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1 June 2014 Estimating Body Mass from the Astragalus in Mammals
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Abstract

Astragalar fossils have been intensively studied as an indicator of the functional morphology and phylogenetic relationships of mammals. However, relatively few studies have investigated the relationship between astragalar size and body mass, usually with a focus on a particular taxonomic group. Here, univariate and multiple regression models are used to analyze the relationship between astragalar size and body mass based on an extensive sample of extant land mammals (11 orders, 48 species, 80 individuals; body mass ranging from 18 g to 3.4 t). The analyses revealed the size of the tibial trochlea to be a better predictor of body mass than the total size of the astragalus. Based on these results, estimates of the body mass of several Paleogene land mammals were calculated and compared to those of previous studies. Thus, for example, the body mass of “Baluchitherium”, the largest terrestrial mammal known to date, was estimated at about 10–15 t.

Introduction

The astragalus (= talus, anklebone) is a moderately compact bone forming part of the mammalian skeleton (Gray 1858). Owing to their robust morphology, astragali are frequently preserved in the fossil record, and more often found undamaged than long bones, vertebrae, or fragile skulls. The morphology of this element is highly diagnostic, easy to identify, and correlates well with the behavior of the animal (e.g., DeGusta and Vrba 2003). As a result, astragalar fossils have been widely used as an indicator of mammalian functional morphology, phylogenetic relationships, and taxonomy (e.g., Martinez and Sudre 1995; Nakatsukasa et al. 1997; Gebo et al. 2000; Plummer et al. 2008; Polly 2008; Dagosto et al. 2010; Parr et al. 2011).

In general, the body mass of an animal strongly correlates with its ecology, physiology, functional anatomy, diet, energetics, and life history (Peters 1983; Calder 1984; Legendre 1986, 1989; LaBarbera 1989; Damuth and MacFadden 1990; McNab 1990; Eisenberg 1990; Mendoza et al. 2004, 2005; Copes and Schwartz 2010), and estimates of the body mass of extinct species consequently form an important part of paleoecological analyses (e.g., Legendre 1986, 1989; Morlo 1999; Burness et al. 2001; Egi 2001; Smith et al. 2010). Several methodologies estimating the body mass of fossil taxa have been suggested (Dagosto and Terranova 1992; Smith 2002; Mendoza et al. 2006), focusing mostly on either craniodental (Gingerich et al. 1982; Legendre 1986, 1989; Conroy 1987; Damuth 1990; Janis 1990; Van Valkenburgh 1990; Fortelius 1990; Egi et al. 2002, 2004; Mendoza et al. 2006; Figueirido et al. 2011) or long bone measurements (Alexander et al. 1979; Anyonge 1993; Ruff 1990; Scott 1990; Gingerich 1990; Egi 2001; Andersson 2004; De Esteban-Triviqno et al. 2008; Figueirido et al. 2011). The cross-sectional diaphyseal and articular dimensions of long bones in particular seem to be good predictors of body mass for a variety of mammals (Gingerich 1990; Ruff 1990, 2003; Scott 1990; Anyonge 1993; Egi 2001; Andersson 2004), and are likely to perform better than either craniodental dimensions or long bone length measurements in the case of extinct mammals with no close phylogenetic links or phenetic similarity to any living species.

The astragalus has broad articular facets for both the tibia and fibula, and thus, like long bones, appears to be well correlated with body mass. However, only a few studies have investigated this relationship, usually with a focus on specific taxonomic groups, such as prosimian primates, artiodactyls, catarrhine primates, pinnipeds, and hominoid primates (Dagosto and Terranova 1992; Martinez and Sudre 1995; Rafferty et al. 1995; Polly 2008; Parr et al. 2011). Because of this taxonomic restriction, the results of these studies are difficult to apply to other mammalian groups.

Fig. 1.

