Body Mass Estimation by Simple Comparison

For Pleistocene species which still have extant representatives, body mass estimates can be made by simple comparison o f Pleistocene skeletal dimensions with modem. If isometric size change is assumed to occur within species, then the size ratio observed between fossil and modem skeletal elements can be used to convert modem body mass data into a Pleistocene mass estimate by use o f simple mles o f geometric similarity (Schmidt-Nielsen 1984). The volume o f an animal (closely related to its mass) will change in proportion to the third power o f linear dimensions. When

be known: modem mass (Mass), average value o f the standard measure in a modem sample (MM), average value o f the standard measure in a Pleistocene sample (PM).

Pleistocene Mass = Mass (PM/MM)^

The assumption o f simple geometric isometry is likely to be flawed however, because if size change o f this type occurs bone cross sectional areas, that provide mass support, will not increase as rapidly as the load placed upon them (Schmidt-Nielsen 1984). Different bone dimensions are likely to scale at different rates. However, simple isometric size change in individual dimensions between species o f similar body plans is also uncommon (Gould 1975). Regular inter-specific aUometry in skeletal dimensions, where body proportions alter with size, appears to be the mle (Scott 1985). This results from other factors that impact on the relationship between body mass and design o f the skeleton, such as the stresses placed on bones during locomotion that lead to theories o f scaling via elastic similarity (McMahon 1975), and the ability o f animals to alter their posture as size increases (Bertram & Biewener 1990).

But once again when case studies are examined size change does not appear to follow any simple theoretical physical or mechanical principle exactly; the pattern o f scaling varies between different taxonomic divisions and even regions o f the body (Scott 1985, 1987). Therefore, whenever possible it is best to apply a multi-species scaling study carried out on the Family concerned to describe the relationship between the skeleton and body mass. When size change occurs within a species, smaller and larger species with the same body plan, i.e. in the same mammalian Family, probably provide the best available model o f how changes in skeletal dimensions relate to changes in body mass.

Obviously, when extinct Pleistocene species are being considered the multi­ species approach will be favoured as no modem material is available for comparison. However, a few extant species recorded in the British Pleistocene have a limited number o f Family representatives e.g. Hippopotamidae and Hyaenidae. This prevents the construction o f effective multi-species scaling studies, so body mass estimates for British Pleistocene H. amphibius (post-crania only) and C. crocuta will be made by comparison with modem material using geometric scaling, taking into account the possibility that this method may over-estimate body masses slightly.

3.2.2 Body M ass Estim ation Using M ulti-Species Scaling Studies

The taxonomic composition o f multi-species studies can vary greatly from all ungulate and carnivore groupings down to single Family level. Total ungulate and carnivore scaling information can be useful for application to extinct species belonging to extinct Families, but where possible Family studies produce the most accurate mass estimates (Scott 1990; Van Valkenburgh 1990). All British Pleistocene mammals are members o f extant Families. The initial stage when carrying out a study on the pattern o f scaling between skeletal dimensions and body mass for a group o f animals is to select the set o f standard measures to be taken from the skeleton. Measures are usually concentrated in the post-cranial weight-bearing elements, as this is where scaling o f dimensions with body mass is most likely to occur. Bones from the axial skeleton are generally excluded. Teeth are often included in scaling studies, despite the fact that they are not directly related to mass support (section 1.3). This is especially true if the study is aimed at estimating mass from fossil material, as teeth are generally better represented in the fossil record than limb bones and can be more easily identified to species or genus level.

The standard measures selected must be easily locatable and repeatable, covering a range o f dimension types. This is necessary as length and width measures may show different relationships with body mass, certain groups o f measures allowing more accurate estimation o f body mass than others. I f the study is to be extended to fossil material then measures must be selected taking account o f the condition o f the fossil specimens available. Very few limb bones survive undamaged so it is rare to be able to take length measures o f fossil long bones. Isolated proximal or distal bone ends are much more common, so it is important to include measures which are restricted to this region. Fossil material is also often damaged at its edges, and projecting parts broken o ff by rolling and abrasion, so internal measures between articular surfaces are more likely to survive intact.

