The Relative Taxonomic Resolving Power Index (Rtax)

The Rtax quantifies the ability of a given SD approach to reveal a high number of potential candidate species, relatively to other approaches. Of the complete set of speciation event hypotheses cumulatively suggested by all approaches, the proportion supported by a given approach becomes its Rtax: for an example with four approaches to be compared (A, B, C, D) with n(AUBUCUD) being the total number of possible speciation events revealed (i.e. supported by A and/or B and/or C and/or D).

High values indicate high relative resolving power of a SD approach, but do not necessarily imply reliability of the results: a high Rtax indicates that an approach can alone retrieve all the species boundaries that have been independently identified by all the approaches, meaning a minimization of the beta-error (false negatives), but possibly a maximization of the alpha-error (false positives).

Calculation of the Relative taxonomic resolving power index (Rtax) and Taxonomic index of congruence (Ctax). Calculations are exemplified on two distinct species delimitation approaches (X and Y) supporting different taxonomies. For a better understanding, calculations are first exemplified on a tree-based taxonomy (a). Although these calculations are based on a underlying phylogenetic perspective, knowledge of tree topology is not mandatory to perform the calculations (b). In (a), speciation event hypotheses supported by the approaches X and Y are represented by black and white circles, respectively. The Ctax between both approaches is defined as the ratio of the total number of speciation events congruently supported ( = shared) by both approaches (dark grey boxes), relative to the total number of speciation events cumulatively suggested by both approaches (in light grey boxes). The Rtax of a given approach represents the proportion of speciation events that it supports ( = single), relative to the complete set of speciation events (set of boundaries cumulatively revealed by all the different approaches – only two approaches in this example). In (b), representing the same taxonomy, the same calculations have been performed without relying on a phylogenetic tree, the number of speciation events being indirectly inferred from the number of species (in a dichotomic species tree, N cladogenetic speciation events = N species – 1). Little black dots represent specimens or populations, and each colored oval represents a distinct species hypothesis according to the approach (or combination of approaches) used.

Figure extracted from PLoS One. 2013 Jul 12;8(7):e68242 doi:10.1371/journal.pone.0068242.g001.