Towards an asymmetric index of community similarity

A number of indices are currently used by ecologists to measure the similarity or difference between community samples. Nearly all are symmetrical, in that the degree of similarity is equal for both parties being compared. There are situations, however, where an asymmetrical measure is more appropriate, most notably in studies of dispersal and its effects. I propose 2 variants of a potentially useful asymmetrical similarity index for use in such circumstances. In most respects, they are well behaved, reflecting the similarity and nestedness of samples, while being relatively insensitive to sample size and species diversity. They are also simple to compute and intuitively meaningful. Nonetheless, they provide anomalous results in cases where one plot contains a nested subset of the commonest species of another. I welcome suggestions for a better asymmetric index of similarity.