The multilevel organismal diversity approach deciphers difficult to distinguish nudibranch species complex

Species identification is a key procedure for broad-scoped ecological, phylogeographic and evolutionary studies. However, to perform a taxonomic study in the molecular era is a complicated task that has many pitfalls. In the present study we use particular examples of common but difficult to distinguish European species within the genus of Polycera (Nudibranchia, Mollusca) to discuss the general issues of the “cryptic species” problem that has broad biological and interdisciplinary importance and can significantly impede ecological, evolutionary, and other biodiversity-related research. The largest dataset of molecular and morphological information for European nudibranchs ever applied encompasses a wide geographical area and shapes a robust framework in this study. Four species are recognized in the species complex, including a new one. It is shown that a lack of appropriate taxonomic analysis led recently to considerable errors in species identity assessment of this complex. Chromatic polymorphism for each species is mapped in a periodic-like framework and combined with statistical analysis of the diagnostic features that considerably facilitates identification of particular species in the complex for biologists and practitioners. The present study evidently shows that “cryptic” and “non-cryptic” components are present within the same species. Therefore, this species complex is well suited for the exploring and testing of general biological problems. One of the main conclusions of this study is that division of biological diversity into “cryptic” and “non-cryptic” components is counterproductive. We propose that the central biological phenomenon of a species can instead be universally designated as multilevel organismal diversity thereby provide a practical set of methods for its investigation.

Nomenclatural acts. The electronic version of this article in Portable Document Format (PDF) will represent a published work according to the International Commission on Zoological Nomenclature (ICZN), and hence the new name contained in the electronic version is effectively published under that Code from the electronic edition alone. This published work and the nomenclatural acts it contains have been registered in ZooBank, the online registration system for the ICZN. The ZooBank LSIDs (Life Science Identifiers) can be resolved and the associated information viewed through any standard web browser by appending the LSID to the prefix http:// zooba nk. org/. The LSID for this publication is: [urn:lsid:zoobank.org:pub:15279E86-D7E2-4765-BF22-C0EB01E48E3D]. The online version of this work is archived and available from the following digital repositories: PubMed Central and CLOCKSS.
Morphological analysis. The external and internal morphology was studied using a stereomicroscope and digital cameras (Nikon D-810, Nikon D-7000, Nikon D-600 and Nikon D-80). The buccal masses were extracted and processed in 10% sodium hypochlorite solution to extract the radula and the jaws. Reproductive systems were examined using the stereomicroscope. The jaws were analyzed under a stereomicroscope and then photographed. The radulae and jaws were rinsed in water and 70% ethanol, then dried, mounted on stubs using carbon tape, coated with gold and palladium and finally examined using scanning electron microscopes (CamScan Series II and JSM 6380). The images were captured using a maximum quality mode (4) in CamScan II and a 80-s capturing mode in JSM 6380.
Statistical analysis. External morphology features (body length; number of frontal veil appendages, rhinophoral lamellae, and gills) were evaluated statistically using nonparametric Mann-Whitney rank sum test.

Molecular analysis.
A total of 102 Polycera specimens of various colour patterns and one Palio dubia were successfully sequenced in the Netherlands and Russia for the mitochondrial cytochrome c oxidase subunit I (COI) gene, and the ribosomal 16S RNA gene (see Supplementary information S1 for Building the periodic-like rows of chromatic variants. Similar chromatic variants within each potential species were aligned using calibration by the degree of light to dark surface pigmentation and transparency of body tissue, including presence of black stripes and brownish/dark pigmentation on the dorsal and lateral sides of the body. These similar forms establish horizontal rows of similar looking specimens within the species (Fig. 1). In total, eight chromatic variants (horizontal rows I-VIII) are recognized: I-body semi-transparent white, orange-yellow spots or brownish/dark colouration completely absent on the dorsal and lateral sides (orange-yellow colouration restricted to the frontal veil appendages, tips of rhinophores, gills, and postbranchial lobes); II-body semi-transparent white, few or indistinct orange-yellow spots present on the dorsal and lateral sides; III-orange-yellow (sometimes with reddish hue) spots are distinct and tend to form lines; IV-in addition to orange-yellow spots blackish or brownish spots or weak lines appeared (in case of lines, mostly in the anterior part of the body); V-in addition to orange-yellow spots, blackish stripes appear (but do not form continuous lines throughout dorsal side), blackish/brownish spots become evident and closer each other; VI-blackish stripes become evident and form continuous lines throughout dorsal side, blackish/brownish spots begin to blend together and form faint stripe-like pattern, orange-yellow spots evident in striped morphs, and less evident or almost absent in spotted morphs; VII-blackish stripes or a brownish (with a greenish hue) colouration pattern become dominant, orange-yellow spots are distinct in striped morphs, and less distinct or almost absent in spotted morphs. VIII-the blackish stripes pattern remains evident or merged, whereas orange-yellow spots (often with more intense reddish colouration) are merged into distinct lines. The proposed scheme of the chromatic variants has a biological basis since it was shown for P. quadrilineata s.l. that during the earlier post larval ontogenetic development orange and blackish colouration is weak or almost absent, and distinct spots, lines and stripes appear only towards later ontogenetic stages 36 and this coincides well with general patterns of the ontogeny among dorid nudibranchs, when colourless or white forms appear first, and intense colouration is added later.

