Prediction of marsupial body mass

P u b l i s h i n g

Volume 49, 2001© CSIRO 2001

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Australian Journal of Zoology, 2001, 49, 99–118

© CSIRO 2001 0004-959X/01/0209910.1071/ZO01009

Prediction of marsupial body mass

Troy J. Myers

Vertebrate Palaeontology Laboratory, School of Biological Science, University of New South Wales, NSW 2052, Australia.

Abstract

Cranio-dental variables are correlated with body mass in marsupials, using a species data-set derived fromextant australidelphian representatives, to predict body mass in fossil species. Thirty-eight extantaustralidelphian species, including 10 dasyuromorphians, 22 diprotodontians, 1 notoryctomorphian and 5peramelemorphians, were analysed. Where sexual dimorphism was prominent, genders were evaluatedseparately. Twenty-nine cranio-dental variables were measured for each specimen and species averagescalculated. Body masses were taken as recorded for each specimen or as published species averages. Thecranio-dental measures for each morpho-species were then regressed against average body mass in fourdistinct data-sets: (1) the entire species sample, (2) only dasyuromorphian taxa, (3) only diprotodontians,and (4) all species excluding dasyuromorphians. Each cranio-dental variable was then ranked according tovarious error statistics and correlation coefficients. Results suggest that predictors of body size ineutherians (such as first lower molar area), commonly used to estimate body mass in marsupials may notbe reliable or accurate indicators. Significant differences in the usefulness of predictor variables betweentaxonomic data-sets were also observed. Total jaw length is the most reliable predictor for diprotodontians,as well as for all species combined, whereas lower molar row length appears to be more appropriate fordasyuromorphians. Multiple variable regressions variably offer more precision than those derived fromindividual parameters. On the basis of these data, body mass estimations are provided for a number ofextinct marsupial taxa. T. J. MyersZO01009M ar supial body- mass pr edi cti onT. J . Myers

Introduction

The prediction of body size in fossil vertebrates serves a number of palaeobiological andpalaeoecological purposes, such as the determination of behaviour or physiology of speciesor individuals (e.g. McNab 1990; Martin 1990; Roth 1990). In recent times, body sizepredictions, specifically body mass, have been utilised in an attempt to elucidatepalaeoecological characteristics such as community structure, home range, populationdensity and biomass. Damuth and MacFadden (1990) suggest that body size ‘… may be themost useful single predictor of that species’ adaptations’. It is therefore not surprising thatthe literature concerning prediction of body size in fossil mammals is extensive. However,this work is biased heavily towards eutherian mammals. Janis (1990) correlated cranio-dental variables with body size in extant macropodoids but only for comparative purposes,with the focus concerning determination of body size in fossil ungulates. Other studies,such as Van Valkenburgh (1990), include marsupials in their data-sets, but sample sizes areusually too small to allow for separate analysis of marsupials. Legendre (1989) correlatesfirst lower molar area with body mass in marsupials, as well as a number of other taxa, butonly to confirm the usefulness of this dental variable for that purpose.

Furthermore, most studies have dealt primarily with the correlation of cranio-dentalelements and body size. Although predictions based on postcranial elements, especiallylimb variables such as cross-sectional area, are generally more reliable estimators of bodysize, it remains the case that most researchers do not have the luxury of access to sufficientnumbers of postcranial elements. In addition, it has long been recognised that, due to therobustness of cranio-dental elements, they are proportionately over-represented in the fossilrecord. Given this taphonomic bias, the relative ease of identifying dental and skull

100 T. J. Myers

elements and, in contrast, the present difficulties associated with recognition of species-specific postcranials, it is likely that cranio-dental elements will remain the tools of choicefor researchers investigating body size in fossil groups.

The focus of this study is therefore the correlation of cranio-dental variables with bodymass in marsupials, using a species data-set derived from extant australidelphianrepresentatives to predict body mass in fossil species. A comparison has also been madebetween regressions previously determined for eutherian groups and the new marsupialversions.

Methods

Thirty-eight extant australidelphian species, including 10 dasyuromorphians, 22 diprotodontians, 1notoryctomorphian and 5 peramelemorphians, were included in this analysis. These included speciesspanning the entire spectrum of body mass, ranging from a 10-g Planigale to a 70-kg Macropus. Inaddition, the wide range of species includes a number of trophic, locomotory and taxonomic groups. Malesand females have been separated for sexually dimorphic species, giving a total of 55 morpho-species(Table 1).

Twenty-nine cranio-dental variables were measured directly using a Wild M5A Microscope, a furthereight variables are composite area measurements combining maximum width and length (sensu Gould1975). These ‘area’ measurements were determined by multiplication of average tooth width by averagetooth length and do not, as such, represent actual molar areas.

Width and length dental measurements were taken as maximum crown distances, in occlusal view.Each tooth in a row was therefore reoriented before measuring, such that the maximum occlusal areawas visible. Janis (1990) found that widths, particularly muzzle width, were poorly correlated withbody mass in kangaroos and ungulates, so measurements of this dimension were not undertaken forskull variables. In addition to measurements on individual teeth, the following cranio-dentalmeasurements were made:

LMORL and UMORL. The ‘lower molar occlusal row length’ and ‘upper molar occlusal row length’variables are measurements from the most anterior portion of the first molar crown to the most posteriorportion of the fourth molar crown.

LMRL and UMRL. These variables are similar to LMORL and UMORL but the measurements aretaken from the respective alveoli instead of the molars, following Janis (1990).

TJL. The ‘total jaw length’ was measured from the most posterior part of the dentary, be that angularprocess or condyle, to the most anterior part of the first incisor. The first incisor is deemed to be a functionalpart of the lower jaw in most diprotodontians, particularly macropodoids (Janis 1990).

TSL. ‘Total skull length’ was taken from the anterior part of the muzzle, including incisors, to themost posterior part of the occipital region.

OCH. The ‘occipital height’ variable was measured from the basioccipital to the most dorsal part ofthe occipital.

PJL. ‘Posterior jaw length’ was determined by measuring from the posterior extremity of the fourthlower molar crown to the most posterior of the lower jaw, be that condyle or angular process.

PSL. Similarly, ‘posterior skull length’ was measured from the posterior extremity of the fourth uppermolar crown to the posterior edge of the occipital condyles.

Body mass measurements are means for species as published in various sources, or determined byaveraging weights from museum records. Ideally, mean weights should be calculated using individualweights recorded for every specimen measured, but these data are rarely available in sufficient numbers formuseum specimens. Martin (1980) found no significant difference between using published means or tagdata in regression analyses.

Where possible, species used were represented by 10 or more individuals of each sex from similargeographic locations so as to provide more accurate averages, although in many cases it was not possibleto obtain this number of suitable specimens. Only ‘adults’ were used in the analysis, as determined by theeruption of the fourth molar. Specimens from older animals, or those exhibiting potentially significant toothwear, were excluded. For dasyuromorphians the second premolar (the tooth anterior to the first molar) wascounted as a third premolar for purposes of the analysis. Third premolar variables such as 3UPW, 3UPL,3LPW and 3LPL are therefore measures of the ‘tooth anterior to the first molar’ for the ‘all species’ data-set.