Linear measurement positions on the astragalus (Li1–9) and their products (area, Ar1–4; volume, Vo1–3). The illustrations are based on a left astragalus of Macaca fuscata (Blyth, 1875) (Primates; Cercopithecidae). Dorsal (= anterior) (A, B), proximal (C), lateral (D), and medial (E) views. Abbreviations: Ar1–3, cross-sectional areas of the tibial trochlea; Ar4, cross- sectional area of the astragalus; Li1, transverse width of the tibial trochlea; Li2, proximodistal length of the lateral trochlear ridge of the tibial tro chlea; Li3, proximodistal length of the medial trochlear ridge of the tibial trochlea; Li4, transverse width of the astragalus; Li5, proximodistal length of the astragalus; Li6, proximodistal length of the central part of the tibial trochlea; Li7, transverse width between the medial and lateral trochlear ridges of the tibial trochlea; Li8, dorsoventral thickness of the lateral part of the astragalus; Li9, dorsoventral thickness of the medial part of the astragalus; Vo1–2, volume of the tibial trochlea; Vo3, volume of the astragalus.

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This article examines the allometric relationship between body mass and astragalar size based on an extensive sample of extant terrestrial mammals, with the ultimate aim of providing formulae capable of estimating the body mass of a variety of extinct taxa. As an example, the present results are applied to four groups of Paleogene land mammals, and their body mass estimates compared with those of previous studies.

Institutional abbreviations.—AMNH and AM, American Museum of Natural History, New York, USA; FAM, Frick Collection, American Museum of Natural History, New York, USA; IVPP, Institute of Vertebrate Paleontology and Paleoanthropology, Beijing, China.

Other abbreviations.—Ar, areas; BM, body mass; CF, correction factor; d.f., degree of freedom; JMP, SAS Institute software; Li, linear measurements; MPE, mean percentage prediction error; n, sample size; P, probability; PE, prediction error; PI, prediction interval; QMLE, quasi-maximum likelihood estimator; RE, ratio estimator; SE, the smearing estimate; SEE, standard error of estimate; R, correlation coefficient; Vo, volumes.

Material and methods

The core data of this study consist of the body mass (in g) and nine linear measurements (in mm) of the astragalus of 80 adult individuals, representing 48 species belonging to 11 orders of extant land mammals, and ranging from 18 g to 3.4 t (see SOM: Supplementary Online Material at  http://app.pan.pl/SOM/app59-Tsubamoto_SOM.pdf). Body masses represent the actual weight of each specimen, and were recorded either while the animals were still alive, or just after their death. Owing to the limited availability of specimens for which such data could be obtained, the dataset is somewhat biased towards primates and carnivores (SOM). Nine linear measurements of the astragalus (Li1–9; Fig. 1) were taken to the nearest 0.01 mm using digital calipers. In addition, four areal (mm2) and three volumetric (mm3) variables were calculated based on these measurements (Fig. 1). For the Paleogene taxa, data were derived from tables and direct measurements of figures in the literature (Osborn 1923; Granger and Gregory 1936; Mellett 1977; Martinez and Sudre 1995; Gebo et al. 2000), on the assumption that the fossil astragali used represented adult individuals. Prior to analysis, all data were transformed to a natural logarithm. Analyses were carried out using Excel (Microsoft), JMP (SAS Institute), and KaleidaGraph (Synergy Software).

To estimate body mass (BM), least squares regression was used instead of major axis or reduced major axis regression, as it can provide prediction intervals for each value (Sokal and Rohlf 1995; Simpson et al. 2003; Zar 2010). However, major axis and reduced major axis regression helped to determine the slope (Gingerich et al. 1982; Natori 2002; Warton et al. 2006). Linear measurements (Li1–9), areas (Ar1–4), and volumes (Vo1–3) were analyzed both together and separately using stepwise multiple regression analyses (Mendoza et al. 2006), with the P values to enter and leave set to 5% in JMP. Accurate 95 % prediction intervals (PIs) for each body mass estimate can be calculated following the formula of Simpson et al. (2003: 238). However, in the case of large sample sizes, approximate PIs can be calculated more easily as ± SEE x t(0.05)(2), d.f., where SEE is the standard error of estimate and the degrees of freedom (d.f.) = sample size (n) - 2 (Ruff 2003). In the case of the present analysis, the 95 % PI for 80 specimens (d.f. = 78) was thus calculated as ± 1.991 × SEE.

When regression is performed using log-transformed data, a systematic detransformation bias is introduced (Smith 1993a, b). To correct for this bias, I calculated three correction factors (CFs): the quasi-maximum likelihood estimator (QMLE), the smearing estimate (SE), and the ratio estimator (RE). The QMLE was calculated following Sprugel (1983), the SE following Duan (1983) and Smith (1993a, b), and the RE following Snowdon (1991) and Smith (1993a, b). The SE value is often similar to the QMLE value, while the RE is an unrelated measure (Smith 1993a). For the purpose of this analysis, I calculated an adjusted CF, consisting of the arithmetic mean of the minimum and maximum values from among the former three CFs. When estimating body mass, the log value determined by the regression analysis was first de-transformed to the actual value (in g), and then multiplied by this adjusted CF.

