, if the flesh alone SG is 1.0, a NSG and SG sans air of 0.992 (0.994 including the cartilage to the skeleton) and 1.045 respectively, are obtained, virtually the same as what is expected (Table 1). This strongly indicates that the SG of the remaining soft tissues sans skeleton in tetrapods, which usually share the same SG without air in their bodies, is very close to 1.0 or 1.01. Despite most of the soft tissues like muscles, blood, tendons, etc. are somewhat above this, the body fats are around 0.9, explaining the relatively low SG of the flesh. Therefore, when necessary, the applied SG for flesh was 1.0.

    2.6 Whole body SGs without air in vertebrates

    The SG without air in the body of extant vertebrates (reptiles, amphibians, fishes, mammals, and many birds), is usually very close to 1.05, although there are a few exceptions (Cott, 1961; Crompton et al., 1996; Davison, 2011; Hamershock et al., 1993; Kodama, 1971; Parker et al., 2006; Pearson et al., 1968; Shafer et al., 2010; Taylor, 1922; Tserveni & Yannakopoulos, 1988; Wilson et al., 1992) that are usually small. The SG without air for reptiles' and mammals' whole bodies is therefore set to 1.05 except for some occasional exceptions (see below; Table 1). For example, Cott (1961) measured an average SG of 1.08 for the Nile crocodile (Crocodylus niloticus) based on nine dead individuals, their lungs were presumably deflated or fluid filled to a least some degree. This relatively high SG is due to the combination of semi-aquatic condition of this clade, which implies particularly dense bones (see Houssaye, Sander, & Klein, 2016), and the extensive dorsal osteoderms of these animals. An SG of 1.08 was, therefore, applied to crocodilian whole bodies without air in the present study (Table 1). Snakes, particularly aquatic and semiaquatic ones, appear to be even denser without air in their lungs. According to Graham, Gee, and Robison (1975), the yellow-bellied sea snake (Hydrophis platurus) is able to dive with their lungs filled to 88.2 ml/kg. In order to do so, during diving should be at least as dense it surrounding seawater (SG = 1.025). Also, Graham et al. (1975) found that they are able to rest on the bottom with lung volume of 7.24 ml/kg, so at this estate, their SG should be somewhat higher than saltwater, probably about 1.05. Both data, therefore, indicate that the SG of H. platurus without air in the lungs is very close to 1.13 (Table 1). The diamondback water snake (Nerodia rhombifer) has probably less dense body composition due to the lower density of the water of its habitat, and therefore, the SG without air in lungs for this species was set to 1.1. The SG without air in healthy (nonobese or overweight) humans has been estimated from 1.038 to 1.097 (Behnke, Feen, & Welham, 1942; Shafer et al., 2010). However, the upper limits appear not to corresponds to what is observable during resting humans in freshwater, and thus, should be considered exceptional. The FRC in humans correspond to about 4–4.5% of the total BM/BV (Withers et al., 1988; Table 2) and VT corresponds to about 6–7 ml/kg (Myrianthefs & Baltopoulos, 2013) or 0.6–0.7% of the BM/BV. Larramendi (2016) noted that the majority of healthy people barely float on freshwater, but once the VT is exhaled, or a just very little more, bodies tend to sink. This is only possible if most human SG without air is at most 1.05, a value in accordance with the average SG (1.049) found by Shafer et al. (2010) for healthy adult men and women. Very similar results have been also found in different domestic mammals (Pearson et al., 1968 and references therein). However, it should be noted that body segments possess different SGs, the head and upper extremities SG is close to 1.1, while lower extremities can be slightly less dense mainly because the low ratio between femur mass and thigh volume and fat in the thigh, and yet less dense is the thorax, that including the abdomen the whole trunk SG is about 1.03 (Crompton et al., 1996; Dempster, 1955; Erdmann, 1997).

    TABLE 2. Different respiratory system capacities relative to body volume and body masses in extant vertebrates
    Species N BM (g) TRSC (ml) FRC (ml) BV without air (ml) TRSC to BV (max) TRSC to neutral BV FRC to BV (resting) TRSC to BM FRC to BM
    Birds
    Gallus gallus domesticus 10 3,756 502 254.5 3,382 12.9% 13.8% 7.0% 13.4% 6.8%
    Gallus gallus domesticus 10 2,905 298 151 2,616 10.2% 10.8% 5.5% 10.3% 5.2%
    Gallus gallus domesticus 1 1,944 209 106.0 1,760 10.7% 11.3% 5.7% 10.8% 5.5%
    Columbia livia 382 80 43 359 18.2% 19.9% 10.7% 20.9% 11.3%
    Columbia livia 1 328 54.5 29.8 308 15.0% 16.1% 8.8% 16.6% 9.1%
    Struthio camelus 1 88,000 13,195 6,695 85,360 13.4% 14.3% 7.3% 15.0% 7.6%
    Passer domesticus 16 27.33 6.72 3.44 24.47 21.5% 24.1% 12.3% 24.6% 12.6%
    Melopsittacus undulatus 12 39.8 6.38 3.325 37.41 14.6% 15.7% 8.2% 16.0% 8.4%
    Colibri coruscans 13 7.3 1.99 1.06 6.86 22.5% 25.1% 13.4% 27.3% 14.5%
    Amazona and Psittacus 8 453 81.06 41.13 425.82 16.0% 17.4% 8.8% 17.9% 9.1%
    Anser indicus 2 2,620 764.8 408 2,462.80 23.7% 26.6% 14.2% 29.2% 15.6%
    Chloephaga melanoptera 2 2,400 796.3 430 2,256.00 26.1% 29.6% 16.0% 33.2% 17.9%
    Branta leucopsis 2 2,120 527.9 227 1,992.80 20.9% 23.8% 10.2% 24.9% 10.7%
    Mammals
    Homo sapiens 162 77,300 6,783 3,327 73,619 8.4% 8.8% 4.3% 8.8% 4.3%
    Macaca radiata 22 5,870 468 310 5,590 7.7% 7.9% 5.3% 8.0% 5.3%
    Macaca mullata 12 7,770 673 333 7,400 8.3% 8.7% 4.3% 8.7% 4.3%
    Canis lupus familiaris 6 18,600 997 17,714 5.3%
    Bos taurus 7 517,000 20,370 492,381 4.0%
    Equus ferus 6 402,000 20,623 382,857 5.1%
    Giraffa camelopardalis 1 1,440,000 73,500 51,700 1,371,429 5.1% 5.2% 3.6% 5.1% 3.6%
    Giraffa camelopardalis 1 775,000 38,540 28,400 738,095 5.0% 5.0% 3.7% 5.0% 3.7%
    Mesocricetus auratus 23 122.3 7.2 2.4 116.5 5.8% 6.1% 2.0% 5.9% 2.0%
    Rattus norvegicus 15 279 5.37 265.7 2.0%
    Spermophilus lateralis 172 12.66 2.81 163.8 7.2% 7.6% 1.7% 7.4% 1.6%
    Reptiles
    Tupinambis nigropunctatus 3 701 105.3 30.7 668 13.6% 15.1% 4.4% 15.0% 4.4%
    Lacerta viridis 6 28 5.3 1.3 26.7 16.6% 18.9% 4.6% 18.9% 4.6%
    Gekko gecko 4 108 33.2 7 102.9 24.4% 30.2% 6.4% 30.7% 6.5%
    Chamaeleo chamaeleon 3 19 22 4.4 18.1 54.9% 97.8% 19.6% 115.8% 23.2%
    Varanus exanthematicus 3 249 126.6 30.3 237 34.8% 47.4% 11.3% 50.8% 12.2%
    Igauna iguana 652 125 29.3 621 16.8% 19.2% 4.5% 19.2% 4.5%
    Caiman yacare 2 27,900 3,984 499 25,833 13.4% 15.1% 1.9% 14.3% 1.8%
    Crocodylus niloticus 1 5,680 558 102 5,259 9.6% 10.4% 1.9% 9.8% 1.8%
    Trachemys scripta elegans(on land) 8 500 147 11.9 439 25.1% 32.6% 2.6% 29.4% 2.4%
    Natrix rhombifera 350 123.3 26.3 318 27.9% 35.8% 7.6% 35.2% 7.5%
    Hydrophis platurus (resting on surface of water) 1 120.7 15.65 107 12.8%
    Hydrophis platurus (diving) 1 120.7 10.65 107 9.1%
    Hydrophis platurus (resting bottom) 1 120.7 8.74 107 7.6%

    On the other hand, birds' SGs without air in their bodies appear to be very variable (Hamershock et al., 1993; Wilson et al., 1992). Since most of the body soft tissues and bones SGs' are over 1.0, it would be expected that birds without internal air should be somewhat denser than freshwater. This is true for house sparrow (Passer domesticus) (SG = 1.05), domestic chicken (Gallus gallus) (SG = 1.044), and quail (Coturnix japonica) (SG >1.053) (Tserveni & Yannakopoulos, 1988; table 3 in Hamershock et al., 1993). SGs in the region of 1.05 have been also found in broiler and Bronze turkey eviscerated carcasses (Becker, Spencer, Mirosh, & Verstrate, 1981; Essary, Dawson, Wisman, & Holmes, 1965; Moran Jr, Summers, & Orr, 1968; Moreng, Whittet, & Enos, 1963). Wilson et al. (1992) observed that the SG without air in ducks (Anatidae and Alcidae), divers (Gaviidae), penguins (Spheniscidae), and cormorants (Phalacrocoracidae) are generally very close to 1.0 or higher. Nevertheless, other clades, especially gulls (Laridae), usually present a SG without air in their bodies significantly below 1.0, with some extreme lowering the SG below 0.9 (Wilson et al., 1992; Hamershock et al., 1993). This figure is even lower than the SG of fat, the less dense body component. The real reasons for such low SGs are difficult to ascertain. Probably some birds of the Wilson et al. (1992) and Hamershock et al. (1993) experiments had some trapped air in the bones and diverticula, however, the air in the bones appear to correspond a very little per cent to BV, usually below 1% (Table 1) and the air in the diverticula is also similar (see below). Another possibility is that some air amount was trapped in the viscera. Although it is more likely that some amount of air was probably trapped in their air sacs because the respiratory system of these species is very large; CT scans generally show air spaces in the cadavers when fairly intact (Allen et al., 2009; Schachner, Cieri, Butler, & Farmer, 2013). For this work, the SG without air in the bodies of birds was set to a conservative 1.0 except for the species these data were already available. On the other hand, in order to be as accurate as possible when measuring the NSG of avian dinosaurs, the feather shell was excluded from the calculations (see below). The plumage in birds usually accounts from 3 to 6% of the BM (Wecke, Khan, Sünder, & Liebert, 2017). Six percent, therefore, was subtracted to obtain the BM of the plucked birds. Three percent was applied to the ostrich due to its less feathered nature (Table 1).

    2.7 Procedure for extinct taxa

    Among the extinct exotic organisms needing the most SG analysis are dinosaurs, which in turn depend upon reexamining the SG's of living amniote tetrapods, which can then be applied to most dinosaurs via use of comparative anatomy, sometimes with minor adjustments. The gigantic sauropods pose a special problem because of their atypical body configuration combined with air-sacs. Wedel (2005) is the only exhaustive work on estimating their density, focusing on the well documented Diplodocus. Although the effort by Wedel (2005) was extensive, some of the methods were crude, including the means of estimating the volumes of vertebrae. Also of note is Bates et al. (2015, 2016) who estimated the SGs of a large number of sauropods, however, several of their assumptions including the applied SGs to body sections and the estimated respiratory system capacities, are questionable. We re-evaluate the SG of Diplodocus based in part on accurate digital 3D reconstruction of the whole skeleton. Further, the data derived from avian dinosaurs was utilized to estimate the SGs of nonavian theropods, and nonpneumatic tetrapods to approximate the densities of ornithischians with particular attention on dense forms such us the armored Stegosaurus, the SG of which is calculated from a multiview profile-skeletal (sensu Paul, 2019). Another exotic group the SGs of which have received considerable attention with highly divergent results are pterosaurs. These densities are reassessed via a set of profile-skeletals, combined with a latter of one of the few birds that matches many pterosaurs in having a very large head including beak, a toucan. The detailed explanations on how we reached to the NSGs of different taxa are given in their corresponding sections below (see Section 21).

    2.8 Confidence ranges

    It is emphasized that all the values calculated and estimated herein are approximations, with the significant ± factors inherent to much of biology. The exact range of the plus minus variations is not determinable in regards to mass estimation (Larramendi, 2016; Paul, 1997, 2019), but in regards to NSGs it is not high, being a few percent. For example, almost all land mammals can float, but barely as noted below, so they cannot have SGs of 1.1 or even 1.05, or 0.9 or even 0.95. Then, 0.98–1.01 is most likely, which can be rounded off to 1.0 in most cases. Because it is always important in scientific endeavors to be as accurate as possible, NSG values need to be as realistic as can be achieved, that said, the proportion of the error inherent in estimating BMs resulting from imprecise NSG values is minor, other errors in volumetric modeling being larger (Larramendi, 2016; Paul, 1997). This is all the more true because healthy individual animals can undergo large fluctuations in BM under normal natural conditions (Larramendi, 2016; Paul, 1997, 2019).

    3 RESULTS AND ANALYSIS

    3.1 EXTANT TAXA

    3.1.1 Plants

    Because wood tissue is itself composed of organic tissues possessing an SG of about 1.5 (Siau, 1984) uncompressed wood cannot exceed or even reach that value. Density variation of wood depends on the air and water content, which affected by many factors including ontogeny (SG increasing with age; Bastin et al., 2015; Cown, 2016). As a result, the SGs of woods are highly variable, ranging from 0.08 for Homalium celebicum which is the lowest density value among organisms, to 1.39 for Caesalpinia sclerocarpa (Zanne et al., 2009), balsa being as low as 0.1, ironwoods reaching 1.35. Typical woods have SGs from 0.3 to 0.95; hardwood angiosperms such as oaks are 0.4–0.93, softwood gymnosperms like pines are around 0.5. The biggest extant conifers, sequoia and redwoods, have a wood density of about 0.4 (see Zanne et al., 2009), while that of the largest living angiosperm, mountain ash (Eucalyptus regnans) is up to 0.55.

    Underground tubers tend to be fairly dense, as per potatoes whose quality is graded in part by their SG that is a little over 1.05 and which increases with size (Kumar et al., 2005). Vegetables are also found to be barely denser than water. Carrots' SG, for example, is 1.04 (Jahanbakhshi, Abbaspour-Gilandeh, & Gundoshmian, 2018). Fruits are variable, and as for potatoes, it has been found that there is a negative correlation between the size and the SG (Ting & Blair, 1965). Most of fruit SGs is around 1.0, being many of them barely buoyant. For example, Valencia oranges SGs vary from 0.92 to 1.01, pineapples from 0.84 to 0.99 (Ting & Blair, 1965), goldenberries from 0.95 to 1.03 (Yıldız et al., 2015), the average SG for African bread fruit is 0.98 (Omobuwajo, Akande, & Sanni, 1999), 0.93 for persimmon fruit (Altuntas, Cangi, & Kaya, 2011), 0.97 for date fruit (Keramat et al., 2008), 0.95 for Golden Delicious and Starking Delicious apples, and 0.89 for Granny Smith variety (Ozturk, Bastaban, Ercisli, & Kalkan, 2010), apples are floaters. However, there are particularly dense fruit. Tomatoes reach a SG of 1.07 (Kaymak, Ozturk, Kalkan, Kara, & Ercisli, 2010) being some varieties barely buoyant (personal observation), kumquat fruit possesses a mean SG of 1.2 (Jaliliantabar, Lorestani, & Gholami, 2013) and Aonla fruit as high as 1.4 (Goyal, Kingsly, Kumar, & Walia, 2007). Selectively adapted to float, coconuts SGs appear to range from ~0.5 to ~0.95 judging from images of floating examples.

    3.1.2 Invertebrates (general)

    SGs of invertebrates are strongly variable and since most of them do not possess lungs, or have lung-like structures known as book lungs, which correspond to a very small percent of total BV, the expected NSGs are high.

    Among the smallest multicellular organisms, nematodes (roundworms), some being microscopic with a length of only 0.1 mm (Margulis & Chapman, 2009), are able to dwell in freshwater, marine, and terrestrial environments. Several studies have been focused on estimating the SGs of adult nematodes (Carta & Carta, 2000 and references therein). Most have found that the SGs of the analyzed nematodes range between 1.05 and 1.1, as is typical of animal soft tissues.

    3.1.3 Invertebrates (aquatic)

    The SG of the shells that make up a large portion of the volume of many thick shelled invertebrates ranges from 2.3 to 3.15 (Mohammad, 2017), because a significant albeit modest portion of the volume of the living animals consists of much less dense soft tissues overall SG must be less. For example, the SG of Green Shelled Mussels (Perna canaliculus) vary from 1.05 to 1.27 (Alçiçek & Balaban, 2014). Rahman and Driscoll (1994) found an SG of about 1.09 and 1.07 on mussel and scallop, respectively. Sponges are rather dense their SGs being between 1.07 and 1.09 (Lowndes, 1938). The generally much denser corals are colonies composed of many individual polyps those secret skeletons from the underside of their skin using calcium carbonate (CaCO3) (see Hughes, 1987). Thus, the upper limit of coral skeleton SG is 2.94 corresponding to their aragonitic skeletons. However, because of the organic matrix included within the coral skeleton, the skeletal micro density is somewhat lower and variable (SG varies from 2.6 to 2.89 [Bramanti et al., 2013; Bucher et al., 1998; Caroselli et al., 2011; Roche, Abel, Johnson, & Perry, 2010]). More importantly, the overall corals' density increases with ontogeny and depth, while the pores in their skeletons reduce the maximum values found in the skeletal micro densities (Bucher et al., 1998; Gladfelter, 1982; Hughes, 1987). Furthermore, there can be a very important variation in porosity within and among branches from individual colonies (Roche et al., 2010). All this makes bulk density (mass divided by the total enclosed volume, including the volume of the enclosed skeletal pores) of corals extremely variable (intra- and interspecific). Taking into account the maximum values found in coral branches (bulk density), the SG of most dense coral is up to 2.6 in Acropora formosa (Oliver et al., 1983), and other species, making these gem quality corals the most dense of known organisms. SG within Acropora (A. palmata and A. cervivornis ) can be as high as 2.41 and 2.48 (Shapiro, 1980; Tunnicliffe, 1983). However, the highly porosus A. horrida has a SG as low as 0.86 (Bucher et al., 1998). For its part, foliaceous corals are in the 1.7–2.4 region (Hughes, 1987), while massive corals are generally about ~1.5, with the exception of Colpophyllia natans with a SG of only 0.84 (Hughes, 1987).

    Bottom dwelling, mobile but nonswimming invertebrates with moderately thick shells such as starfish, sea urchins, should be significantly denser than water, perhaps well over 1.05. Other bottom walking, thinner shelled invertebrates such as certain crabs and lobster can swim for extended periods, but are also able to easily walk on the bottoms, and their SGs are therefore considerably higher than their surrounding water. Blake (1985) found that the NSG of three crab species of different families (Cancridae, Portunidae, and Lithodidae), all from Decapoda clade, was very close to 1.16. On the other hand, Lowndes (1943) found an NSG of 1.28 for a large male crab Cancer pagurus (Cancridae) and 1.19 for a Homarus vulgaris lobster (Nephropidae), similar results were found in larger samples on other works which also includes other large crab species such as Maja squinado (NSG = 1.18) (Lowndes, 1942; Spaargaren, 1979). Based on the sinking factors (1,000 times the ratio of the density of the aquatic animal to that of its surrounding water) of the different aquatic organism presented by Lowndes (1942), the NSG of small and thin-shelled crustaceans within Branchiopoda, Ostracoda, Copepoda, Leptostraca, Amphipoda, and Decapoda (shrimp in this case) clades and excluding in berry specimens, is on average 1.08, being the lightest one Artemia salina with an NSG as low as 1.014 and the most dense Herpetocypris reptans sports an NSG of 1.2.