Marsupial body-mass prediction 101

Table 1. Species used in analysisSource for data: 1, Flannery (1994); 2, Flannery (1995a); 3, Strahan (1995); 4, Flannery (1995b); 5, averages from Australian Museum specimens (NSW only); 6, averages from Australian Museum specimens; 7, Janis (1990); 8, median of weight range presented in

Strahan (1983); 9, Paddle (2001)

Species Sample size Mean body mass (g) Source (M/F)

DiprotodontiansAepyprymnus rufescens 2 –/2500 7Bettongia penicillata 2 1300 3Cercartetus caudatus 12 30 3Dactylopsila trivirgata 10 423 3Dendrolagus goodfellowi 6 –/8150 2Dorcopsis atrata 2 7500/– 4Dorcopsis hageni 3 –/5500 2Dorcopsulus vanheurni 4 1750/– 2Macropus giganteus 7 43000/– 7Macropus robustus 4 39000/20000 7Macropus rufus 8 66000/26500 3Petauroides volans 15 1068/1130 1Petaurus norfolcensis 9 230 3Phascolarctos cinereus 16 6254/5281 5Pseudocheirus peregrinus 12 987/878 1Setonix brachyurus 3 –/2900 3Spilocuscus maculatus 23 4567 1Thylogale billardierii 4 –/3900 3Thylogale stigmatica 8 5100/4100 3Trichosurus vulpecula 18 2701/2362 1Vombatus ursinus 14 26000 3Wallabia bicolor 2 17000/13000 3

PeramelemorphiansEchymipera kalubu 18 1313/604 2Echymipera rufescens 7 1450/– 6Isoodon macrourus 13 2100/1100 3Microperoryctes longicauda 16 478/598 2Perameles nasuta 15 1441/895 6

DasyuromorphiansAntechinus flavipes 9 56/34 3Antechinus minimus 6 65/– 3Antechinus stuartii 20 35/20 3Antechinus swainsonii 4 65/– 3Dasyurus maculatus 15 3210/1830 5Dasyurus viverrinus 11 1300/880 3Planigale maculata 4 12/10 3Sminthopsis crassicaudata 5 15/– 3Sminthopsis macroura 3 20/– 3Thylacinus cynocephalus 12 29500 9

NotoryctomorphiansNotoryctes caurinus 3 –/55 8

102 T. J. Myers

Cranio-dental variables were correlated against mean body mass for species using least-squaresregression methods. The data were analysed, using SigmaStat (1992), as four separate species data-sets [(1)all species, (2) all species excluding dasyuromorphians, (3) diprotodontian species, and (4)dasyuromorphian species] as previous studies (e.g. Damuth 1990) have suggested that prediction estimatesimprove with regressions based on taxonomically restricted data-sets. The dasyuromorphians, in particular,as carnivore–insectivores with specialised skull modifications, may not follow allometric equations derivedfor non-carnivorous taxa (Van Valkenburgh 1990).

For each regression, Studentised residuals were calculated such that outliers, those data-points lyingoutside of the regression population’s 95% confidence limits, were removed from the data-set before theregression equation was computed.

As the correlation coefficient, and its derivatives, are (1) affected by the range of data being analysed,(2) influenced by the slope of the regression, and (3) poorly reflect the confidence with which predictionscan be made (Smith 1984), it has been necessary to include other determinators of a regression’s ability topredict and ‘goodness-of-fit’. The indicators used in this analysis, besides the correlation coefficient, arethe percent standard error of the estimate (SEE%) and percent prediction error (PE%). Determination ofPE% and SEE% follow Smith (1981,1984). All regressions have been ranked, in order of decreasingaccuracy, according to these determinators and, where necessary, the adjusted determination coefficient(adjusted R2).

Due to logarithmic transformation bias (Smith 1993) predicted body mass, presented here asdetransformed values, are almost certainly underestimates. To correct for this bias the smearing estimate(SE) (Duan 1983; Smith 1993) has been applied to all predictor variables (Table 2). Application of the SEto a predicted body mass estimate will largely correct for transformation bias.

Accuracy and precision of regressions have been further tested by predicting body mass for a numberof extant taxa, not used in the original data-sets, as well as for a variety of extinct species (Tables 7, 8).

Specimens used in this analysis are held in the Australian Museum, Queensland Museum (QMF, QMJand QMJM) and the University of New South Wales zoology and palaeontology collections (UNSW andAR respectively).

Results

Single-variable regressions

All species

For the data-set comprising all species the ‘best predictor’ variable is TJL, followed byTSL and UMORL (Table 2). The best dental predictor is UMORL followed closely byLMORL. In general, composite ‘area’ variables are slightly better predictors than thosebased solely on length or width. Premolar variables are poorly correlated with body mass,having high percent standard errors greater than 88% and as high as 124%, as well assimilarly high PE% values. Only the 4th upper molar width (4UMW) exhibits accuracystatistics below those for premolar variables. Additionally, lower molar width regressionsare better predictors than those derived from upper molar widths. For regressions using theentire sample the standard error of the estimate (SEE%) has a large range (39–160%).

All non-dasyuromorphian species

The most accurate predictor variable for the data-set excluding dasyuromorphians isUMRL, followed by UMORL and TJL. As for the ‘all species’ data-set, premolar variablesare among the least accurate variables to use for predicting body mass, as highlighted bythe relatively low accuracy statistics for these variables (Table 3). First lower and first uppermolar variables are also poor predictors. In general, the SEE% and PE% are lower forregressions in this data-set than they are for those including all species. Exclusion ofdasyuromorphians from the data-set results in a SEE% range for the regressions of 34–110%.

The highest-ranked individual predictor variable for the ‘all species’ sample is TJL.Interestingly, UMRL in the non-dasyuromorphian data-set has lower error statistics, and is


therefore a better predictor than the former. Comparing just UMRL, ranked first in the non-dasyuromorphian data-set and fourth for ‘all species’, SEE% is 34 in the former and 52 inthe latter, despite both data-sets exhibiting similar correlation coefficients for thisparameter.

In contrast to the ‘all species’ regressions (1) there is no evidence for upper molar widthsbeing less accurate predictors than lower molar widths, (2) TSL is ranked far lower as apredictor variable, and (3) 4UMW is ranked far higher.

Table 2. Ranked body-mass equations for the ‘all species’ data-set

Regression Variable SEE PE SEE% PE% Total Adjusted Smearing (x) % % rank rank rank R2 estimate

(%)

log y = –3.036 + 3.464(log x) TJL 39 27 1 1 1 0.980 5.2log y = –3.733 + 3.641(log x) TSL 40 28 2 2 2 0.979 5.5log y = –0.914 + 3.320(log x) UMORL 51 35 3 3 3 0.967 8.6log y = –0.944 + 3.372(log x) UMRL 52 36 4 4 4 0.970 8.9log y = –1.253 + 3.540(log x) LMORL 55 38 5 5 5 0.962 9.4log y = –1.302 + 3.602(log x) LMRL 60 39 6 6 6 0.962 10.3log y = 1.385 + 1.536(log x) 4UMA 61 42 7 8 7 0.959 12.1log y = 1.005 + 1.857(log x) 2LMA 63 41 8 7 7 0.951 11.9log y = 0.914 + 3.327(log x) 3UML 66 44 9 9 8 0.953 13.4log y = 1.124 + 1.710(log x) 3LMA 66 44 9 9 8 0.952 13.7log y = 1.422 + 3.396(log x) 3LMW 68 45 10 10 9 0.950 14.0log y = 1.657 + 3.112(log x) 4LMW 69 45 11 10 10 0.948 14.9log y = –1.295 + 3.529(log x) OCH 69 47 11 11 11 0.949 14.7log y = 0.909 + 3.245(log x) 4LML 69 47 11 11 11 0.948 15.1log y = 1.360 + 1.546(log x) 4LMA 71 47 12 11 12 0.947 14.9log y = 1.423 + 3.495(log x) 2LMW 71 47 12 11 12 0.942 14.3log y = 0.751 + 3.525(log x) 3LML 71 48 12 12 13 0.945 14.5log y = 0.606 + 3.846(log x) 2LML 72 48 13 12 14 0.939 15.3log y = 1.865 + 2.408(log x) 4UML 72 50 13 14 15 0.946 16.6log y = 1.278 + 1.759(log x) 1LMA 75 50 14 14 16 0.933 16.3log y = –1.448 + 3.443(log x) PJL 79 49 16 13 17 0.936 16.3log y = 0.633 + 3.782(log x) 2UML 77 50 15 14 17 0.933 16.1log y = 0.737 + 1.951(log x) 1UMA 77 51 15 15 18 0.931 16.6log y = 1.669 + 3.345(log x) 1LMW 79 50 16 14 18 0.928 16.7log y = 0.662 + 1.942(log x) 2UMA 80 52 17 16 19 0.930 16.7log y = 0.421 + 4.146(log x) 1UML 81 54 18 17 20 0.924 18.4log y = 1.685 + 2.377(log x) 3LPL 88 50 21 14 20 0.914 18.6log y = 0.813 + 1.791(log x) 3UMA 84 54 20 17 21 0.933 18.6log y = 0.792 + 3.770(log x) 1LML 82 56 19 19 22 0.923 19.5log y = 1.015 + 3.681(log x) 1UMW 88 55 21 18 23 0.916 22.0log y = 0.634 + 4.073(log x) 2UMW 88 57 21 20 24 0.920 20.1log y = –2.789 + 3.885(log x) PSL 91 57 22 20 25 0.920 20.8log y = 2.052 + 2.753(log x) 3UPW 100 72 23 23 26 0.902 33.2log y = 0.638 + 3.953(log x) 3UMW 110 66 24 22 26 0.900 26.9log y = 1.494 + 2.626(log x) 3UPL 115 64 25 21 26 0.880 28.4log y = 2.327 + 2.806(log x) 3LPW 124 82 26 24 27 0.868 40.0log y = 1.072 + 3.418(log x) 4UMW 160 95 27 25 28 0.835 49.9