The degree of correlation (accuracy) between body mass and astragalar size was evaluated using the coefficient of determination adjusted for the number of variables (adjusted R2), the percent standard error of estimate (%SEE), and the mean percentage prediction error (%MPE). %SEE for natural log-transformed data was calculated as %SEE = (eSEE - 1) × 100 (Smith 1984a; Egi et al. 2002; Ruff 2003), while the percentage of prediction error of the de-transformed value (%PE) was calculated as %PE = (original value - estimated value) / estimated value × 100 (Smith 1981, 1984a, b). %MPE is the arithmetic mean of the absolute values of %PE for each variable calculated for each individual (Smith 1981, 1984a, b; Dagosto and Terranova 1992). Finally, %MPE for the values corrected using the adjusted CF was also calculated (%MPEad-CF).

Results and discussion

The three stepwise multiple regression analyses retained only a single predictor per analysis: loge(Li1) for the linear, loge(Ar3) for the areal, and loge(Vo1) for the volumetric measurements, with Li1 and Ar3 being more accurate than Vo1 (Table 1; Fig. 2).When all predictors were included in a single multiple regression analysis, only loge(Li1) was retained in the final model. These results were corroborated by individual bivariate regressions carried out for all 16 variables, which showed Li1, Ar3, and Vo1 to be the best predictors, respectively (Table 1; Figs. 2, 3). Additionally, Ar1 was also found to be a powerful predictor, as its adjusted R2, %SEE, and %MPEs were better than those of Vo1 (Table 1; Figs. 2, 3).

Table 1.

Results of the bivariate regression analyses of the linear, areal, and volumetric measurements. Abbreviations: N, sample size; SEE, standard error of estimate; adjusted R2, coefficient of determination adjusted by the number of variables; adjusted CF, adjusted correction factor (see text for details); %SEE, percent standard error of estimate; %MPE, mean percentage prediction error; %MPEad-CF , %MPE for the values corrected using the adjusted CF.

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Fig. 2.

Comparison of %SEE, %MPE, and %MPEad-CF arising from the bivariate regression analyses of the 16 astragalar measurements (Li1–9, Ar1–4, and Vo1–3). Abbreviations: ad-CF, adjusted correction factor; MPE, mean percentage prediction error; SEE, standard error of estimate.

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Fig. 3.

Scatter plots of the best-performing body mass (BM [g]) regressions, based on A, Li1 (mm); B, Ar1 (mm2); C, Ar3 (mm2). The black line indicates the line of best fit, while the dashed lines represent the upper and lower 95% prediction limits.

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All of the slopes of the major axis and reduced major axis analyses were identical to or slightly lower than the values inferred from the isometric hypothesis (Table 1; SOM). The adjusted R2, %SEE, and %MPE of the regressions for Li1, Ar1 and Ar3 (Table 1; Fig. 2) were comparable to those of previous studies focusing on craniodental or limb bone measurements (Damuth 1990; Janis 1990; Scott 1990; Van Valkenburgh 1990; Dagosto and Terranova 1992; Egi et al. 2002; Figueirido et al. 2011). Some of the measurements illustrated in Fig. 1 were difficult to define for some taxa, owing to a high degree of morphological variation. However, Li1, Li2, and Li9 were more easily determined and more stable than other measurements, thus making them and their products (Ar1, Ar3, and Vo1) most suitable for this study in terms of practical measurement procedures.

In conclusion, the width (Li1) and cross-sectional areas of the tibial trochlea (Ar1 and Ar3) are better predictors of body mass than indicators of the overall size of the astragalus (Li4, Li5, Ar4, and Vo3) (Table 1; Fig. 2). Judging from the adjusted R2, %SEE, %MPE, and %MPEad-CF, Li1 is as powerful a predictor as Ar1 and Ar3 (Table 1; Fig. 2), suggesting that the width of the tibial trochlea in terrestrial mammals is well constrained by body mass.

