Schematic representation of work protocols in taxonomy. Workflow in (a) integrative taxonomy by congruence and (b) by cumulation; (c) work protocol to define Unconfirmed Candidate Species (UCS), Confirmed Candidate Species (CCS) and Deep Conspecific Lineages (DCL) in an automated approach that starts with DNA barcoding [8]; and (d) a general work protocol for integrative taxonomy proposed here that combines advantages of cumulative and congruence approaches. Increasing black color intensity in a-d represents increasing uncertainty about species status and the need of a more thorough evaluation of data.

The "taxonomic circle" representation of work protocol for species recognition. This protocol (redrawn from [49]) is a schematic representation of the congruence approach to taxonomy proposed by DeSalle and collaborators [49]. Dotted lines in (a) connect lines of evidence used to discover species or support previous hypotheses. The recognition of a species is considered when congruence between a taxonomic character and geography allows breaking out of the circle (arrows). For example, in classical taxonomy (b) the occurrence of morphologically distinct specimens at different locations can be used to propose and support a species hypothesis. In the case of cryptic species (c), morphology fails to support the hypothesis but other characters (e.g. molecular) do provide support.

Schematic representation of two approaches of integrative taxonomy. Background yellow, red, and blue colors represent the spectrum of character variation, each dot being an independent evolutionary linage that requires identification and delimitation as separate species. Integration by cumulation (left) identifies species limits with divergence in one or more not necessarily overlapping taxonomic characters (e. g. mtDNA or morphology), whereas the integration by congruence (right) identifies species limits with the intersection of evidence from two or more independent taxonomic characters (e. g. mtDNA plus morphology). Both methods of integration have relevant limitations. The integration by cumulation approach may over-estimate the number of species by identifying distinct species where there is intraspecific character variation only. As an example, conspecific populations can be very distinct in terms of morphology but will be erroneously regarded as distinct species (alpha error or false positive). On the contrary, integration by congruence is a highly stringent approach that might under-estimate the number of species by being unable to detect cryptic or young species (beta error or false negative, represented here by three encircled species among all the undetected ones). Actually, there is a trade-off between the lack of reliability of the species detected by integration by cumulation, and the lower taxonomic resolving power of the integration by congruence.

Schematic representation of character divergence and fixation in several speciation scenarios. Character divergence varies quantitatively during lineage evolution, with later stages being characterized by marked differentiation (character fixation) at multiple levels, reciprocal monophyly of most gene genealogies, and reproductive isolation [21]. In situations of neutrality or when species are not subjected to novel selective regimes (a, and left lineage of b)-- character fixation is stochastic, due to neutral processes as random genetic drift or because characters are not acquired and fixed in the same order under balancing selection-- a situation known as mutation-order speciation [94]. In cases of speciation along new selective pressures (right lineage of b, c and d), characters subjected to selection are expected to become fixed at early stages of divergence [57,58]. This is especially evident in sympatry or parapatry (c) when disruptive selection causes fitness-dependent character fixation [57,95]. In most scenarios the origin of reproductive incompatibilities will be the result of the epistatic effect of new mutations, under divergent or balancing selection [96]. Reproductive isolation is expected to proceed more rapidly if there is divergent selection, both in allopatry (b, c; [e.g. [97]]), and in sympatry or parapatry (d; [reviewed by [57]]), or in those situations where a character mediating species recognition becomes fixed [77,78]. However, recent evidence indicates that reproductive incompatibilities do not necessarily need to have an adaptive origin, and that they can be the cause of lineage splitting in a neutral or nearly neutral scenario. For example, when the accumulation of new mutations, gene movement, or gene duplication lead to hybrid dysfunction [55]. A textbook-example could be the recurrent cases of polyploidy speciation in plants [98].