Once the standard measures have been determined, they must be taken on a sample o f individuals o f both sexes from a range o f modem species within the group under consideration. The average value o f the standard measure for each species is then determined. Averages from the two sexes may be kept separate, but identification o f sex in the fossil material to which the scaling equations will be applied is often not possible.

Body mass information is available in the literature for the majority o f modem mammalian species. It would be most suitable to concentrate only on skeletal

specimens for which an individual live body mass is known. However, this is not possible in practice as only very limited amounts o f material with such documentation are available in museum collections. Seasonal mass variations o f up to 10% can occur in large mammals due to food and water availability. This means that the weights o f individuals at capture may not provide an accurate representation o f the usual mass condition in any case (Scott 1983). Instead, an average o f as many different individual mass determinations from both sexes as possible is used. This forms a suitably accurate and convenient measure o f species body mass, for association with mixed-sex skeletal material where body mass at capture is not available (Martin 1990).

For each o f the standard measures the scaling relationship with body mass shown by the entire size range o f the Family is determined by least squares regression o f average species measure against average species mass data (fig 3.2). Logio

transformed data is used to produce a linear relationship between the measure and mass on which linear regression can be carried out, as the scaling relationships are usually allometric (Scott 1985). The equation o f the regression line given is o f the form:

log body mass = mlog measure + c m = slope o f line c = y intercept

Substituting the value o f the standard measure for any individual o f a species (living or fossil) into the equation for the Family/group o f mammals concerned, will produce an estimate o f its body mass.

Certain skeletal elements or individual measures provide more accurate estimators o f mass than others. For example, the lengths o f distal limb elements are poorer predictors o f mass than the length o f the femur or humerus or dimensions o f articular surfaces for bovids, as these dimension are more greatly affected by locomotor specialisations (Scott 1983). This is illustrated in figure 3.2, where the observations fall more closely along the fitted regression line for measure R2 o f the proximal radius (fig.3.2a) than for the metacarpal length measure (fig 3.2b).

1000 5 0 0 00 JZ O ' 5_J 50 æ 0.9 l.O 2.0 3 0 5 0 9. 0 R2 (cm)

Fig.3.2a: Log-log plot o f measure R2 o f the proximal surface o f the radius against body mass for bovids

1000 5 0 0 ^ 100 50 8 10 15 20 30 4 5 Metocorpol length (cm)

Fig.3.2b: Log-log plot o f metacarpal length (M c l) against body mass for bovids.

Fig.3.2: The relationship between body mass (kg) and two different skeletal measures in bovids (modified from Scott 1983).

The accuracy o f the linear regression equations for estimating mass can be determined by calculating the values o f three different statistical parameters: r^, %PE and %SEE (Smith 1981,1984; Van Valkenburgh 1990).

1) r^ (coefficient o f determination).

This is a measure o f the proportion o f variability in the data set that is explained by the regression equation. Values close to one indicate a high proportion o f variation

explained by the regression and suggest a close relationship between the standard measure and body mass. However, r^ can be a poor indicator o f the predictive power o f the independent variable. Therefore, two additional parameters that reflect residual variation are necessary.

2) %PE (percentage prediction error).

%PE = 100 X (Observed mass - Predicted mass) Predicted mass

As discussed above, the species used to produce the equation all have an observed average mass. The regression produces a predicted mass for each o f these species according to the fitted equation. The percentage prediction error compares the values o f the observed and predicted masses for each species, and expresses the deviation

between the two values (the error) as a percentage o f the predicted mass. The mean o f %PE values for all species included in a regression provides a comparative index o f predictive accuracy between the regressions based on different standard measurements.

3) %SEE (percentage standard error o f the estimate)

The %SEE provides a measure o f the overall ability o f the independent variable to predict the dependent variable.

%SEE = antilog (2+logioSEE)-100

Standard error o f the estimate (SEE) is given by the STATISTICA regression program

Assuming a normal distribution 6 8% o f the actual mass values would be expected to

fall within ±%SEE o f the predicted mass. A %SEE o f 25 indicates that 6 8% o f the

observed masses fall within ±25% o f the predicted mass. The smaller the %SEE, the more accurate the estimating equation.