Results
Morphological and statistical analyses. The scheme of description of the chromatic polymorphism among the monophyletic group of closely related species of Polycera which inhabit European waters is consistently applied to each of the four potential species in this complex ( Fig. 1, vertical columns). Among specimens whose external and internal morphology correspond to the descriptions of Polycera quadrilineata and P. capitata, specimens with the colour patterns which correspond to the rows II-VIII were detected (Fig. 1, horizontal rows show eight different color patterns). In P. faeroensis specimens with colour patterns for the rows I-III and VIII were found, whereas for P. kernowensis sp. nov. (holotype ZMMU Op-755, ZooBank registration: urn:lsid:-zoobank.org:act: 5C821EFD-FB12-49D5-A9C3-026A325F6D21) specimens with colour patterns corresponding only to row I were found. Afterwards, an additional morphological study in order to detect morphological differences between similar specimens of I-III rows (semitransparent white body and absence/presence yellow-orange spots/lines, that was observed in 42% among P. quadrilineata specimens, used for statistical analysis, 47% P. capitata, 88% P. faeroensis, and 100% of P. kernowensis sp. nov.) (Fig. 1). In the present study it is shown that these similar white-and-yellow specimens of all four species reveal significant statistical differences in number of rhinophoral lamellae (p = 0.023 between P. quadrilineata and P. kernowensis sp. nov.; p < 0.001 between all other species). For the number of frontal veil appendages there were no significant statistical differences between P. quadrilineata and P. capitata. However, such differences were revealed between P. faeroensis and P. kernowensis sp. nov. (p < 0.001); P. faeroensis compared with P. quadrilineata or P. capitata (p < 0.001); P. kernowensis sp. nov. compared with P. quadrilineata or P. capitata (p < 0.001). There were no significant statistical differences in number of gills for P. quadrilineata, P. capitata, and P. faeroensis. But P. kernowensis sp. nov. shows statistically significant fewer gills compared with P. quadrilineata, P. capitata, and P. faeroensis (p < 0.001) ( Fig. 2A, Table 1, Table S2). It is unmistakably visible that P. faeroensis commonly possesses more than one pair of postbranchial lobes (Fig. 2B). Significant statistical differences in external morphology were revealed for specimens of all colour patterns (Supplementary information, Fig. S1). Mean P. faeroensis body length is statistically significantly bigger than mean body length of P. www.nature.com/scientificreports/ quadrilineata, P. capitata, and P. kernowensis sp. nov. Mean P. capitata and P. kernowensis sp. nov. body length is statistically significantly smaller than mean body length of P. quadrilineata and P. faeroensis (p < 0.001, Fig. S1, Table S2). In addition, differences in internal morphology were revealed (Fig. 2B). P. capitata have clear differences from the other species in shape of the copulative spines. P. faeroensis have clear differences in shape and size of the lateral teeth of radula.