    A large array of aquatic invertebrates, some with shells, others without, are full time swimmers and floaters, their NSGs are generally quite close to that of the salt water they are immersed in. These include jellyfish, slugs and cephalopods. Rahman and Driscoll (1994) after analyzing a large number of fresh seafood specimens found that the SG of squid body sections varies from 1.05 to 1.07. Very similar results were found for the common octopus. Also, Martins et al. (2010) found that the SG of the African chokka squid (Loligo reynaudii) paralarve ranges from 1.04 to 1.07. Since the SG of jellyfish mesoglea is just 0.001 below to that of seawater, the NSG of most jellyfish is, therefore, approximately equal to 1.025, while others could be somewhat denser (Alexander, 1979). Some, marine invertebrates, such as nautiloids, use internal gas chambers to counter the density of their soft tissues and especially shells (Longridge, Smith, Rawlings, & Klaptocz, 2009; Ward, 1987), and thus, are able to be negatively, neutrally and positively buoyant (Bidder, 1962). Lowndes (1938) found that ragworm (Hediste diversicolor) NSG is 1.07.

    The SG of the static, bottom dwelling sea anemone Anemonia sulcata lacking any hard tissues was measured in 1.04 (Lowndes, 1943).

    3.1.4 Invertebrates (terrestrial and aerial)

    Lacking other bones or internal airspaces, worms slowly sink in water, indicating they SGs are in the area of 1.05–1.1 as per nematodes and Nereis (SG = 1.07 [Lowndes, 1938]). Arthropod exoskeletons or cuticle, is principally composed of chitin and other organic components (Darvas, 1997). Chitin nanofibers SG is approximately 1.6 (Vincent & Wegst, 2004) and thus, the NSG of arthropods has the potential to be high. Images of swimming spiders, scorpions, ants, centipedes, and other insects often show them with considerable freeboard, but this can be misleading. Peripheral “fur” and long legs utilizing surface tension can allow small arthropods to high float. But once they are soundly submerged, nonvolant taxa often do not float and some can easily walk on the bottoms, including those normally covered with oxygen supplying “air bags” all around their bodies. Immersion of a pillbug (Oniscidea) left it suspended in the water neither floating at the surface despite a few tiny air bubbles attached to its legs, and so on, nor sinking to the bottom probably because of the bubbles. The data set strongly indicates that the NSGs of most of these arthropods are probably higher than 1.1, approaching what is observed in marine arthropods.

    Based on direct observation and available images, insects that are highly developed fliers or have modest flight performance via folding wings float. A 15 mm caterpillar beetle (Calosoma) was highly buoyant even after being forced submerged, with an observed NSG of ~0.85, perhaps because of air trapped within the folded wings. A cockroach (Blattella) floated but with a little freeboard indicating an NSG close to 0.95. A 17-year cicada (Magicicada cassini) with minimal air bubbles floated moderately well with a NSG ~0.85–0.9. A stinkbug (Halyomorpha halys) exhibited an NSG of ~0.85. Ladybugs (Coccinella) floated to varying degrees that observed SGs of about 0.5, 0.8, and 0.85, differing amounts of air trapped under folded wings may have been responsible for the variation, and the densest result was of an individual that had flapped its wings just before immersion and is the most reliable value. Turning to more volant taxa a firefly (Photinus) barely floated indicating an NSG of about 0.98. A small housefly (Musca) barely floated with a few extremely small bubbles on its wings, NSG was ~1.0, a large housefly more readily floated indicating an NSG of 0.9–0.95. A bumblebee (Bombus) floated with about 15% of its body above the waterline, but that was partly because of numerous ting air bubbles trapped by its fuzz, so the NSG was probably around 0.95. The general lightness is probably due to the combination of the insect's thin shelled exoskeletons and an extensive system of air filled trachea. This probably applies to the best insect aerialists, dragonflies, but actual observational data is lacking.

    3.1.5 Fish

    To efficiently live underwater, fish that spend much of their time swimming must have a NSG very close to or scarcely higher than the surrounding water they normally dwell in, as per the variation depending on its salt content. From an energetics point of view, being considerably denser than water can be problematic for such fish, so close neutral buoyancy should be optimal for them. Since most of the body composition of fish is denser than water (Baldrige Jr, 1970; Davison, 2011; Goolish, 1992; Stewart & Hughes, 2014; Taylor, 1922) and in the absence of conventional lungs (except some clades see below), the majority of teleosts possess a hydrostatic organ known as swim bladder—which contrary to previous thinking, recent phylogenetic analysis indicates is itself a modified lung (Longo, Riccio, & McCune, 2013)—which allow fish to regulate their buoyancy by secreting gas into it. The swim bladder usually corresponds to about 3–5% of the total BVof fish (Davenport, 1999; Stewart & Hughes, 2014) and this is in accordance with the SG (1.04–1.08) found in most of them without gas in their swim bladders (Davison, 2011; Parker et al., 2006; Taylor, 1922). In this sense, it has been found that the NSGs of marine pinksnapper (Pagrus auratus), mulloway (Argyrosomus japonicus), and cod (Gadus morhua) are 1.026, 1.038, and 1.033 or very close to the density of seawater (Davenport, 1999; Stewart & Hughes, 2014). Freshwater species NSG should be below marine ones due to the lower density of freshwater. Thus, as expected, the NSG found for Eurasian ruffe (Gymnocephalus cernua) for example, is 1.018 (Davenport, 1999). Several freshwater fish, Polypteriformes, and lungfish, possess lungs instead swim bladders, and they are also used for buoyancy control (Perry, Wilson, Straus, Harris, & Remmers, 2001). In this type of fish, as happens in the rest of freshwater examples; the NSG is expected to be very close to 1.0 for neutral buoyancy.

    On the other hand, the cartilaginous fish (Chondrichthyes), having neither lungs nor swim bladders for buoyancy control, instead using low density oily livers work as their primary hydrostatic organ (Baldrige Jr, 1970). However, in sharks for example, their livers are not light enough for achieving neutral buoyancy in most cases. The NSGs of these cartilaginous fish are, therefore, barely higher than seawater's (Lingham-Soliar, 2005; Lowndes, 1943; Nakamura, Meyer, & Sato, 2015). Nevertheless, recently, contrary to the previous understandings, it has been found that some deep-sea sharks are positively buoyant in their natural habitats (Nakamura et al., 2015). To determine the NSG of these sharks shall be very difficult until more data is collected.

    It is logical that some demersal fish that spend the great majority of their time on the bottom, and even buried in sediments (e.g., stingrays, flatheads, cottids, flatfishes, several sharks, and stargazers), have NSGs distinctly, but not greatly, above that of water. For example, based on sinking factors, it was found that the NSG of catshark (Scyllium catulus [=Scyliorhinus stellaris]) is 1.08, the same as for sculpin (Cottus bubalis [=Taurulus bubalis]) and 1.06 was observed for European plaice (Pleuronectes platessa; Lowndes, 1942).

    3.1.6 Amphibians

    There appears to be little data on extant amphibians. Strongly aquatic salamanders, frogs, and tadpoles are able to walk or lay on bottoms and presumably have NSGs somewhat above 1.0, and this was probably true of the large array of highly aquatic amphibians of the Paleozoic and Mesozoic. Images of surface swimming terrestrial salamanders are too scarce to assess. Swimming shoreline frogs and toads are awash suggesting NSGs of about 1.0. However, they are able to show appreciably buoyancy, as well as resting fully submerged underwater. This indicates that like reptiles (see below), they can widely regulate their FRCs.

    3.1.7 Reptiles

    Reptiles have high lung volumes (Paul, 2002; Tables 1 and 2). However, it is usually claimed that the total respiratory system capacity of them is about 8–10% of the BV, which is comparable to mammals (Alexander, 1989; Henderson, 2018; Mallon et al., 2018). In fact, the lung volumes in reptiles are extremely variable (Perry, 1983; Table 2). In golden tegu (Tupinambis nigropunctatus) the TLC corresponds to 13.6% of the total BV, while in tokay gecko (Gekko gecko) is nearly twice this (Table 2). Chameleons possess an incredible lung capacity which can be up to 55% of their total BV (Table 2). Snakes also have relatively huge lungs (Perry, 1983; Table 2). Crocodilians have large lungs though generally smaller than lizards. The TLC of yacare caiman (Caiman yacare) is 13.4% of the BV whereas in Nile crocodile is only about 10% (Table 2). However, it was found that there is a negative correlation between lung capacity and BM in crocodiles and other reptiles (Klein, Abe, & Perry, 2003; Perry, 1988; Tenney & Tenney, 1970; Wright & Kirshner, 1987). According to Wright and Kirshner (1987) the lung volume in submerged Crocodylus porosus decreases with mass with an exponent of 0.906. So, large crocodiles may have a TLC to BV comparable to most mammals (<8%). Despite the large lung capacity of reptiles, their FRC to BV is relatively small allowing them to have NSGs close to freshwater (Table 1). However, in early and not replicated since attempts to determine amniote tetrapod SGs via direct measurement of animals, Colbert (1962) obtained a SG of 0.9 for a juvenile alligator and 0.8 for a Gila monster. These values are problematic for a number of reasons. It appears that the subjects measured by Colbert were living when measured, but this is not certain. Nor were the means and method for measuring their volumes described, so the accuracy of the procedure is not knowable. The degree of lung inflation during the procedure in Colbert (1962) is not known, and how fluctuations in such were accounted for if the animals were breathing were not detailed. Via CT-scanning, Allen et al. (2009) estimated the SGs of a juvenile and an adult Crocodylus johnstoni cadaver, obtaining SGs of 0.860 and 0.948, respectively. These are very low results; the scans of the crocodiles showed air spaces, although these were not specifically inflated apparently (Hutchinson, personal communication).

    Crocodilians are heavily armored and their skeletons robustly built; although the juvenile nature of the alligators in Colbert (1962) and Allen et al. (2009) may have reduced its SG a little, probably due to less bone mass and density, and proportionally larger lungs (Perry, 1988; Wright & Kirshner, 1987). Images of surface swimming crocodilians, juveniles included, and most of lizards do not show 10–20% of their bodies above the waterline, it is more like a few percent (Alexander, 1985). Able to rest on the bottoms of water bodies, crocodilians can readily control their SG via variable lung in/deflation via a specialized liver pump system featuring a mobile pubis to sink and rise in water (Paul, 2002; Uriona & Farmer, 2008). Ergo crocodilian NSGs are in the 1.0 region, being denser on land (see below). So, the SGs from Colbert (1962) and Allen et al. (2009)—specially the result for juvenile specimens—do not correspond to what is observed in living individuals.

    The calculated results (Table 1) indicate that reptile NSGs are often very close to 1.0. However, there are notable exceptions. Crocodiles are among the densest of extant reptiles with a NSG of about 1.06 (Table 1). In diving saltwater crocodiles (C. porosus), Kirshner (1985) found that they possess an average SG of 1.028, which corresponds to the SG of their surrounding water. Lung volumes appear to be filled nearly to the half of their capacity during voluntary dives in small crocodiles (Uriona, Lyon, & Farmer, 2019; Wright & Kirshner, 1987), which is much more than when they are resting outside water. Filling the lungs to the 50% of their capacity in C. niloticus, a SG of 1.026 is obtained, confirming the accurateness of the method here proposed. The very high FRC to BV of common chameleon (Chamaeleo chamaeleon) (20%, compared to 5% typically observed in mammals [Table 2]) leaves its NSG as low as 0.845 (Table 1). Their remarkably high buoyancy observed in swimming chameleon videos corroborates this low value, their freeboards sometimes being so extreme and metacentric height therefore so low (also because of their narrow bodies) that they are at risk of rolling over and sometimes do so, indicating that they can greatly control their FRC. The enormous lungs of chameleons allow them to expand their BV up to 80% relative to a resting state on land. At maximum inhalation, therefore, their SG decreases below 0.5 (calculated from Tables 1 and 2). Savannah monitor (Varanus exanthematicus) are as well, particularly light with a NSG of 0.931, a result that is supported by filmed swimming specimens where a significant body part is over the water level. On the other hand, semi-aquatic monitors like Mertens' water monitor (Varanus mertensi) among others, are much denser; being able to rest and walk on the bottom of water bodies, their NSGs are probably in the 1.05 area.

    Images of other surface swimming lizards, including the marine iguana, show them from nearly awash to with significant body freeboard. This indicates their NSGs are near 1.0, with the ability to take in enough air to increase buoyancy as needed. Whether or not extensive lung capacity was responsible for Gila monsters adopting the low density apparently observed by Colbert (1962) is not known. Data on snake densities appears to be scarce. Images of swimming snakes continental and marine are interesting in that while some of both types are awash with just the head above water, others of both types show considerable free board, but also possess the capacity to rest fully submerged underwater (Table 1). This pattern indicates that snake NSGs are again close to 1.0 (Table 1), but that they are able to inflate themselves with enough air in their long lungs to high float thanks to their very large respiratory system (Graham et al., 1975; Perry, 1983). Because of their extensive belly scutes and bony shells, 25% of BM consists of bone in turtles on average, with some species reaching up to 40% (Iverson, 1984), compared to the ~15% average for mammals (see below). Moreover, the shells can account 30–35% of the BM in turtles according to (Jackson, 1969, 2000; Miller & Birchard, 2005; Zani & Claussen, 1994) and the SG of the shells has been found to be around 1.44 (Jackson, 1969), so tortoises/turtles are expected to be particularly dense. Jackson (1969) found that the SG of the Red-eared slider (Trachemys scripta elegans) without air is 1.14. On the other hand, turtles have generally very large lungs for buoyancy control, allowing them to regulate their FRC as required with practically no effort (Hochscheid et al., 2007; Jackson, 1969, 1971; Patterson, 1973; Zani & Claussen, 1994), so their SG is highly variable depending the situation (swimming, diving, resting on the bottoms or resting on land). The maximum lung capacities of semiaquatic species vary from 5 to more than 30% of the BM (Jackson, 1971; Patterson, 1973; Perry, 1978), implying up to a third of the total BV. In marine species the TLC is somewhat smaller being less than 20% of the BM (Lutcavage & Lutz, 1997; Minamikawa et al., 2000; Tenney et al., 1974). On yet another hand, terrestrial tortoises possess much larger lungs because the high domed shells grant more space to them. This makes the TLC usually about 50% of the BM, with some species reaching up to a 72% (Patterson, 1973) or about 10 times that commonly found in mammals. Agassiz (1857) estimated even higher TLC volumes, for example, he found a TLC of 93% to BM in one box turtle (Terrapene carolina), however, the technique, and the technology of the mid-nineteenth century compel us to treat his results with caution.

    Jackson (1969) found that the FRC in the red-eared slider (T. scripta elegans) varied from 2.6 to 16.9 % of its BV. The lowest value can be assumed as the potentially most relaxed state for the turtle, indicating a NSG of 1.11 (Table 1). The shell mass in red-eared slider corresponds to about 30% of its BM (Jackson, 1969), contributing to most armored freshwater turtles having NSGs up to 1.13. These NSGs are probably achieved when resting on land. However, in a relaxed position underwater, freshwater turtles are found to possess a SG usually from 1.01 to 1.04 (Jackson, 1971, 2011; Peterson & Gomez, 2008), but they are also able to be positive buoyant if they fill their lungs to about 14 ml/100 ml (Jackson, 1969), permitting them to more easily swim. The highest NSGs calculated here are in accordance with the highest mean values found by Zug (1971), however, some of his estimates appear to be problematic. For example, he found a SG as high as 1.4 for one loggerhead musk turtle (Sternotherus minor). This is hardly possible because the SG of turtle's shells alone is roughly the same. The other highest NSGs reported by Zug (1971) are in the 1.2 area, which appears to be extremely high but possible. On the other hand, terrestrial box turtles (T. carolina) have the highest TLC reported in any Testudines (Patterson, 1973), and are correspondingly able to surface swim with high freeboards that indicate a floating density as low as 0.73 (Williams & Han, 1964; Zug, 1971), yet able to increase their SG up to 0.96 (Zug, 1971) if not more according to internet footages. Other giant terrestrial tortoises are very good swimmers as well. Gaymer (1968) and Van Denburgh (1914) noted that Aldabra (Aldabrachelys gigantea) and Galápagos (Chelonoidis nigra) giant tortoises float. Those, along with leopard tortoise (Stigmochelys pardalis) are confirmed to swim with high freeboards in video recordings, probably with a SG in 0.9 area. However, this does not mean that tortoises resting on land are this light, fully relaxed on land at midbreath they should be significantly denser, albeit probably a bit less than semiaquatic species. Finally, marine turtles use the air of their lungs to achieve neutral buoyancy (Milsom, 1975; Minamikawa et al., 2000), and therefore, their NSG in their environment is close to 1.025.

    3.1.8 Mammals

    Estimating the NSGs of continental mammals is generally easier than it is for some other animal groups like birds because mammalian postcranial skeletons are not pneumatized, and there appears to be little variation of the NSGs among different nonaquatic mammalian clades regardless of the huge differences in body size (see Alexander, 1985; Larramendi, 2016; Table 1).

    The estimated NSGs for mammals varying in BM from 0.122 to 1,440 kg, are listed in Table 1. The results indicate that most of the land mammals' NSGs are consistently very close to 1.0. However, several SG results obtained from carcasses of large mammals are significantly less than this (Buchner et al., 1997; Garrett, 1967). For example, Buchner et al. (1997: table 1) found a mean SG of 0.89 on six horses, and Henderson and Naish (2010) assigned a SG of only 0.93 to their horse model. However, if one observes riderless swimming horses, only the head which correspond to just 5% of the BV (Buchner et al., 1997), plus a small part of the neck, corresponding to a very little percent of the BV, will be seen above the water, even though by swimming the body is propelled toward the surface. This is comparable to what is observed in a human while swimming (dog paddle style), that only the head is over the water level, which correspond about the 7–8% of the BV (Clauser, McConville, & Young, 1969; Drillis, Contini, & Bluestein, 1964). In these examples, the mass of the head and neck above water is negating the air space in the lungs. Most humans, authors included, have failed to pass safety floating tests related to organized swimming activities because their NSGs matched or slightly exceeded that of freshwater. Thus, the NSG of horses and humans is very similar at ~1.0. This is supported by the method here proposed where the NSG of the horse is found to be 0.996 (0.984 including VT) and 1.003 (0.996 including VT) in human (Table 1). The very low SG in Buchner et al. (1997) for the horse can be explained because of their sample suffered from infaust prognosis of abdominal colic, containing an excessive gas volume in their tested abdomens (see Buchner et al., 1997). Perusal of a wide variety of images of large land marsupials and placentals including elephants produces similar near total immersion while swimming, and an SG value of 1.0 is applied to most land mammals. This is in accord with Larramendi (2015, 2016) who found that human beings and elephants in relaxed position possess the same overall average density of 0.99 g/cm3 and predicted that most of the extinct proboscideans' NSGs would vary between 0.99 and 1.01 depending on their tusks relative size, demonstrating that plesiomorphic forms possessing very robust skeletons may have had higher NSGs.

    Among the few large mammals with relatively low body densities appear to be domestic suids, because images of swimming pigs show a significant portion of their backs above the waterline. This probably reflects a combination of extensive fat deposits due to selective farm breeding with a skeletal frame that is not as robust as typical of aquatic mammals. This information suggests suid NSGs are in the area of 0.95. However, this data should not be taken as representative since obesity is not observable in nature so this artificial permutation should not be applied to any extinct vertebrates (Paul, 1997, 2019). Swimming nondomestic suids show a more normal pattern of only the head above water, indicating they carry less fat and have a typical land mammal NSG.