104 T. J. Myers

Dasyuromorphian species

For dasyuromorphian species alone, LMRL, followed by UMRL, are the best predictorvariables, being separated in the accuracy rankings by only 1 PE%. The second upper molararea (2UMA) is the best individual dental predictor. Lower molar row length (LMRL) is thebest correlated non-dental variable, with a SEE% of 18. The dasyuromorphian regressionsexhibit the lowest range of SEE% values (18–74%) (Table 4).

Table 3. Ranked body-mass equations for the ‘all species excluding dasyuromorphians’ data-set

Regression Variable SEE PE SEE% PE% Total Adjusted Smearing(x) % % rank rank rank R2 estimate

(%)

log y = –0.229 + 2.880(log x) UMRL 34 23 1 1 1 0.961 3.9log y = –0.366 + 2.936(log x) UMORL 36 25 2 2 2 0.963 4.6log y = –3.027 + 3.475(log x) TJL 37 25 3 2 3 0.957 4.7log y = 1.743 + 1.305(log x) 4LMA 41 28 4 3 4 0.946 7.2log y = 1.301 + 1.527(log x) 3UMA 42 29 5 4 5 0.946 5.6log y = 1.591 + 1.408(log x) 3LMA 42 30 5 5 6 0.944 5.8log y = 1.810 + 1.257(log x) 4UMA 43 30 6 5 7 0.956 6.2log y = 1.291 + 2.927(log x) 3LML 44 31 7 6 8 0.926 5.5log y = –0.370 + 2.978(log x) LMRL 46 30 9 5 9 0.935 6.7log y = –3.273 + 3.425(log x) TSL 45 32 8 7 10 0.951 6.6log y = –0.549 + 3.056(log x) LMORL 45 32 8 7 10 0.947 6.8log y = 1.210 + 3.326(log x) 3UMW 50 31 10 6 11 0.929 7.2log y = 1.310 + 2.908(log x) 3UML 46 32 9 7 11 0.925 6.6log y = 1.262 + 1.568(log x) 2UMA 46 33 9 8 12 0.912 7.1log y = 1.989 + 2.609(log x) 4LMW 51 32 11 7 13 0.920 9.0log y = –1.043 + 3.230(log x) PJL 53 32 13 7 14 0.935 8.1log y = 2.077 + 2.074(log x) 4UML 52 39 12 10 15 0.924 8.3log y = 1.801 + 2.809(log x) 3LMW 57 38 16 9 16 0.907 9.9log y = 1.423 + 2.804(log x) 2UML 54 41 14 12 17 0.889 10.1log y = 1.586 + 1.436(log x) 2LMA 56 40 15 11 17 0.881 9.2log y = 1.299 + 3.193(log x) 2UMW 59 38 18 9 18 0.869 9.5log y = 1.142 + 3.204(log x) 2LML 58 40 17 11 19 0.836 8.8log y = –2.410 + 3.724(log x) PSL 61 39 19 10 20 0.918 10.6log y = 1.665 + 2.391(log x) 4LML 61 41 19 12 21 0.894 12.5log y = 1.675 + 2.778(log x) 4UMW 65 41 21 12 22 0.914 11.2log y = 1.815 + 2.815(log x) 2LMW 66 45 22 14 23 0.846 12.7log y = –0.850 + 3.232(log x) OCH 68 43 24 13 24 0.904 12.3log y = 1.314 + 1.558(log x) 1UMA 66 46 22 15 24 0.846 10.0log y = 2.307 + 2.141(log x) 3UPW 67 45 23 14 24 0.843 14.1log y = 1.762 + 2.578(log x) 1UMW 68 45 24 14 25 0.792 9.8log y = 2.112 + 1.747(log x) 3LPL 62 71 20 20 26 0.828 42.6log y = 1.249 + 3.081(log x) 1UML 71 52 25 18 27 0.827 12.7log y = 1.688 + 1.431(log x) 1LMA 73 51 26 17 27 0.817 13.1log y = 1.964 + 2.769(log x) 1LMW 78 50 27 16 27 0.799 13.3log y = 1.568 + 2.694(log x) 1LML 88 62 28 19 28 0.761 18.3log y = 1.871 + 2.102(log x) 3UPL 110 62 30 19 29 0.763 29.9log y = 2.640 + 1.966(log x) 3LPW 91 86 29 21 30 0.747 45.6


Diprotodontians only

TJL is again the best overall predictor of body mass. The most accurate dental predictorappears to be UMORL. Surprisingly, 4UMW, a lowly ranked variable in other data-sets, andthe worst predictor variable for ‘all species’, is a more accurate predictor of body mass fordiprotodontian species.

For diprotodontians, first molar variables are ranked among the least accurate of bodymass predictors, with errors far exceeding those exhibited by their dasyuromorphiancounterparts (Table 5). Only third upper and lower premolar length and third lower

Table 4. Ranked body-mass equations for the dasyuromorphian data-set

Regressions Variable SEE PE SEE% PE% Total Adjusted Smearing(x) % % rank rank rank R2 estimate

(%)