Molecular phylogenetic analysis. Phylogenetic analysis was performed using 197 specimens of
Polycera, including data for 178 P. quadrilineata species complex (102 of which were preliminarily divided into four groups using the methods described above and data for 76 downloaded from GenBank), and 24 outgroup specimens. The dataset consisted of 356 nucleotide sequences including COI and 16S genes. Bayesian Inference (BI) and Maximum Likelihood (ML) analyses based on the combined dataset for the COI, and 16S genes yielded similar results (Fig. 3). To define species, we use a set of methods 12,37 including phylogenetic tree topologies, ABGD analysis, pairwise distances and the haplotype network containing phylogeographic data rendered using PopART (Fig. 4, Table 2). The results of this study confidently confirmed the presence of four species among P. quadrilineata similar specimens that coincided with species detected before the molecular study: P. quadrilineata, P. capitata (that do not show any differences from the recently described P. norvegica), P. faeroensis, and P. kernowensis sp. nov. A clade containing P. quadrilineata (n = 92, PP = 1, BS = 99) has the closest position to the clades containing P. capitata (n = 34) combined with former P. norvegica (n = 17, PP = 1, BS = 100), P. faeroensis (n = 2, PP = 1, BS = 100), P. kernowensis sp. nov. (n = 33, PP = 1, BS = 100), and two Polycera sp. A from South Africa (PP = 1, BS = 100). P. quadrilineata and P. capitata (combined with former P. norvegica) clustered in two distinct and well separated sister clades that formed the sister group to P. faeroensis, P. kernowensis sp. nov., and P. sp. A, which are clustered together in a separate clade, wherein P. faeroensis has sister position to P. kernowensis sp. nov. The ABGD analysis of the COI data set run with two different models are fully concordant with the clades in the molecular phylogenetic analysis (Fig. 3). Results obtained by PopART showed a network of haplotypes that clearly clustered into four distinct groups coincident with P. quadrilineata, P. capitata (combined with former P. norvegica), P. faeroensis, and P. kernowensis sp. nov. (Fig. 4). While no correlation was found between the molecular characteristic for each of the four species and the geographical www.nature.com/scientificreports/ distribution of each of the four species from this complex, P. capitata and "P. norvegica" recently described from Norway have a widespread distribution in England, Ireland and Norway, and do not show separate clustering. Regarding the supposedly fast-evolving COI marker, uncorrected p-distances within the P. quadrilineata clade range 0-3.36%. Whereas minimal uncorrected p-distances between the P. quadrilineata clade and P. capitata (combined with P. norvegica), P. faeroensis, and P. kernowensis sp. nov. clades are 9.44%, 11.09%, and 10.79% respectively. Uncorrected COI p-distances within the P. capitata (combined with P. norvegica) clade range from 0.15 to 3.04%. Minimal uncorrected p-distances between the P. capitata (combined with P. norvegica) clade and P. faeroensis, and P. kernowensis sp. nov. clades are 8.52%, and 8.66% respectively. Uncorrected COI p-distances within the P. faeroensis clade are 0.61%; within the P. kernowensis sp. nov. clade range 0-2.33%. Uncorrected COI p-distances between P. faeroensis and P. kernowensis sp. nov. clades range from 5.47 to 6.38% (Table 2). Polycera aurantiomarginata García-Gómez & Bobo, 1984, which was described from Spain and which is also distributed on the West African coasts 22 belongs to a different Polycera clade, considerably different morphologically, and hence is not part of the complex of the European species closely related to P. quadrilineata. Therefore P. aurantiomarginata is included in the present molecular phylogenetic analysis, www.nature.com/scientificreports/ but not considered in this study in detail (Fig. 3). An undescribed species ("Polycera sp. A") which was included to a molecular phylogenetic study without any morphological data 14 is basal to the clade of the European Polycera ( Fig. 3) but occurs exclusively in South Africa and is out of scope in the present study.
For Polycera marplatensis Franceschi, 1928 38 which is partly similar to P. quadrilineata molecular data are not available, but this species occurs exclusively in South America and therefore is also out of scope of the present study. The morphological analysis data were confirmed by molecular phylogenetic results. P. quadrilineata, P. capitata, P. faeroensis, and P. kernowensis sp. nov. are four separate species in the genus Polycera. P. capitata and former P. norvegica are the same species.
Difficult to distinguish European species within the genus Polycera: recognition of the involved species. We obtained a very robust framework of four closely related species from European waters: Polycera quadrilineata, P. capitata, P. faeroensis and P. kernowensis sp. nov. (Figs. 3, 4, for detailed systematic account of all four species see Supplementary information S2). Polycera quadrilineata and P. capitata are the two common European species and usually present in the shallow marine waters at depths easily accessible for diving (ca. 5-40 m), making these species always a focus of attention of various environmental associations, ecological studies and currently also citizen scientists. Therefore it is of high general importance to present a framework for morphological identification of these species complex based on robust molecular data (Tables 1, 2).
Throughout the history of nudibranch studies in Europe, a species similar, but distinct from P. faeroensis has been confused with the latter and was never taxonomically recognized 14,39,40 . In the present study this species using robust molecular framework based on a broad geographical sampling and significant external and internal morphological differences (Figs. 1, 2, 9; Table 1) it is for the first time recognized and described as a new species, Polycera kernowensis sp. nov. (see details in Supplementary information S2). This species has significantly more rhinophoral lamellae (14-15) than in P. capitata (8) and P. quadrilineata (11)(12) and same is true for the frontal veil appendages (7-8 vs. 4-5) including specimens of similar sizes (Figs. 2, Supplementary information Fig. S1). Polycera quadrilineata can reach a similar large size as P. faeroensis (commonly the former species is smaller), but the mean number of rhinophoral lamellae in P. quadrilineata is significantly smaller (11)(12), than in P. faeroensis (18)(19) (Figs. 2, Fig. S1) and even in largest specimens of P. quadrilineata the number of rhinophoral lamellae is smaller than in P. faeroensis. In addition, the number of the frontal veil appendages differs with a high support among these three species (Fig. 2, Supplementary information S2, Fig. S1).
