The Taxonomic index of congruence (Ctax and mCtax)

The Ctax allows the comparison of the congruence of taxonomies inferred by two different SD approaches. The Ctax is the ratio of the number of speciation event hypotheses (pairwise species boundaries) congruently supported by the two approaches, relative to the total number of such hypotheses cumulatively supported by them: where A and B represent two different SD approaches, n(A∩B) represent the total number of speciation event hypotheses congruently supported both by A and by B, and n(AUB), the total number of speciation event hypotheses congruently supported by A and/or by B.

Thus, the highest value (Ctax = 1) indicates that both approaches give identical taxonomies, supporting exactly the same species hypotheses (thus suggesting a reduced alpha-error). If the index is low, this indicates incongruence between the SD approaches (underestimation, overestimation, or mis-estimation by at least one of them).

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.