    The salt free H2O density equivalent NSG does not apply to all mammals, especially those that are semiaquatic and aquatic because in general they are prone to being denser than water for buoyancy control (Wall, 1983). These animals' appendicular and/or axial skeletons are particularly dense because the SG of their bones is increased by the replacement of cancellous bone with compact bone, by increasing cortical bone thickness at the expense of the medullary cavity, and by increasing the percentage of volume that consists of bone (Coughlin & Fish, 2009; Houssaye et al., 2016 and references therein). As a result of such pachyostosis, animals like hippos walk along the bottom of rivers or lakes (Colbert, 1962; Gregory, 1905), while images unambiguously showing them surface floating or swimming appear to be absent. Hippos are the densest continental mammals possessing an SG probably over 1.1 (Larramendi, 2016). Other nonmarine mammals with aquatic habits and with swimming capacities that bear legs rather than flippers are also denser than water. Tapirs and mouse deer have the ability to walk underwater (Coughlin & Fish, 2009; Larramendi, 2016), and internet videos show that capybaras also possess this density dependent skill. Thus, all these mammals should possess a NSG very close to 1.05.

    Many small monotremes, marsupials and placentals whether terrestrial, such as echnidas, mice, and rabbits, or aquatic sometimes show more freeboard than large land mammals, presumably because their relatively heavy fur coats are trapping air. Sans the fur the NSG of small terrestrial animals is generally close to 1.0. Nevertheless, very small rodents appear to be somewhat denser (NSG = 1.03) than many other mammals due to their very small FRC (Tables 1 and 2). This relatively high density can be seen in the forced swimming test in rats, where once the swimming act is stopped, rats tend to sink in many occasions (see Nishimura, Tsuda, Oguchi, Ida, & Tanaka, 1988). Nonsinking rats in these experiments reflect a lower level of emotional reactions compared to sinking ones (Nishimura et al., 1988), probably allowing them to fill their lungs above FRC thanks to their composure.

    The fur shell as a buoyancy vest is especially well developed in highly aquatic examples in which the fur can be effectively waterproof (Fish, Smelstoys, Baudinette, & Reynolds, 2002). For example, it has been found that the SG of muskrats (Ondatra zibethicus), via a sample of ten individuals, was as low as 0.79. However, when they were measured with water saturated fur their NSGs increased to 0.98–1.04 (Johansen, 1962). The sea otter (Enhydra lutris) probably shows the greatest buoyancy among all mammals. This is first due to their possessing the highest hair density ever measured (up to 1340 hairs/mm2; Fish et al., 2002; Tarasoff, 1972), allowing the retention of larger volumes of air in the pelage, and second, because their lung volume to BV ratio is twice as high as any other marine mammal (Kooyman, 1973; Tarasoff & Kooyman, 1973). In water saturated fur conditions, or without fur, the NSG of the sea otter is expected to be close to 1.0. As for fully aquatic mammals, despite usually possessing very large fat stores in the form of blubber, and considerably greater lung capacity compared to continental examples (Kooyman, 1973), an NSG equals or barely over that of fresh or saltwater is expected for efficient buoyancy control as in fishes. In this sense, it has been found that whales and seals mean SGs are very close to 1.03 (Aoki et al., 2011; Miller et al., 2016; Narazaki et al., 2018; Watanabe et al., 2006).

    A few highly terrestrial land mammals like rhinos are barely denser than water (Larramendi, 2016). For example, when a Javan rhinoceros (Rhinoceros sondaicus) swims only a little part of the head, representing about 1–2% of the BV, rises above the water level (~7% in humans and horses for comparison). This would indicate that its NSG should be close to 1.05. One of the main reasons for the relatively high overall density of rhinos is the relation between SM and BM as their skeletons are particularly sturdily built, and the white rhinoceros (Ceratotherium simum), may be the densest rhinoceros species due to its extremely massive skeleton (see fig. 1 in Chang & Jang, 2004). Bellmann et al. (2005) calculated a SG as high as 1.15 for an embalmed black rhinoceros (Diceros bicornis) specimen which weight was recorded previous to death. However, such high SG—higher even than recorded in the body without air of Trachemys turtle with hypertrophied skeleton—in the living animal would, very probably, make it unable to swim. Not known are how precise the embalming process was, or when the animal was weighed prior to its death, it's mass may have been significantly changed by the events that led to its demise. These uncertainties may explain the questionable result obtained by Bellmann et al. (2005). Pangolins, the only mammals covered with keratin scales covering their skin, are expected to be denser than water. According to Pietersen et al. (table 11.1 in Pietersen et al., 2020) the scales of Temminck's pangolin (Smutsia temminckii) if dried accounts about 25% of the animal's BM. Assuming that the NSG Temminck's pangolin without scales is 1.0 as in the rest of land mammals, and scales SG is that of keratin (1.33), a NSG of 1.033 is therefore obtained for the whole animal. This can be observed in swimming pangolins where only their little head and a very small part of the back can be seen above the water level while they propel their body upward mainly thanks to their large and powerful tails. This indicates again that NSG of pangolins is probably slightly over 1.0 albeit lower than that of armadillos (see below).

    A few species of are expected to have had NSGs close to extant rhinos in the area of 1.05. For example, the nine-banded armadillo (Dasypus novemcinctus) can walk under water (Larramendi, 2016; Taber, 1945) indicating a density higher than fresh H2O. Larramendi (2016) predicted that the NSG of armadillos should be very close to 1.05, while Kalmbach (1943) measured the NSG for a specimen he captured as 1.06. However, armadillos are also able to swim with their backs above water level, are reputed to be able to increase their buoyancy by gulping air into their digestive tracts (McBee & Baker, 1928; Vijayaraghavan, 2009).

    Turning to the mammalian aerialists, images and videos of swimming bats show them almost entirely awash, with little or none of their back above the waterline, and a portion of the head above. This indicates that the NSGs of these membrane winged powered fliers with nonpneumatic albeit slender bones approached that of water, in the area of 1.0 as is typical of most mammals.

    3.1.9 Avian dinosaurs (birds)

    Unlike all nonornithodire animals and many dinosaurs, birds have extensive air-sacs within and outside of their postcranial elements. This major expansion of the volume of the avian respiratory complexes is why birds' SG are prone to being low and somewhat more variable than the tetrapod norm. At the same time, birds are usually covered by dense plumage—some flightless examples being an exception—which can effectively increase their total volume as well as total mass. Most birds, mainly those that fly, possess uropygial glands that secrete waxes the preening birds use to impregnate their plumage (Moyer, Rock, & Clayton, 2003). The resulting water-repellent coating forms the body feathers into an outer shell that further increases buoyancy, to the degree that some waterfowl float high above the water. That is why it's important to exclude the feather shell when calculating the NSG.

    According to King (table 3 in 1966) data, the air in lungs and air sacs of several analyzed birds can occupy about 10–20% of the BM, but those results must be taken with caution. Much of his data correspond to the birds' greatest capacity of the lungs and air sacs, which according to him, those far exceeds any physiological values. Lasiewski and Calder Jr (1971) and Dubach (1981) also listed different avian respiratory variables against BM or BV. Following their data, the air within lungs and air sacs to BV in birds account 12–15% and 15–23%, respectively (Table 2), but again, these data overestimates what would be expected from a normal breathing because their information corresponds to the maximum capacity of the respiratory system. As noted above (see Section 2), in resting birds the air in the respiratory systems correspond to about half of the total air system maximum capacity. When Hazlehurst and Rayner (1992) obtained an average SG of 0.73 with a sample of 25 birds from twelve different unidentified species by artificially inflating the respiratory tracts of carcasses. The resulting respiratory volumes were again correspondingly excessive relative to the state of normal breathing, so that value should be closer to an average of ~0.85. Hamershock et al. (1993) measured the SG of 12 bird species. Their results should be analyzed with great caution for several reasons. First of all, the SGs were measured in dead specimens, so that they are not representative of what would be found in living animals because their air system is primarily empty. In their table 1, there are listed a number of SGs, these should be not taken as reliable because those were measured with the feather shell included, leading to extremely low results. This became obvious when comparing these results with those of their table 3, where the SGs, in some cases, are nearly up to 50% higher than in Table 1 because in the latter, the SGs were measured in plucked birds.

    There is also the issue of inappropriately using the respiratory capacity of flying birds to derive SGs for flightless nonavian theropods. In order to meet the high oxygen demands of energetic powered flight nonbasal volant birds have exceptionally well developed lung and air sac complexes, featuring an oversized sternum that helps ventilate the air spaces in the trunk (Paul, 2002).

    The results of flying birds here listed indicate that their NSGs are considerably higher than previously thought (Table 1). Most of the NSG are in the region of 0.9 in the pigeon (Columba livia), house sparrow (P. domesticus), some geese species, and parrots. Among the lightest are the sparkling violetear (Colibri coruscans) with a NSG of 0.866, bar-headed geese (Anser indicus) with a NSG of 0.858 and the high-altitude Andean geese (Chloephaga melanoptera) with an NSG of 0.840, being 0.830 including VT. The last birds possess the highest TRSC and FRC of the measured specimens. On the other hand, it is the domestic chicken (Gallus gallus domesticus) with a surprisingly high NSG ranging from 0.971 to 0.987; Allen et al. (2009) estimated an SG of up to 0.968 for chickens, although the degree of respiratory tract inflation is not certain in that study. That only the small heads and short sections of the necks of water immersed chickens whose feathers are well soaked are above water level in videos, indicates that chicken NSGs really are very close to 1.0.

    The extraskeletal diverticulum was not taken into account in the present sample, however, recent CT-scans on ostrich show that these diverticula are very small, particularly compared with the living organism BV (see Taylor & Wedel, 2013; Wedel, 2007). Moreover, the below analysis on Diplodocus suggests, that based on surrounding diverticula volume of bones, the impact of the extraskeletal diverticula on the NSG is probably minimal.

    So although it is possible that the total air in the air sacs and lungs together of lightest flying birds may reach over 30% of BV, at resting state the percentage of air is about half that. Another very small percentage of air could be in their pneumatic bones or their extraskeletal diverticulum. In the case of these less dense volant birds their NSG would be around 0.8. However, birds with very large beaks appear to possess even lower NSGs. The biological equivalent of Styrofoam that has a standard density SG of 0.05, 0.1 for stronger versions, extreme avian beaks consist of an extremely pneumatic bone foam with NSGs as low as 0.1 (Seki, Kad, Benson, & Meyers, 2006), and account for a large portion of BV, ~17% in the toucan used in this study, compared to ~0.3% in the small beaked pigeon (Table 11; Figure 1). Assuming that NSG of the body in toucans is comparable to what is found in parrots (see Table 1), a NSG of 0.772 is obtained for Ramphastos (Table 3).

    Details are in the caption following the image
    Multi-view profile-skeletals to same scale. (a) Common pigeon (Columbia); (b) Toucan (Ramphastos)
    TABLE 3. Volumes, masses, and NSG of pigeon (Columba) and toucan (Ramphastos)
    Species Specimen number Beak (ml) Head/trunk/tail (ml) Wings (ml) Legs (ml) BV (ml) BM (g) BM with plumage (g) NSG
    Common pigeon (Columba) Uncatalogued 1 226 38 40 305 275 293 0.903
    Toucan (Ramphastos) USNM 344094 144 558 65 71 838 647 689 0.772
    • Note: The applied NSG to the pigeon is the average found in Table 1.

    The SG situation is significantly different for secondarily flightless birds, especially those that have a long phylogenetic and morphological heritage of nonvolance. Respiratory systems of ratites have a total capacity that is considerably lower than that of most flying birds (Table 2). The TRSC of an adult ostrich (Struthio camelus) is around 14% of the animal's total volume (Schmidt-Nielsen et al., 1969; Table 2). However, this percentage greatly exceeds the physiological volume of the respiratory system in resting breathing, and therefore, should be lowered by about half. On the other hand, the tidal volume represents 10% of the total respiratory system (Schmidt-Nielsen et al., 1969), which is comparable to some terrestrial mammals. Moreover, with the muscular system, solid bones, and most body tissues having a density greater than 1.0 an NSG of over 0.9 is expected for this bird. It is possible that the volume of the kiwi (Apteryx) respiratory tract, which appears to lack large abdominal air sacs posterior to its very short sternum, is even lower (Huxley, 1882; Paul, 2002). The NSG obtained for the ostrich is 0.925 and 0.913 including VT (Table 1), the results would increase to 0.968 if a SG without air in the body of about 1.05 is assumed, as is observed in quail, house sparrow or domestic chicken. If one observes large terrestrial birds like emus and ostriches swimming, it appears that they have a SG approaching 0.95, albeit lower than those of land mammals. When one of these big birds swims, only the head, neck, and a small part of the back are visible, which represent about 10–15% of the BV (Molina-Pérez & Larramendi, 2019), and although the body being propelled toward the surface when swimming must be taken into account, denser swimming land mammals have still less freeboard. Therefore, the NSG here calculated is reasonable.

    Another avian types are divers, including those that are flightless. That these are able to submerge, including in ocean water, might seem to indicate that their NSGs are typically above 1.0. So does a tendency toward reduced skeletal pneumaticity (as per Gutzwiller, Su, & O'Connor, 2013). For example surface swimming anhinga are waterlogged, with only the neck and head above water, so their NSGs are about 1.0. But the situation is more complicated. Surface floating boobies, gannets, pelicans, diving ducks, grebes, loons, auks, and penguins float with considerable freeboard, so their SGs, at least in part because of their feather shells, are below 1.0, in some cases significantly so. This is confirmed by the need of these birds including penguins (Sato et al., 2002) to propel their dives underwater, and their lesser need for active propulsion while returning to the surface. This is true even if the feather shell is collapsed due to water pressure at depth. At this time, it can only be said that the NSGs of diving birds excluding any feather shells, are probably in the area of 0.95.

    3.2 EXTINCT TAXA

    3.2.1 Basal chordates and fish

    All in all, basal chordates and extinct fishes' NSGs are expected to be very close, or just barely more (1.01–1.04), to that of their surrounding waters. During Silurian and Devonian the armored placoderms existed. Their plates indicate that the bodies of these fishes were particularly dense, however, their NSG should not have differed greatly from the neutral buoyancy that is optimal for reducing the energetic cost of horizontal swimming. This probability appears to be supported with the discovery of the placoderm Bothriolepis canadensis which possess air-filled organs that likely were for buoyancy control (Perry et al., 2001).

    3.2.2 Mammals

    Most of extinct species would have shared the same NSG to those of living relatives at 1.0. However, several extinct species of different clades are expected to have had NSGs close to extant rhinos in the area of 1.05. For example, the extremely robust skeletons and/or armor of extinct Xenarthrans (giant sloths, glyptodonts, and armadillos) and many other species within Desmostylia, Hyracoidea, Pholidota, Embrithopoda, Brontotheriidae, Toxodontidae, Dinocerata, and Pantodonta clades, are expected to have possessed a NSG of this category, as their skeletal robustness or aquatic habits indicate. Extinct armored forms may have used the same air gulping tactic as living armadillos to facilitate swimming. Interestingly, the gigantic Hippopotamus antiquus has much more slender ribs than H. amphibius (personal observations), suggesting the former was markedly less dense and may have been able to surface swim.

    3.2.3 Parareptiles

    As in current reptiles, the extinct parareptilians' NSGs are expected to be very similar, in the area of 1.0. However, most of the species within Pareiasauria would have been particularly dense. Apart from being armored animals (Lee, 1997), the skeletons of some genera were most robustly built than any extant reptile or mammal known, these include Anthodon, Arganaceras, Bradysaurus, Bunostegos, Deltavjatia, Embrithosaurus, Nochelesurus, Pareiasaurus, Provelosaurus, Scutosaurus, among others. These animals should have possessed a NSG in the area of 1.1, rendering them unable to surface swim as per hippos.

    3.2.4 Basal synapsids

    Being either similar to extant reptiles, or closely related and anatomically similar to modern mammals, the NSG for the majority of basal synapsids is expected to be analogous, and therefore very close to 1.0. However, the robustly built skeletons of several clades, especially within Therapsida, should have made them denser. As per the extremely massive dinocephalians, among which the skeletons of some families are more robust than most of extant mammals. Such include at least Estemmenosuchidae, Tapinocephalidae, Styracocephalidae, and probably others. The species within these clades generally might have had an NSG comparable to extant rhinos of about 1.05. Even more massive were dicynodonts, some forms possessing the most massive skeletons of any reported synapsid, particularly the large species within Stahleckeriidae. Their NSG probably ranged between 1.05 to more than 1.1, approaching or exceeding that of hippos.

    3.2.5 Basal archosaurs

    Most archosaurs outside Ornithodira are lizard like forms with little or no armor, and they lack solid evidence of the air-sac complexes present in some derived archosaurs (Butler, Barrett, & Gower, 2012; Paul, 2002), in which case their NSGs should have been ~1.0, although it may have been a little less if they had incipient nonbony air-sacs (as suggested by Butler et al., 2012). Heavily armored aetosaur NSGs probably were 1.05–1.1, and they probably had difficulty swimming unless they could gulp air. Presumably phytosaur NSGs should have been similar to the ~1.05 NSG of their aquatic crocodylomorph analogs. What is not known is whether phytosaur buoyancy control was as sophisticated as that of the latter. Terrestrial basal and usually gracile crocodylomorph NSGs too were likely to have been similar to that of water.

    3.2.6 Protodinosaurs and basal dinosaurs

    Basal nondinosaur dinosauromorphs, as well as eoraptors and herrerasaurs, appear to have lacked the skeletal pneumaticity indicative of the presence of air-sacs (Butler et al., 2012; Paul, 2002). In that case their NSGs were probably close to or at 1.0 unless they had the beginnings of a nonbony respiratory complex beyond the lungs, in which case NSGs would have been a few percent lower. That prosauropod basal sauropodomorphs appear to possess modest skeletal pneumaticity (Yates et al., 2012) suggests their NSGs were intermediate to the nonpneumatic tetrapod norm and more pneumatic sauropods (see below) in the area of ~0.97 (compared to the 0.95 used by Paul, 1997, 2016).

    3.2.7 Ornithischian dinosaurs

    Apparently having inherited the air-sac free condition of basal dinosaurs, or lost the structures if they were incipient in the latter, the SG of most ornithischians should have been comparable to extant mammals because of their absence of skeletal pneumaticity, contrary to Paul (1997, 2016) who applied a 0.95 NSG to the group. In general, species lacking armor would possess an NSG very close to 1.0. Ceratopsians are a likely exception because their skeletons are massive (Christiansen & Paul, 2001; Paul, 1997, 2016) along with their horns and frills probably made them denser than water. So, the NSG for this clade should be comparable to that of extant rhinos, if not higher in which case their ability to swim may have been limited. The large skulls, especially those with very large upward projecting frills, of ceratopsids may have rendered them front heavy in a manner that, along with nostrils placed rather low on their deep snouts, could have hindered their swimming on the surface. Because protoceratopsid skeletons were less heavily constructed those dinosaurs probably had more normal NSGs, and their nostrils tend to be high placed (Paul, 2016), so they should have been able to swim without undue trouble.

    Stegosaurs should have been considerably denser than water due to their dorsal midline plates and spikes. These osteoderms would be close in density to compact bones, and therefore, would have helped to increase the overall animals' density.

