Trinchesia from European waters to reveal three new species and demonstrate that they show a dual nature: on one hand, they can be considered a ‘cryptic’ species complex due to their overall similarity, but on the other hand, stable morphological differences as well as molecular differences are demonstrated for every species in that complex. Thus, this species complex can equally be named ‘cryptic’, ‘pseudocryptic’ or ‘non-cryptic’. We also present evidence for an extremely rapid speciation rate in this species complex and link the species problem with epigenetics. Available metazoan-wide data, which are broadly discussed in the present study, show the unsuitability of a ‘cryptic’ species concept because the degree of crypticity represents a continuum when a finer multilevel morphological and molecular scale is applied to uncover more narrowly defined species making the ‘cryptic’ addition to ‘species’ redundant. Morphological and molecular methods should be applied in concordance to form a fine-scale multilevel taxonomic framework, and not necessarily implying only an a posteriori transformation of exclusively molecular-based ‘cryptic’ species into morphologically-defined ‘pseudocryptic’ ones. Implications of the present study have importance for many fields, including conservation biology and fine-scale biodiversity assessments.‘Cryptic’ species are an emerging biological problem that is broadly discussed in the present study. Recently, a cryptic species definition was suggested for those species which manifest low morphological, but considerable genetic, disparity. As a case study we present unique material from a charismatic group of nudibranch molluscs of the genus  The term ‘cryptic species’ became popular relatively recently5 and has supplanted the term ‘sibling species’ which was commonly used in previous cases with difficult-to-distinguish species6. Despite the fact that the ‘cryptic species’ concept has received considerable attention and is now used in various applications, it is intrinsically contradictory and might also be confused with other uses of the word ‘cryptic’. For example, the exact same ‘cryptic species’ term is used in ecology to denote that some species are very well camouflaged on some substrates7.The ‘cryptic species’ concept is widely used in modern biodiversity studies8. In a further discussion, Struck et al.9 rather disagreed and attempted to build a definition of ‘cryptic’ species on a lower degree of phenotypic  disparity than non-cryptic relatives. However, to define an exact degree of morphological disparity is very difficult, if it is possible at all, so Heethoff10 further concluded that the current ‘cryptic species’ concept represents either conceptual or terminological chaos. Additional complications arise from the most recent practice in different animal groups such as crustaceans11, insects12 or echinoderms13 when the term ‘cryptic’ species is used for morphologically diagnosable species.Recently, the difficulty of delineating the ‘cryptic species’ concept from the basic biological species definition was highlighted, and it was suggested that this concept should be used with care and only as a temporary formalization for taxonomic complexes for which a robust morphological framework is not yet established15. The term ‘cryptic species’ is also commonly vaguely applied, making its definition uncertain10, which prompts the necessity of its revision. The present case is of special importance since it links a taxonomic problem in a particular organism group with the most general biological problem of the species concept, using broad-scope material on marine animals. Here, we show that a very colourful species of nudibranch mollusc Trinchesia caerulea , which was originally described from the UK, but common throughout European waters , is revealed to actually be a complex of four species (three of which are new). According to the present study, these species are robustly distinguished by their molecular data and were never taxonomically separated previously and thus fit within the ‘cryptic species’ concept and its