log y = –1.075 + 3.209(log x) LMRL 18 13 1 1 1 0.996 3.0log y = –0.992 + 3.279(log x) UMRL 18 14 1 2 2 0.996 1.2log y = –1.098 + 3.350(log x) UMORL 19 14 2 2 3 0.996 1.2log y = –1.225 + 3.340(log x) LMORL 20 16 3 3 4 0.995 1.6log y = –2.551 + 3.496(log x) PSL 24 16 4 3 5 0.993 2.0log y = –2.722 + 3.207(log x) TJL 26 18 5 4 6 0.991 2.3log y = –3.465 + 3.436(log x) TSL 27 19 6 5 7 0.991 2.2log y = –1.409 + 3.183(log x) PJL 28 20 7 6 8 0.990 2.6log y = 0.426 + 1.890(log x) 2UMA 31 21 8 7 9 0.989 2.9log y = 0.379 + 4.038(log x) 2UMW 31 21 8 7 9 0.989 3.0log y = 0.290 + 3.945(log x) 1UML 31 22 8 8 10 0.989 3.0log y = 0.567 + 3.400(log x) 3LML 33 22 9 8 11 0.987 3.5log y = –1.341 + 3.434(log x) OCH 34 24 10 10 12 0.986 3.7log y = 0.775 + 3.143(log x) 3UML 35 23 11 9 12 0.985 4.0log y = 0.528 + 3.381(log x) 4UMW 36 23 12 9 13 0.977 3.8log y = 0.559 + 1.720(log x) 3UMA 36 24 12 10 14 0.984 4.2log y = 2.053 + 3.372(log x) 3UPW 36 24 12 10 14 0.977 16.3log y = 0.878 + 1.777(log x) 3LMA 37 25 13 11 15 0.984 4.4log y = 0.771 + 3.116(log x) 4LML 37 25 13 11 15 0.984 4.4log y = 0.560 + 1.977(log x) 1UMA 38 24 14 10 15 0.983 4.5log y = 0.511 + 3.622(log x) 2LML 38 25 14 11 16 0.983 4.5log y = 1.085 + 1.622(log x) 4LMA 37 26 13 12 16 0.983 4.5log y = 1.156 + 1.724(log x) 4UMA 38 26 14 12 17 0.983 4.4log y = 0.312 + 3.780(log x) 3UMW 39 25 15 11 17 0.982 4.8log y = 0.811 + 3.984(log x) 1UMW 40 25 16 11 18 0.982 4.7log y = 1.432 + 3.374(log x) 4LMW 39 27 15 13 19 0.982 4.8log y = 0.519 + 3.497(log x) 2UML 39 27 15 13 19 0.982 4.9log y = 0.890 + 1.845(log x) 2LMA 40 27 16 13 20 0.981 5.0log y = 0.723 + 3.688(log x) 1LML 42 27 17 13 21 0.980 5.3log y = 1.228 + 3.702(log x) 3LMW 44 29 18 14 22 0.978 6.2log y = 1.163 + 1.845(log x) 1LMA 44 30 18 15 23 0.978 5.9log y = 1.806 + 3.231(log x) 4UML 46 30 19 15 24 0.977 5.9log y = 1.253 + 3.337(log x) 3UPL 49 29 21 14 25 0.974 6.6log y = 1.298 + 3.734(log x) 2LMW 48 31 20 16 26 0.975 6.8log y = 1.612 + 3.664(log x) 1LMW 52 34 22 17 27 0.971 8.0log y = 2.248 + 3.302(log x) 3LPW 55 35 23 18 28 0.968 9.0log y = 1.575 + 2.694(log x) 3LPL 74 46 24 19 29 0.949 13.7

106 T. J. Myers

premolar width (3UPL, 3LPL and 3LPW) rank lower than the first molar variables. Incontrast, third upper premolar width (3UPW) is the third most accurate predictor variablefor diprotodontians, despite being a particularly poor predictor in other data-sets. TheSEE% range for diprotodontians is 29–165%.

The first lower molar crown area has been extensively cited as one of the most accuratedental estimators of body mass in mammals. However, 1LMA ranked as one of the leastaccurate estimators in the diprotodontian, dasyuromorphian and non-dasyuromorphiandata-sets. In the ‘all species’ data-set this variable was ranked higher, albeit only as the 16th

Table 5. Ranked body-mass equations for the diprotodontians data-set

Regression Variable SEE PE SEE% PE% Total Adjusted Smearing (x) % % rank rank rank R2 estimate

(%)

log y = –2.884 + 3.426(log x) TJL 29 20 1 1 1 0.977 2.8log y = –0.567 + 3.072(log x) UMORL 37 25 3 2 2 0.962 4.7log y = 1.775 + 2.991(log x) 3UPW 36 26 2 3 2 0.954 1.3log y = –0.418 + 3.011(log x) UMRL 38 25 4 2 3 0.906 4.4log y = –3.410 + 3.508(log x) TSL 38 26 4 3 4 0.962 4.9log y = 1.774 + 1.291(log x) 4UMA 40 29 5 6 5 0.959 5.4log y = 1.733 + 1.322(log x) 4LMA 41 28 6 5 5 0.955 5.8log y = 1.275 + 1.559(log x) 3UMA 42 28 7 5 6 0.957 5.5log y = 1.804 + 2.706(log x) 4UMW 42 28 7 5 6 0.956 5.5log y = 1.371 + 1.555(log x) 3LMA 43 28 8 5 7 0.953 5.9log y = 1.907 + 2.719(log x) 4LMW 44 27 9 4 7 0.950 6.2log y = 1.809 + 2.400(log x) 4UML 44 31 9 7 8 0.953 6.4log y = 1.303 + 3.242(log x) 3UMW 46 29 10 6 8 0.948 6.3log y = –0.719 + 3.236(log x) LMRL 47 28 11 5 8 0.865 6.4log y = 1.348 + 2.890(log x) 3UML 46 32 10 8 9 0.949 6.8log y = –0.783 + 3.222(log x) LMORL 46 32 10 8 9 0.945 7.1log y = 1.225 + 3.019(log x) 3LML 47 32 11 8 10 0.944 7.1log y = –2.748 + 3.964(log x) PSL 53 33 13 9 11 0.937 8.4log y = 1.587 + 3.114(log x) 3LMW 53 33 13 9 11 0.932 8.3log y = 1.640 + 2.490(log x) 4LML 51 35 12 11 12 0.937 8.3log y = 0.951 + 1.778(log x) 2UMA 54 34 14 10 13 0.919 8.6log y = –0.952 + 3.313(log x) OCH 55 35 15 11 14 0.931 8.7log y = –0.998 + 3.211(log x) PJL 61 36 17 12 15 0.918 9.6log y = 1.039 + 3.340(log x) 2UML 57 38 16 13 15 0.912 9.6log y = 1.016 + 3.582(log x) 2UMW 63 36 18 12 16 0.898 10.1log y = 1.214 + 1.708(log x) 2LMA 61 39 17 14 17 0.902 10.5log y = 0.959 + 3.442(log x) 2LML 65 43 19 15 18 0.890 12.8log y = 1.543 + 3.257(log x) 2LMW 71 45 20 16 19 0.876 12.5log y = 1.109 + 3.470(log x) 1UMW 73 43 21 15 19 0.858 13.2log y = 0.910 + 1.821(log x) 1UMA 75 48 22 17 20 0.851 15.0log y = 0.848 + 3.632(log x) 1UML 82 58 23 19 21 0.828 18.5log y = 1.682 + 3.226(log x) 1LMW 89 56 24 18 21 0.805 19.2log y = 1.271 + 1.740(log x) 1LMA 89 60 24 20 22 0.807 20.6log y = 0.971 + 3.515(log x) 1LML 106 75 25 21 23 0.750 28.6log y = 2.424 + 2.377(log x) 3LPW 119 75 26 21 24 0.706 34.3log y = 1.841 + 2.116(log x) 3UPL 132 78 27 22 25 0.692 39.2log y = 2.263 + 1.703(log x) 3LPL 165 107 28 23 26 0.587 64.5


Tab

le 6

.M

ulti

ple-

vari

able

reg

ress

ions

Dat

a-se

tR

egre

ssio

n eq

uatio

nA

djus

ted

SEE

%PE

%Sm

eari

ng R

2es

tim

ate

(%)

All

spec

ies

log

y =

–2.

23 –

3.0

1(lo

g 2U

ML

) +

6.08

(log

UM

RL

)0.

983

3627

1.2

All

spec

ies

log

y =

1.3

8 +

2.0

6(lo

g 1L

MW

) +

1.2

8(lo

g 4L

ML

)0.

959

5537

10.1

All

spec

ies

log

y =

1.2

7 +

0.9

89(l

og 1

UM

A)

+ 1

.25(

log

4UM

L)

0.95

658

379.

9A

ll sp

ecie

slo

g y

= –

3.1

+ 0

.853

(log

OC

H)

+ 2

.74(

log

TS

L)

0.97

742

296.

7A

ll –

dasy

urom

orph

ians

log

y =

–0.

919

+ 1

.27(

log

4LM

W)

+ 1

.86(

log

TSL

)0.

972

3223

5.6

All

– da

syur

omor

phia

nslo

g y

= 1

.22

+ 1

.55(

log

1UM

W)

+ 0

.915

(log

4U

MA

) 0.