    In order to estimate the NSG of particularly dense thyreophoran armored dinosaurs, the largely complete skeleton of Stegosaurus stenops USNM 4934 with further data from the identical sized DMSN 2818 were used for a rigorous blueprint style profile-skeletal (Figure 2), that has previously appeared elsewhere (Paul, 1997, 2016)—the basic methods used for restoring profile-skeletals are detailed in Paul (Paul, 1987, 1988a, 1988b, 1997, 2002, 2016, 2019; Paul & Chase, 1989). The distal caudals are scaled in from USNM 4714, the tail spikes are scaled in under the presumption that the one 4934 spike is a posterior element; note that the spikes as restored here are a little larger than in past versions by Paul (1997, 2016). The volume of the fairly simple shaped tail spikes was estimated by Graphic Double Integration (GDI) volumetric method (Hurlburt, 1999; Jerison, 1973; Larramendi, 2016), and the BV of the profile-skeletal without dermal plates, was calculated through plasticine model and water displacement (WD) method as per Paul (Paul, 1988a, 1988b, 1997, 2002, 2016, 2019), because the finer physical details possible with the latter method are likely to produce more accurate results than is dimensionally grosser GDI (Larramendi & Paul, unpublished observations). Dermal plate volumes were estimated based on their areas and thickness.

    Details are in the caption following the image
    Multi-view profile-skeletal of Stegosaurus USNM 4934

    The volume of the full animal without dermal plates and spikes was first measured (Table 5). Considering the high robustness of the postcranial skeleton, the SG of the body without air is expected to have been significantly higher than the typical 1.05 found in extant vertebrates, and probably approaching to that of rhinos. The latter's NSG is about 1.05, indicating that the body sans air SG is 1.1. For this study, a median SG of 1.075, as well as 1.1, were applied to Stegosaurus BV to get its NSG. On the other hand, the relative lung volume of Stegosaurus was probably more comparable to extant mammals than to reptiles due to its probably sharing a metabolic physiology more similar to that of the former (Erickson, 2014; Paul, 2002, 2016; Reid, 1997). According to Harrison, Pingel, and Bülow (2019) the TLC in mammals equals 0.046b × M1.06. Assuming that Stegosaurus USNM 4934 weighed 2,600 kg (see below) 192 L of TLC are obtained, which correspond to the 7.4% of the animal BM, however, if Stahl's (1967) equation is applied, an 8.6% of TLC to BM is obtained. For this analysis, 8% of TLC to BM was assumed. However, the FRC should have been about half of TLC/TRSC as is observed in mammals and birds.

    TABLE 4. Stegosaurus USNM 4934 dermal plates, spikes volumes, and masses
    One side plate area (cm2) Plate volume (ml) Plate mass (g) One side keratin area (cm2) Keratin volume (ml) Keratin mass (g) Full plate volume (ml) Full plate mass (g)
    Plate 1 39 98 185 47 47 63 145 248
    Plate 2 47 118 223 57 57 76 174 299
    Plate 3 105 263 499 127 127 169 390 668
    Plate 4 112 280 532 136 136 180 416 712
    Plate 5 140 350 665 169 169 225 519 890
    Plate 6 375 938 1,781 454 454 603 1,391 2,385
    Plate 7 595 1,488 2,826 720 720 958 2207 3,784
    Plate 8 1,890 4,725 8,978 2,287 2,287 3,042 7,012 12,019
    Plate 9 1,930 4,825 9168 2,335 2,335 3,106 7,160 12,273
    Plate 10 2,595 6,488 12,326 3,140 3,140 4,176 9,627 16,502
    Plate 11 2,616 6,540 12,426 3,165 3,165 4,210 9,705 16,636
    Plate 12 2,945 7,363 13,989 3,563 3,563 4,739 10,926 18,728
    Plate 13 3,283 8,208 15,594 3,972 3,972 5,283 12,180 20,878
    Plate 14 3,845 9,613 18,264 4,652 4,652 6,188 14,265 24,452
    Plate 15 2,760 6,900 13,110 3,340 3,340 4,442 10,240 17,552
    Plate 16 1,215 3,038 5,771 1,470 1,470 1,955 4,508 7,727
    Plate 17 485 1,213 2,304 587 587 781 1,799 3,084
    Total plates 24,977 6,2443 118,641 30,222 30,222 40,195 92,665 158,836
    Spike 1 3,300 6,270 2,537 3,375 5,837 9,645
    Spike 2 3,300 6,270 2,537 3,375 5,837 9,645
    Spike 3 1,235 2,347 950 1,263 2,185 3,609
    Spike 4 1,235 2,347 950 1,263 2,185 3,609
    Total spikes 9,070 17,233 6,974 88,953 160,44 26,508

    As for the dermal plates, the areas of each plate was measured based on (Gilmore, 1914) measurements and here restored skeletal-profile (Figure 2). Afterward, the mean thickness was calculated to estimate the volume of each plate. Those of S. stenops appear to be quite thin (Gilmore, 1914, Plates 12 and 13; Brown, 1932; Brassey et al., 2015), while those of S. ungulatus appear to be markedly thicker in some cases (In Galton, 2010, fig. 3 contra in Lull, 1910b, Figures 3 and 4). Specifically, although S. stenops plates are thick on their bases (>10 cm in some cases [Gilmore, 1914]), they are very thin (<1 cm) at the extremes. Lull (figs. 8 and 9 in Lull, 1910a) illustrated the anterior, middle, and posterior dermal plates in anterior views based of Stegosaurus ungulatus. Scaling the anterior, middle and posterior dermal plates to a height of 24, 76, and 63 cm, corresponding to the approximate heights of USNM 4934 6, 14, and 15 plates, areas of 50, 193, and 160 cm2 are obtained, or average thickness of 2.1, 2.53, and 2.54 cm, respectively. This is in accord with the plate 14 of USNM 4934 illustrated by Gilmore (1914, Plate 13) which at 76 cm in height, 2.4 cm of average thickness is obtained. This plate appears to be somewhat crushed, so the real thickness should have been more. For this work, a conservative average thickness of 2.5 cm was applied to all plates to get their volumes. This gives a total of 62.4 L and nearly 119 kg of mass, which is about half that calculated recently by Maidment, Henderson, and Barrett (2014), but about proportionally twice that calculated by Brassey et al. (2015) for the juvenile NHMUK R36730 specimen. Tail dermal spike volumes were obtained applying GDI to the detailed spikes illustrations in different views of USNM 4714 specimen in Gilmore (1914, Plates 13 and 15). The posterior spike length was scaled to 53.7 cm to match the length of USNM 4934 (Gilmore, 1914), resulting in a length of about 63 cm for the anterior spike. It was assumed that both side spikes were approximately symmetrical giving a total volume of about 9 L and 17 kg of mass. Moreover, the dermal armor was entirely covered by keratin, but to what extent is difficult to ascertain. However, the work on the osteoderms including the keratin sheathes of the nodosaur Borealopelta TMP 2011.033.0001 gives some clues (Brown, 2017). Brown (2017) noted that keratinous coverings are positively allometric respect to the size of the bony core with a slope of 2.3. However, if one groups the osteoderms to by shape (see Brown, 2017:supporting information 2), one would realize that the keratin covering thickness is determined by the morphology rather than by bony core size. For example, in the more rounded cervical osteoderms of Borealopelta (C1CL, C2AL, C2AR, and C2CL) keratin thickness increase range, is from 10 to 15% regardless of bony core size. The same goes for spikier osteoderms in cervical region (C1BL, C1BR, C2BL, C2BR, C3BL, and C3BR) which most of them possess an extra ~20% of keratin covering being the most keratinous osteoderm the smallest of all (C1BL). The most keratinous spike, as would be expected, is the very pointed parascapular spine which the keratinous sheath increases the bone length by 33% (Brown, 2017). Judging the rounded nature of dorsal plates of Stegosaurus, for this contribution, it was conservatively assumed that they were covered by an extra 10% of keratin on the extremes. However, the keratin thickness around the large flat walls of the plates, would probably have been different, being very thin at just a few millimeters in thickness, and quite constant among all plates. So, the keratin thickness on each side of plates was set in 5 mm, and the keratin volume was calculated accordingly (Table 4). On the other hand, it was assumed that the long dermal spikes keratin of Stegosaurus would have increased the length in 33% as in Borealopelta parascapular spine. In this case, the keratin around all of the spike would have been very thick, increasing the bony core size in about similar per cent, or much more, all around it, as appear to be the case of Borealopelta (figs. 10 and 11a in Brown, 2017). In this sense, the volume of the Stegosaurus tail spikes was estimated increasing the body core volume by 33% in all dimensions minus the actual bony core volume (Table 4).

    Details are in the caption following the image
    Comparison between the CM84 Diplodocus skeleton photogrammetric model presented in this study based on Hatcher (1901) plus multiple photographs in different angles, and the same individual skeleton cast at Paris Natural History Museum and genuine skeleton at Carnegie Museum of Pittsburgh. (a) Full CM84 Diplodocus photogrammetric skeleton created for this study in old classical pose. (b) Full CM84 Diplodocus skeleton photogrammetric model based on the cast skeleton mounted at Paris Natural History Museum after Rogez (2017). (c and d) Digital morphological and proportional comparison between Paris Natural History Museum skeleton and 3D model created for this study. (e) Same comparisons as previous with the original CM 84 skeleton at Carnegie Museums of Pittsburgh
    Details are in the caption following the image
    CM84 Diplodocus skeleton photogrammetric model in anatomical position based on Hatcher (1901), multiple photographs in different angles, and after careful comparison with the Paris Natural History Museum cast and genuine skeleton at Carnegie Museums of Pittsburgh

    The present analysis on Stegosaurus USNM 4934 produces a total dermal plates mass of 159 kg with a SG of 1.71 and 26.5 kg and a SG of 1.65 for tail dermal spikes (Tables 4 and 5). The NSG of the animal was found to be 1.057 or 1.080 if the body SG without air was similar to that of extant rhinos, which is equally possible. Similar NSGs would be expected for most of stegosaur species. It is found that keratin amount has no relevant impact Stegosaurus SG. For example, if the keratin bulk of dorsal plates is doubled, the NSG of the animal would be maintained, because, while the keratin increase adds mass, it also adds volume to the dorsal plates which lowers the SG of them. This is because the bony core (which is denser than keratin) volume to full plate volume reduces. So, important changes in keratin amount would have no impact in the Stegosaurus NSG. With their heavy armor set so high, stegosaurs may have been top heavy and prone to capsizing. The rather narrow trunks of some taxa such as Stegosaurus would have added to their low metacentric height and instability, although the broad bellies of most stegosaurs (Paul, 2016) would have aided stability. Combined with their overall high density and low set heads, stegosaurs may have been poor swimmers.

    TABLE 5. Stegosaurus USNM 4934 volumes, masses, and NSG
    BV excluding dermal plates (L) Plates volume (L) Spikes volume (L) Total BV (L) TRSC (L) FRC (L) BM excluding dermal plates (kg) Plates mass (kg) Spikes mass (kg) Total BM (kg) NSG
    2,360 92,7 16 2,469 208 104 2,425 158.8 26.5 2,611 1.057

    Basal armored dinosaurs in the form of scutellosaurs and scelidosaurs should have been denser than normal for unarmored ornithischians, less so than more derived and more heavily plated examples, between 1.0 and 1.05. Being fairly dense and somewhat top heavy should have made swimming a less than ideal activity.

    The extensive armor over much of ankylosaur bodies very probably made them the densest of all dinosaurs, with NSGs possibly higher than today hippos in some especially armored species. Armadillos are probably the closest living analogs to ankylosaurs which the formers have NSG around 1.05. Turtles are, surprisingly, not particularly good ankylosaur analogs because they have extensive belly scutes lacking in the dinosaurs, and because of their lung capacities are remarkably variable. Ankylosaurs' NSGs would vary significantly depending the amount of scutes, nodules, and spines of different forms, probably the lighter ones would have NSGs around 1.05 and the most heavily armored genera such as Saichania, Gargoyleosaurus, or Borealopelta probably had a NSG close to 1.1. Such may have rendered them unable to swim as is true of hippos, unless they could gulp enough air and bloat themselves, as armadillos appear to do, or possessed an unusually large respiratory system and were able to regulate their FRCs extensively. But the narrow, shallow chests characteristic of the group (Brown, 1908; Carpenter, 2004; Paul, 1997, 2016) suggest that lung capacity was not high relative to total volume in these dinosaurs whose vast bellies made up the bulk of body capacity, and if anything internal air space may have been on the low side. And lacking belly armor to counterweight the dorsal plating, ankylosaurs should have been top heavy, albeit perhaps not as much so as stegosaurs in view of the ankylosaurs broad bodies.

    The recent “bloat-and-float” model explanation proposed by Mallon et al. (2018) to explain why so many ankylosaur specimens are found on their backs is problematic. Their results were obtained on the basis that nonbloated Euoplocephalus and Sauropelta had implausibly low SGs of 0.87 and 0.887, respectively. This is highly improbable—especially for their lifeless condition—because such body densities are comparable to alive flying birds, and considerably lower than what is observed in large flightless birds that possess pneumatized skeletons and air sacs (Table 1). The reasons Mallon et al. (2018) underestimated ankylosaur densities include their exclusion of the layer of small scutes all around the back. Their estimated SG of 1.0 excluding lungs for the dinosaurs' bodies is too low because this value includes lungs in nonarmored living animals. Likewise, the SG of 0.9 for the combined head and neck would be too low by ~15% or considerably more. Their assumption that 10% of BV was filled by the lungs can only occur when the vacuities are at maximum inflation, which is especially improbable when the animals are deceased and lung volume would be below the norm, and/or the spaces filled at least partly with water.

    The most plausible reasons for upside down ankylosaurs found in fluvial or marine environments are as follows. In one situation the high density dinosaurs could not swim, and an ankylosaur found itself in a lethal situation either because faulty navigation or swift currents placed it in deep stream waters or out at sea where even rearing hippo style did not allow contact with the surface. That would have caused the top heavy ankylosaur to sink and to flip upside-down, drowning the animal as it sank toward the river or seabed. In another scenario, an intact ankylosaur carcass was swept into a river or out to sea because of a flood, high tide, or wave action. Regardless of its orientation on land and its bloated or nonbloated condition, the body would quickly capsize belly up because of its armored back. The bloating process would be irrelevant in the first situation and slightly significant in the second one for the upside down orientation. However, in case a recent submerged carcass (nonbloated) was not flipped, because the river/sea was not deep enough, the currents were too weak, or other circumstances, the bloating process would always occur with the body sunken, and the flipping would occur underwater and not in the surface as Mallon et al. (2018) proposed, thus, when the carcass floated it would already be upside down. These scenarios may also apply to the dorsally armored glyptodont fossils that are often are reported to occur upside-down (Thrasher, 2000).

    3.2.8 Avian dinosaurs (birds)

    Giant extinct flightless birds, paleognaths, dromornithids, and phorusrhacids, which were somewhat more robustly boned than living ostrich, especially in their limb elements, should have been a little denser, with an NSG of around 0.95.

    The SGs of Mesozoic basal winged avians with limited flight performance, especially those with sterna shorter than the volant ornithurine standard, were likely to be somewhat above the norm of more derived avian fliers, perhaps approaching NSG of about 0.9.

    Because of the complications found in penguins (see above), it is not possible to further pin down the SGs of extinct, exotic diving birds such as hesperornithiforms, and thus, the best guess is to assume a similar NSG to those of living Sphenisciformes of around 0.95.

    3.2.9 Nonavian avepod theropod dinosaurs

    Turning to the nonavian tridactyl footed avepod theropods (sensu Paul, 2002: theropods that either possess a foot in which metatarsal I does not contact the tarsals, or descended from such theropods, and belong to the clade to the clade that includes Neotheropoda), estimating these dinosaurs' densities is complicated because like their close avian relations, they probably had air sacs linked with their pneumatic postcranial skeletons (Henderson, 2018; O'Connor, 2004; O'Connor & Claessens, 2005; Paul, 1988b, 1997, 2002, 2016). But their body form was sufficiently different to complicate matters. Being flightless with few exceptions, lacking large sterna, and having large, airless tails, it is highly improbable that any nonavian theropod had as a large a neutral respiratory space as derived flying birds. Instead, it is terrestrial birds that run but do not fly that are superior density models for such dinosaurs. It follows that a NSG comparable to big ground birds would be expected for nearly all nonavian avepods, or a very little higher in the case of large theropods as their limb-bones, contrary of what is found in extant terrestrial birds, were not comparably pneumatized. As a result, the NSG for large avepod theropods, would be about 0.95, or a bit higher, somewhere between 0.95 and 0.99 in some cases, compared to 0.85 used for derived nonavian avepods in Paul (1988a, 1988b, 1997, 2016). The highly derived nonavian paravian theropods—being the closest to the basal avian fliers yet unable to fly in most cases, the microraptor dromaeosaurs excepted (Paul, 2016)—may have had a less-developed respiratory systems than modern flying birds, so their SGs would have been higher than those of the latter. In this sense, a NSG of ~0.9–0.95 for the most derived and small theropods (<30 kg) would be expected.

    A few extinct theropods appear to have been particularly dense, in particular the supposedly amphibious Spinosaurus (Ibrahim et al., 2014; Ibrahim, Maganuco, et al., 2020; Ibrahim, Sereno, et al., 2020 contra Henderson, 2018). Lines of evidence that appear to indicate an aquatic lifestyle for Spinosaurus, including recently discovered material attributed to S. aegyptiacus, reveals that these dinosaurs sported a transversely flattened tail with exceptionally developed caudal neural spines and chevrons apparently suitable for aquatic locomotion (Ibrahim, Sereno, et al., 2020), long bones which are about 30–40% denser than those of any other known theropod (Ibrahim et al., 2014), very poorly pneumatized or even apneumatic vertebrae (Rauhut, 2003; Ibrahim, Maganuco, et al., 2020; Ibrahim, Sereno, et al., 2020), retracted nares (Ibrahim et al., 2014; Ibrahim, Sereno, et al., 2020), piscivorous adaptations of jaws and teeth (Dal Sasso, Maganuco, Buffetaut, & Mendez, 2005), an elongated body, short hind limbs (Ibrahim et al., 2014; Ibrahim, Maganuco, et al., 2020; Ibrahim, Sereno, et al., 2020)—although that needs to be verified by more complete remains—stable isotopes (Amiot et al., 2011) and apparently too short femur relative to its center of mass for a feasible bipedal locomotion on land (Ibrahim, Sereno, et al., 2020), which is further supported by its remarkably small ilium and hindlimbs proportions relatively to its large BM (Larramendi & Paul, unpublished observations) suggesting a limited terrestrial performance.

    So, it is likely that the NSG of it, and perhaps other spinosaurs, was comparable to that of current crocodilians and other semi-aquatic animals at around 1.05. In the case of Spinosaurus it was probably able to regulate its FRC to achieve neutral buoyancy when diving. A recent study by Henderson (2018) that tested the hypothesis of a semi-aquatic Spinosaurus concluded that it was unsinkable. However, the study, which was based on a skeletal restoration that now appears obsolete, applied a too low SG to soft tissues and body parts, omitted that Spinosaurus vertebrae are largely apneumatic—which may suggest a restricted air-sacs system—and assumed an air-system similar to extant birds (although he tested an alternative model lacking air sacs, he committed the here mentioned errors) with the respiratory system normally fully inflated. Also excluded were possible gastroliths which despite their possibly limited mass (Cott, 1961), could have increased the Spinosaurus NSG while lowering its center of gravity. As a result, Henderson (2018) obtained overly low SGs for all the analyzed animals in his study including a mean SG for Spinosaurus at only 0.833. Finally, the thoracic region of the 3D reconstruction of Henderson (2018) appears to be too transversely narrow, nonavian theropod anterior trunks tended to be somewhat wider and more rounded (Paul, 1997, 2016), especially so in view of the strongly arced rib illustrated by Stromer (1915 Plate 1, fig. 15). That combined with the seemingly shallow pelvis would have resulted in a high and therefore more stable metacentric height. If the Ibrahim, Sereno, et al. (2020) skeletal reconstruction is correct, then the sail backed dinosaur should have had better hydrodynamic stability than indicated by Henderson (2018).