Scaling studies are available in the literature for a number o f mammalian Families represented in the British Pleistocene (table 3.1). No scaling studies are available for Hippopotamidae or Hyaenidae because o f the small numbers o f extant species representing these Families. The scaling o f teeth with body mass for the Hippopotamidae and Suidae is based on a taxonomically heterogeneous group o f species (Damuth 1990). The grouping used is a fimctional one, including species with bunodont and lophodont teeth. Teeth o f these two forms scale similarly with body mass, as opposed to the selenodont grouping (Fortelius 1985). Using a mixed non- selenodont group increases the number o f species and the size range o f the regression. A grouping higher than Family level is also used for scaling o f teeth in equids and rhinos, with all perissodactyls and hyracoids included.

Table 3.1: Summary o f previous scaling studies carried out on mammalian Families or functional groupings.

Family Post-crania Teeth

Bovidae Scott 1983,1985,1990 Janis 1990

Cervidae Scott 1987,1990 Janis 1990

Hippopotamidae

Damuth 1990

Suidae Scott 1990

Equidae Scott 1990

Alberdi et al. 1995 _{Janis 1990} Rhinocerotidae

Canidae Anyonge 1993 Van Valkenburgh 1990

Ursidae Anyonge 1993 Van Valkenburgh 1990

Hyaenidae

Felidae Anyonge 1993 Van Valkenburgh 1990

For the majority o f the Families shown above, the standard measures and mass estimating equations that had already been developed by previous authors were used in this project. The listed studies have all demonstrated that the methods o f mass

estimation described operate with sufiQcient accuracy, using both statistical indicators and testing against the masses o f modem species o f known body weight. Scott (1983) estimates from her approach that mass estimates within 15% o f actual should be possible for most fossil Bovidae. The equations have even been applied to extinct species that do not belong to modem Families.

There were two areas where it was considered that fiirther scaling studies o f the type described should be carried out for application to the Pleistocene body size

project. No scaling study on the post-cranial bones o f the Rhinocerotidae is available in the literature. Guerin (1980) lists the average values for a set o f standard measurements taken on all five extant species o f rhino. By combining this data with information on the average mass o f each species via the regression methods described, mass estimating equations were produced by the author (Appendix 3.1.5).

The only bone scaling relationships available for carnivore Families were produced by Anyonge (1993). All o f the mass-estimating equations are based on the femur and humerus. Also a number o f the standard measurements are cross sectional areas and cortical thicknesses requiring X-ray techniques. It was decided that it would not be possible to take biplanar radiographs o f all o f the Pleistocene carnivore material fi*om widely dispersed museums all over the country, so new carnivore Family scaling studies were carried out. A set o f more suitable measures, as equivalent as possible to those taken on the ungulate material, and covering a wider range o f bone elements, was devised for this project (section 3.3.8).

The scaling o f the standard measures with body mass was determined for the Canidae, Ursidae and Felidae. This was achieved by taking the standard measures on all suitable skeletal specimens o f members o f these Families present in the collections o f the Zoology Department o f the Natural History Museum, London. For each Family the widest possible size range o f species was used. Specimens bred in captivity were generally avoided, but if no other material was available they were included if the skeleton did not appear too aberrant. Because o f the small sample sizes for most species, zoo specimens captured in the wild as adults had to be included. Any skeleton displaying major deformities in the limbs was excluded, whether it was a wild or zoo animal. Only bones with fused epiphyses were measured; no juvenile material was included in the samples.

Species belonging to the three carnivore Families could only be used in the scaling studies if a suitable amount o f mass information was available jfrom the

literature. As many recorded weight measurements as possible were combined together to give an average body mass for each species. A scaling study could not be carried out on the Hyaenidae as only three species, very similar in size, are available. The aardwolf

{Proteles cristatus) also belongs to this Family but no suitable skeletal material could

be found. In any case this species is a highly modified and unusual member o f the Family. Body masses o f Pleistocene spotted hyaenas (C. crocuta) were therefore

determined by simple comparison with the sample o f modem skeletons o f this species in the Natural History Museum’s collection.