Application to Paleogene Mammals

The body mass of four groups of Paleogene land mammals with no close extant relatives were estimated using Li1 and Ar1 with adjusted CFs (Table 2; Fig. 4). The preferred areal measure, Ar3 (=Li1 × Li9), was not used here, as Li9 is often difficult to obtain from the literature. However, among the individual bivariate regression analyses, Ar1 performed almost as well as Ar3 (Table 1; Fig. 2).

Largest terrestrial mammal.—Several previous studies have provided estimates for the body mass of the largest terrestrial mammal known to date, the rhinocerotoid perissodactyl “Baluchitherium” (= Paraceratherium or “Indricotherium”). The present study slightly overestimates the body mass of rhinoceroses using Li1 and slightly underestimates them using Ar1 (Fig. 3, SOM). Therefore, the mean of these two estimates likely provides a better prediction for rhinocerotoids. In the case of “Baluchitherium”, this (geometric) mean was 12.7 t, with the 95% prediction interval ranging from 10.9–13.7 t (Table 2). It should be noted that, owing to its large size, the body mass of “Baluchitherium” could only be estimated by extrapolation, which may be subject to large errors (Draper and Smith 1998; Reynolds 2002; Zar 2010). Nevertheless, the estimate of the present study is consistent with those of Fortelius and Kappelman (1993) (11 t) and Gingerich (1990) (9–15 t), who used several measurements of body length, as well as limb bone diameters and lengths.

Table 2.

Body mass predictions for several Paleogene mammals based on Li1 and Ar1 (= Li1 × Li2), corrected using the adjusted CF (Fig. 1; Table 1). Abbreviations: BM, body mass; LPL and UPL, lower and upper 95% prediction limits.

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Although the present estimate for “Baluchitherium” was lower than that of Economos (1981) (<20 t, based on “gravitational tolerance”), the latter still lies within its maximum upper prediction limits (Li1: 44.2 t; Ar1: 23.7 t; Table 2). By contrast, the estimate of Alexander (1989) (34 t), which was based on the head-body length as measured from the restoration drawings of “Baluchitherium” by Granger and Gregory (1935: figs. 1, 2), lies well beyond the maximum upper prediction limit of Ar1, and hence might be considered unlikely.

Hyaenodontids.—Hyaenodontids are archaic carnivorous mammals with a unique molar morphology. Here, the body mass of Hyaenodon crucians and Hyaenodon horridus was estimated at 11 kg and 26–29 kg, respectively (Table 2). These values are similar to previous estimates based on head-body length (9 kg and 32 kg, respectively; Van Valkenburgh 1987) and limb bone dimensions (10–25 kg and 25–60 kg; Egi 2001), but much lower than reconstructions based on the length of the skull (23 kg and 150 kg; Van Valkenburgh 1987). Because head-body length is considered to be a reliable predictor of body mass (Creighton 1980; Damuth 1990; Van Valkenburgh 1990), these comparisons may indicate that the astragalus performs well in estimating the body mass of hyaenodontids.

Asian Eocene primate.—The body mass of fossil primates has been used extensively in their identification, taxonomy, phylogeny, and functional morphology (e.g., Gingerich et al. 1982; Dagosto and Terranova 1992; Fleagle 1998; Gebo et al. 2000). Gebo et al. (2000) described an astragalus (IVPP V11846) of the anthropoid primate Eosimias sp. from the Middle Eocene of Central China, and estimated the body mass of the animal to be 90–147 g based on the equations of Dagosto and Terranova (1992). However, the latter were exclusively derived from data on prosimian, rather than anthropoid, primates. Using the present equations, I estimate the body mass of IVPP V11846 to be 147–177 g, with a 95% PI of 84–295 g (Table 2). This estimate is slightly higher, but overall consistent, with than that of Gebo et al. (2000).

European Paleogene artiodactyls.—Martinez and Sudre (1995) estimated the body mass of several European Paleogene artiodactyls based on the astragalus and m1, with their astragalar estimate consisting of the product of the tibial trochlear width (∼ Li1) and the astragalar length (∼Li5). A recalculation of the body mass of these artiodactyls using Li1 (∼“l” in Martinez and Sudre 1995: fig. 2) resulted in somewhat lower estimates, with the exception of Diplobune minor, which has a proximodistally much shorter proportion of the astragalus than other artiodactyls (Martinez and Sudre 1995) (Fig. 4). However, the prediction intervals of the present analysis included the estimates of the earlier study, except for Doliochoerus quercyi from Pech Desse (Fig. 4), which has a proximodistally long and mediolaterally narrow astragalus (Martinez and Sudre 1995).