956

5841

22.9

All

– da

syur

omor

phia

nslo

g y

= 1

.38

+ 1

.85(

log

3LM

W)

+ 0

.72(

log

4LM

A)

0.95

762

4325

.4A

ll –

dasy

urom

orph

ians

log

y =

–2.

54 +

0.9

19(l

og O

CH

) +

2.5

5(lo

g T

JL)

0.97

742

2811

.7D

asyu

rom

orph

ians

lo

g y

= –

3.75

– 5

.91(

log

2UM

L)

+ 8.

61(l

og L

MR

L)

0.99

323

132.

5D

asyu

rom

orph

ians

log

y =

0.3

69 –

1.1

5(lo

g 2L

MA

) +

5.51

(log

3L

ML

)0.

987

3322

3.5

Das

yuro

mor

phia

nslo

g y

= –

2.28

+ 0

.789

(log

OC

H)

+ 2

.7(l

og P

SL)

0.99

323

161.

1D

ipro

todo

ntia

nslo

g y

= –

2.83

– 1

.07(

log

PSL

) +

4.3

(log

TJL

)0.

973

3122

3.9

Dip

roto

dont

ians

log

y =

1.6

1 +

0.8

19(l

og 1

UM

W)

+ 0

.985

(log

4U

MA

)0.

955

3624

3.8

Dip

roto

dont

ians

log

y =

1.5

6 +

1.5

4(lo

g 3L

MW

) +

1.3

4(lo

g 4L

ML

)0.

963

3723

2.3

108 T. J. Myers

most accurate predictor. Indeed, composite-area measurements of other lower molarsconsistently ranked far higher than 1LMA (Tables 2–5).

Multiple-variable regressions

In addition to correlating body mass against individual variables, ‘best subsets’ analyseswere performed on each data set such that the ‘best’ pair of predictor variables could bedetermined. Using multiple variables does not necessarily lessen the percent standard errorof the estimate or the prediction error.

All species

For the data-set comprising all species the best overall subset of cranio-dental variablesis a combination of second upper molar length (2UML) and UMRL (Table 6). The relevanterror statistics are slightly lower for the multiple linear regression than they are for thehighest-ranked individual estimator, in this case TJL. The most reliable combination ofindividual teeth variables is first lower molar width and fourth lower molar length (1LMWand 4LML). However, the PE% and SEE% figures for this regression are far higher thanthose for TJL alone, potentially making the former redundant. For upper molars only, thebest pair of variables are first upper molar area (1UMA) and fourth upper molar length(4UML). Using cranial variables only, the two best variables are OCH and TSL. The latterhas a lower SEE% and PE% than the multiple variable regressions based on individual teeth(Table 6).

All non-dasyuromorphian species

The best pair of overall variables is fourth lower molar width (4LMW) and TSL. Thiscombination exhibits marginally better error statistics than the highest-ranked individualvariable (UMRL). First upper molar width (1UMW) and fourth upper molar area (4UMA)are the most reliable combination of single dental variables. For lower dentition only thebest subset is a combination of third lower molar width and fourth lower molar area (3LMWand 4LMA). Using cranial data, the best variable pair is OCH and TJL. The last two multi-variable regressions do not exhibit error values smaller than those for the best individualvariable regression (UMRL).

Dasyuromorphians only

The best pair of predictor variables is 2UML and LMRL. For lower dental and cranialvariables the best combinations are second lower molar area and third lower molar length(2LMA and 3LML) and PSL and OCH respectively. A ‘best’ subset of upper dentalvariables could not be determined as the second variable was consistently redundant. Noneof the bivariate regressions had lower predictive error margins than the best individualpredictor, LMRL (Tables 4, 6).

Diprotodontians only

The most reliable pair of cranial, and overall, variables is PSL and TJL. The best pair ofdental predictors for upper molars is the 1UMW and 4UMA, while the best pair for lowermolars is 3LMW and 4LML. The multiple variable regressions are better predictors thanmost individual variable regressions, although none approach the predictive power of thebest individual variable regression (TJL).


The smearing estimate (SE)

For variables derived from the ‘all species’ data-set the smearing estimate correction factoris 5.2–49.9%; for the data-set excluding dasyuromorphians it is 3.9–45.6%, for‘dasyuromorphians’ 1.2–16.3% and for the ‘diprotodontian’ data-set 1.3–64.5% (Tables 2–5). Prediction equations derived from the dasyuromorphian data-set exhibit the lowestrange and absolute figures for SE, suggesting that the geometric mean is more closelyapproximating the arithmetic mean for these variables relative to the other data-setsanalysed.

For the multiple-variable regressions presented the smearing estimate correction factorranged as follows: (1) 2.3–3.9% for diprotodontians, (2) 1.1–3.5% for dasyuromorphians,(3) 5.6–25.4% for all species excepting dasyuromorphians, and (4) 1.2–10.1% for thewhole sample (Table 6).

Body-mass estimations

Body-mass predictions were made for seven extinct taxa, based on the ‘best’ and second‘best’ predictor variables for the taxon concerned. The predictor variables used were notalways the first and second most highly ranked for the data-set employed, due to thelimitations associated with the completeness of specimens. These estimates vary between1 and 18% of the most reliable. Predictions made for these taxa using first lower molar area(1LMA) differ significantly from those derived from more reliable variables.

In addition, body-mass predictions are given for 10 randomly selected extantAustralidelphian taxa, derived from the most reliable variables. These exhibit PE% valuesranging from 4 to 41%, with a mean of 27.4% (Table 8).

Discussion

Fortelius (1990) suggested that within Mammalia ‘… it is always possible to get anapproximate idea of body size … In the case of morphologically similar, closely relatedspecies, quite precise relative sizes can also be determined, no matter how imprecise theestimates of absolute size’. One would therefore expect that regression equations derivedfrom restricted taxonomic subsets would result in more-precise body-mass predictions thanthose employing paraphyletic or polyphyletic groupings. In the present study this assertionholds true for the dasyuromorphian subset, which consistently exhibits the lowest errorstatistics. Only nine variables, eight in the dasyuromorphian data-set and one in thediprotodontian, have a SEE% equal to or less than 30% and none represent individual toothparameters. This is consistent with the findings of Damuth and MacFadden (1990) thatstandard errors less than 30% are rare in dental regressions.

However, this hypothesis is less robust when applied to the monophyletic‘diprotodontian’ data-set which, although possessing minimum error statistics below thosefor the ‘all species’ and ‘all species excluding dasyuromorphians’ data, has a larger errorrange for SEE% and PE% than any other data-set. This suggests that the predictive powerof the regressions derived from data-sets incorporating diprotodontian, peramelemorphianand notoryctomorphian species, with or without dasyuromorphians, is greater than that forthe diprotodontians alone. Likewise, the range of adjusted R2 coefficients is substantiallysmaller for the ‘all species’ and ‘all species excluding dasyuromorphian’ data-sets relativeto ‘diprotodontians’ only, implying a stronger relationship between body size and cranio-dental variable in the former.

110 T. J. Myers

Tab

le 7

.B

ody-

mas

s pr

edic

tion

s fo

r ex

tinc

t m

arsu

pial

tax

a

Taxo

nFa

mily

Ord

erSp

ecim

enV

aria

ble

Dat

a-se

tS

mea

ring

W

eigh

tes

tim

ate

(%)

(g)

Hyp

sipr

ymno

don

bart

holo

mai

iH

ypsi

prym

nodo

ntid

aeD

ipro

todo

ntia

QM

F13

051

UM

RL

All

sp

ecie

s ex

clud

ing

dasy

urom

orph

ians

3.9

696

H. b

arth

olom

aii

Hyp

sipr

ymno

dont

idae

Dip

roto

dont

iaQ

MF

1305

11U

MW

& 4

UM

AD

ipro

todo

ntia

ns3.