    3.2.10 Sauropod dinosaurs

    The proposition by Gregory (1905) that sauropod SGs were well above 1.0 in order for what were then seen as semi-aquatic dinosaurs to walk on river and lake bottoms as per hippos is not possible, in part because their highly pneumatic vertebrae precluded a density very close to much less above that of water. The pneumatic sauropods would have been incapable of bottom walking water deeper than the tops of their shoulders, and when swimming would have had more freeboard than elephants (Henderson, 2004). Because sauropod legs were solid boned compared the pneumatic skeleton vertebral series, the super dinosaurs would have had a high metacentric height and been correspondingly stable on the roll axis when swimming.

    Other than sauropod NSGs being distinctly below 1.0, restoring their densities is exceptionally complicated, even more so than for nonavian theropods, by a number of factors. On the one hand like birds they had air-sacs (Paul, 1988a, 1997, 2016; Schwarz & Frey, 2008; Schwarz, Frey, & Meyer, 2007; Wedel, 2005). But with sauropod size and body form being unavian, and avepod versus sauropod air-sac complexes probably evolved independently to at least a great degree, bird SGs, even those of the large flightless examples, cannot simply be transferred to sauropods without further analysis. Sauropods may have been more pneumatic in parts of their vertebral series than birds, and their presacrals and sacrals tended to be exceptionally large relative to their bodies compared to avepods including birds, yet were generally not pneumatic in their large tails, the limb elements were not air filled, and nearly all adult sauropods were far larger than even the biggest flightless avians.

    Another complication specific to sauropods is the potential need to apply the SG of their necks separately from the rest of their bodies (Paul, 1988a, 1997, 2016). The size of the neck relative to the rest of the body is not extremely different in most animal groups. But the neck/rest of the BV ratio of sauropods is very highly variable. In the biggest necked sauropods known to date, mamenchisaurs, the organ makes up a fifth of total BV. The necks of shunosaurs, the smallest necked sauropods, are just a twentieth of overall volume, a fourfold differential from mamenchisaurs. At the same time, necks are the most pneumatic portion of sauropod bodies, markedly more so than the trunk, and much more so than the tail and limbs. It follows that if a uniform SG is applied to all sauropods, then those with longer necks will be calculated to be more massive than they were, especially relative to short necked forms. Paul (1988a, 1997, 2016, 2019) provisionally addressed this problem by applying an SG of 0.6 to sauropod necks, and 0.9 to the rest of their bodies. This study tests the value applied to sauropod necks.

    We follow Wedel (2005) in focusing on Diplodocus CM 84, supplemented by USNM 10865, to volumetrically model. We do so because the taxon is more completely known and morphologically documented than most sauropods, and has long been a subject of research including restoring its form, volume and mass. In order to estimate the SG of Diplodocus we first digitally sculptured the complete fleshed dinosaur bone by bone, based on the high-quality images in different views of each vertebrae and postcrania in Hatcher (1901), plus a large amount of photographs in different angles, and with further help from the profile-skeletal published in Paul (1997, 2016). In order to ensure the most accurate representation possible, the 3D sculpted model was carefully compared and fitted it with a full photogrammetric model of the Paris museum CM 84 replica (Rogez, 2017; Figure 3). The results were corroborated with another, but less complete 3D photogrammetric model created by us from the genuine mounted skeleton of Diplodocus CM 84 at Carnegie Museums of Pittsburgh (Figure 3). Additionally, the 3D restoration process, permitted us to correct distorted, crushed and broken bone elements, which helped to generate more reliable results. The full skeletal model was obtained using the 3D sculpting software Zbrush and carefully scaled to the recorded femur length of 1,542 mm. The resulting skeletal dimensions match very closely with the published measurements in Hatcher (1901) and Gilmore (1932). Because fossils have no articular cartilages, the works by Holliday, Ridgely, Sedlmayr, and Witmer (2010) and Taylor (2014) were followed to quantify the cartilage thickness in limb-bones edges and vertebrae articular surfaces, respectively. According to Holliday et al. (2010), a space of 6.5% of the bone lengths, with equal cartilage thicknesses on the proximal and distal ends of appendicular skeleton elements should be added. However, this percentage applies only when the limb joints were not bearing any load, when loaded the cartilage must have been flattened a considerable amount. Apparently no research on the degree of compression has been conducted. So, the space between joints was set to about half of proposed by Holliday et al. (2010). For the dorso-sacral-caudal series an intervertebral cartilage 10% of the functional length of the short centra was added (the half on the condyle and the other half on the cotyle) as per Taylor (2014). Note that, Hatcher (1901) only published the vertebrae centra maximum lengths, not functional lengths where the cotyle depth should be subtracted. Unfortunately, to our knowledge, no study of any sauropod has been published which includes vertebrae functional lengths. However, the depth of the cotyles maybe not significantly more than the 10% of the vertebrae centra maximum lengths and was restored accordingly in the present contribution. Attempting to use the 10% of cartilage value (Taylor, 2014) with the very elongated cervicals produced implausibly long spacing between the centra, and restoring the articulation of sauropod cervical series is inherently problematic for a number of reasons, including distortion of the delicate fossil bones (Paul, 2017; Taylor, 2014). So a best fit approximation of the ball-in-socket articulations and zygapophyses was used (Figure 4). The fleshed-out Diplodocus 3D model is restored in lean-healthy condition, in which the animal is fit but possesses minimal fat deposits (Figures 5 and 6), as is frequently true of terrestrial animals (Paul, 1988a, 1988b, 1997, 2019). Not carrying large amounts of fat may have been a necessity for giant sauropods already hard pressed to carry their great mass of bones, organs, muscles, blood, gut fauna, digesting food, any gastroliths, and other items in 1G.

    Details are in the caption following the image
    Step by step reconstruction process of CM84 Diplodocus. (a) Skeletal reconstruction. (b) Postulate muscle restoration after Paul (1987). (c) Fleshed version showing the internal skeleton. (d) Life restoration
    Details are in the caption following the image
    Comparison between Paul (1997, 2010, and 2019) multi-view profile skeletal (a) and present study multi-view life restoration (b) CM84 Diplodocus

    Because the highly pneumatic vertebrae presumably had a significant impact on the sauropod's SG, the volumes of the cervical, dorsal and caudal series, as well as the complete sauropod reconstruction, were precisely calculated. The volumes were calculated using the software PreForm. The Air Space Proportion (ASP) is the proportion of the volume of a bone occupied by air (Wedel, 2005). After studying the vertebrae of a large number of sauropod taxa, Wedel (2005) applied a mean ASP of 0.60 to Diplodocus whole vertebrae from the cervicals to the caudals. However, if one wishes to estimate the air proportion inside the vertebrae alone, the obtained average values by ASP would not be accurate because this method actually, apart from measuring the internal air proportion (in cotyle and condyle), also measures some part of the diverticula surrounding the midcentrum of the vertebrae (see fig. 7.5 in Wedel, 2005). So, the ASP assumes any airspace that occupies a volume that would otherwise be bone. Thus, intraosseous diverticulum sensu (Wedel, 2005), apart from the diverticula inside the vertebrae, also includes the diverticula surrounding them. Therefore, the extraskeletal diverticula sensu (Wedel, 2005), would include only the diverticula that are not connected with the skeleton (visceral, intermuscular, and subcutaneous diverticula) excluding the surrounding diverticula around vertebrae despite these are not inside the bones. We think it is relevant to realize these clarifications because these concepts were not sufficiently explained, and could cause confusion. It is important to note that estimating the ASP of certain parts of the vertebrae, especially around the different apophysis, can be problematic because it is hard to exactly ascertain how much bone was displaced by the diverticula. In fact, apneumatic vertebrae of tetrapods also show deep concave shapes.

    On the other hand, the average ASP obtained by summing three different points of the vertebral centra (condyle, midcentrum, and cotyle) and dividing the result by 3 (Taylor & Wedel, 2013; Wedel, 2005) is not accurate enough because each of these parts occupies a different percentage to the total centra volume. Moreover, how much air is inside other parts of the vertebrae like spines or cervicals ribs has never been measured, although probably they were similarly pneumatized (Wedel, 2005). For all these factors and uncertainties, provisionally a factor of 0.6 was applied to calculate the air inside the Diplodocus vertebrae, which is the data derived from ASP values of the condyle and cotyle but excluding mid-centra (Taylor & Wedel, 2013; Wedel, 2005), bearing in mind that is not entirely accurate. For this and future studies, we propose the VIASP (vertebral internal air space proportion) concept to quantify the relative air amount is inside the vertebrae solely.

    To better address the special SG problems posed by the exotic sauropods, we conducted the most sophisticated and meticulous restoration of the SG of a sauropod yet attempted. One reason this was necessary is because after analyzing a composite of the relatively complete and very similar sized Diplodocus CM 84 and USNM 10865, Wedel (2005) obtained an overall SG of 0.8 for the taxon. Because this density is comparable to, if not lower than, extant flying birds as detailed above, it appears to be too low. Also, although the effort by Wedel (2005) was extensive, some of the methods were crude, including the means of estimating the volumes of vertebrae. Nor did Wedel (2005) calculate the SG of the neck distinct from the rest of the sauropod, a potentially important absence because of the great variability of the volume of the neck relative to the rest of the body in the group (Bates et al., 2016; Paul, 1988a, 1997, 2019).

    Rather than carefully modeling the cervicals, Wedel (2005) arrived at a broad approximation of gross vertebral volumes by treating the centra as cylinders based on the greatest lengths and heights published by Hatcher (1901) and Gilmore (1932). He then calculated the volume of the spinal processes as follows: for cervicals he assigned the same volume obtained for the centra, for the dorsal and sacral vertebrae, multiplied by 2 the volume obtained in their respective centra, and for caudals assigned half of the estimated volume of the centra. The obtained results were much above probable reality, because sauropod's vertebral centra have strongly pronounced concave shapes, including those that are apneumatic (e.g., the cervicals of the giraffe). The actual volumes of Diplodocus CM 84/USNM 10865 vertebrae are listed in Table 6. The total vertebral column volume from cervical 2 to caudal 19 is 800 L, and around 893 L including intraosseous diverticula at minimum expansion (see below), which gives an overall ASP of 0.64. The resulting total volume is about the half that calculated by Wedel's (2005) method (table 7.3 in Wedel, 2005). The real vertebral column volume could be even lower, because using photogrammetry it is difficult to obtain the precise thickness of the extremely thing walls of the vertebrae, especially of the cervicals. Thus, our results on vertebrae volumes could be slightly high, but should be more realistically close to the true volumes.

    TABLE 6. Diplodocus CM 84/USNM 10865 vertebral and air volumes
    Cervicals Total volume (L) Volume of air (L)
    C2 0.43 0.26
    C3 1.29 0.77
    C4 2.66 1.60
    C5 3.69 2.21
    C6 4.98 2.99
    C7 8.34 5.00
    C8 11.03 6.62
    C9 14.7 8.82
    C10 15 9.00
    C11 19.82 11.89
    C12 26.84 16.10
    C13 31.96 19.18
    C14 35.19 21.11
    C15 34.63 20.78
    Subtotal cervicals 210.56 126.34
    Dorsals
    D1 32.31 19.39
    D2 23.57 14.14
    D3 23.07 13.84
    D4 24.64 14.78
    D5 21.58 12.95
    D6 21.86 13.12
    D7 23.93 14.36
    D8 24.72 14.83
    D9 27.71 16.63
    D10 25.44 15.26
    Subtotal dorsals 248.83 149.30
    Sacrals
    S1–S5 76.09 45.65
    Caudals
    C1 24.86 14.92
    C2 23.78 14.27
    C3 23.22 13.93
    C4 20.18 12.11
    C5 19.78 11.87
    C6 17.5 10.50
    C7 15.17 9.10
    C8 16.08 9.65
    C9 13.56 8.14
    C10 12.33 7.40
    C11 11.57 6.94
    C12 9.96 5.98
    C13 10.24 6.14
    C14 9.23 5.54
    C15 8.15 4.89
    C16 7.75 4.65
    C17 6.88 4.13
    C18 7.04 4.22
    C19 6.74 4.04
    Subtotal caudals 264.02 158.41
    Total vertebral column 799.5 479.70

    It is questionable whether the respiratory system of sauropods was as relatively large as those of birds. Sauropods lacked either the extremely large sterna most birds use to ventilate large abdominal sacs, or the gastralia baskets that theropods may have used for that purpose (O'Connor, 2004; O'Connor & Claessens, 2005; Paul, 2002). Nor were sauropod limb elements pneumatic in the manner of birds. So sauropod air sac complexes were probably less capacious in total than those of birds. Even the enormous size of Diplodocus does not indicate a relatively much larger respiratory systems because the relative lung volumes of mammals, reptiles and birds generally increase with BM near to isometry (Mania et al., 1989; Harrison et al., 2019; Peixoto, Klein, Abe, & Luis Da Cruz, 2018; Stahl, 1967; Wright & Kirshner, 1987). Thus, the combined air sac plus lung volume to BV in Diplodocus is likely to have been lower than any of the analyzed birds in this study, including the least volant species that possess the smallest avian respiratory system volumes (the TLC plus maximum air sacs capacity is ~11–14% of the neutral BV, Table 2). Hence it was assumed the air in lung and air sacs of Diplodocus was 10% of neutral BV excluding the trachea, intraosseus skeletal diverticula and extraskeletal diverticula. Since diverticula tissue is an extremely thin and membraneous, and because it is not possible to exactly restore the sacs' true volumes, the volume of the air inside them was assumed to be their entire volume. Wedel (2005) in his analysis did not take into account that the lungs and the air sacs would not be fully inflated most of the time. With bird and mammal air systems filled to about half of total capacity at mid breath this is assumed to have been true for Diplodocus. And Wedel (2005) assumed that entire animal without air would have an SG of only 1.0. But as pointed above, this is not possible.

    Wedel (2005) calculated the tracheal dead space as 104 L assuming that the Diplodocus BM was 12 t, and by then applying the allometric equation by Hinds and Calder (1971) for birds. Because sauropod body proportions are different from that of birds, such extrapolations are problematic. One hundred and four liters appear to be far from possible taking into account the very small head (comparable in absolute measure to that of an otherwise much smaller horse) and the relatively skinny neck featuring especially small anterior cervicals. These factors would highly reduce and limit the diameter of the larynx and trachea of Diplodocus. To put this in perspective, the estimated internal tracheal volume by Wedel (2005), is comparable to the entire body of a very thick and adult green anaconda (Unectes murinus), the most massive modern snake—a huge specimen procured by the New York Zoological park measured 5.7 m long, had a 91 cm circumference on the thickest part, and weighed 107 kg (Ditmars, 1931). Furthermore, based on the 6.8 m long trachea calculated by Wedel (2005), a cylinder of 14 cm in diameter is required, however, taking into account that in an adult giraffe the outer tracheal diameter is 20% greater than inner diameter (calculated from table 1 in Cano & Pérez, 2009)—about the same observed in the trumpet manucode bird (Clench, 1978)—, including the tracheal walls to the present example, the tracheal outer diameter could have been about 17 cm. This diameter is considerably greater than the average cervicals' centra diameter of Diplodocus CM 84 (calculated from Hatcher, 1901), and increases the whole tracheal volume to about 155 L of air plus tube tissues. These figures therefore appear to be excessive for Diplodocus. Long necked giraffes offer a more reliable means for estimating tracheal dead space volume in sauropods. It has been observed that giraffe internal tracheal diameter (ITD) decreases with the increase in length, so that the trachea becomes relatively narrower with increasing body size, decreasing the diameter/length ratio (Mitchell & Skinner, 2011). This is probably because along with the neck lengthening, the tracheal dead space volume increases, so a thick trachea is dysfunctional. Such should have been true for long necked sauropods as well. In giraffes inner tracheal diameter scales very close to isometry with BM (table 1 in Mitchell & Skinner, 2011, 147 kg—ITD: 2.3 cm; 775 kg—ITD: 4.1 cm; 1441 kg—ITD: 4.8 cm), the same is true in birds (Hinds & Calder, 1971) implying that a Diplodocus weighing 14.5 t (Table 9) would have an ITD of about 10 cm. However, this calculation may overestimate the size of the sauropods ITD, which might not be significantly larger than that of an adult giraffe because the latter has even larger skull (60 vs. 74 cm [Spinage, 1968; Woodruff et al., 2018]), a similarly thick throat, and a much shorter neck. Also, horses being much smaller than giraffes, have a tracheal diameter comparable, if not larger, than the latter's (see Carstens, Kirberger, Grimbeek, Donnellan, & Saulez, 2009; Rex, 1972). This is probably due to their shorter necks. This supports that ITD in large long necked animals is more related to the anterior part of the axial skeleton dimensions and neck length, rather than to the BM. Assuming that the ITD of Diplodocus was of an intermediate size between the actual giraffe and that of predicted by BM, about 7.5 cm is obtained. This is a rough estimation but is probably the best approach with the currently available data. Our 3D fleshed Diplodocus restoration has a neck length along the vertebral centra of 6.4 m (Figure 5) and trachea should have been as long as the neck or just barely longer (Wedel, 2005), although a longer organ looping around in the chest as per some long necked birds (Fitch & Hauser, 2003) cannot be ruled out, that is highly speculative. Using the geometric formula for calculating the volume of a cylinder, ~28 L of air volume in the trachea are, therefore, obtained, which is nearly seven times more than what is found in a very large giraffe (Table 1; Mitchell & Skinner, 2011).

    For the estimation of Diplodocus NSG, the body was divided into different segments: head, neck, body trunk, forelimbs, hindlimbs, tail, and dermal spines. Based on the above described parameters for the bones, the approximate SG of Diplodocus limb bones and skeletal parts can be estimated. The legs of sauropods should have been particularly dense because their limbs' marrow cavities are mostly filled by trabecular bone, and the limb-bone walls are very thick increasing the overall bone density. The limb bones of giant columnar proboscideans are very similarly designed to that of sauropods, in which the cortical walls are thick and the presence of marrow cavity is absent or minimal (Boschian, Caramella, Saccà, & Barkai, 2019; Shoshani, 1996). Elephants are, therefore, very good analogues. It should be noted however, that sauropods femurs are relatively much more robustly built compared to proboscideans, possessing very massive femoral shafts that are on average about 30% proportionally thicker than extant elephants, and in case of Diplodocus CM84, close to 18% (Larramendi & Paul, unpublished observations). As a result, sauropod legs' SGs would have been notably dense. The Boschian et al. (2019) recent CT-scan analysis on the appendicular skeleton of the massive fossil elephant Palaeoloxodon antiquus, allows estimation of Diplodocus limb bones SGs (Table 7). The resulting values for the elephant are 1.56 and 1.67 for two femora, 1.51 for the tibia, and 1.55 for a humerus half (Table 7). The upper value for the femur surpasses in density all recorded terrestrial mammals including the semi-aquatic hippo (see Wall, 1983). This is because the percentage of the compact bone in Palaeoloxodon antiquus is likewise higher than any reported land mammal (Wall, 1983; Table 7). When the bone type percentages are the same, the obtained SG is also identical, supporting the accuracy of the herein proposed values, for example, the Hippopotamus femur SG is 1.51 with a compact bone that accounts for 44% of the same whole limb element. The same values were found for the Palaeoloxodon tibia (Table 7). Nevertheless, we would like to note that some, but not all, data from Wall (1983) should be taken with special caution. Since Wall's (1983) sample is composed of dry bones, without organic material (cartilage and periosteum) around the elements, it is also possible that in case of those limb elements with large medullar cavities containing yellow marrow, could be partially, or fully empty, and may contain large “airbags” inside them. This does not involve the aquatic or semi-aquatic mammals within his study, as well as rhinos whose marrow cavities are filled by trabecular bone. Our hypothesis would explain why the SGs of some limb bones of “Terrestrial group” of Wall (1983) study are very close or even below 1.0.

