Sciuridae, Fischer de Waldheim, 1817

Kielan-Jaworowska, Zofia & Lancaster, Terry E., 2004, A new reconstruction of multituberculate endocranial casts and encephalization quotient of Kryptobaatar, Acta Palaeontologica Polonica 49 (2), pp. 177-188 : 183-185

Sciuridae Sciurus vulgaris (1) Protoxerus stangeri (2)

Sciurus carolinensis (2) Spermophilus

Ratufa indica (2) tridecemlineatus (2)

Spermophilus citellus (2) Anomaluridae Anomalurus pusillus (2) Hystricidae Atherurus africanus (2) Caviidae Cavia porcellus (3) Dasyproctidae Dasyprocta leporina (4) Chinchillidae Chinchilla lanigera (4) Chinchilla brevicaudata (2) Cricetidae Ondatra zibethicus (2) Heteromyidae Peromyscus maniculatus (2)

For estimation of body mass we employed the allometric equation:

Y = kX a (3)

in which Y is the body mass, X is the bone length/diameter measurement, k is the proportionality coefficient (or the Y−intercept) and a is the slope of the regression line of the log transform ( Jerison 1973; Schmidt−Nielsen 1984; Zar 1999). We used the reported length measurements from Sereno and McKenna (1995) along with the hind limb lengths for ZPAL MgM−I/ 41 in the first regression calculation. The step−wise regression of all variables measured for Kryptobaatar showed the diameter of the tibia in the plane through the tibial crest to be the largest contributor to the estimation of body mass.

1 The term tibial crest (crista tibiae), which we use, has been replaced in Nomina Anatomica Veterinaria (see Schaller 1992) by cranial border (margo cranialis).

We produced a multivariable regression equation (3a) based on the lengths of the humerus, radius, ulna, and the lengths and midshaft diameters of the femur and tibia. We also formulated another multivariable regression equation (3b) based solely on the lengths of the humerus, radius, ulna, femur and tibia as well as a multivariable regression equation (3c) generated from the length and diameter measurements of the femur and tibia only. We further derived simple regression equations for each length variable and diameter variable (3d 1, 3d 2, 3d 3, 3d 4, 3d 5, 3d 6, 3d 7, 3d 8, and 3d 9). The regression equations and the resulting predicted body masses are shown in Table 4. Although the hind limbs of K. dashzevegi (ZPAL MgM−I/41, see Kielan−Jaworowska and Gambaryan 1994: fig. 2) are nearly complete, the femur and tibia are the only long bones of which the all the measurements could be taken. The complete humerus, radius, and ulna of Kryptobaatar have been preserved in specimen PSS−MAE−103, referred to originally by Sereno and McKenna (1995) to Bulganbaatar nemegtbaataroides , but regarded by Sereno (in press) as belonging to Kryptobaatar dashzevegi . The humerus PSS− MAE−101, figured by Dashzeveg et al. (1995: fig. 3a, referred to as “compare Chulsanbaatar vulgaris ”) lacks the humeral head. The humerus from Ukhaa Tolgod GI5/302, figured by Kielan−Jaworowska (1998: figs. 1, 2) is almost complete but lacks the compact layer of the bone in the middle of the shaft, and therefore the diameter of the shaft could not be measured. While lengths were reported for the humerus, radius, and ulna in Sereno and McKenna (1995), the midshaft diameters were not recorded. Thus, the regression of the midshaft diameters could not be completed for these bones.

From the same 32 rodent specimens used to create the body mass regression equations, we derived a brain mass prediction equation using known body and brain masses and simple linear regression ( Bonin 1937; Crile and Quiring 1940; Pilleri 1959; Eisenberg 1981; Damuth and MacFadden 1990; Silva and Downing 1995). True brain masses were averaged to provide one mean brain mass variable per species. Body masses were determined as described above. The resulting equation is:

Y = 0.070(X 0.697) (4)

in which Y is the brain mass and X is the body weight (r = 0.909). We determined the predicted brain mass from each body mass calculated from our derived equations (3a, 3b, 3c, and 3d 1–9). Equation (4) predicts brain weight in grams, but brain volume is needed to calculate EQ. Therefore, we used the specific density of water, 1.036 g /cm 3, to convert each predicted brain weight in grams to a volume in milliliters ( Hopkins and Marino 2000) for comparison to the measured endocast volume for Kryptobaatar dashzevegi . We used the equation:

E = 0.25πlwh (5)

in which E is the estimated endocast volume and l, w, and h are the length, width and height of the endocast, to determine the estimated volume of the total endocast for Kryptobaatar dashzevegi , which is 0.84 ml.

We then calculated the encephalization quotient (EQ) for each predicted brain volume of Kryptobaatar dashzevegi using the equation:

E

EQ = (6)

V

in which E is the estimated volume of the endocast, 0.84 ml, and V is the predicted brain weight from the regression equation converted into milliliters, 1.186 ml.

The resulting EQ’s are shown in Table 4.

Discussion of body mass prediction methods and resulting EQ values.—The predicted body mass using Jerison’s method was 62.9 g and the resulting EQ was 0.71. The predicted body mass using McDermott et al.’s method (2) was 36.6 g and the resulting EQ was 1.06. Body masses predicted from our derived equations (3a, 3b, 3c, 3d 1–9) range from 30.6 to 268.0 g with a mean weight of 85.3 g. The EQs predicted from these body masses range from 0.25 to 1.15, with a mean EQ of 0.73. The single variable regression equations we generated using only one measurement from a long bone resulted in a wide range of mass predictions, 30.6 to 268.0 g,

compared to the multiple regression equations we generated using multiple measurements or multiple bones, 32.6 to 56.2 g. The predicted mass from McDermott et al.’s tooth measurement regression, 36.6 g, is comparable to the low range of mass predictions we produced with our derived equations (3a, 3b, 3c, 3d 1–9) and, therefore, the resulting EQ from McDermott et al.’s mass prediction, 1.06, was in the high range of our calculated EQs. The mean of our mass predictions, 85.3 g, was similar to the predicted mass from Jerison’s single variable regression of body length, 62.9 g, and the mean EQ from our predictions was very similar to the EQ calculated from Jerison’s method (1), 0.73 and 0.71 respectively.