updated definition including “low morphological disparity9”. However, the apparent cryptic morphology for that complex had previously been noted and questioned17 and in the present study those morphological distinctions have been supported by novel molecular data. Thus, these ‘cryptic’ species can be distinguished morphologically (and hence can be defined as ‘pseudo-cryptic’ species) not only a posteriori after molecular study, as was commonly suggested and has become a notable modern tendency19, but by using multilevel morphological information as a primary source. This adds a new perspective to the understanding of the core biological species problem, which should not just be to adhere to a putative cryptic notion, but methods should rather follow the idea “from cryptic to obvious species” with the rapid progress of various molecular analyses and aids to morphological differentiation21 in order to reveal an immense hidden multilevel biological diversity.The ‘cryptic’ species problem is not merely a theoretical problem. The strong trend to distinguish ‘cryptic’ and ‘non-cryptic’ species, and the explosive growth of exploration and description of ‘cryptic’ diversity, without a clearly defined terminological ground, is already resulting in recent outstanding controversies in important fields such as conservation biology - particularly regarding suggestions for special regulations of species names, that will affect the core of taxonomy25. Additional molecular data for 13 specimens of nudibranchs were obtained from GenBank  and Maximum Likelihood (ML), were used to infer evolutionary relationships. To evaluate the genetic distribution of the different haplotypes, a haplotype network for the COI molecular data was reconstructed using Population Analysis with Reticulate Trees . Also, the minimum uncorrected p-distances between all the sequences as well as maximum intra- and minimum intergroup genetic distances were examined. Automatic Barcode Gap Discovery (ABGD)28 was used to define species. See supplementary information Text for methods in detail.Material for this study was obtained by scuba diving at widely separated locations across Europe: from the United Kingdom, Ireland, Norway, Sweden, Spain, Italy, France, Croatia and Russia. The specimens were deposited in the Zoological Museum of Lomonosov Moscow State University (ZMMU), in the Gothenburg Natural History Museum (GNM), National Museums Northern Ireland (BELUM.Mn), and the Department of Science of the Roma Tre University (RM3). Integration of molecular and morphological data as well as phylogenetic and biogeographical patterns were used. The external and internal morphology of the 28 specimens was studied using digital cameras, under a stereomicroscope and scanning electron microscope. For molecular analysis 17 specimens were successfully sequenced for the mitochondrial genes cytochrome c oxidase subunit I (COI), 16S rRNA, and the nuclear genes Histone 3 (H3). The DNA extraction procedure, PCR amplification options, and sequence gathering are described in detail in previous studiesTrinchesia, including data for 21 Trinchesia caerulea species complex specimens, four other congener species of the genus Trinchesia and two outgroup species. All supposedly morphologically cryptic morphs of Trinchesia caerulea illustrated in Thompson & Brown (1984)16 were collected in European waters and examined. In addition, specimens collected in the Black Sea that are taxonomically close to T. caerulea were also included in the study. We apply the concept ‘Trinchesia caerulea species complex’ here as the designation for all these studied specimens. The dataset consisted of 80 nucleotide sequences including mitochondrial COI and 16S, and the nuclear H3 genes. The SYM + G model was chosen for the concatenated dataset. Bayesian Inference (BI) and Maximum Likelihood (ML) analyses based on the combined dataset for the COI, 16S and H3 genes yielded similar results , T. cuanensis sp. n. , T. morrowae sp. n. , and T. diljuvia sp. n. . ZooBank registration for the paper is: urn:lsid:zoobank.org:act: 