    TABLE 7. Palaeoloxodon antiquus limb bone SGs
    Element Femur Femur Tibia Humerus
    Specimen number CdG29 CdG30 CdG26 CdG36
    Yellow marrow (ml) 306 358 114 78
    Trabecular bone (ml) 12,280 18,412 8,893 13,603
    Compact bone (ml) 25,309 19,370 7,018 12,978
    Total bone volume (ml) 37,895 38,140 16,025 26,659
    Percentage of yellow marrow 0.8% 0.9% 0.7% 0.3%
    Percentage of trabecular bone 32.4% 48.3% 55.5% 51.0%
    Percentage of compact bone 66.8% 50.8% 43.8% 48.7%
    Yellow marrow (g) 300 351 112 76
    Trabecular bone (g) 14,858.8 22,279 10,761 16,460
    Compact bone (g) 48,087 36,803 13,334 24,658
    Total bone mass (g) 63,246 59,432 24,206 41,194
    Bone SG 1.67 1.56 1.51 1.55

    Returning to the SGs of sauropods' limb bones, there is not available CT-scan data in which the trabecular and compact bone amounts can be determined. However, mid-cross-sectional areas could be a very good approximation to estimate their SG. Based on the cross-sectional area of the Palaeoloxodon femur figured by Boschian et al. (2019: fig. 10b), 48% of compact bone and 52% of trabecular bone are obtained, suggesting a SG of 1.54, which is in very good agreement with the SG estimated via CT-scans (Table 7). Mid-cross-sections can therefore be used to estimate the approximate SG of sauropod limb bones. Recently, Wedel (2018) calculated the approximate SG of the radius and ulna of the sauropod Haestasaurus NHMUK R1870 based on their cross sectional areas. He obtained a SG of 1.72 and 1.67 for the aforementioned elements. Applying the bony tissue SG values of the present work, however, SGs of 1.53 and 1.58 are obtained for Haestasaurus radius and ulna, respectively. Hatcher (fig. 23 in 1901) reported two photographs of the middle cross-section of Diplodocus CM 84 femur. Those display about 63 and 66% of compact bone, respectively, indicating an average SG of about 1.65. This is just 8% more than Haestasaurus forelimb elements and comparable to the Palaeoloxodon antiquus femur. It is correspondingly arguable that especially large columnar graviportal animals such as sauropods typically had limb bone SGs on the order of 1.6, in some cases somewhat more, others somewhat less. For this contribution, a SG of 1.65 was applied in accordance with what is observed in the Diplodocus femur. This gives a SG of 1.128 and 1.080 for the forelimb and hind limb, respectively. These are in good consonance with what is found in primate and horses extremities where their SGs are usually between 1.06 and 1.1 (Buchner et al., 1997; Clauser et al., 1969; Crompton et al., 1996; Drillis et al., 1964). The limb bones of these last, as would be expected, are slightly lighter than those of sauropods because their bones are relatively thinner and filled with yellow marrow. It should be stressed that a recent study (Aguirre et al., 2020) found that the trabecular spacing, unlike in mammals, is negatively correlated with BM in dinosaurs—although no sauropods were included in their analysis, and the sample, of several juveniles was very small—. However, even lowering the trabecular bone density of by half, the SG of the femur to Diplodocus would barely decline from 1.65 to 1.62. This is because the trabecular bone is itself light and corresponds to just a few percent of the bone material. This indicates that even relatively low density trabecular bone in the marrow spaces would not have a significant impact on the SM or SG of dinosaurs.

    The bone material SG of the pneumatic vertebra of Diplodocus, however, would have been higher, although the SG of overall element would be much lower. This is because once the intraosseous diverticula penetrate inside the bone marrow cavity, it replaces bony trabeculae bone, occupying most of the cavity by epithelium-lined air sacs (O'Connor, 2004; Wedel, 2005; Witmer, 1990), leaving only the remaining compact bone. So, the SG applied to the pneumatic bones volumes without air (cervicals, dorsals, sacrals, anterior caudals, and ribs), was 1.9. Sauropod dorsal ribs, including those of diplodocids, are also pneumatic because foramina lead to an internal cavity (Lovelace, Wahl, & Hartman, 2003; Wedel, 2005). The ASP for these was assumed to be 0.6 based on the rest of the pneumatic skeleton, although this might overestimate the air within these elements. According to current knowledge the rest of the skeleton was not pneumatized, including the ilium apparently (Wedel, 2005). The internal cavities of apneumatic bones would have been mainly filled by trabeculae bone, and those SGs would probably, on average, not vary greatly to that of limb elements. For comparison, if the yellow marrow is extracted from the human skeleton without cartilage, the obtained SG for the skeleton is 1.65. However, as in all tetrapods, yellow marrow should have been placed somewhere in the skeleton. In adult birds, the red marrow volume is displaced in correlation to increasing pneumaticity with age, and converting it into yellow marrow (Canoville et al., 2019; Schepelmann, 1990; Tavassoli, 1974). A similar ontogenetic pattern may have occurred in sauropods. Adding the yellow marrow to the previous example with the human skeleton, a SG of 1.4 is obtained, it is not, however, possible to know if the yellow marrow percentage in the sauropod apneumatic skeleton would have been similar, but it must have been lower than 1.65. For this article, a middle value was applied. The yellow marrow would not be uniformly distributed within the skeleton, but locally in some parts (see Canoville et al., 2019). But as the purpose of this work is to estimate the overall NSG, the distribution was assumed to be proportionally the same along with nonpenumatic skeletal elements. So, the SG for apneumatic skeletal parts (skull, ilium, ischium, pubis, and mid-posterior caudals) was set to 1.5. In any case, a significant change of this value would not have a noteworthy impact in overall animal NSGs. The SG of Diplodocus without air was found to be 1.056 (Table 9), as it would be expected for a tetrapod, supporting the accuracy of the parameters applied herein.

    The pneumatic diverticula surrounding the vertebral column were restored following Schwarz et al. (2007) and Schwarz and Frey (2008), plus several considerations explained below. The purpose of this article is not, however, to reconstruct the extraskeletal diverticula with extreme accurateness, that not being possible for a number of reasons (Paul, 1988a, 1997, 2019; Perry, Christian, Breuer, Pajor, & Codd, 2009; Schwarz et al., 2007; Schwarz & Frey, 2008; Wedel, 2005) but evaluate the impact of the approximate volumes of these upon the sauropods' NSGs within a range of plausible variations. Therefore, the distribution of the diverticula was simplified without subdivisions, and supramedullary diverticula were excluded for practical purposes, which in any case, would have not added a significant volume to the whole diverticula system complex due to its very small size. A large supravertebral diverticula between the metapophyses of bifurcate neural spines of cervicals and anterior dorsals was added (Figures 7 and 8), however, this space was probably mostly filled by ligaments, muscles, or depression (see Woodruff, 2017). To our knowledge, no study has been focused on restoring postcervical diverticula in detail, so the diverticula for dorsals, sacrals, and caudals (Until C19 [Wedel, 2005]) was built based on the presence of potential osteological correlates for vertebral pneumaticity that includes different fossae, which extend over the vertebrae (Figure 8). It is very difficult to ascertain how big the sacs emerging form these openings could have been, but they were probably constrained by the muscles and other soft tissues to some degree. Therefore, these diverticula were restored to the minimum expansion (see below), though they might have been somewhat larger, or maybe not (see later discussion). However, in case of the neck, the pneumatic diverticula could have been much larger because lateral vertebral diverticula may have developed through the whole canal between cervical ribs. For this contribution, three possible neck diverticula volumes were restored following in part Schwarz and Frey (2008): (1) the minimum expansion where the diverticula volume is approximately that of the displaced bones, which correspond exclusively to the fossae and foramina in the vertebrae (Figure 7); (2) the intermediate expansion model which correspond the half of the maximum expansion. This reduction affects the entire diverticula of the cervicals, and in case dorsals, to those are placed on the anterior bifurcated neural solely (Figure 8); (3) the maximum expansion model where the lateral vertebral and supravertebral diverticula goes into a long continuous tube that runs along the entire length of the neck, and through the anterior dorsals in case of supravertebral diverticula, without being pinched out between each vertebrae and the lateral spinal diverticula are larger than the osteological correlates (Figures 7 and 8). The minimum expansion is probably the least likely of three models because the enlargement of the pneumatic diverticula had an important impact in different aspects of sauropods necks. The pneumatic diverticula expansion increases the support and strength of sauropods necks and it constitutes an important factor in increasing the length of the necks while lightening them (Schwarz & Frey, 2008; Schwarz et al., 2010; Taylor & Wedel, 2013). Additionally, the large hollows produced in the parapophysis and diapophysis fusion probably evolved in order to contain a large lateral vertebral diverticula. If so, relatively well developed lateral cervical diverticula appear to be biomechanically advantageous.

    Details are in the caption following the image
    CM84 Diplodocus cervical series with postulated and simplified pneumatic diverticula restorations. (a) Lateral view of minimum expansion of pneumatic diverticula based on osteological correlates. (b) Lateral and dorsal views of maximum expansion of pneumatic diverticula with lateral spinal diverticula exceeding osteological correlates
    Details are in the caption following the image
    Full CM84 Diplodocus skeleton in lateral and dorsal views. The cervicals and anterior dorsal bifurcate neural spines shows a postulated pneumatic diverticula at maximum expansion. Posterior cervicals pneumatic diverticula are based on osteological correlates

    Since the neck diverticula were connected with the respiratory apparatus (Schwarz et al., 2007; Schwarz & Frey, 2008) the maximum expansion model would have been only possible at the maximum inflation of the respiratory system, while at resting or neutral state, like the rest of the respiratory system, the diverticula were probably filled to half of its capacity as observed in York et al. (2018) experiments. Thus, the intermediate expansion model is the most plausible model for the relaxed animal. In the now classical skeletal-latex preparation of a black-headed gull (Larus ridibundus) (O'Connor, 2004, 2006; O'Connor & Claessens, 2005), the lateral vertebral diverticula, as well as the intermuscular diverticula, are very large compared to cervical vertebrae size, however, this is because of the respiratory system appears to be inflated to the maximum its capacity (see O'Connor, 2004). At this state, the volume of the air sacs is more than twice the size respect to the resting stage (York et al., 2018). Thus, the latex in O'Connor's work markedly overestimates the volumetric values of the avian cervical respiratory air system in neutral condition. For comparison, the CT-scan of a deceased ostrich neck cross-section in Wedel (fig. 5 in Wedel, 2003) shows much smaller lateral vertebral diverticula, although it is possible that these are partly collapsed. Even so, the postcervical diverticula of the vertebral column in O'Connor (fig. 1 in 2004) are extremely small. So, the intraosseous diverticula volume of Diplodocus dorsals, sacrals and caudals probably was not significantly larger than the minimum expansion model. Finally, to take into account the possible air amount within the nasal passages and closed mouth, which was at least partly filled with a tongue, a factor of 0.95 was applied to the flesh of the head of Diplodocus.

    In order to be as comprehensive as possible, dermal spines running along the dorsal midline were included. The spines observed and described in Czerkas (1992, 1994) were limited to the tail, but they may well have extended along the entire animal, so the NSG of the sauropod was calculated based on both possibilities. Blunt spines, presumed to be on the side of the animal (Czerkas, 1994) were excluded. The Diplodocus tallest recorded dermal spine belonging to a 14 m long individual, was estimated as 18 cm (Czerkas, 1992). The tallest dermal spines in the present and much larger model (26 m), were, therefore, set to about 35 cm. The SG applied to these spines was that of keratin (1.33).

    The full restoration of Diplodocus (Figures 5 and 6) depicts an animal exactly 26 m along the vertebral centra, 4.32 m high to the top of the tallest dermal spines, and 15,258 L in volume. A BV is greater than those of previous volumetric analysis (Henderson, 2013; Paul, 1997, 2010, 2016) by a modest amount, with no dramatic differences being visually observable in any particular body section (Figure 6). The NSG of Diplodocus was found to be in the area of 0.95 (Table 9), which is significantly higher than previously thought for sauropods (Henderson, 2004; Paul, 1988a, 1997; Wedel, 2005). Based on the intermediate model for the neck, the obtained NSG for the entire body is 0.948, while in accordance with minimum and maximum expansion models, the NSGs are 0.955 and 0.939, respectively (Tables 8 and 9). Also, even tripling the volume of the diverticula surrounding the postcervical vertebrae, the NSG of the animal barely reduces about 0.01 points. This indicates that large changes in diverticula volume are irrelevant for the whole animals' NSG, and thus, even the exclusion of subcutaneous and intermuscular diverticula of the analysis, indicates that those would not affect the animal's NSG significantly. The most notable change is found if important alterations are made in lung and air sacs volume together, however, even if those are doubled in volume, which is highly implausible, the obtained NSG only lowers to 0.9. Also, it was found that dermal spines have no appreciable effect in Diplodocus NSG, because excluding them, the NSG only reduces only about 0.2%. And, excluding the presumed spines along the neck and back, but keeping those of the tail, the NSG of the animal is reduced only from 0.948 to 0.947. The addition of blunt spines, or large changes in dorsal spines size, is therefore, irrelevant in Diplodocus NSG. This is as a result of their extremely small size compared to the sauropod BV.

    TABLE 8. Diplodocus neck SGs to different expansion models
    Outer contour Volume (L)
    Neck 1,398.78
    Dermal
    Spines 9.67
    Skeketal
    Cervicals 210.56
    Air
    Trachea air 28.23
    Cervicals inside air volume 126.30
    Cervical divercticula min. expansion 29.83
    Cervical divercticula int. expansion 139.88
    Cervical divercticula max. expansion 279.8
    Dermal Mass (kg)
    Spines 12.86
    Outer contour
    Neck min. expansion 1,303.1
    Neck int. expansion 1,193.1
    Neck max. expansion 1,053.2
    Specific gravities
    Minimum expansiona 0.922
    Minimum expansionb 0.925
    Intermediate expansiona 0.844
    Intermediate expansionb 0.847
    Maximum expansiona 0.744
    Maximum expansionb 0.748
    • a Excluding dermal spines.
    • b Including dermal spines.
    TABLE 9. Diplodocus CM 84/USNM 10865 volumes, masses, and NSG
    OUTER Volume (L)
    Head 28.08
    Neck 1,398.78
    Trunk 9,603.64
    Forelimb 382.15
    Hindlimb 1,464.89
    Tail 2,307.39
    Total 15,184.95
    Skeletal
    Cervicals 210.56
    Skull 4.76
    Dorsals 248.84
    Sacrum 76.09
    Ribs 96.75
    Appendicular trunk (scapulae; ilium, ischium, and pubis) 299.50
    Skeletal forelimb 74.98
    Skeletal hind limb 179.89
    Pneumatized caudals 264.03
    Not pneumatized caudals 71.36
    Skeleton volume 1,526.76
    Dermal
    Neck dermal spines 9.67
    Trunk dermal spines 20.96
    Tail dermal spines 41.92
    Air
    Head 1.17
    Trachea 28.23
    Cervical divercticula intermediate expansion 139.88
    Cervicals inside air 126.30
    Lung and air sacs 759.25
    Dorsal diverticula 55.23
    Dorsal inside 149.30
    Sacrum diverticula 17.74
    Sacrum inside 45.65
    Ribs air 58.05
    Caudal diverticula 27.41
    Caudal inside air 158.41
    Total air 1,566.61
    Body parts without air Volume (L) SG
    Head 26.91 1.088
    Neck 1,104.37 1.069
    Trunk 8,518.42 1.035
    Forelimb 382.15 1.128
    Hindlimb 1,464.89 1.080
    Tail 2,121.57 1.095
    Dermal spines 72.55 1.330
    Full animal 13,691 1.056
    Body parts with air (living animal) Mass (kg) NSG
    Head 29.29 1.043
    Neck 1,180.20 0.844
    Trunk 8,819.98 0.918
    Forelimb 430.89 1.128
    Hindlimb 1,581.82 1.080
    Tail 2,323.66 1.007
    Dermal spines 96.49 1.330
    Full animal 14,462 0.948

    The neck alone SG varies from 0.744 to 0.925 depending on different variables, being the most plausible a value 0.844 (0.847 including dermal spines) in a neutral state (Table 8). As pointed above, the subcutaneous and intermuscular diverticula of the neck were not taken into account, however, they were likely to be relatively small, and their volumes were probably reduced in favor of the very large supravertebral vertebral diverticula. Moreover, is possible that supravertebral vertebral diverticula was significantly smaller than estimated here in favor of large nuchal and interspinal ligament (Woodruff, 2017). In any case, even taking into account the maximum expansion of the diverticula plus a large amount of possible intermuscular diverticula, the SG of the neck can hardly be below 0.75. The previously suggested neck SG values as low as 0.6, or less (Henderson, 2013; Paul, 1988a, 1988b, 1997, 2016, 2019; Taylor & Wedel, 2013; Wedel, 2005) are, therefore, too low (see Bates et al., 2016 for further discussion). Because the NSG of sauropod necks is not so dramatically lower than the rest of their bodies, the impact on the overall mass due to the great variation in neck volume in sauropods is less than calculated by Paul (1988a, 1988b, 1997, 2016, 2019), but is still significant—it follows that reducing their weight was not as strong a factor behind the pneumatic nature of long sauropod necks—. Also, the relative high SG of Diplodocus body excluding head, neck and dermal spines, indicates that it had an impact on BM greater than estimated by Paul (1988a, 1997, 2016, 2019) by a 6%, because this section NSG of sauropods was from about 0.943 to 0.986 (0.957 on average) and 0.956 in Diplodocus (calculated from Tables 8 and 10).

    TABLE 10. Different sauropod volumes, masses, and NSGs
    Clade Specimen number Head volume (L) Neck volume (L) Trunk volume (L) Forelimbs volume (L) Hindlimbs volume (L) Tail volume (L) BV (L) Head mass (kg) Neck mass (kg) Trunk mass (kg) Forelimbs mass (kg) Hindlimbs mass (kg) Tail mass (kg) BM (kg) NSG
    Early sauropods
    Tazoudasaurus CPSGM collection 21 399 2,736 204 423 378 4,161 21.8 359.1 2,503.4 230.5 456.8 378 3,950 0.949
    Spinophorosaurus GCP-CV-4229 15 506 5,395 287 763 570 7,536 15.6 455.4 4,936.4 324.3 824.0 570 7,126 0.946
    Shunosaurus ZDM 5402 11 156 2,219 147 381 454 3,368 11.4 140.4 2,030.4 166.1 411.5 454 3,214 0.954
    Barapasaurus IRIS collection 20 490 4,862 302 864 844 7,382 20.8 441.0 4,448.7 341.3 933.1 844 7,029 0.952
    Cetiosaurus OUMNH collection 28 1,078 8,214 700 1,274 1,310 12,604 29.1 970.2 7,515.8 791.0 1,375.9 1,310 11,992 0.951
    Patagosaurus PVL 4170 26 635 5,604 420 1,103 1,825 96,13 27.0 571.5 5,127.7 474.6 1,191.2 1,825 9,217 0.959
    Mamenchisauridae
    Mamenchisaurus IVPP 3 28 3,372 10,511 438 1,104 1,020 16,473 29.1 2,748.2 9,617.6 494.9 1,192.3 1,020 15,102 0.917
    Mamenchisaurus ZDM 0083 18 1,384 5,190 183 610 485 7,870 18.7 1,128.0 4,748.9 206.8 658.8 485 7246 0.921
    Omeisaurus ZDM T5701 63 1,397 6,229 420 870 824 9,803 65.5 1,138.6 5,699.5 474.6 939.6 824 9142 0.933
    Early neosauropods
    Jobaria MNN TIG3 54 994 13,157 850 2,315 1,290 18,660 56.2 894.6 12,038.7 960.5 2,500.2 1,290 17,740 0.951
    Early Diplodocoidea
    Haplocanthosaurus CMNH 10380 20 751 10,024 518 1,943 1,102 14,358 20.8 675.9 9,172.0 585.3 2,098.4 1,102 13,654 0.951
    Dicreosauridae
    Nigersaurus MNN composite 8 75 1,227 93 442 242 2,087 8.3 70.5 1,141.1 105.1 477.4 252 2,054 0.984
    Dicraeosaurus HMN m 32 432 3,370 190 832 816 5,672 33.3 406.1 3,134.1 214.7 898.6 849 5,535 0.976
    Amargasaurus MACN-N 15 18 318 2,625 130 485 800 4,376 18.7 298.9 2,441.3 146.9 523.8 832 4,262 0.974
    Diplodocidae
    Apatosaurus CMNH 3018 31 2,720 11,282 926 2,728 2,751 20,438 32.2 2,284.8 10,323.0 1,046.4 2,946.2 2,751 19,384 0.948
    Barosaurus AMNH 6341 23 3,010 7,408 440 1,374 1,820 14,075 23.9 2,528.4 6,778.3 497.2 1,483.9 1,820 13,132 0.933
    Early Macronaria
    Camarasaurus CMNH 11393 86 1,163 11,164 585 1,530 1,348 15,876 89.4 1,017.6 10,215.1 661.1 1,652.4 1,348 14,984 0.944
    Titanosauriformes
    Giraffatitan HMN MB.R.2181 113 5,119 25,135 2,260 2,888 1,577 37,092 117.5 4,300.0 22,998.5 2,553.8 3119.0 1,577 34,666 0.935
    Euhelopodidae
    Euhelopus PMU R233(B) 11 567 2,621 174 251 289 3,913 11.4 462.1 2,398.2 196.6 271.1 289 3,628 0.927
    Titanosauria
    Patagotitan MPEF-PV 3400 160 6,362 40,242 2,808 4,930 5,590 60,092 166.4 5,344.1 36,821.4 3,173.0 5,324.4 5,590 56,419 0.939
    • Note: Volumes are obtained from profile-skeletal volumetric models after Paul (2010, 2016, and 2019). Any possible dermal spines were excluded.