862

1N

imio

koal

a gr

eyst

anes

iPh

asco

larc

tidae

Dip

roto

dont

iaQ

MF

1637

83U

PWD

ipro

todo

ntia

ns1.

327

14N

. gre

ysta

nesi

Phas

cola

rctid

aeD

ipro

todo

ntia

QM

F16

378

3LM

W &

4L

ML

Dip

roto

dont

ians

2.3

2220

N. g

reys

tane

siPh

asco

larc

tidae

Dip

roto

dont

iaQ

MF

3048

71L

MA

All

sp

ecie

s ex

clud

ing

dasy

urom

orph

ians

13.1

4448

Kut

erin

tja

ngam

aIl

arii

dae

Dip

roto

dont

iaQ

MF

2330

63L

MW

& 4

LM

LD

ipro

todo

ntia

ns2.

313

378

K. n

gam

aIl

arii

dae

Dip

roto

dont

iaQ

MF

4032

41U

MW

& 4

UM

AD

ipro

todo

ntia

ns3.

813

861

K. n

gam

aIl

arii

dae

Dip

roto

dont

iaQ

MF

4032

44U

MA

Dip

roto

dont

ians

5.4

1155

9K

. nga

ma

Ilar

iida

eD

ipro

todo

ntia

QM

F23

306

1LM

AA

ll

spec

ies

excl

udin

gda

syur

omor

phia

ns13

.121

493

Dji

lgar

inja

gil

lesp

iei

Pilk

ipil

drid

aeD

ipro

todo

ntia

QM

F13

028

3LM

W &

4L

ML

Dip

roto

dont

ians

2.3

415

D. g

ille

spie

iPi

lkip

ildr

idae

Dip

roto

dont

iaQ

MF

1302

84L

MA

Dip

roto

dont

ians

5.8

411

D. g

ille

spie

iPi

lkip

ildr

idae

Dip

roto

dont

iaQ

MF

1302

81L

MA

All

sp

ecie

s ex

clud

ing

dasy

urom

orph

ians

May

igri

phus

orb

usD

asyu

rida

eD

asyu

rom

orph

iaQ

MF

2378

0L

MR

LD

asyu

rom

orph

ians

3.0

17M

. orb

usD

asyu

rida

eD

asyu

rom

orph

iaQ

MF

2378

03L

ML

Das

yuro

mor

phia

ns3.

516

M. o

rbus

Das

yuri

dae

Das

yuro

mor

phia

QM

F23

780

1LM

AD

asyu

rom

orph

ians

5.9

13N

gam

alac

inus

tim

mul

vane

yiT

hyla

cini

dae

Das

yuro

mor

phia

QM

F16

853

LM

RL

Das

yuro

mor

phia

ns3.

057

43N

. tim

mul

vane

yiT

hyla

cini

dae

Das

yuro

mor

phia

QM

F168

53 &

Q

MF

3030

02U

ML

& L

MR

LD

asyu

rom

orph

ians

2.5

5201

N. t

imm

ulva

neyi

Thy

laci

nida

eD

asyu

rom

orph

iaQ

MF

1685

31L

MA

Das

yuro

mor

phia

ns5.

912

912

Yara

la b

urch

fiel

diY

aral

idae

Per

amel

emor

phia

QM

F16

860

UM

RL

All

sp

ecie

s ex

clud

ing

dasy

urom

orph

ians

Y. b

urch

fiel

diY

aral

idae

Per

amel

emor

phia

QM

F16

860

2UM

L &

UM

RL

All

spec

ies

1.2

53Y.

bur

chfi

eldi

Yar

alid

aeP

eram

elem

orph

iaQ

MF

1686

01L

MA

All

sp

ecie

s ex

clud

ing

dasy

urom

orph

ians

13.1

66


Admittedly, it is difficult to understand why predictive power should be improved byinclusion of unrelated and morphologically dissimilar species. Damuth (1990) suggeststhat grouping taxa on the basis of crown morphology and diet increases a regression’spredictive power, and that groups defined on morphological or functional criteria arebetter than those based on taxonomy alone. The inclusion of peramelemorphians, which,as generalist omnivores feeding largely upon arthropods and succulent plant material, fillsimilar dietary niches to many small-to-medium diprotodontians, may therefore accountfor the observed increase in predictive power of ‘all species excluding dasyuromorphians’regressions over those from the diprotodontian data-set. Although dasyuromorphians areprimarily faunivores they exhibit a dental morphology that is largely congruent with thatof most peramelemorphians, differing largely only in the position and size of themetaconule. The increased overlap in tooth morphology and diet with the increase inspecies sample size may explain the slightly lower error range for the ‘all species’regressions compared with the ‘diprotodontians’ alone. However, the removal ofdasyuromorphians from the entire sample results in a significantly smaller error range,perhaps suggesting that trophic overlap is a more important factor than tooth morphology.Additionally, it is apparent that removing dasyuromorphians from the ‘all species’ data-set reduces the usefulness of cranial variables, the implication being that there is greatervariability in diprotodontian skull morphology than there is in dasyuromorphian. Theincreased predictive power of cranial variables in the ‘all species excludingdasyuromorphians’ data-set over the diprotodontian data-set may therefore be due tosimilar factors. As peramelemorphians share a relatively uniform skull shape theiraddition in the data-set increases overall uniformity of this character such that thecorrelation between body size and cranial variable also improves.

Damuth and MacFadden (1990) also state that ‘… care should be taken to recognisefossil species that may be aberrant in one or more characters that for most species yieldgood estimates’. Using dental regression equations derived from the ‘diprotodontian’ data-set to predict the body weight of any thylacoleonid, for example, would result in highlymisleading estimates due to the hypertrophy of the carnassial P3, a feature not found in anyother diprotodontian family. It is also questionable whether any cranial variable derivedfrom the ‘diprotodontian’ data-set is appropriate to use for thylacoleonids, given theinfluence the P3 has had on the morphology of the skull. None of the predictor variablesmentioned here should be used without first considering the overall cranial morphology ofthe species in question, relative to the data-set sample employed in determining theregression equation.

Dental variables

Premolar variables are poorly correlated throughout all groups, with the exception of3UPW, actually the second upper premolar for dasyuromorphians, which ranks as the thirdmost reliable predictor for diprotodontians. These results reaffirm the findings of Janis(1990), where premolar variables were found to be generally poor predictor variables. Thegreatly varied functional roles of the third premolar, even among closely related taxa,accounts for most of the inconsistency in the degree of correlation between body size andthe dental parameters of this tooth. Ultimately, the third premolar may play a greater role inthe initial acquisition of food items than it does in later processing and, subsequently,metabolic rate. In many diprotodontian groups, for instance, the shape and size of theplagiaulacoid premolar is largely controlled by the amount of pressure this tooth needs toexert on the food item, rather than by the quantity of food to be processed.

112 T. J. Myers

An interesting contrast between dasyuromorphians and diprotodontians is in the relativeusefulness of regressions based on first molar dimensions. At least with respect to themorphology of the first molar, it would seem that diprotodontian species exhibit far greatervariation in tooth design and size, with a weaker relationship between body size and anytooth parameter. First molar variables rank below all variables, other than those based onthe third premolar, in the ‘diprotodontian’ data-set. These variables are also very poorpredictors in the ‘all species excluding dasyuromorphians’ data-set. A factor that mayaccount for lower variation in dasyuromorphian first molars is the increased responsibilityof this tooth in food processing, through greater carnassialisation of the tooth row. A greaterrole in this process would ensure that the first molar scales with metabolic rate andconsequently with body size. Whatever the reason, it is clear that regressions derived fromfirst molar variables will not provide accurate or precise predictions when used in relationto diprotodontian species.

