Summary
Ecological studies using measures of overlap or similarity often treat these measures as free of sampling error. If sample sizes are relatively small, however, the estimates of overlap may not be accurate, and misleading interpretations may result. Two methods are presented here for estimating the variance of a general weighted measure of similarity. First, an approach based on the mutinomial model is discussed. Because the multinomial model is not valid when data are clustered, a second more general approach is given. The more general approach is applicable when the data may be broken into units; in diet analysis, for example, a stomach may be used as a unit. Two examples illustrating the usefulness of the methods are given.
In this paper, statistical formulas are presented for estimating the variance of a general weighted measure of overlap. The simpler, multinomial case, in which data are categorical, is considered first. A second more general approach is then presented for data that are categorical but need not be multinomial or even discrete. Although the second approach is more valid than the simpler model, the simpler model results in easier computations and generally will give smaller variance estimates if the multinomial assumption is valid. Examples are presented for the proportional similarity measure, one of the most common measures of overlap (Schoener 1970; Wallace 1981).
Methodology
Keast (1977) presented data on the diets of several year classes of yellow perch Perca flavescens collected at different times from Lake Opinicon, Ontario, and on the availability of several prey taxa (Table 1) in Lake Opinicon. As availabilities may be highly variable, the prey availabilities were ranked and weights based on these ranks were used (high = 1, moderate = 2, low = 3). Although the unweighted proportional similarity measure changed only slightly from May to August (Table 1), the weighted measure and the adjusted weighted measure decreased considerably.