Remarkably, in this study we also recovered two closely related species P. quadrilineata and P. capitata as sister species (Fig. 3), in contrast to a previous study 14 , because taxon selection was previously not exhaustive. True P. faeroensis is a more rarely encountered species than P. quadrilineata and P. capitata (at least in the relatively shallow water environments) and verified molecular data which were aligned with the fine-scale morphological data are presented in this study for the first time (Figs. 1, 2, 3, 4, 5, 6,7,8,9,10). Previously real P. faeroensis were misidentified 14,40 with its new sister species, here described as P. kernowensis sp. nov. (Figs. 8, 9). Our verified data on the morphology of the radula matched well with the original description of P. faeroensis from the Faeroe Islands 41 and a morphological redescription from Sweden 42 . www.nature.com/scientificreports/ www.nature.com/scientificreports/ The results of the statistical test in key diagnostic external features (number of rhinophoral lamellae, frontal veil appendages and gills) in the Polycera species complex (Fig. 2, Supplementary information S2), showed that easily accessible external morphological features are distinguishing factors among adult individuals between the species in the complex, with high statistical support (Figs. 2, Supplementary information S2, Fig. S1). Particularly, the number of the rhinophoral lamellae differs with high support among all four species (Figs. 2, 10, Supplementary information S1). It must be noted that differences in rhinophoral lamellae are partly related to the animal length, due to the fact that larger specimens may have larger numbers of rhinophoral lamellae, starting from 0 (i.e. smooth rhinophores) and reaching a mean number of lamellae towards mature stages 43,44 . However, even most closely related sister species P. quadrilineata and P. capitata were revealed as having smaller, but statistically significant differences in the mean number of the rhinophoral lamellae (mean 8 in P. capitata and 11-12 in P. quadrilineata) including specimens of similar sizes (Figs. 2, 10, Supplementary information S2). The significant differences can be further used for the fine-scale diagnostics of these species. This is a very important result for further assessment of the general reliability of the "cryptic species" concept. Figure 10. Presentation of the multilevel organismal diversity approach using the example of closely related Polycera quadrilineata and P. capitata: presence of conditional "non-cryptic" and putative "cryptic" components among the same species and provision of fine-scale morphological diagnostic characters even among the "cryptic component" within a single species. Scale bars-10 μm.

Discussion
Importance of the true, and not a formal integration of the molecular, morphological, and taxonomic data for applications in ecological and evolutionary studies. The present study is very relevant for the investigation of the general species concept and so-called "cryptic species" concept and also for the currently commonly claimed "integration" of molecular and morphological data. It was already highlighted that the challenge represented by cryptic species has great importance for general biological problems and represents "a window into the paradigm shift of the species concept" 20 . We therefore present in this study the largest currently possible molecular and morphological dataset on a particular nudibranch species complex, which is widely distributed over the vast European region. Molecular data of 178 specimens belonging to four species were involved in the molecular phylogenetic analysis (Fig. 3). Furthermore, for the practitioners, and for researchers who perform environmental monitoring in the European marine waters, it is very important to trustworthily distinguish the four species, including the most difficult to distinguish P. quadrilineata and P. capitata, in the field and, above all, without complicated, time-consuming and expensive molecular analysis. This is especially important since P. quadrilineata complex represents an indicator of biodiversity shifts in relation to climatic changes 27 .
In order to develop a robust framework to make it possible to identify all four species using only easily accessible external characters and applying in the majority of cases, we hereby provide a summary of an exhaustive analysis of molecular and morphological data for all European Polycera species (Figs. 1, 2, 3, 4, 5, 6, 7, 8, 9, Tables 1, 2), i.e. every newly available specimen or sequence from European waters belonging to each of the four recognized species (Fig. 3, Tables 1, 2) and not to any other potential "hidden" lineages.
Polycera quadrilineata (O. F. Müller, 1776) is one of the oldest species names amongst European nudibranch molluscs 45,46 . Since then there were numerous attempts to separate more species similar to P. quadrilineata (see the Supplementary information S1 for details on the systematics of P. quadrilineata), however all of them without a detailed morphological analysis were later considered to be synonyms of P. quadrilineata 40 . Using molecular data, Driessen et al. 21 showed two lineages among European "P. quadrilineata" for the first time. Recently one of these lineages has been formally described as Polycera norvegica 14 . The description proposed the species to occur exclusively in Norway. According to our data, applying a very broad geographic sampling in frames of the present study (see e.g., Figs. 3, 4) the recently named "Polycera norvegica" definitely is not distributed solely in Norway, but is a species widely distributed in other European countries, such as the United Kingdom and Ireland (Supplementary information, Table S1). Furthermore, in that publication, the numerous synonyms of P. quadrilineata were neither listed nor investigated, and its synonymy was just referred to the internet database MolluscaBase 47 .
