Fig. 1

RQE as it applies to specificity. In this example, two matrices are shown, D and W. D is an environmental dissimilarity matrix, describing how different are several environment types, A through D, with multiple samples represented for each environment type. Note that diagonals are empty because they are not used; see Eq. 1. Matrix W is the pairwise product of species weights p (Eq. 1). In this example, the focal species is perfectly specific to habitat A, which can be seen in p. Data corresponding to species detections are colored in red, and species absences in blue. The product \(D \circ W\) (=\(D_{ij}p_ip_j\)) will be all zeroes for this example, because this example shows perfect specificity. Thus, the sum of that product, RQE, will be zero. If p had relatively small values instead of its zeroes, for example 0.25, those small values would still down-weight their corresponding larger differences in D and produce a signal of specificity, compared to random permutations of p which produce much higher RQE values