4B5F968F-69B6-4FB0-BB7B-43ABC4B09EBB. Information about the taxonomy of these four species can be found in the descriptions below, in the Figs Phylogenetic analysis was performed using 28 specimens of ART Fig. –S5. The Trinchesia caerulea species complex: T. caerulea , T. cuanensis sp. n. ,T. morrowae sp. n. , and T. diljuvia sp. n. . The maximum genetic distance values within the T. caerulea group are 1.25% for COI, 0.25% for 16S, and 0.66% for H3 markers. The maximum genetic distance values within the T. cuanensis sp. n. group are 1.88% for COI, 0.46% for 16S, and 0% for H3 markers. The maximum genetic distance values within the T. morrowae sp. n. group are 2.18% for COI, 0.23% for 16S, and 0.65% for H3 markers. The maximum genetic distance values within the T. diljuvia sp. n. group are 0.16% for COI, 0.46% for 16S, and 0% for H3 markers. Regarding the supposedly fast-evolving COI marker, minimum genetic distance values between the T. caerulea and the T. cuanensis sp. n., T. morrowae sp. n., and T. diljuvia sp. n. groups are 7.20%, 10.95% and 11.89% respectively. The minimal COI p-distance (2.98%) was found between T. morrowae sp. n. and T. diljuvia sp. n.; the maximal COI p-distance (12.99%) was found between T. cuanensis sp. n. and T. diljuvia sp. n. The minimal 16S p-distance (1.39%) was found between T. caerulea and T. cuanensis sp. n.; the maximal 16S p-distance (6.47%) was found between T. caerulea and T. diljuvia sp. n. The minimal nuclear H3 p-distance (0.98%) was found between T. caerulea and T. cuanensis sp. n. and between T. morrowae sp. n. and T. diljuvia sp. n.; the maximal nuclear H3 p-distance (1.63%) was found between T. caerulea and T. morrowae sp. n. and T. caerulea and T. diljuvia sp. n and between T. cuanensis sp. n. and T. morrowae sp. n. All minimum intergroup genetic distances for every marker are larger than the maximum intragroup distances. 34, Thompson & Brown, 198416 .Non NE Atlantic, Mayo, Killary Harbour, Rusheen Point, Ireland (53° 37′ 31″ N 9° 51′ 26″ W), 10–20 m depth, stones with hydroids, 30.04.2017, coll. M. Larsson & B.E. Picton .Sertularella polyzonias, with spawn, 02.07.2013, coll. B.E. Picton, one specimen , 02.07.2013, coll. B.E. Picton. NE Atlantic, Gulen Dive Center, Norway (60° 57′27.11″ N 5° 07′ 47.10″ E), depth 15–20 m, stones, collectors T.A. Korshunova, A.V. Martynov, 05.03.2017, one specimen . Mediterranean Sea, Ugljan Island, Karantun, Croatia (44° 04′ N 15° 09′ E), depth 15–20 m, collectors Đ. Iglić, A. Petani, 21.01.2018, 2 specimens . Mediterranean Sea, Ugljan Island, Karantun, Croatia (44° 04′ N 15° 09′ E), depth 15–20 m, collectors Đ. Iglić, A. Petani, 21.01.2018, one specimen . Mediterranean Sea, Tor Paterno, Latium, Italy, one specimen (41° 40′ N 3° 12′ 20″ E), 25 m depth, collector G. Furfaro, 26.04.2013 (RM3 333). Mediterranean Sea, Tor Paterno, Latium, Italy, one specimen (41° 40′ N 3° 12′ 20″ E), 25 m depth, collector G. Furfaro, 01.05.2013 (RM3 860). Mediterranean Sea, Tor Paterno, Latium, Italy, one specimen (41° 40′ N 3° 12′ 20″ E), 25 m depth, collector G. Furfaro, 01.05.2013 (RM3 861). Mediterranean Sea, Tor Paterno, Latium, Italy, one specimen (41° 40′ N 3° 12′ 20″ E), 25 m depth, collector G. Furfaro, 26.04.2013 (RM3 309). Mediterranean Sea, Catalonia, L’Estartit, Girona, Spain (42° 02′ 32″ N 3° 13′ 38″ E), depth 16 m, stones, collector M. Pontes, 22.04.2017, one specimen . Mediterranean Sea, Catalonia, L’Estartit, Girona, Spain (42° 02′ 32″ N 3° 13′ 38″ E), depth 16 m, stones, collector M. Pontes, 22.04.2017, one specimen .NE Atlantic, Wales, Pembrokeshire, Martin’s Haven, United Kingdom (51°44′15.57″ N 5°14′43.37″ W), 10–20 m depth, rocky reef, feeding on Body up to 21 mm with long foot corners; cerata with distinct colour zones, digestive gland basally greenish to light grayish occasionally with a narrow or diffuse dotted yellow band at the surface, an upper blue broad band, and towards the top of cerata a broad orange or yellow band; up to 12 rows of cerata, commonly four anterior rows; radular formula 57–63 × 0.1.0, penial stylet relatively short and bent at the top, seminal receptacle is 