Spatial confusion or clarity? Reply to Ricotta & Avena



Abstract. This communication is a response to a recent suggestion that ordinal data of the Braun-Blanquet type (BB) can be directly or, after conversion to ranks, indirectly analysed by metric methods. I show that the proposals on structure in topological spaces made by Ricotta & Avena in a recent contribution to this Forum are confounding because (1) they use the term ‘topological’ in the inappropriate way, and (2) the measure they propose is in fact a metric, rather than merely topological. In addition, I illustrate with a few examples how a truly topological measure functions, so that the reader can appreciate the ideas behind their definitions. By reference to axiomatic measurement theory, I argue that whenever vegetation scientists know exactly at the outset what attributes they wish to express by relevé data, what questions they are asking and whenever they are aware of the basic properties of the BB scale, ordinal data analysis is still the most logical choice.