    On the other hand, in the present intermedium expansion model the TRSC to BM represents the 17.2% (15.6% to BV and 16.4% to neutral BV), which is comparable to the less volant birds, while the FRC (including the air in the bones) to BM is 10.8% (10.3% to BV) being considerably larger than the aforementioned birds (Table 2) because of the well-developed intraosseous diverticula of the sauropod.

    Based on Diplodocus results, the NSG of a large number of sauropods known from reasonably complete remains was estimated (Table 10) upon the following considerations. Note that the air-sacs and lung capacities, and SM to BM ratio among different sauropods probably having varied, the calculated results are correspondingly approximate. The SGs corresponding to the neck, trunk and tail, were rounded down in order to take into account the possible impact of the extraskeletal diverticula. The heads SG was set to 1.04, and the used SG for the fore and hind limbs was 1.13 and 1.08, respectively. Based on the ASP values recorded by Taylor and Wedel (Table 2 in 2013), the approximate SG values for the necks were calculated. Because of when applying divergent vertebral internal ASP values (from 0.5 to 0.8) to the trunk and tail vertebrae no significant variations on SGs were observed (excluding Dicraeosauridae), the applied SGs to these sections, were the same to that of Diplodocus, 0.915 and 1.0, respectively. In a recent study (Windholz et al., 2019) was found that the ASP in a posterior cervical of the dicraeosaurid Pilmatueia, was only 0.26. Following this data, the applied SGs for Dicraeosauridae neck, trunk and tail were 0.94, 0.93, and 1.04, respectively. In the case of Apatosaurus and Giraffatitan, the neck SG (0.84), was the same as that of Diplodocus because the average ASP values of these taxa are roughly similar. In the absence of present data in titanosaurs, the SG of the previous sample was applied to the neck of Patagotitan. Based on the relatively high ~0.7 ASP of Tornieria the SG of the neck of Barosaurus was set at 0.815. In the absence of information on the ASP, the same were applied in the very long-necked Mamenchisauridae and Euhelopus. In case of Camarasaurus with vertebral ASP close to 0.5, the resulting SG was 0.875 for the neck. With regard to Haplocanthosaurus with an ASP of 0.4 in cervical condyle, the obtained SG for its neck was 0.9. The same SG was applied to other plesiomorphic sauropods (early sauropods and Jobaria, Table 10).

    The resulting NSG values in analyzed sauropods range from 0.917 to 0.984. These are significantly higher than estimated by Bates et al. (2016) which included most of the sauropod genera calculated here. They found very low SGs ranging from 0.776 to 0.929—excluding their minimum convex hull models which further reduce the SGs—. Their low results are because the authors applied an overly low SG of just 1.0 to different apneumatic sections, and estimated extremely large respiratory systems for most of the sample which generally far exceed even what is expected in flying birds in a neutral state.

    Because the poorly pneumatized vertebrae of dicraeosaurids, the species in this clade were found to be the densest (Table 10), while the lowest NSG were found in the sauropods with the longest necks like mamenchisaurids, Giraffatitan, Barosaurus, and Euhelopus with a NSG approaching to 0.93 in some cases. Colossal sized titanosaur carrying relatively large necks (Paul, 2019), were probably in this region (Table 10), or slightly below because their very wide torsos may have allowed them to possess relatively larger respiratory systems. If the lesser density of the neck of the neck relative to the rest of the body is not taken into account when calculating total BM, the later will be overestimated by up to ~3% among very large necked sauropods such as mamenchisaurs and brachiosaurs relative to short necked examples such as shunosaurs. The BM results herein are ~5–12% higher than for the same specimens volumetrically massed by Paul (2016, 2019) for the same specimens due to the lower NSGs used in those efforts.

    3.2.11 Pterosaurs

    Few studies have focused on estimating pterosaur SGs because their BMs have been usually estimated by nonvolumetric methods (see Bramwell, 1971; Brower, 1983; Hankin & Watson, 1914; Stein, 1975; Witton, 2008; Witton & Habib, 2010). Bramwell and Whitfield (1974) made the first serious attempt to estimate the SG of a large Pteranodon 695 cm wing span. However, some of their calculations were obscure, leading to SGs as low as 0.2 or 0.3. Paul (1991, 2002) proposed less implausible SGs of 0.57–0.7, Henderson (2010) was in a similar range. Bramwell and Whitfield (1974) made numerous problematic assumptions. Attempting to estimate the SG of the neck of Pteranodon, they first examined those of the lizard Lacerata vivipara and goose Anser domesticus, asserted that they trachea and esophagus made up 40 and 20% of cross-sectional space, respectively. But no illustrations of the modern animal neck cross-sections were provided, nor was it detailed what the ratios are in the lizard versus the bird, nor whether the volumes included just the air spaces or tissues of the tubes although it seems to include the latter, and the esophagus is not normally filled with air in a living animal in any case (Blomquist & Mahoney, 1960). The cross-section of the Pteranodon neck in their fig. 27 does not appear to correspond to their estimates of solid (30%) versus air-filled space (70%). Even more, they applied their extremely low estimated SGs of the neck to the Pteranodon body trunk in their “normal and light estimate” models. These estimations led Henderson (2004, 2006, 2010) to erroneously state that the SG of goose neck is as extremely low as 0.3 (see also Macaulay et al., 2017). The Bramwell and Whitfield (1974) observations are therefore dismissed as of no technical value.

    To assess the NSG of pterosaurs, multi-view profile-skeletals were prepared (for Paul, 2021) of a set of taxa representing the major morphological types and grades, with some preference for those represented by a number of complete articulated specimens (Figures 9 and 10). In the case of Rhamphorhynchus and Pterodactylus the specimens include some that present the lateral view of the crania and postcrania, others preserve the dorso-ventral views (Bennett, 2001; Bennett, 2007; Eaton, 1910; Wellnhofer, 1970; Wellnhofer, 1975; Wellnhofer, 1985; Wellnhofer, 1991a, 1991b). Some specimens of those two taxa preserve individual elements that retain their 3-D shape. The latter is also true of Anhanguera, while Anurognathus and Pteranodon are known only from specimens with flattened bones, and neither Anhanguera or even famed Pterandon are known from complete adult specimens. The Pteranodon skeletal is centered on the uniquely large partial P. longiceps UNSM 50130, with other elements scaled in from other large adults, the Anhanguera is scaled to NSM-PV 19892, with dorsal view of the axial skeleton primarily after AMNH 22555. The toucan, which in addition to its very large head including an oversized beak shares with pterosaurs a modest sized sternal complex, is based on a USNM display mounted skeleton of Ramphastos (uncatalogued) for the lateral view supplemented by the dorsal view of a R. toucans USNM 344094 (Figure 1). Contrasting to pterosaurs and the toucan with its small beak and very large sternal complex, the pigeon (C. livia) is based on a commercial lab skeleton (Figure 1). Pterosaurs' BVs were estimated by WD. The volumes of the birds were estimated using GDI. Because it was difficult to replicate the very slender nonpterodactyloid tail in plasticine, it is volume was also estimated by using a series of the wooden handles of bristle free paint brushes of declining diameter, and by GDI, these results were satisfactorily within a few percent of each other. Pterosaur wing membrane profiles were based in part on preserved examples, and present a best estimate that is at the low end for wing loading in the clade as per Paul (2021), the values are correspondingly highly approximate.

    Details are in the caption following the image
    Multi-view profile-skeletals of basal and derived pterosaurs. Scale bars equal 20 cm in small species and 50 cm in large. (a) Anurognathus BSPG 1922 (wingspan 37 cm); (b) Pterodactylus BSPG 1937 (wingspan 43 cm); (c) Rhamphorhynchus BSP 12927 (wingspan 110 cm); (d) Anhanguera NMS—PV 19892 (wingspan 525 cm); (e) Pteranodon UNSM 50130 (wingspan 650 cm)
    Details are in the caption following the image
    One side wing and membrane profiles of basal and derived pterosaurs to same half wingspan, scale bars equal 5 cm in small species and 50 cm in large. (a) Rhamphorhynchus BSPG 12927 (membrane area 364 cm2); (b) Anurognathus BSPG 1922 (membrane area 58.6 cm2); (c) Pterodactylus BSPG 1937 (membrane area 49.5 cm2); (d) Anhanguera NMS—PV 19892 (membrane area 5,665 cm2); (e) Pteranodon UNSM 50130 (membrane area 8,918 cm2)

    Pterosaurs were highly pneumatic in their axial and in some cases their appendicular skeletons and skulls, sometimes exceptionally so (Bramwell and Whitfield, 1974; Bonde & Christiansen, 2003; Buchmann & Rodrigues, 2019; Claessens, O'Connor, & Unwin, 2009; Martin & Palmer, 2014). The ASP in some limb bone elements of large and derived taxa can be ~0.9 (see Bramwell & Whitfield, 1974; Currey & Alexander, 1985; Martin & Palmer, 2014; Table 7). In all nonpterodactyloids and small pterodactyloids postcranial pneumatization appears to usually be restricted to the axial skeleton and absent in limb bones, this covers basal and derived pterosaurs with wings less than 2.5 m span (Buchmann & Rodrigues, 2019; Claessens et al., 2009).

    To estimate the NSGs of the pterosaurs, several considerations have been taking into account. First, the bodies were divided into different sections and then the volumes were calculated separately. Not all pterosaurs had beaks, there being none among the short snouted anurognathids. Among the great majority that had them the size of the beak is ambiguous in that the transition to the main body of the head is not clear, unlike toucans in which the extent of the beak is externally visually obvious. For pterosaurs the posterior beak edge is designated as being in the posterior section of the preorbital opening, in which case beaks make up 4–17% of total volume in the pterosaurs that had them in this study (Table 15; Figure 9). Among pterosaurs that, like some birds, combined large beaks with short bony tails there would been selective pressure to make the rostrum as low density as possible to prevent being front heavy in flight. Because large toothless pterosaur beaks were largely bone foam in the manner of extant toucans, the SG of 0.1 observed as noted below was applied to such rostrums. The density of tooth bearing beaks would have been higher than for toothless beaks both because of the bone anchoring the teeth would likely have been denser, and because teeth have high SGs of 2.0–3.0 for enamel and dentine, respectively (Boyd, Drain, & Deakins, 1938; McIntosh & Anderson, 2010; Weidmann, Weatherell, & Hamm, 1967). The greater the collective bulk of the teeth, many of which were replacement teeth not externally visible, the greater beak density would have been. A major problem is that the absence of modern analogs to help estimate the SGs of tooth bearing beaks. Lacking better information SGs of 1.0 are applied to beaks featuring very large teeth (Rhamphorhynchus), and much less to those with increasingly smaller dental arrays (0.2 for Pterodactylus and 0.3 Anhanguera). Because head volumes contain the posterior section of the nasal passages, for the head alone the SG applied was 1.0, somewhat less than what is typically found in vertebrate heads sans nasal passages air (1.03–1.1, Buchner et al., 1997; Crompton et al., 1996; Dempster, 1955; Erdmann, 1997). Ignored are pterosaur throat pouches, they being made of such thin elastic tissues that they had no significant effect on overall mass.

    Arm volume and mass is that of the appendages cut off at the shoulder joint on out, so the proximal flight muscles are included with the trunk. Pterosaurs trunks are prone to be small, in some case very much so compared to the rest of their bodies, mainly due to their large wings that —in part because they include bones all the way out to the tips, and because pterosaur sterna and associated inner arm muscles are modest in size—make up a markedly larger portion of total mass, 12.3–19% (excluding membrane) according to the results herein (Table 15), than they do among birds (9.4–13%, excluding feathers; Table 3). These features indicate that pterosaur lung plus air sac/BVs were relatively smaller than in extant birds. In the latter, the average TRSC to neutral BV (including heads, wings, and legs) is on average 19% (calculated from Table 2). Small sterna render toucans better suited than most modern avians for comparison to pterosaurs. Applying a 19% respiratory space to the toucan model without the beak, a TRSC of 23.6% to neck, trunk, and tail neutral volume is obtained (calculated from Table 3). However, if the percentage applied to the toucan is that of parrots (17.4%; Table 2), which also have relatively small sterna, a 21.6% of TRSC is obtained for the neck, trunk and tail neutral volume. On the other hand, since pterosaurs exhibited greater axial skeleton pneumaticity than birds, a higher TRSC of 25% for neck, trunk, and tail neutral volume was assumed for the pterodactyloids concerning the same body sections. In case of the less pneumatic nonpterodactyloids the percentage was lowered to 20%. However, as in extant tetrapods, the lungs and air sacs together were probably filled to its half in neutral position. Because of the light skeletal built of pterosaurs, a SG of 1.0 was applied to pterosaurs' neck, trunk, and tail combined without air.

    To begin to approximate the amount of air contained in the appendicular skeletons of large derived pterosaurs, the internal air volume of each Pteranodon hollow wing long bone was measured as a cylinder proximal to the wrist. Pterosaur wing finger elements are markedly dorso-ventrally flatter than they are antero-posteriorly broad for streamlining (as per fig. 2 in Palmer, 2018; Figs. 21f,g and 24 in Wellnhofer, 1985, the less flattened cross-sections with those figures are not in accord with the overall form of the bones; figure on p. 55 of Wellnhofer, 1991b). The Palmer (2018) first wing phalanx scans indicate that the actual cross sectional area is about two thirds (~66%) of a circle (Table 11), and the cross sectional area of humerus, ulna, radius and metacarpals in Wellnhofer (1985) also indicate that those areas, are less than a perfect circle (Table 11), so the volumes of Pteranodon wing bones were calculated accordingly of the obtained values (Table 12), with a result of 3,739 ml (Table 15). Since the UNSM 50130 specimen restored herein (Figure 9) is similar in size to the material described by Bramwell and Whitfield (1974), part of their data listed in their table 11 was used, namely the outer diameters and bone wall thickness. Subtracting the wall thickness to the outer shaft diameters, the inner diameters are therefore obtained, and the volume of air can be calculated (Table 12). The average ASP found in the wing bones is 0.86 (Table 12) and the air volume in bones to the wing volume represents 28%. On the other hand, it was found that the ASP in the wing bones of nine specimens from Ornithocheiromorpha is on average 0.77 (table 1 in Martin & Palmer, 2014), or about 10% less to what was found in Pteranodon. Therefore, to estimate the possible air volume in the wing bones of Anhanguera, a factor of 0.25 to wing volume was applied. Any extraskeletal diverticula that may have been used to blend the arm bones into the wing membrane for streamlining should have been as thin as possible in antero-posterior view to minimize frontal drag, which in turn would have minimized the volume of air they contained. For this reason, to estimate the mass of the wings in Pteranodon and Anhanguera, a factor of 1.0, somewhat lower than the usual 1.05 (for comparison, the SG of turkey wing is 1.036 [Moreng et al., 1963]), was applied to the wings without air. The air in Pteranodon hind limbs was estimated extrapolating the air volume calculated by Bramwell and Whitfield (table 10 in 1974) to UNSM 50130 size. It was found that the total air corresponds to about 9% of the legs volume, and this percentage was applied to Anhanguera. The applied SG those pterosaur legs lacking air was a conservative 1.05.

    TABLE 11. Pterosaur wing bone cross-sectional areas
    After Wellnhofer, 1985 Diameter Actual cross-sectional area Circle area % of the circle
    Humerus 100 59.9 78.5 76.3%
    Ulna 100 68.8 78.5 87.6%
    Radius 100 75.7 78.5 96.4%
    Metacarpal IV 100 53.7 78.5 68.4%
    Phalanx II 100 59.8 78.5 76.1%
    Phalanx IV 100 54.3 78.5 69.1%
    After Palmer, 2018
    Phalanx section 1 100 43.2 78.5 55.0%
    Phalanx section 2 100 53.3 78.5 67.9%
    Phalanx section 3 100 49.6 78.5 63.2%
    Phalanx section 4 100 54.6 78.5 69.5%
    Phalanx section 5 100 51 78.5 64.9%
    Phalanx section 6 100 51.3 78.5 65.3%
    TABLE 12. Pteranodon USNM 50130 wing bone air volumes and ASP values
    Length (cm) Outer diameter (cm) Wall thickness (cm) Bone volume (ml) Inner diameter (cm) Volume of air (ml) ASP
    Humerus 35 4.7 0.16 606.9 4.38 527.1 0.87
    Radius 41.5 2.4 0.13 187.6 2.14 149.2 0.80
    Ulna 46.5 4.1 0.09 613.6 3.92 560.9 0.91
    1st metacarpal 63.5 3.6 0.15 646.0 3.3 542.8 0.84
    1st phalanx 66.2 3.1 0.15 499.4 2.8 407.4 0.82
    2nd phalanx 54.6 2.46 0.06 259.4 2.34 234.7 0.90
    3rd phalanx 41 1.3 0.05 54.4 1.2 46.3 0.85
    4th phalanx 19.4 0.9 0.05 12.3 0.8 9.7 0.79
    Total 2478

    Relative to wingspan the Pteranodon membrane area restored herein (Figure 10) is very close to just half the very high area arrived at by Bramwell and Whitfield (1974), and is 61% that by Palmer (2018, 2.48 m2 wing area for his 6 m span restoration in Figure 2), but is an only 20% less the low chord restoration by Brower (1983). Pterosaur wing membrane sheets were probably thin, in part because adding thickness can considerably boost total mass loads (Palmer, 2018). Efforts to estimate absolute membrane thickness for giant pterosaurs as per Palmer (2018) are problematic for a number of reasons. First, rather than being fairly uniform across broad areas as in bats which use many fingers to support the membranes along much if its length, it is very possible that pterosaur membrane thickness varied considerably within a given wing, it being especially plausible that their cross-sections became much thinner progressing aft from the anterior wing bones to the trailing edge. For purposes of estimating wing membrane mass this issue can be dealt with by using a median between maximum and middle thickness that, applied as a gross average to the membrane as a whole, allows the mass of the sheet to be calculated for a given total area. To get the mass of the membranes, a SG of 1.1, the same that is found in humans skin (Leider & Buncke, 1954; McIntosh & Anderson, 2010) could be applied, however, this is somewhat conservative since the membranes were probably reinforced by keratin (Palmer, 2018; Paul, 2021). Assuming that half of the membranes material was keratin (SG ~1.33), a SG of ~1.2 is obtained and was accordingly applied.