Fig. 4.

Comparison of body mass estimates for European Paleogene artiodactyls based on Li1 (this study) with those of Martinez and Sudre (1995). Where shown, mean estimates refer to the results of the latter study.

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Concluding remarks

Tibial trochlear size is the best astragalar predictor of body mass, based on data from a wide variety of extant mammals, and yields estimates comparable in their accuracy to those based on long bone data. When applied to a range of Paleogene mammals, the equations derived here yield estimates similar to those of previous studies, thus further supporting the use of tibial trochlear size as a reliable indicator of body mass. The present results thus have the potential to contribute significantly to quantitative taxonomic, ecological, and physiological studies of fossil land mammals, particularly those with no close phylogenetic links and/or similar morphological proportions to any extant species.

Acknowledgements

I am grateful to the following individuals involved in access to the specimens used in this research: Masanaru Takai, Takeshi Nishimura, and Naoko Egi (all Primate Research Institute, Kyoto University, Inuyama, Japan); Shin-ichiro Kawada (National Museum of Nature and Science, Tokyo, Japan); and Kensuke Yasui and Keiji Matsuoka (both Toyohashi Museum of Natural History, Toyohashi, Japan). Thanks are also due to Masahito Natori (Okayama University of Science, Okayama, Japan), who helped with the statistical analysis. This research was supported by the MEXT/JSPS Grants-in-Aid for Scientific Research (KAKENHI, nos. 21770265 and 23370044) and the Cooperation Program (nos. 2011-A-3 and 2012-B-2) of Primate Research Institute (Kyoto University, Inuyama, Japan).

References

1.

R.M. Alexander 1989. Dynamics of Dinosaurs and Other Extinct Giants. 167 pp. Columbia University Press, New York. Google Scholar

2.

R.M. Alexander , S.A. Jayes , G.M.O. Maloiy , and M.E. Wathuta 1979. Allometry of the limb bones of mammals from shrews (Sorex) to elephant (Loxodonta). Journal of Zoology (London) 189: 305–314. Google Scholar

3.

K. Andersson 2004. Predicting carnivoran body mass from a weight-bearing joint. Journal of Zoology (London) 262: 161–172. Google Scholar

4.

W. Anyonge 1993. Body mass in large extant and extinct carnivores. Journal of Zoology (London) 231: 339–350. Google Scholar

5.

G.P. Burness , J. Diamond , and T. Flannery 2001. Dinosaurs, dragons, and dwarfs: The evolution of maximal body size. PNAS 98: 14518–14523. Google Scholar

6.

E. Blyth 1875. Catalogue of mammals and birds of Burma. Journal of the Asiatic Society of Bengal 44 (2, extra no. ): i–xiv, 1–167. Google Scholar

7.

W.A. Calder 1984. Size, Function, and Life History. 431 pp. Harvard University Press, Cambridge. Google Scholar

8.

G.C. Conroy 1987. Problems of body-weight estimation in fossil primates. International Journal of Primatology 8: 115–135. Google Scholar

9.

L.E. Copes and G.T. Schwartz 2010. The scale of it all: postcanine tooth size, the taxon-level effect, and the universality of Gould's scaling law. Paleobiology 36: 188–203. Google Scholar

10.

G.K. Creighton 1980. Static allometry of mammalian teeth and the correlation of tooth size and body size in contemporary mammals. Journal of Zoology (London) 191: 435–443. Google Scholar

11.

M. Dagosto , L. Marivaux , D.L. Gebo K.C. Beard , Y. Chaimanee , J.-J. Jaeger , B. Marandat , A.N. Soe , and A.A. Kyaw 2010. The phylogenetic affinities of the Pondaung tali. American Journal of Physical Anthropology 143: 223–234. Google Scholar

12.

M. Dagosto and C.J. Terranova 1992 Estimating body size of Eocene primates: a comparison of results from dental and postcranial variables. International Journal of Primatology 13: 307–344. Google Scholar

13.

J. Damuth 1990. Problems in estimating body masses of archaic ungulates using dental measurements. In : J. Damuth and B.J. MacFadden (eds.), Body Size in Mammalian Paleobiology: Estimation and Biological Implications, 229–253. Cambridge University Press, Cambridge. Google Scholar

14.

