**Part 1: Body Mass Estimates**

Body mass is the single most important attribute to be determined during paleobiological reconstructions of extinct species. The singular importance of body mass is based on the strong correlations of this attribute and a broad range of ecological and physiological factors, such as, population density, diet, community structure, metabolism, thermoregulation, and growth rates. Mammalian paleobiologists have been particularly active in the various aspects of size estimation, ranging from the comparisons of methodologies to the analysis of functional morphology and the evaluation of paleoecological inferences.

The immense size of many
of the larger extinct animals requires that mass estimates are huge extrapolations
from data on extant species. Extrapolations beyond available data are always
risky. Where these extrapolations must be a factor of two or more larger
than the data base, mass estimates must be especially suspect. For example,
the giant white shark,
*Carcharocles megalodon*, has teeth more than
twice the height of the living great white shark,
*Carcharodon carcharias*.
The results of two studies on the body mass for white sharks (data from
J. Randall. 1973. Size of the great white shark (*Carcharodon*). *Science*
181: 169-170 and L. J. V. Compagno. 1984. *FAO species catalogue, vol.
4, parts 1 & 2. An annotated and illustrated catalogue of shark species
known to date.* FAO Fisheries Synopsis 125, 655 pp.) are shown in Figure
1.

Both studies produce body mass estimates that agree for individuals
up to about 500 cm body length, which approximates the largest *C. carcharias*
individuals in each study. But at larger body lengths commensurate with
the size of *C. megalodon* teeth, the estimates diverge rapidly. At
the largest size (estimated at about 16 m), the difference in the estimates
is 14 metric tons, with the larger estimate 39% greater than the smaller!

Which of these two estimates is more reliable? Both studies have reasonable numbers of individuals (68 and 98). Both studies also cover a similar range of body lengths; 148-510 cm and 127-554 cm. In this case, there is no clear preference for one estimate over another.

In first part of this exercise you will evaluate body masses for the group of animals (i.e., dinosaurs) that requires the most extreme extrapolations from measurements on extant animals. The problem of estimating dinosaur body masses is further complicated by the absence of living reptiles with erect leg postures, like the dinosaurs. Instead, paleobiologists and artists attempting to reconstruct the size and appearance of dinosaurs must rely on observations of large mammals. Unfortunately, while dinosaurs and mammals both have erect leg postures, there are many other aspects of their morphologies, and presumably biologies, that are very different.

You will be evaluating models of five dinosaurs that have been reconstructed by two different, and equally reputable, museums. These models are based on the same fossil material, but use different assumptions about the actual appearance of the dinosaurs. In both cases, reconstructions were made as collaborative efforts between paleontologists and artists. The main questions you will address in this exercise are:

- how much variablity is there in mass estimates between different researchers?

- how reliable are mass estimates of dinosaurs?

- what are the possible causes of discrepancies between different reconstructions?

In the laboratory are two
sets of model dinosaurs. One set was produced by the British Museum at
one forty-fifth scale. The other set was produced by the Carnegie Museum
at one fortieth scale. We have the same five dinosaurs from each set; a
carnosaur (*Tyrannosaurus*), a ceratopsian (*Triceratops*), a
stegosaur (*Stegosaurus*), and two sauropods (*Diplodocus* and
*Brachiosaurus*).
These models will be used to evaluate the reliability and variability of
mass estimates for extinct animals.

Mass estimates will be obtained
by obtaining water displacement volumes for each of the models (based on
procedure in R. McN. Alexander. 1985. Mechanics of posture and gait of
some large dinosaurs. *Zoological Journal of the Linnean Society*
83: 1-25):

1. Zero the readout on one of the elevated electronic scales in the laboratory.2. Suspend a dinosaur model (head upward) with thread from the undercarriage hook of the scale. The model should be within the tall water container positioned below the scale,

but several centimeters above the surface of the water.3. With thread, attach a small weight to the lower end of the model.

The thread must be long enough so that the weight is completely submerged in the water.4. Gently shake the weight to dislodge any adhering air bubbles. Record the initial mass (I) from the scale.

5. Lengthen the thread attaching the model to the undercarriage hook of the scale so that the model is

completelysubmerged in the water.6. Gently shake the model to dislodge any adhering air bubbles. Record the final mass (F) from the scale.

7. Since 1 g of water occupies a volume of 1 cm

^{3}, the volume of the model (v) can be calculated from the two recorded masses asv = I - F.8. Repeat this procedure for all models.

9. Determine the volume of the full-sized dinosaur (V) with the appropriate scaling factor. For the British Museum models (one forthy-fifth scale) the scaling factor is 45

^{3}, or 91,125. The one fortieth scale models from the Carnegie Museum have a scaling factor of 40^{3}, or 64,000. Multiply V for each model by the appropriate scaling factor.10. Since terrestrial vertebrates have a mass very close to 1 g per cm

^{3}, the calculated live volume (V) is equal to the body mass in grams. Convert this to a live body mass (BM) in metric tons, by dividing V by 1,000,000.

**Body Mass Estimates from Leg Bone Dimensions**

Body mass reconstructions
based solely on artistic renditions in models are not the only means of
reconstructing the size of dinosaurs or other extinct animals. There is
a strong correlation between the total circumference of the femur and humerus
of quadrupedal mammals and body mass. Mammalian data can be used for obtaining
independent estimates of body mass for quadrupedal dinosaurs. In this exercise
will we only make estimates for the two largest dinosaurs studied (*Diplodocus*
and *Brachiosaurus*), since these represent the most extreme extrapolations
from living animals.

1. Construct a dedicated spreadsheet to derive the regression equation and correlation coefficient for the quadrupedal mammal data in Table 1 (data from J. F. Anderson, et al. 1985. Long-bone circumference and weight in mammals, birds and dinosaurs.Journal of Zoology(A) 207: 53-61). Plot the data and insert a trendline.2. From skeletal material, the total leg bone circumference was 725 mm for

Diplodocusand 1384 mm forBrachiosaurus. Calculate estimated body masses based on these measurements. Divide by 1,000,000 to convert the mass to metric tons.3. There are too few bipedal mammals to construct a similar regression for estimating body masses of bipedal dinosaurs. However, it is possible to logically derive an appropriate equation for bipedal animals based on the circumference of the femur (Cf): log M = 2.73(log Cf) - 0.796. If Cf for

Tyrannosaurusis 534 mm, calculate an estimated body mass.

**Questions**

1. How comparable are your estimates of body mass for each dinosaur?

2. What factors may lead to large disparities between different reconstructions?

3. Which estimates seem most likely to be correct, and why?