In the present study we carefully investigated all existing available synonyms of P. quadrilineata (Figs. 1, 2, 3, 4, 5, 6, 7, Table 1, Supplementary information Fig. S1). Therefore, being part of the difficult to distinguish P. quadrilineata complex, for which more than ten synonyms have been suggested, and having a broad distribution in Europe, "P. norvegica" could have already been described. If "P. norvegica" had no clear recognizable chromatic variants which immediately distinguished it from P. quadrilineata it would be difficult to assess a potential synonym. However, "darker" chromatic variants (Fig. 1IV-VII) are clearly different between P. quadrilineata and "P. norvegica", which makes a solid base for the search for such previously described variants within taxonomic synonyms. During this study we identified two available taxonomic names that contain chromatic variants with darker colouration without evident stripes, and those can be thus excluded from the striped variants of true P. quadrilineata (Figs. 1, 2, 5, 7). These available names are Polycera ornata d'Orbigny, 1837 and Thecacera capitata Alder & Hancock, 1854. For Polycera ornata a main morph with red-orange lines was described 48 and in addition a morph with weaker orange and black spots was mentioned. Because of a main morph with orange-reddish lines in Polycera ornata, and having only an old painting published, it is difficult to surely distinguish the morph from P. quadrilineata. Furthermore, for P. ornata a "tiger-like" colouration was indicated for the darker morph 48 , that may imply stripes, as in true P. quadrilineata. Thus, to assign Polycera ornata to this species would be ambiguous. Also, the type material of Polycera ornata was not saved.
Instead, for Thecacera capitata in the original description by Alder & Hancock (1854) the colouration was solely indicated as "freckled with brownish greenish" 49 that immediately allows exclusion of any morphs with evident black stripes, that are present only in true P. quadrilineata (Figs. 1, 5). Thecacera capitata was later confirmed as belonging to the genus Polycera and not to Thecacera, including study of the type material 40 ; presence of rhinophoral sheaths for P. capitata was thus indicated mistakenly 49 . Polycera capitata was partly redescribed with aid of the type material regarding external features and the external colouration 40 and exactly matched the chromatic variant V in P. norvegica but not any chromatic variants of P. quadrilineata (Figs. 1, 7M). In this study we additionally studied the saved radula from the type specimen of Polycera capitata as was figured in the original description 49 . The radula has only four outer lateral teeth and thus fits well to the most rigorous assessment of the radular characters in this species, including "P. norvegica" 14 .
This combination of the external and internal data excludes the possibility that Polycera capitata is a synonym of P. quadrilineata but instead conforms closely to the characters that were recently described for P. norvegica 14 . We have involved numerous specimens from the United Kingdom and Ireland-that matched well morphologically to the original description of P. capitata (Figs. 1, 7)-in the present molecular analysis. The present study shows that darker chromatic variants V-VII without distinct stripes are characteristic solely for P. capitata (Figs. 1, 7, 10). Furthermore, these darker chromatic variants of P. capitata are very common throughout the United Kingdom from Cornwall in the south to the Scotland in the north, including the type locality at St. Ives, Cornwall according to the available photographic data 50 www.nature.com/scientificreports/ These data were already available, but an essential external similarity of "P. norvegica" to P. capitata was missed and it was incorrectly stated that the species is restricted to Norway 14 . "P. norvegica" syn. nov. thus becomes a junior synonym of Polycera capitata. Additionally, (with permission) we present a copy of plate 18c from Thompson & Brown (1984) 40 where the external features illustrated for Polycera capitata correspond exactly with our morphological data for P. capitata (Fig. 7M). Therefore, our present taxonomic assignment of P. capitata is robustly supported by the abundant morphological (including statistical study), molecular and distributional data (Figs. 1, 2, 3, 4, 5, 6, 7, Table 1, Supplementary information, Table S1, Fig. S1). In the present study we therefore restore the species P. capitata and P. norvegica becomes its junior synonym.
Importantly, what appears to be a particular taxonomic problem, has in reality general importance for an array of biological fields since it clearly shows that without true integration of an "old" taxonomic knowledge, that tends to be neglected currently, with modern morphological and molecular data, an appropriate study of world biodiversity cannot be performed. The "cryptic species problem" therefore does not emerge only recently, but was always part of taxonomy since the Linnean era. A formal integration of the molecular and morphological data and inaccurate claim for "cryptic species" led to omission of a synonym for a common, species which is important for ecological monitoring. Therefore, the importance of true and not just a formal integration of molecular, morphological and taxonomic data are here specially highlighted and a practical set of methods is proposed below.