J. Damuth and B.J. MacFadden 1990. Introduction: body size and its estimation. In : J. Damuth and B.J. MacFadden (eds.), Body Size in Mammalian Paleobiology: Estimation and Biological Implications, 1–10. Cambridge University Press, Cambridge. Google Scholar

15.

S. De Esteban-Triviqno , M. Mendoza , and M. De Renzi 2008. Body mass estimation in Xenarthra: a predictive equation suitable for all quadrupedal terrestrial placentals? Journal of Morphology 269: 1276–1293. Google Scholar

16.

D. DeGusta and E. Vrba 2003. A method for inferring paleohabitats from the functional morphology of bovid astragali. Journal of Archaeological Science 30: 1009–1022. Google Scholar

17.

N.R. Draper and H. Smith 1998. Applied Regression Analysis. 736 pp. 3rd edition. John Wiley & Sons, Inc., New York. Google Scholar

18.

N. Duan 1983. Smearing estimate: a nonparametric retransformation method. Journal of the American Statistical Association 78: 605–610. Google Scholar

19.

A.C. Economos 1981. The largest land mammal. Journal of Theoretical Biology 89: 211–215. Google Scholar

20.

N. Egi 2001. Body mass estimates in extinct mammals from limb bone dimensions: the case of North American hyaenodontids. Palaeontology 44: 497–528. Google Scholar

21.

N. Egi , M. Takai , N. Shigehara , and T. Tsubamoto 2002. Body mass estimates for Pondaung primates [in Japanese with English summary]. Primate Research 18: 1–18. Google Scholar

22.

N. Egi , M. Takai , N. Shigehara , and T. Tsubamoto 2004. Body mass esti mates for Eocene eosimiid and amphipithecid primates using prosimians and anthropoid scaling models. International Journal of Primatology 25: 211–236. Google Scholar

23.

J.F. Eisenberg 1990. The behavioral/ecological significance of body size in the Mammalia. In : J. Damuth and B.J. MacFadden (eds.), Body Size in Mammalian Paleobiology: Estimation and Biological Implications, 25–37. Cambridge University Press, Cambridge. Google Scholar

24.

B. Figueirido , J.A. Pérez-Claros , R.M. Hunt Jr. , and P. Palmqvist 2011. Body mass estimation in amphicyonid carnivoran mammals: A multiple regression approach from the skull and skeleton. Acta Palaeontologica Polonica 56: 225–246. Google Scholar

25.

J.G. Fleagle 1998. Primate Adaptation and Evolution. 2nd edition. 596 pp. Academic Press, New York. Google Scholar

26.

M. Fortelius 1990. Problems with using fossil teeth to estimate body sizes of extinct mammals. In : J. Damuth and B.J. MacFadden (eds.), Body Size in Mammalian Paleobiology: Estimation and Biological Implications, 207–228. Cambridge University Press, Cambridge. Google Scholar

27.

M. Fortelius and J. Kappelman 1993. The largest mammal ever imagined. Zoological Journal of Linnean Society, London 108: 85–101. Google Scholar

28.

D.L. Gebo , M. Dagosto , K.C. Beard , T. Qi , and J. Wang 2000. The oldest known anthropoid postcranial fossils and the early evolution of higher primates. Nature 404: 276–278. Google Scholar

29.

P.D. Gingerich 1990. Prediction of body mass in mammalian species from long bone length and diameters. Contributions from the Museum of Paleontology, University of Michigan 28: 79–92. Google Scholar

30.

P.D. Gingerich , B.H. Smith , and K. Rosenberg 1982. Allometric scaling in the dentition of primates and prediction of body weight from tooth size in fossils. American Journal of Physical Anthropology 58: 81–100. Google Scholar

31.

W. Granger and W.K. Gregory 1935. A revised restoration of the skeleton of Baluchitherium, gigantic fossil rhinoceros of Central Asia. American Museum Novitates 787: 1–3. Google Scholar

32.

W. Granger and W.K. Gregory 1936. Further notes on the gigantic extinct rhinoceros, Baluchitherium, from the Oligocene of Mongolia. Bulletin of the American Museum of Natural History 72: 1–73. Google Scholar

33.

H. Gray 1958. Anatomy: Descriptive and Surgical. 750 pp. J.W. Parker, London. Google Scholar

34.

