118 Joshua Laerm and James L. Boone 



studies because of statistical and conceptual difficulties. Discriminant 

 analysis based on two characters has a similar result of separating 

 groups based on the magnitude of two measurements. It also has the 

 benefits of potentially better separation of groups by stretching the 

 axes (weighing measurements with discrimination function coefficients) 

 and an associated probability of group membership. Therefore, we 

 have presented results (Table 2) that use one or two measurements 

 rather than ratios to separate pairs of species with discriminant functions. 



We agree with Choate (1973) that habitat and external features 

 (e.g., tail coloration, penciled tail, color, and degree of fur luxuriance) 

 can yield important information for classifying these species. For 

 example, we believe that the best ways to identify P. polionotus are 

 that it is found on sandy soils and by its short, strongly bicolored tail, 

 and the best ways to identify P. leucopus are that it is found in low 

 elevation exeric sites and that it has more reddish-orange on the sides 

 than P. gossypinus. Other qualitative characters may also be useful. 

 For example, Linzey et al. (1976) found that the skulls of P. leucopus 

 tend to be lighter and more fragile than those of P. gossypinus. However, 

 our goal was to identify these species with quantitative characters 

 rather than qualitative characters, and preferably with the skull alone, 

 as noted by Feldhamer et al. (1983), these qualitative characteristics 

 can be variable within species. Most of the classification problems 

 we encountered involved old skulls without associated skins. 



Use of the discriminant function — Discriminant analysis combines 

 variables to generate a set of linear, independent axes upon which 

 specimens, after appropriate scoring, can be plotted and their classification 

 determined. The appropriate scoring method is to multiply each morphological 

 character variable (e.g., foot length, skull length) by its discriminant 

 function coefficient, sum the products, and add a constant (for each 

 axis separately). In general: 



D, = Bw + BuX^ + £,2X2 + #13*3+ ... + BlnXn 

 Di = £20 + B2^X^ + £22*2 + Bz>X> + ... + BlnXn 



where D\ is the specimen's discriminant score on the first axis, the 

 Bus are discriminant function coefficients estimated from the data 

 for the first axis (Bins are constants), and the Xt's are the values of 

 the original variables. This is done separately for each axis, and the 

 scores, D\, D2, ..., D«, form the coordinate of the specimen's location 

 in the ^-dimensional discriminant space. For example, to separate P. 

 gossypinus from P. leucopus using external and skull measurements, 

 the appropriate transformation is (only one axis is needed) 



D = -34.125 + 0.593(hindfoot length) + 0.821(skull length). 



