Selection of an Appropriate Index for the Study of the Variability of Lizard and Snake Body Scale Counts

Frequency distributions of body scale counts show a positive skewness. Plots of sample standard deviations against sample means confirm the log-normal nature (i.e., the variance proportional to the mean) of scale count distributions. Moreover, variation is conservative, so that related species tend to possess similar coefficients of variation for homologous counts. If certain conditions are fulfilled (approximation to linear relationship, origin intercept, and proportio-nality of scatter to standard deviation), the mean coefficient of variation not only serves as a short-cut method of obtaining a least squares regression estimate of variation, but simultaneously serves as an index of variability uneffected by changes in the mean scale count. The bodies of lizards and snakes are covered by an epidermal coat of scales. The scales are folds of tissue, capped by a keratinized layer, that assume highly variable configurations. The purpose of this paper, however, is not to review the diversity of external scale morphology, a subject adequately covered by a number of general texts (e.g., Smith, 1946; Ludicke, 1962), but to examine statistically the degree and kind of variation in the number of body scales in naturally occurring local populations of lizards and snakes. As a first step, some means of mathematically describing the variability of scale counts is necessary. Basically, all statistical symbols and terminology follow Snedecor (1966). I have added subscripts to avoid confusion in certain circumstances. Early work by Klauber (1941b) demonstrated that the ventral scute counts of snakes and the body scale counts of some lizards (Sceloporus, Cnemidophorus) appear to conform to a normal distribution. Table 1, summarizing Klauber's calculations, presents the probability that the observed scale counts of the corresponding species fit a normal distribution. The probability that the differences are due to chance is tabulated. This close fit has allowed the use of normal statistics in the systematic study of lizards and snakes. The level of treatment of this subject historically has been largely a taxonomic one. Often the degree of dispersion of scale counts about a calculated sample mean is used to compare the significance of an observed difference between two or more means, or the departure of an isolated value (by the familiar "t" test). Occasionally (Klauber, 1940, etc.; Fox, Gordon, and Fox, 1961; Duellman and Wellman, 1960; and others to a lesser extent), the relative dispersion of scale counts about the same or different mean values has been compared using the coefficient of variation. At this point it should be noted that all the larger samples examined by Klauber (1941b) showed a slight positive skewness, an indication of a log-normal distribution, viz., the variance is proportional to the mean (Simpson, Roe, and Lewontin, 1960: 145-146). In the normal distribution, the mean and the variance are independent. If the distribution of scale counts is indeed log-normal, rather than normal, then the coefficient of variation could be valuable for comparing the relative variability of scale coiunts between different taxa. To date the application of the coefficient of variation as a systematic tool has not been justified for meristic scale counts in lizards and snakes. The use of the coefficient of variation, which is the sample standard deviation (s) divided by the sample mean (x), assumes the parametric