C.M. Janis 1990. Correlation of cranial and dental variables with body size in ungulates and macropodoids. In : J. Damuth and B.J. MacFadden (eds.), Body Size in Mammalian Paleobiology: Estimation and Biological Implications, 255–299. Cambridge University Press, Cambridge. Google Scholar

35.

M. LaBarbera 1989. Analyzing body size as a factor in ecology and evolution. Annual Review of Ecology and Systematics 20: 97–117. Google Scholar

36.

S. Legendre 1986. Analysis of mammalian communities from the late Eocene and Oligocene of southern France. Palaeovertebrata 16: 191–212. Google Scholar

37.

S. Legendre 1989. Les communautés de mammifères du Paléogène (Eocène supérieur et Oligocène) d'Europe occidentale: structures, milieux et évolution. Münchner Geowissenschaftliche Abhandlungen (Reihe A, Geologie und Paläontologie) 16: 1–110. Google Scholar

38.

J.-N. Martinez and J. Sudre 1995. The astragalus of Paleogene artiodactyls: comparative morphology, variability and prediction of body mass. Lethaia 28: 197–209. Google Scholar

39.

B.K. McNab 1990. The physiological significance of body size. In : J. Damuth and B.J. MacFadden (eds.), Body Size in Mammalian Paleobiology: Estimation and Biological Implications, 11–23. Cambridge University Press, Cambridge. Google Scholar

40.

J.S. Mellett , 1977. Paleobiology of North American Hyaenodon (Mammalia, Creodonta). Contributions to Vertebrate Evolution 1: 1–134. Google Scholar

41.

M. Mendoza , B. Goodwin , and C. Criado 2004. Emergence of community structure in land mammal-dominated ecosystems. Journal of Theoretical Biology 230: 203–214. Google Scholar

42.

M. Mendoza , C.M. Janis , and P. Palmqvist 2005. Ecological patterns in the trophic-size structure of mammal communities: a taxon-free characterization. Evolutionary Ecology Research 7: 505–530. Google Scholar

43.

M. Mendoza , C.M. Janis , and P. Palmqvist 2006. Estimating the body mass of extinct ungulates: a study on the use of multiple regression. Journal of Zoology (London) 270: 90–101. Google Scholar

44.

M. Morlo 1999. Niche structure and evolution in creodont (Mammalia) faunas of the European and North American Eocene. Geobios 32: 297–305. Google Scholar

45.

M. Nakatsukasa , M. Takai , and T. Setoguchi 1997. Functional morphology of the postcranium and locomotor behavior of Neosaimiri fieldsi, a Saimiri-like middle Miocene platyrrhine. American Journal of Physical Anthropology 102: 515–544. Google Scholar

46.

M. Natori 2002. Allometric scaling in the molars of titi monkeys [in Japanese with English summary]. Primate Research 18: 59–67. Google Scholar

47.

H.F. Osborn 1923. Baluchitherium grangeri, a giant hornless rhinoceros from Mongolia. American Museum Novitates 78: 1–15. Google Scholar

48.

W.C.H. Parr , H.J. Chatterjee , and C. Soligo 2011. Inter- and intra-specific scaling of articular surface areas in the hominoid talus. Journal of Anatomy 218: 386–401. Google Scholar

49.

R.H. Peters 1983. The Ecological Implications of Body Size. 344 pp. Cambridge University Press, Cambridge. Google Scholar

50.

T.W. Plummer , L.C. Bishop , and F. Hertel 2008. Habitat preference of extant African bovids based on astragalus morphology: operationalizing ecomorphology for palaeoenvironmental reconstruction. Journal of Archaeological Science 35: 3016–3027. Google Scholar

51.

P.D. Polly 2008. Adaptive zones and the pinniped ankle: A 3D quantitative analysis of carnivoran tarsal evolution. In : E. Sargis and M. Dagosto (eds.), Mammalian Evolutionary Morphology: A Tribute to Frederick S. Szalay, 165–194. Springer, Dordrecht. Google Scholar

52.

K.L. Rafferty , A. Walker , C.B. Ruff , M.D. Rose , and P.J. Andrews 1995. Postcranial estimates of body weight in Proconsul, with a note on a distal tibia of P. major from Napak, Uganda. American Journal of Physical Anthropology 97: 391–402. Google Scholar

53.

