The degree of intransitivity and its measurement in an assemblage of encrusting cheilostome bryozoa

The outcome of spatial encounters between 12 species of encrusting bryozoans is largely dependent on the angle formed between the direction of growth of the two species. An index has been devised which describes the degree to which the pattern of interspecific overgrowth is an hierarchical, perfectly transitive one, where each species invariably overgrows those beneath it in the hierarchy or an intransitive one, where all of the species have an equal probability of being overgrown; these two states therefore form quantifiable and opposite ends of a continuum. Frontal encounters alone produced a value closer to the transitive end than did encounters from all directions. Since the latter are more likely in nature, the underlying pattern of overgrowth in assemblages of encrusting bryozoans will be a highly intransitive one.