Periodic-like framework for the recognition diagnosable characters in the species complexes. Periodic-like as well as parallel-like patterns in biological applications have been discussed for a long time and successfully applied for protein structure 52 , but they are still not widely used practical tools for taxonomy and phylogeny. Several recent studies on different groups, such as rodents 53 and fishes 54,55 robustly confirmed the existence of periodic patterns during development of morphological characters at a genomic level, particularly concerning chromatic variants and thus are directly connected with the present Polycera case. Notably, the ontogenetic periodicity is based on periodicity of homeobox and other developmental gene systems in animals and plants 56,57 , thus approaching chemical periodicity. Recently an evident periodicity was revealed for a higher-level organism group using an ontogenetic phylotypic periods/stages approach, that consistently links the genomic and morphological levels 44 . There were attempts to describe chromatic variants within another nudibranch family Chromodorididae under the term "colour groups" 58 or as different colour morphs in frames of a phylogeny 59,60 , but not in a periodic framework. However, when similar morphs of different closely related species are mapped in the same horizontal sections, the partial periodicity can be clearly revealed 18 .
During individual development, this was investigated for Polycera quadrilineata 36 , the darker colouration appeared during later stages of the ontogeny, and similar patterns of the ontogeny of the sister species P. capitata must present in parallel, which makes the biological grounds for the periodic-like approach. Such an approach is a practical one and helps to reveal fine distinguishing details among apparently very similar morphs (e.g. chromatic variants) and also potentially not yet discovered morphs of the closely related species. Currently we have no information about which particular genes underlie any common genetic basis in the polychromatic nudibranchs 61 , but it must inevitably imply similar developmental genes basis and it was recently used for delineation of a very difficult nudibranch species complex of the genus Amphorina 18 . A North Pacific species, Polycera atra MacFarland, 1905, provides evidence for the existence of the underlying similar genomic basis, that appears in parallel in various phylogenetic lineages. According to the present analysis it represents a taxon which is only distantly related to the P. quadrilineata complex (Fig. 3), and potentially may belong to a separate genus (a general revision of the family Polyceridae is pending), but nevertheless exhibits similar chromatic variants 62 . As in the P. quadrilineata complex, about eight chromatic variants of P. atra are recognized. These are used in the present study to align the chromatic variants found within the European Polycera species (Fig. 1). Such parallel appearance of the similar chromatic variations in relatively distantly related clades is well matched to the parallel appearance of the shell morphs within gastropod molluscs 63 , for which a similar genomic base has already been confirmed 64 .
The present Polycera chromatic polymorphism is a clear case of periodic appearance of similar colour morphs among phylogenetically related but different species which has robust support from a large molecular dataset (Figs. 1, 3). Polycera quadrilineata also possesses stripe patterns in their colouration (Fig. 1V-VIII), and similar patterns were recently showed as underlain by ontogenetic periodicity in various groups 54,55 . Within P. capitata instead darker forms (Fig. 1V-VIII) appear in parallel, without distinct stripes, but with remnants of a faint stripe-like pattern (Fig. 1VI). In both P. faeroensis and P. kernowensis sp. nov. the chromatic variants IV-VII are not yet discovered (Fig. 1). This makes the method a practical tool for revealing a diagnosable character within putative "cryptic species complexes". While biologists from non-taxonomic fields or experienced practitioners have the task to identify Polycera in the field, they will be guided by a periodic-like mapping (Fig. 1) which is based on accurate taxonomy and robust molecular phylogenetic data (Figs. 3, 4). It will be easier to exclude these variants that do not occur (as striped or heavily spotted variants are not yet found in P. faeroensis and P. kernowensis sp. nov.), and instead carefully investigate similar chromatic variants II and III in two sister species P. quadrilineata and P. capitata (Fig. 1).