Janis (1990) found third molar variables to be poorly correlated with body size inungulates, but the best estimator for kangaroos, thereby supporting the hypothesis that thethird molar in kangaroos is analogous to the second molars of ungulates. This present studycould find no evidence to support this hypothesis. For diprotodontians, fourth and thirdmolar variables rank higher than first or second molar variables. Excepting the fact that twoof the three highest-ranking individual dental variables are derived from the fourth uppermolar, there is no clear indication as to whether the fourth or third molar is the betterestimator. Similarly, for the ‘all species’ data, all molar variables were interspersed, withnone clearly ranking higher than another. A restriction of the diprotodontian data-set suchthat only macropodoids are included would clarify Janis’s hypothesis.

The results from this analysis do not concur with the prevalent assertion that the lowerfirst molar crown area is the most accurate estimator of body mass in marsupials (e.g.Conroy 1987; Legendre 1988, 1989; Gunnell 1994; Morgan et al. 1995; Gagnon 1997; Kayand Madden 1997). Indeed, for diprotodontians and dasyuromorphians, and for regressionsderived from the ‘all species excluding dasyuromorphians’ data-set, 1LMA is one of theleast accurate predictors of body mass, exhibiting high error statistics. According to thedata presented here, 2LMA and third lower molar area (3LMA) are always better estimatorsof body weight in marsupials than 1LMA. This is clear despite the high correlationcoefficients for this variable against body weight, further supporting the hypothesis (Smith1981) that correlation coefficients do not reflect the ability of a regression to make accurateor precise predictions.

The inability of 1LMA to predict accurate or precise mass estimates is bestdemonstrated in Table 7. For the extinct taxa Nimiokoala greystanesi (Phascolarctidae),Kuterintja ngama (Ilariidae), Djilgaringa gillespiei (Pilkipildridae), Ngamalacinustimmulvaneyi (Thylacinidae) and Yarala burchfieldi (Yaralidae), using 1LMA results inbody-mass predictions 5–398% greater than that derived from more reliable estimators.Conversely, the dasyurid Mayigriphus orbus is significantly underestimated by 1LMA,with an estimate 24% lower than that derived from the ‘best’ variable.

In addition to highlighting the degree of usefulness of 1LMA as a predictor variable,Table 7 provides a number of body-mass estimates for a series of Australian Oligocene andMiocene taxa utilising (1) the most reliable regressions for the specimen used, asdetermined by error statistic rankings, and (2) the next most reliable variable(s) for thespecimen concerned. Ignoring the 1LMA values in Table 7 (the purpose of which were tomerely illustrate the unreliability of this variable), it is apparent that most body massestimates are in broad agreement with one another. Variation between ‘best’ and ‘second


best’ estimates is as little as 1% for Djilgaringa gillespiei and only as large as 18% forNimiokoala greystanesi. This range of body mass compares favourably with that for sixOligocene predators exhibiting a range of 5–323% of the ‘best’ estimate (Van Valkenburgh1990). Janis (1990) predicts body mass for a number of extinct ungulates, using three‘constant’ cranio-dental variables, for which the range of estimates differs by up to 87% (forStenomylus hitchcocki) from that of the most reliable variable. While body-mass estimatesare presented here for only a few marsupial taxa it would appear that they are at least asprecise as any previously published for eutherian taxa.

4UMW varies substantially in its usefulness as a predictor variable between data-sets. Itis the least reliable for the ‘all species’ sample and is poorly ranked, with similarly poorerror statistics, in the ‘all species excluding dasyuromorphians’ data-set. Yet fordasyuromorphians and diprotodontians alone, 4UMW ranks far higher with improved errorstatistics. It must therefore be concluded that either 4UMW is poorly correlated with bodymass in peramelemorphians or else it has vastly disparate scaling rates between marsupialorders.

Janis (1990) found length measures to be better correlated than width or area, at least forkangaroos. Results from diprotodontian data used here, which include a number ofmacropodoid species, do not confirm this hypothesis, although a restricted data-set may.Fortelius (1990) also postulates that tooth length is a better estimator of body size than toothwidth, and subsequently area, which includes width. This argument is based primarily onthe assertion that tooth width better measures shape than size, and is more significantlyinfluenced by adaptation than length. No evidence for one dental dimension being a betterestimator of body size was found in this analysis, with the possible exception of the data-set incorporating all species (Table 2). In the latter, width variables appear to cluster towardsthe bottom of the rankings, indicating more error in predictions based on these variables.For the remaining taxonomic groupings the variables are freely interspersed throughout therankings.

As noted earlier, UMRL ranks as a far better predictor of body size than LMRL for alldata-sets other than that comprising dasyuromorphian species. This implies that there is anintrinsic factor of UMRL that causes it to scale with body size at a more predictable ratethan LMRL. A possible explanation can be provided by focusing on the diastema andprocumbent incisor, features present in most diprotodontians. As TJL is the most preciseestimator of body size for both the diprotodontian and ‘all species’ data-sets, and given thelack of variation in LMRL, it is probable that part of the lower jaw other than the molar rowmust be scaling with body size. The diastema, part of the jaw directly involved in foodprocessing (and, subsequently, metabolic rate), and the first lower incisor, also a functionalpart of the jaw in many species (e.g. macropodoids: Janis 1990), are the obvious candidatesfor expansion with body size.

For dasyuromorphians, the lack of a diastema and/or procumbent incisors limits theareas of the lower jaw available for expansion. Hence, the molar row, again directlyresponsible for processing food and metabolic rate, is more likely to be acted upon bynatural selection than are other parts of the jaw. Similarly, the slightly lower error statisticsin the dasyuromorphian data-set for LMRL, compared with UMRL, may be theconsequence of greater potential for expansion in the typical dasyuromorphian snout orposterior skull region, compared with the molar row.

The results from this study contrast with the conclusions of Janis (1990) who foundlower molar row length to be ‘… superior to any single dental variable’ as well as ‘… aconsistently good predictor in herbivores with enlarged individual cheek teeth’. While

114 T. J. Myers

LMRL is the most highly ranked predictor variable in the dasyuromorphian data-set andranks higher than any individual dental variable in the ‘all species’ data-set, it is only thesixth most reliable predictor in the latter. When dasyuromorphians are removed from the‘all species’ data-set LMRL drops to be the ninth most reliable predictor variable, and isranked equal eighth in the diprotodontian sample. LMRL appears to be a very goodpredictor for faunivorous dasyuromorphians, but far less so for insectivorous/omnivorousperamelemorphians. At least for herbivorous diprotodontian marsupials LMRL is not ‘…a consistently good predictor’, with many single dental variables exhibiting a superiorranking. Despite this, LMRL may still be an appropriate variable to use in many cases,given its relatively fair ranking combined with the relatively high preservational potentialand taphonomic advantage typically attributed to dentaries.

Janis (1990) found molar row length to be highly correlated with body mass inungulates, but less well correlated for kangaroos, which was ascribed to molar progression.Results presented here suggest UMRL to be a substantially better estimator of body sizethan LMRL in all but the dasyuromorphian data-set. For diprotodontians UMRL is highlycorrelated, ranking as the third most reliable predictor. Perhaps the use of macropodoidspecimens with all four molars present accounts for the high correlation, eliminating theeffects of molar progression. The fact that the diprotodontian data-set was not restricted tomacropodoids may confound these results.

Non-dental variables

OCH was found to be a poor estimator of body mass in all data-sets. This variable wasequally most highly ranked in the ‘all species’ and dasyuromorphian data-sets but exhibiteda SEE% of 69 and PE% of 47 in the former. While ranked lowly relative to all othervariables in the dasyuromorphian data-set the SEE% and PE% were far lower than othersample groups (SEE% = 34, PE% = 24). These figures compare favourably with thosefound for OCH in ungulates when suines are excluded (SEE% = 42.5, PE% = 28.1) (Janis1990).