8-shaped without a long convoluted additional chamber, egg mass spiral with several whorls.The live length of the neotype is  17 mm Fig. . The lenThe basal colour is whitish to light greenish, occasionally yellow, never forming any continuous broad white line dorsally Fig. . CommonlThe jaws are triangularly ovoid Fig. . The masFig. . The ampThe egg mass is a white or very pale pinkish spiral cord forming about 3 whorls or an irregular cord. It may contain 1000 eggs or more.Sertularella ) but also on S. crassicaulis  and S. gayi  for which it has a strong preference40, and it is also reported feeding on Eudendrium racemosum 41, Hydrallmania falcata  and Halecium halecinum 16. We provide references to the potential food sources here, but this information should be used carefully since food associated with T. caerulea may now be the food preference of one of the other T. caerulea complex species. In the French Mediterranean, T. caerulea was recorded as feeding on S. crassicaulis. In the present study T. caerulea was confidently found commonly in L’Estartit  area as associated with S. polyzonias and much less frequently on Eudendrium racemosum.Reliably confirmed from Britain and Ireland, Norway, and the Mediterranean Sea . Found in stony, relatively shallow areas, often covered with various algae, usually at 10–25 m depth, occasionally at only 1–2 m. Feeds on hydrozoans of the genus T. caerulea can be distinguished from the partly sympatric (in the NE Atlantic) T. cuanensis sp. n. by this set of morphological data: 1). Greenish to light grayish basis of the cerata, not blackish to dark grayish as in T. cuanensis sp. n. 2). Absence on the cerata of a narrow blackish band above the broad blue band, which is present in T. cuanensis sp. n. 3). Long anterior foot corners, not short ones as in T. cuanensis sp. n.; 4). Relatively short penial stylet, whereas T. cuanensis sp. n. has an extraordinarily long stylet. T. caerulea can be distinguished from the partly sympatric, predominantly Mediterranean species, T. morrowae sp. n., by this set of morphological data: 1). Greenish to light grayish basis of cerata, not light grayish to yellowish as in T. morrowae sp. n.; 2). Absence of a distinct white dorsal line and thin white lateral lines, which are instead always present in T. morrowae sp. n.; 3). White opaque or light yellowish tips of rhinophores and oral tentacles, but not orange ones as in T. morrowae sp. n. 4). Long anterior foot corners, not just angular projections as in T. morrowae sp. n.; 5). The penial stylet is curved towards the tip, whereas in T. morrowae sp. n. it is curved rather basally; 6). T. caerulea has up to two times the adult body size of T. morrowae sp. n. T. caerulea can be distinguished from the exclusively Black Sea species T. diljuvia sp. n. by this set of morphological data: 1). Presence of distinct colour zones on the cerata, which are absent in T. diljuvia sp. n.; 2). T. caerulea has up to five times larger adult body size compared to T. diljuvia sp. n.; 3). Absence of a white dorsal line, which is always present in T. diljuvia sp. n.; 3). Long anterior foot corners, which are completely absent in T. diljuvia sp. n.; 5). Precise shape of the penial stylet is different between T. caerulea and T. diljuvia sp. n.caerulea neotype specimen and T. cuanensis sp. n., T. morrowae sp. n. and T. diljuvia sp. n. specimens are 7.36%, 11.11%, and 12.05% respectively. See also Discussion, Fig. Minimum uncorrected COI p-distances between the T. Figures –S5.Cuthona caerulea sensu lato auct., e.g. Thompson & Brown (1984)16, Schmeckel & Portmann (1982)34 .NE Atlantic, Strangford Lough, Down, Ballyhenry, Northern Ireland, United Kingdom (54°23′22.2″ N 5°34′23.4″ W), 15–20 m depth, coll. B.E. Picton, 24.05.2014 . Paratypes. NE Atlantic, Strangford Lough, Portaferry, Northern Ireland, United Kingdom , ca. 10 m depth, coll. B.E. Picton, 22.05.2014, one specimen . NE Atlantic, Strangford Lough, Down, Ballyhenry, Northern Ireland, United Kingdom (54°23′22.2″ N 5°34′ 23.4″ W), 10–25 m depth, coll. B.E. Picton, 24.05.2014, one specimen . NE Atlantic, Portrush, Antrim, S