When such periodic-like mapping becomes a routine part of biodiversity studies, the accumulated data will allow the presentation of small, fine-scale distinguishing characters even between such highly similar orange-spotted chromatic variants that are present in both P. quadrilineata and P. capitata. At www.nature.com/scientificreports/ present, they remain difficult to distinguish, but using available data we can preliminarily conclude that in P. capitata orange spots are more commonly smaller and more rarely form lines, than in P. quadrilineata (Figs. 1, 2, 5, 7). A statistical test of the diagnostic value of the external characters, that were mapped in the periodic-like framework, revealed that number of the rhinophoral lamellae, though it may overlap in juvenile specimens, in adult specimens is different with a statistical high support including among these difficult to distinguish chromatic variants II and III between P. capitata and P. quadrilineata (Fig. 2, Supplementary information S1, Fig. S1). Thus, the number of the rhinophoral lamellae (a very easy to check character even on the photographs), can be used as an additional verification in case of similar chromatic variants II and III between P. capitata (commonly less than ten rhinophoral lamellae in adults) and P. quadrilineata (commonly more than ten rhinophoral lamellae in adults). The periodic-like mapping of the chromatic variants revealed that orange dots on the body sometimes occur, as well as potentially darker morphs in true P. faeroensis (Fig. 1II-VIII), but patterns and quantity differ between P. quadrilineata and P. capitata (Fig. 1II-VIII). Previously all four species of the European Polycera complex have been confused with each other 40,65 also because these chromatic variants were previously never accurately mapped with each other, but instead it was commonly noted that similar to P. quadrilineata and P. capitata yellow-orange dots were sometimes present on the body in P. faeroensis, which immediately misled practitioners that have had tasks to identify animals in the field. Further, this profound confusion among identification of European Polycera persists even using modern molecular tools as P. faeroensis until the present study was not distinguished from P. kernowensis sp. nov., despite the presence of robust external, internal, and molecular differences (Figs. 1, 2, 3 , 4, 8, 9). Thus, the periodic-like mapping of the polychromatic variants in combination with statistical analysis of the diagnostic characters is an important tool in addition to the molecular phylogenetic analysis. It will be particularly important since P. quadrilineata and P. capitata are two of the most common nudibranch species in Europe, and particularly in the UK the further testing of their chromatic variance already attracted attention 51 and further attraction of various environmental and educational organizations and citizen scientists is expected. Our present study builds a major framework for further broader testing of the colour polymorphism and other distinguishing features in the Polycera species complex that will have importance for the development of documenting the fine-scale diversity not only in other nudibranchs, but in the variety of multicellular organisms.
Practical guidelines how to perform a taxonomic study in the molecular era. The present study evidently shows that "cryptic" and "non-cryptic" components are present within the same species. This further significantly undermines the "cryptic species" concept, which recently was already questioned 4,10-12 . The presence of both "cryptic" and "non-cryptic" components is demonstrated here for sister species P. quadrilineata and P. capitata sharing externally similar chromatic variants II and III (Fig. 1), which however can be distinguished by the morphological features of another level (Figs. 5, 7). Particularly, the internal features of the shape and size of copulative spines allow in 100% cases to confirm the identity of both species (compare Figs. 5K, L, Q, R, V-X and 7E, F, L, R, S, W-Z), even without aid of molecular data this undermines the proposal that these species are morphologically "cryptic". In our recent study 12 we already showed how the underestimation of the taxonomic and morphological data resulted in a long-term omission of reliable multilevel differences in the nudibranch Trinchesia species complex. Recently, there are proposals that taxonomy should be an integrative study [66][67][68] . However, in current common practice "integration" unfortunately mainly means performing a molecular study on some selection of specimens and then morphological features listed "in addition", rather as an auxiliary information. The best confirmation of this is the recent Polycera study 14 , when crucial previous taxonomic information was omitted, and while some morphological diagnostic features were revealed, both their stability and variability (and hence, their usefulness for taxonomic diagnostics) were over-or underestimated that subsequently led to an incorrect statement about "general crypticity" of the involved species.
To avoid this, practical guidelines proposing how to perform a taxonomic study in the molecular era are outlined here: (1) make a selection of a taxonomic group and appropriate specimens; (2) make a relevant morphological study in a given group, including for example scanning electron microscopy of previously commonly used diagnostic characters in the given group; (3) ensure that ontogenetic information is considered during taxonomic assessment, because adult diagnostic characters can be considerably transformed at different ontogenetic stages, whereas adult paedomorphic characters can be easily misidentified with juvenile transitive features 44,69-71 ; (4) make an appropriate bibliographic study, to exhaustively study the synonymy of a studied taxa/species group, importantly, not just as a reference to a taxonomic data base, but to perform a real study of original sources; (5) molecular study selected and taxonomically checked specimens with commonly used genetic markers in a given group; (6) compare the results of the morphological (step 2) and taxonomic investigation (steps 3, 4) with the molecular (step 5) results; (7) in case of finding discrepancies between previously commonly assessed diagnostic characters in a given species group and results of molecular phylogeny, respective diagnostic features of specimens in question should be presented in a periodic-like framework of the parallel rows, that will enable their detailed comparison and further search for fine-scale differences between given rows for each of the closely related species; (8) in case difficult to distinguish variants are present among the same parallel rows, a statistic study of the relevant diagnostic features should be performed in order to reveal fine-scale differences among closely related species; (9) a complete study at a given time and using current research possibilities should result in fine-scale taxonomic diagnoses for all closely related species in a given taxa/complex (including new taxa); (10) test the established framework by further investigation of a given group with new materials and data.