P.S. Reynolds 2002. How big is a giant? The importance of method in estimating body size of extinct mammals. Journal of Mammalogy 83: 321–332. Google Scholar

54.

C. Ruff 1990. Body mass and hindlimb bone cross-sectional and articular dimensions in anthropoid primates. In : J. Damuth and B.J. MacFadden (eds.), Body Size in Mammalian Paleobiology: Estimation and Biological Implications, 119–149. Cambridge University Press, Cambridge. Google Scholar

55.

C.B. Ruff 2003. Long bone articular and diaphyseal structure in Old World monkeys and apes. II: Estimation of body mass. American Journal of Physical Anthropology 120: 16–37. Google Scholar

56.

K.M. Scott 1990. Postcranial dimensions of ungulates as predictors of body mass. In : J. Damuth and B.J. MacFadden (eds.), Body Size in Mammalian Paleobiology: Estimation and Biological Implications, 301–335. Cambridge University Press, Cambridge. Google Scholar

57.

G.G. Simpson , A. Roe , and R.C. Lewontin 2003. Quantitative Zoology. Revised edition. vii + 440 pp. Dover Publications, Mineola. Google Scholar

58.

F.A. Smith , A.G. Boyer , J.H. Brown , D.P. Costa , T. Dayan , S.K.M. Ernest , A.R. Evans , M. Fortelius , J.L. Gittleman , M.J. Hamilton , L.E. Harding , K. Lintulaakso , S.K. Lyons , C. McCain , J.G. Okie , J.J. Saarinen , R.M. Sibly , P.R. Stephens , J. Theodor , and M.D. Uhen 2010: The evolution of maximum body size of terrestrial mammals. Science 330: 1216–1219. Google Scholar

59.

R.J. Smith 1981. On the definition of variables in studies of primate dental allometry. American Journal of Physical Anthropology 55: 323–329. Google Scholar

60.

R.J. Smith 1984a. Allometric scaling in comparative biology: problems of concept and method. American Journal of Physiology 246: R152–R160. Google Scholar

61.

R.J. Smith 1984b. Determination of relative size: the “criterion of subtraction” problem in allometry. Journal of Theoretical Biology 108: 131–142. Google Scholar

62.

R.J. Smith 1993a. Bias in equations used to estimate fossil primate body mass. Journal of Human Evolution 25: 31–41. Google Scholar

63.

R.J. Smith 1993b. Logarithmic transformation bias in allometry. American Journal of Physical Anthropology 90: 215–228. Google Scholar

64.

R.J. Smith 2002. Estimating of body mass in paleontology. Journal of Human Evolution 42: 271–287. Google Scholar

65.

P. Snowdon 1991. A ratio estimator for bias correction in logarithmic regressions. Canadian Journal of Forest Research 21: 720–724. Google Scholar

66.

R.R. Sokal and F.J. Rohlf 1995. Biometry: the Principles and Practice of Statistics in Biological Research. 887 pp. 3rd edition. W.H. Freeman and Co., New York. Google Scholar

67.

D.G. Sprugel 1983. Correcting for bias in log-transformed allometric equations. Ecology 64: 209–210. Google Scholar

68.

B. Van Valkenburgh 1987. Skeletal indicators of locomotor behavior in living and extinct carnivores. Journal of Vertebrate Paleontology 7: 162–182. Google Scholar

69.

B. Van Valkenburgh 1990. Skeletal and dental predictors of body mass in carnivores. In : J. Damuth and B.J. MacFadden (eds.), Body Size in Mammalian Paleobiology: Estimation and Biological Implications, 181–205. Cambridge University Press, Cambridge. Google Scholar

70.

D.I. Warton , I.J. Wright , D.S. Falster , and M. Westoby 2006. Bivariate line-fitting methods for allometry. Biological Review 81: 259–291. Google Scholar

71.

J.H. Zar 2010. Biostatistical Analysis. 944 pp. 5th edition (Pearson International edition). Pearson Education, Inc., New Jersey.  Google Scholar
© 2014 T. Tsubamoto. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.
Takehisa Tsubamoto "Estimating Body Mass from the Astragalus in Mammals," Acta Palaeontologica Polonica 59(2), 259-265, (1 June 2014). https://doi.org/10.4202/app.2011.0067
Received: 17 June 2011; Accepted: 20 September 2012; Published: 1 June 2014
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