In contrast, TSL is variably useful as a predictor of body size throughout the samplesanalysed. This variable is a good predictor for marsupials in general, but significantly moreso for diprotodontians than dasyuromorphians when considering error statistics as opposedto ranking. The error statistics for TSL in the diprotodontian sample compare favourablywith those of ungulates (Janis 1990), perhaps suggesting that this cranial variable scaleswith body size in herbivores better than it does in carnivores. Van Valkenburgh (1990)found skull length to rate second only to head–body length as a predictor of body size incarnivores, although the PE% and SEE% were substantially larger than they are for thefaunivorous dasyuromorphians, for which TSL ranks seventh in the present study. VanValkenburgh (1990) also notes that the inaccuracy of the total sample regressions can beexplained as a result of differences in scaling among families or size groups.

Multiple-variable regressions

Damuth and MacFadden (1990) found that the use of multiple variables in body-sizeregressions could increase accuracy of predictions. Best subset analyses performed heresuggest that multiple variables may result in a significant improvement in predictive power,although significance disappears if more than two variables are used (Table 6). For the ‘allspecies’ and ‘all species excluding dasyuromorphians’ data-sets analysed at least onemultiple-variable regression exhibited error statistics lower than those found for the bestindividual-variable regression. For example, utilising the regression derived from the best


Tabl

e 8.

Com

pari

son

of b

ody-

mas

s pr

edic

tion

s an

d pu

blis

hed

body

mas

ses

for

exta

nt s

peci

es

Spec

ies

Fam

ilyS

peci

men

Var

iabl

eS

ampl

ePr

edic

ted

Act

ual

Sour

ce f

or a

ctua

l wei

ght

wei

ght (

g) w

eigh

t (g)

Sarc

ophi

lus

hari

ssii

Das

yuri

dae

UN

SWZ

456

LM

RL

Das

yuro

mor

phia

ns14

066

9000

Mea

n fo

r m

ales

: Str

ahan

(19

95)

Pse

udoc

heir

ops

arch

eri

Pseu

doch

eiri

dae

AR

2534

UM

RL

All

sp

ecie

s ex

cept

dasy

urom

orph

ians

1801

1190

Spec

ies

mea

n: S

trah

an (

1983

)

Bet

tong

ia le

sueu

rPo

toro

idae

AR

1573

5U

MR

LA

ll

spec

ies

exce

ptda

syur

omor

phia

ns16

44~1

500

App

roxi

mat

e m

ean:

Str

ahan

(19

95)

Pet

auru

s au

stra

lis

Peta

urid

aeU

NSW

Z45

5U

MR

LA

ll

spec

ies

exce

ptda

syur

omor

phia

ns42

658

2M

ean

for

mal

es: C

raig

(19

85)

Pot

orou

s tr

idac

tylu

sPo

toro

idae

AR

1568

PSL

& T

JLD

ipro

todo

ntia

ns19

3113

00Sp

ecie

s m

ean:

Gra

inge

r et a

l. (1

987)

Mac

ropu

s do

rsal

isM

acro

podi

dae

AR

1580

UM

RL

All

sp

ecie

s ex

cept

dasy

urom

orph

ians

1145

816

000

Mea

n fo

r m

ales

: Str

ahan

(19

83)

Ant

echi

nus

godm

ani

Das

yuri

dae

QM

J367

3L

MR

LD

asyu

rom

orph

ians

5658

Mea

n fo

r fe

mal

es: S

trah

an (

1995

)Sm

inth

opsi

s hi

rtip

esD

asyu

rida

eQ

MJM

5239

LM

RL

Das

yuro

mor

phia

ns20

15M

ean

for

mal

es: S

trah

an (

1995

)Sm

inth

opsi

s yo

ungs

onii

Das

yuri

dae

QM

JM61

86L

MR

LD

asyu

rom

orph

ians

1610

Mea

n fo

r m

ales

: Str

ahan

(19

95)

Thy

loga

le th

etis

Mac

ropo

dida

eA

R62

7U

MR

LA

ll

spec

ies

exce

ptda

syur

omor

phia

ns62

1670

00M

ean

for

mal

es: S

trah

an (

1983

)

116 T. J. Myers

overall pair of variables (2UML and UMRL) substantially improves predictive power formarsupials in general (based on the ‘all species’ data). Likewise, predictive power isincreased by using a combination of 4LMW and TSL for ‘all species excludingdasyuromorphians’. However, the single variables LMRL and TJL are better predictorsthan their bivariate counterparts in the dasyuromorphian and diprotodontian data-setsrespectively.

To determine the actual usefulness of the predictive regression equations, as alreadyoutlined, average body masses were determined for selected extant marsupials. Thehighest-ranking appropriate variable from a suitable data-set, exhibiting the lowest errorstatistics, was used to make the predictions (Table 8). The results confirm the reliability ofthe regression equations, with the average difference being 27.4% between actual andpredicted average species body mass. It is important to remember that these predictions (aswith the extinct species’ predictions) are average species masses as determined from onerandomly selected, but hopefully typical, specimen. Undoubtedly, better estimates will bederived by using as many specimens as possible for a species and averaging the resultantestimates.

How useful is all this?

Fortelius (1990) noted that any body-size distribution ‘… will inevitably be a trivialisedversion of the real thing’ as the use of allometric body-mass equations involves averaging.This should not be forgotten. When a body-mass estimate is derived from allometricequations, such as those presented here, we are given an average for a species’ (or particularsex’s) weight based on the fossil specimen used. Arguments concerning the predictivepower of a particular regression, based on error statistics for the variable in question, havemore to do with the precision of an estimate than its accuracy. We will probably never becertain of a particular fossil species’ body mass, but by using the most appropriate dentalvariable(s), or combination of dental, cranial and post-cranial variables, we can maximisethe likelihood of precision and accuracy, given Recent scaling trends.

Precautions

Several factors should be taken carefully into consideration when estimating body size:

(1) When predicting morphological features, such as body mass, of extinct animals anassumption inherent in our models is that regarding similarity of scaling trends andsimilarity of rates of evolution with extant taxa. This may not be justified. Alroy(1998) concludes that for North American Cainozoic mammals, at least, new specieshave, on average, been 9.1% larger than their predecessors in the same genera, affirm-ing Cope’s rule (Cope 1887). On its own, this is not a problem if it can be demon-strated that scaling rates have remained the same for marsupials over time, otherwiseadjustments in body-mass estimates will be required.

(2) As always, extrapolation beyond the range should be avoided, as it can result in erro-neous predictions, due to potential changes in regression slope (Underwood 1997).

(3) When deciding on the most appropriate regression variable and data-set to use it isimportant to take into consideration the specimen being used as well as the species inquestion. Where possible, a restricted taxonomic data-set should be used, but only ifthe variable to be used exhibits error statistics lower than those from another sample.Additionally, the highest ranked variable in any sample should be used ahead of thosemore lowly ranked.


(4) The relationship between correlation coefficients and range is well known (e.g. Smith1981, 1984). Certainly, the ‘all species’ data-set includes five orders of magnitude ofbody size. For dasyuromorphians the correlation coefficients would appear to be amore realistic guide for determining a regression’s predictive power, given the lownumber of species included and the fact that the species’ body-mass range over onlythree orders of magnitude. The correlation coefficient (r), coefficient of determina-tion (r2) and adjusted r2 are not reliable indicators of the prediction power of a regres-sion. Take, for example, 4UMW in the ‘all species’ data-set, with the highest SEE%and PE% statistics for any sample, but with a correlation coefficient suggesting a verystrong relationship: use of this variable as a predictor of body size would result inhighly inaccurate and imprecise estimates, despite the apparent goodness-of-fit.

Acknowledgments

Extant mammal specimens were kindly lent by the Australian and Queensland Museums.Vital assistance in finding and providing appropriate specimens came from Dr SandyIngleby. Helpful suggestions for this manuscript were provided by Dr Suzanne Hand, MaryKnowles and two anonymous referees. Matthew Crowther kindly provided some body massdata. Many thanks to all of them.

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Manuscript received 19 February 2001; accepted 8 May 2001

Prediction of marsupial body mass

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