Applying the above described methodology and using a large dataset we were able to exhaustively investigate the European Polycera species complex (Figs. 1, 2, 3, 4)  www.nature.com/scientificreports/ as a "cryptic one" 14 . As a result, we definitely assessed every particular specimen (or sequence data) to a particular species: P. quadrilineata, P. capitata, P. faeroensis, and P.kernowensis sp. nov. (Figs. 1, 3 , 5, 9). For each of these species we provided diagnostic characters that are based not just on traditional taxonomic "listing" of some features, but on statistically supported analysis of key external features. Particularly, in addition to the molecular phylogenetic study and periodic-like mapping of the chromatic variance we tested the most commonly used diagnostic characters within the Polycera species complex, such as number of the rhinophoral lamellae, number of frontal veil appendages and number of gills using statistical tests (Fig. 2). As a result, we discovered that the four species differ in number of rhinophoral lamellae with high statistical support (Fig. 2, Supplementary information S2). With this study, we integrated molecular and morphological data and moreover recovered the multilevel diagnosable diversity within the given species complex, including presenting the distinguishing characteristics between closely related and most difficult to distinguish species from this complex: P. quadrilineata and P. capitata. When specimens of these species belong to similar chromatic variants II and III, it will be possible to diagnose it using not only clearly different micromorphological features of copulative spines, but also easily accessible external morphological features (Figs. 2, 5, 7, Supplementary information, Fig. S1). They possess consistent molecular and morphological units, and importantly, there are no signs for further hidden molecular lineage among European Polycera species.
Multilevel organismal diversity approach and conclusions on "cryptic species" problem. According to the suggested approach, when knowing more difficult to distinguish species within a species-complex in other organism groups 8,12,72 , putative crypticity means that characteristics were not investigated at a maximally possible fine-scale level (despite considerable efforts) using fine morphologybased comparative rows of parallel characteristics. Without comparative rows of parallel characters it is especially difficult to distinguish species with a highly simplified morphology, for example tiny paedomorphic, decelerated burrowing polychaete worms 13,73 . Using a lineage-based approach, as shown recently 1 , is not enough for species definition. Every new specimen, even a clone must have either smaller or larger differences from any other specimens 12 . It is therefore biologically impossible that a species can be morphologically "completely cryptic". Conclusions about a "cryptic species" appeared when fine-scale differences (either macro-or micromorphological) were not detected at a present level of knowledge in given groups. It was already concluded most recently that in several cases, potential diagnostic characters were hidden within broadly overestimated "intraspecific variations" 14 and that a search for the fine-scale morphological differences using various modern methods is important part of future research, because otherwise, for example in palaeontology, species diagnostics will be greatly compromised 74 .
The present data evidently imply that both P. quadrilineata and P. capitata species comprise putative "cryptic" and conditional "non-cryptic" components. We generated a scheme to clearly show this phenomenon (Fig. 10). P. quadrilineata and P. capitata have similar chromatic variants (Fig. 1II-III, 10) at a "macromorphological" level. Therefore they conditionally represent a "cryptic component" but are readily different by other chromatic variants (IV-VIII). This additionally has a strong statistical support in other external macromorphological features, such as the number of rhinophoral lamellae, and therefore manifesting a "non-cryptic component" for the diversity within Polycera (Figs. 2, 10). Subsequently, at a "micromorphological" level, the differences in shape and size of the copulative spines allow clear and unambiguous distinction of P. quadrilineata and P. capitata by "non-cryptic components" (Fig. 10). Further, at a molecular level all four Polycera species demonstrate significant genetic distances (Figs. 3, 4; Table 2).
Particularly, the special emphasising about "crypticity" of P. capitata in Norway 14 did not help to correctly recognize taxonomic and distributional data for this species, but instead led to important omission that in reality P. capitata is not restricted to Norway, but common throughout waters of the middle and Northern Europe (Figs. 3, 4; Supplementary information Table S1). By results of the present study, we can further extend and strengthen our recent arguments 4,12 and conclude that it is highly counterproductive to divide the biological diversity into "cryptic" 8,14,75 and "non-cryptic" components since both may be presented within a single species. Additionally, the term "cryptic species" can be misleading because of its continued usage in recent publications, but in a completely different ecological meaning of a well camouflaged species 76,77 .
We propose that the central biological phenomenon of a species that currently attempted to be disrupted into "cryptic" and "non-cryptic" ones can be instead universally designated as multilevel organismal diversity (Fig. 10). This term will avoid artificial division of the very complex biological phenomenon of diversity. Multilevel organismal diversity encompasses numerous patterns and processes of various levels, from which most notable and readily recognizable are morphological and molecular levels, each with numerous intersected sublevels, ultimately forming complex functional living organisms.

Data availability
Sequences will be deposited in GenBank, and can be consulted accessing GenBank, with sequence IDs listed in Table S1. www.nature.com/scientificreports/