    The absence of preserved flight membranes that reliably record any thickness at any location, or even their actual area is a major difficulty. Another is that the modern powered fliers with membrane airfoils, bats, in which membrane thickness ranges from about 0.02 to 0.15 mm in species of 5 g to ~1 kg (Table 13) are much smaller than the giant pterosaurs, their skin sheets are supported along much of their span by multiple fingers that should allow the membranes to be thinner than those supported by just one finger, and bat membranes lack the internal supporting fibers of pterosaurs. As a result, bat membrane thickness may not informative regarding those of pterosaurs, especially the giants. Nor is it known what aerodynamic stresses pterosaur membranes were exposed to. If, for example, wing membrane chord and area/span were very high, then there would have been strong selective pressure to minimize membrane thickness in order to minimize wing mass. That in turn should compel low flight speeds in order to avoid damaging the fragile membrane, as suggested by Palmer (2018). But such an aerial limitation could be avoided with a much lower wing chord and area that would allow the same membrane mass while being much thicker, the result being a correspondingly stronger membrane suitable for markedly higher flight velocities, the latter aided by the lower surface drag of the narrower chord membrane. It is quite possible that minimizing membrane mass tended to force pterosaur wings to be low chord in order to allow the membranes to be sufficiently resilient to allow high flight performance, especially among larger taxa (Paul, 2021). Palmer (2018) could have executed his calculations over a range of membranes chords and areas in order to test the alternatives. Membrane thicknesses of just 0.3–0.5 mm as offered by Bramwell and Whitfield (1974) and Palmer (2018) appear too thin and flimsy for fliers weighing tens of kilograms stretched behind single span wings 5 plus meters wide. If the membrane averaged a more structurally plausible 2 mm, then a ~6.5 m span narrow chord membrane of ~1.8 m2 would have had a mass of 4 kg (15 and 16), a tenth or less of total mass, while offering the stiffness and the high total mass/wing area loading needed to exploit the full speed potential of the streamlined pterosaur airframe. In living bats there is close relationship between BM and membrane thickness and the last is found to be proportional to M0.342 (Table 13), very close to geometric similarity (McMahon, 1975). A similar relationship may have been also true in pterosaurs. Scaling down membrane thickness to smaller pterosaurs results in broadly similar wing membrane/total mass values (Tables 13 and 14). Although this appears to render pterosaur membranes relatively heavier than the thinner sheets of bats, this is compensated by some degree by the former having less outer wing mass in the form of multiple fingers; in other words, pterosaurs put their outer airfoil mass into internal membrane structure, bats more into an array of supporting fingers. Lessening the thickness of the airfoils reduces the NSG by only 1–2.5% in the examples restored herein.

    TABLE 13. Bat membrane thickness and body masses
    Species Average body masses (g) Membrane thickness (mm) Reference
    Myotis yumanensis 4.75 0.023 (Christy & West, 1993; Studier, 1972)
    Myotis thysanodes 6 0.0243 (Christy & West, 1993; Studier, 1972)
    Myotis lucifugus 8 0.0298 (Studier, 1972; Kalcounis & Brigham, 1995)
    Plecotus townsendii 10.5 0.032 (Christy & West, 1993; Studier, 1972)
    Eptesicus fuscus 18 0.0376 (Christy & West, 1993; Studier, 1972)
    Antrozous pallidus 20 0.033 (Hermanson & O'Shea, 1983; Studier, 1972)
    Pteropus giganteus 1122 0.15 (Bramwell & Whitfield, 1974; Perveen & Faiz-ur-Rehman, 2014)
    TABLE 14. Pterosaurs membrane areas and volumes
    Rhamphorhynchus Anurognathus Pterodactylus Anhanguera Pteranodon
    Specimen number BSP 12927 BSP 1922 BSP 1937 NSM-PV 19892 UNSM 50130
    Propatagium area (cm2) 9.7 4.2 2.67 300 308
    Cheiropatagium area (cm2) 338 53 39.8 5,188 8,362
    Cruropatagium area (cm2) 16 1.35 7 177 248
    Total area (cm2) 364 59 49 5,665 8,918
    Both wings total area (cm2) 727 117 99 11,330 17,836
    Membrane thickness based on bats (mm) 0.1 0.05 0.05 0.4 0.55
    Membrane thickness based on this work (mm) 0.35 0.17 0.2 1.5 2
    Wing membrane volume based on bats (ml) 7.3 0.6 0.5 453 981
    Wing membrane volume based on this study (ml) 25.5 1.99 2.0 1,700 3,567

    Based on the parameters defined above the NSGs for pterosaurs are summarized in the Table (15). The results suggest that their NSGs were much higher that proposed by Bramwell and Whitfield (1974) and similar to that of birds and bats (Table 15). The lowest NSGs, as would be expected, are found in most derived and large pterosaurs sporting large toothless beaks and pneumatized limbs, those of toothless Pteranodon and of Anhanguera with wings that are as extremely large as they were highly pneumatic being 0.746 and 0.843, respectively, comparable to toucan and high-altitude geese, the lightest birds analyzed in this study. The less pneumatized, small tooth bearing basal pterodactyloid Pterodactylus NSG is 0.886, comparable to small beaked modern pigeons (Table 1). The classic nonpterodactyloid with large teeth Rhamphorhynchus is nearly one, note that its long tail made up a significant 6% of overall mass. Anurognathus had the same high density (NSG of 0.966) in the range of bats and the denser range of volant birds, in part because it lacked a low density beak that is 4–17% of total volume in the other restored pterosaurs (but only 1.9–4.8% of mass, Table 15). Note that, if the SG sans air in the neck, trunk and tail was actually in the order of 1.05, as generally observed in all tetrapods, the NSG should be about 2.5–5% higher. For example, in the case of the densest genus (Rhamphorhynchus), the NSG would increase to 0.993, and in case of the lightest pterosaur (Pteranodon), the NSG would barely increase to 0.776.

    TABLE 15. Different pterosaur volumes, masses, and NSGs
    Rhamphorhynchus Anurognathus Pterodactylus Anhanguera Pteranodon
    Specimen number BSP 12927 BSP 1922 BSP 1937 NSM-PV 19892 UNSM 50130
    Beak (ml) 12.4 0 3 1,948 11,400
    Head (ml) 20.4 6.3 2.9 1,860 4,707
    Neck (ml) 22.8 3.3 4.5 3,010 8,558
    Trunk (ml) 140 17.1 31.4 8,500 20,753
    Tail (ml) 16.5 0.1 1.92 88.5 342
    Arms and fingers (ml) 42.3 4.2 5.7 4,516 13,265
    Air in arms and fingers bones (ml) 0 0 0 1,129 3,739
    Legs (ml) 13.3 3.7 3.6 1,770 5,134
    Air in leg bones 0 0 0 159.3 468
    Membrane (ml) 25.5 2.05 2 1,700 3,567
    BV of the animal (ml) 293 37 55 2,3392.5 67,726
    Beak (g) 12.4 0 0.6 584 1,140
    Head (g) 20.4 6.3 2.9 1,860 4,707
    Neck, trunk, and tail (g) 161.4 18.5 33.1 10,149 25,946
    Arms and fingers (g) 44.4 4.4 6.0 3,387 9,526
    Legs (g) 14 3.9 3.8 1,691 4,899
    Membrane (g) 30.6 2.46 2.4 2,040 4,280
    BM of the animal (g) 283.2 35.5 48.8 19,711 50,499
    NSG 0.966 0.966 0.886 0.843 0.746

    4 SKELETAL MASS AS A PERCENTAGE OF TOTAL MASS

    Other interesting data derived from this analysis concerns the relationship between skeletal mass (SM) and BM. It was found that the fresh skeleton (without cartilage and periosteum) mass (1,665 kg) corresponds to 11.5% of the Diplodocus BM. This appears low for a vertebrate of this large size even though diplodocines were among if not the most gracile of sauropods (Paul, 1997, 2016); as emphasized by Paul (1988a, 1997, 2019), skeletal robustness relative to mass varied tremendously in sauropods in a manner that does not correspond closely to mass, with modest sized apatosaurines being exceptionally stoutly built in almost all respects, their close diplodocine relatives being the opposite, and the quite high BM brachiosaurs having quite gracile skeletons, while the titanic titanosaurs are fairly average for sauropods. According to Prange, Anderson, and Rahn (1979), the relationship between avian or mammal dry SM and BM in 14.5 t animal, should be 12.8 and 14.4%, respectively. On the other hand, Martin-Silverstone et al. (2015) found that phylogeny is a primary control of SM to BM in birds, indicating that this relationship is not appropriate for estimating the BM of species outside of crown birds. That situation suggests that estimating dinosaur BMs by extrapolating from mammals BM/skeleton mass ratios may also be unreliable, especially regarding pneumatic theropods and sauropods. Also of very serious concern is that the database utilized by Prange et al. (1979) to derive their equation for mammals is very problematic because the data was not taken directly using consistent standards, but from the literature which contains variables in the measurements. In particular, they mixed dry with wet SMs. The Prange et al. (1979) analysis was meant to consist of dry skeletons, lacking cartilage, periosteum, and water. The actual dry SM of adult male human is about 4 kg, corresponding to about 5–6% of BM (ICRP, 1995). However, Prange et al. (1979) list 12.16 kg of SM to 67.3 kg of BM, corresponding 18%. So, their human SM likely refers to wet SM, not dry. But even this data is not accurate since in a healthy human of 73 kg, the wet SM is only 10.5 kg (9.15 kg excluding cartilage and periosteum: ICRP, 1995; Avtandilashvili & Tolmachev, 2019), corresponding only to 14.4%. According to Prange et al. (1979) the dry SM of a 81 kg ostrich can be more than 7.7 kg. If this data is accurate it would imply that the dry SM of the ostrich is relatively about twice that of humans, such would be at least surprising, it is more likely that the big bird data included wet tissues, or that the reported BM came from a much smaller individual than that of the skeleton. Also remarkable is the 1,782 kg of SM for a 6,600 kg elephant based on Crile & Quiring, 1941 (table A2 in Prange et al., 1979)—that ratio led Christiansen (2002) to estimate an implausible 10 t of SM for Giraffatitan—. To start with: the data is not even mentioned in Crile and Quiring (1941) so it is impossible to know where it came from, second: the skeleton which corresponds to an animal less than the half of the mass of Diplodocus, cannot be heavier than the latter, and third: if the full elephant wet skeleton SG alone is comparable to that of human (~1.35), which is something expected because while the elephant limbs are denser than that of human, the elephant pneumatic the skull is lighter, giving probably an overall similar SG, would indicate that with that SM, the NSG of the elephant would be 1.03, but again, this not correspond to the reality as human and elephant both sharing much the same NSG very close to 1.0 (Larramendi, 2015, 2016; Table 1). In fact, the wet SM on the adult female Asian elephant Iki, was found to be 355 kg in the 2,267 kg animal (Shoshani et al., 1982; Shoshani, Kupsky, & Marchant, 2006), corresponding to the 15.7% of the BM. This is virtually the same (15.9%) as found in a much smaller brown hyena (Hyaena brunnea; Shoshani et al., 1982) or somewhat more than the 14.4% found in humans. However, after 20 months Iki's skeleton was again weighed and it was found that the dry SM was thereafter of 216 kg corresponding to the 9.5% of the BM, although it is unknown if cartilage and periosteum were still remaining. Assuming that the cartilage and periosteum in elephants accounts for a similar percent to that of humans, the wet SM sans those two tissues on the elephant, would account to about 13.6%. The expected wet full SM for a 6,600 kg male elephant would be, therefore, 1,050 kg and of about 775 L in volume, and 900 kg and 640 L excluding cartilage and periosteum—or a little higher due the slightly most robust skeleton of tusked male elephant—that being nearly half the value reported by Prange et al. (1979). So, the size increase, as it would be predicted by allometric scaling models in which the larger the animal is, the more robust skeleton it would possess (McMahon, 1975; Prange et al., 1979), is not fully met in this case. It is therefore probable that from a certain size on up that skeletal robustness is more closely tied to ecology, body proportions, biomechanics, and other factors than to body size (Larramendi & Paul, unpublished observations). This is why hippos regardless of not being the largest living land mammals, are the densest because their skeletons are proportionally the heaviest relative to their BMs among extant mammals, due to its semiaquatic condition. Something similar happens with rhinos, despite being much smaller than elephants, their mediportal condition and wide bodies give them a much more robust limb bones and an overall more sturdily built skeleton. This indicates, for example, that dense ceratopsians and thyreophorans would have a proportionally heavier skeleton to their BMs than much larger yet highly pneumatic sauropods, especially gracile examples like Diplodocus. One of the reasons for this is because the skeletons of sauropods are highly pneumatized, however, their skeletons relative volumes were probably greater or similar compared to other smaller taxa. For instance, Diplodocus skeletal volume—without cartilage and periosteum—makes 10.6% of its BM, which is comparable or barely greater than what is expected for a an elephant which has relatively heavier skeleton. Another reason for the light skeleton of Diplodocus could be the articular cartilages of sauropods. For example, in humans, the cartilage corresponds to only to ~10.5% of the whole skeleton mass (ICRP, 1995), however, the enormous epiphysial cartilage of sauropods were several magnitudes greater than that of mammals and possibly than any extant tetrapod (see Holliday et al., 2010), so the cartilage in sauropods should have accounted to a much higher percent of the skeleton, in which case the skeleton mass plus cartilage mass would have been probably relatively close to that of extant tetrapods. The current data indicates that the NSG can be a marker of the SM to BM ratio, where denser animals would have a higher per cent of SM than lighter ones, and thus, the SM can be potentially predicted with a reasonable reliability from the NSG and BM data, as long as the respiratory system capacity of the analyzed clade remains fairly constant regardless the body size (e.g., mammals).

    5 CONCLUSIONS

    Within organisms, living body SGs vary tremendously, from 0.08 to around 2.6, a differential exceeding thirtyfold, and a maximum that is nearly equal to the ~2.7 SG of aluminum. The greatest variations occur within plants and invertebrates, respectively, with the former ranging from 0.08 to 1.35 for a seventeenfold differential, and the latter from about 0.8 to 2.6 for a variation of about three. Animals therefore skew toward being denser than plants, with the densest creatures being twice as dense as the highest mass/volume ratio plants. Density variation within vertebrates is limited, with NSGs ranging from about 0.75 to around 1.2, a differential of about two thirds.

    The last fact means that the application of NSGs to vertebrates needs to be done with some technical care, particularly in certain circumstances. For example, if it is assumed that the NSG of a pneumatic boned giant sauropod with an estimated BV of 50,000 L is that of a modern lightest flying bird at 0.8, then its mass will be 40 t, if it is assigned a hippo like NSG of 1.1 then it will be 55 t. If the applied NSG is the most probable of 0.93 then tonnage is 46.5 t. On the other hand, even this variation is markedly less than the ± range for the same specimen that results from extrapolating mass from limb bone strength factors, which can differ by a factor of over two (Paul, 1997, 2019, Larramendi & Paul, unpublished observations). And in any case, it is essentially impossible for the highly pneumatic sauropods to have been as dense as hippos or even water, while it is equally improbable that the solid limb boned, small sterna sauropods were as lightly built as birds, so the NSG estimate error is only going to be in the region of a few percent going forward. The fact is that the great majority mobile animals, aquatic, and terrestrial, have an NSG very close to that of water, and those that do not can be determined by obvious factors, such as pneumatic skeletons and other evidence for air-sacs, such archosaurs that also have well developed wings for flight, or at the opposite end of the density spectrum exceptionally heavily constructed skeletons and/or heavy armor coverings. Likewise, a low density fossil wood microstructure will indicate an SG below 0.5, a dense composition indicates a value closer to water. On the other hand, it cannot be assumed that the tonnage of a giant extinct tree can be estimated by directly extrapolating from a comparison of its dimensions to those of giant redwoods. Such is likely to be correct if the fossil giant is a softwood conifer, but if it is hardwood it's density was probably closer to those of denser wooded angiosperms, including the titanic eucalyptus, which are about half again as dense.

    The most simple situation applies to all animals that spend most of their time suspended in and/or swimming in water. For most practical purposes of deriving mass from volume, it can be presumed that the SG is 1.0 or 1.025 depending on the type of water they live, or lived in. So if the volume of an intact shell of a giant ammonoid is directly measured, then the SG of the swimming cephalopod can be presumed to be 1.025 in the strict technical sense, but this is not significantly different from 1.0. The 1.0 value is even more true regarding volumes derived from restorations.

    Regarding extant animals of the continents and the air, all insects sampled so far appear to be less dense than water, although that might not be true of some freshwater aquatic examples. No mammal has an NSG appreciably below 1.0 including bats, some semi-aquatic and armored mammals are significantly above that value to the point that they cannot surface swim. Birds are denser than thought, with some being only a little lighter than water, especially but not only flightless examples, with the lowest NSG being about a fifth below 1.0. Contrary to what is widely assumed, the densest vertebrates, reptiles, paradoxically possess the largest respiratory systems, which can be up to more than twice than lightest birds in case of some terrestrial Testudines. This implies that the most important factor for possessing high or low NSGs is not the TRSC itself, but the amount of air in FRC. Reptiles, contrary to mammals at least, have a great ability to take enough air to increase or decrease buoyancy with no effort, indicating that they can regulate their FRC extensively. This capacity allows them to possess the lowest and the highest NSGs among vertebrates.

    The great majority of extinct amniotes NSGs were just shy of or at 1.0. Exceptions were heavily armored and some semi-aquatic examples, including specialized theropods, whose densities were probably up to 10% higher, precluding the more dense examples from surface swimming. At the other end of the density spectrum none of the pneumatic pterosaurs, avepod theropods or sauropods were as dense as H20, although some were fairly close. Probably no sauropod was less than 0.9, and their necks no less than 0.75. Theropods lacking wings were in the area of 0.95 with large and robust prone to be the densest, approaching to 1.0 in some cases. The lowest density animals were very probably giant marine soaring pterosaurs as light as three quarters the density of water.

    The array of SG values presented in this single united study are intended to provide a foundation for future work by researchers on a wide range of organisms including volume based mass estimates. Although this is the most extensive examination of organic SGs yet executed, it is not a truly comprehensive accounting because major data gaps remain. Such includes the need for more widespread and accurate observations of the densities of a large number of extant taxa. Also anticipated is further work on the NSGs of certain fossil taxa, especially those that were pneumatic, although the results are likely to differ from those offered here by minimal amounts. Also needing further investigations are the ratios of skeletal masses to those of entire bodies.

    ACKNOWLEDGMENTS

    The authors would like to express our gratitude to Julia York for her useful discussion and clarifications on her work about geese respiratory system and to Rubén Molina-Pérez for his comments on keratin sheaths. Thanks are extended to John Hutchinson and another anonymous reviewer for their comments which have improved the manuscript.

      AUTHOR CONTRIBUTIONS

      Asier Larramendi: Conceptualization; data curation; formal analysis; investigation; methodology; project administration; resources; software; supervision; validation; visualization; writing-original draft; writing-review and editing. Gregory Paul: Conceptualization; data curation; formal analysis; investigation; methodology; resources; supervision; validation; writing-original draft; writing-review and editing. Shu-yu Hsu: Resources; software.