of Little Skerry, Northern Ireland, United Kingdom (55°′12′59.238″ N 6° 38′39.292″ W), 24.3 m max depth, coll. B.E. Picton, 23.08.2006, three specimens . Bohuslän, outside of Smögen, Sweden , 10–20 m depth, coll. Klas Malmberg, 02.05.2015, one specimen .urn:lsid:zoobank.org:act: 77629514-DDB5-4757-86FE-78DDD7672563.After Lough Cuan, an alternative name for Strangford Lough in Northern Ireland, where many marine biological studies have been undertaken over the past 100 years.Body up to 15 mm (live), cerata with distinct colour zones, digestive gland basally dark grayish to blackish with commonly a narrow or reduced dotted orange or yellowish band, then narrower black zone, then a blue broad band, and towards the top of cerata there is broad orange or yellow band, up to 10 rows of cerata, commonly four anterior ceratal rows, radular formula 64 × 0.1.0, penial stylet extraordinarily long, rounded seminal receptacle with a long convoluted additional chamber, egg mass spiral with several whorls.The length of the preserved holotype is 7 mm Fig. . The livThe basal colour is whitish to light greenish, sometimes with some diffuse pigment of a similar colour scattered over the body, but never forming any continuous broad white line dorsally Fig. . The cerThe jaws are triangularly ovoid Fig. . The masFig. . The ampThe egg mass is a spiral cord forming a minimum of 2 whorls, or an irregular cord. Number of eggs is commonly more than 300.Sertularella polyzonias, and possibly other Sertularella species.Confirmed records in Ireland, United Kingdom and Swedish west coast. Found in stony, relatively shallow areas, at 10–20 m depth. Feeds on hydrozoans T. cuanensis sp. n. can be distinguished from the partly sympatric (both are common in the North Atlantic) type species of the genus, T. caerulea, by this set of morphological data: 1). Blackish to dark grayish basis of the cerata, not greenish to light grayish as in T. caerulea; 2). Presence on the cerata of a narrow blackish band above the broad blue band, but not in T. caerulea; 3). Short anterior foot corners, not long as in T. caerulea; 4). Extraordinarily long penial stylet , whereas T. caerulea has a normal, short one. T. cuanensis sp. n. can be distinguished from the partly sympatric, predominantly Mediterranean species, T. morrowae sp. n., by this set of morphological data: 1). Blackish to dark grayish basis of the cerata, not light grayish to yellowish as in T. morrowae sp. n.; 2). Presence on the cerata of a narrow blackish band above the broad blue band, not present in T. morrowae sp. n.; 3). Absence of a white dorsal line and thin white lateral lines, which are instead always present in T. morrowae sp. n.; 4). Short anterior foot corners, not just angular projections as in T. morrowae sp. n.; 5). Extraordinarily long penial stylet, whereas T. morrowae sp. n. has a normal short one. T. cuanensis sp. n. can be distinguished from the exclusively Black Sea species T. diljuvia sp. n. by this set of morphological data: 1). Presence of distinct colour zones on the cerata, which are absent in T. diljuvia sp. n.; 2). Absence of a white dorsal line, which is always present in T. diljuvia sp. n.; 3). Short anterior foot corners, which are completely absent in T. diljuvia sp. n.; 4). Extraordinarily long penial stylet, whereas T. diljuvia sp. n. has a relatively short one.T. cuanensis sp. n. type specimen and T. caerulea, T. morrowae sp. n. and T. diljuvia sp. n. specimens are 7.98%, 12.05%, and 13.77% respectively. See also Discussion, Fig. Minimum uncorrected COI p-distances between Figures –S5.Cuthona caerulea auct., e.g. Thompson & Brown (1984)16, Schmeckel & Portmann (1982)34, Picton & Morrow (1994)31 non Doris caerulea Montagu, 1804.Mediterranean Sea, Catalonia, L’Estartit, Girona, Spain (42° 02′ 32″ N 3° 13′ 38″ E), depth 16 m, stones, collector M. Pontes, 22.04.2017 . Paratypes. Mediterranean Sea, Banyuls-sur-Mer, France (42° 28′ 53.0″ N 3° 08’ 17″ E), depth 5–12 m, stones, collector T.A. Korshunova, A.V. Martynov, 08.09.2010, two specimens . Mediterranean Sea, Banyuls-sur-Mer, France (42° 28′ 53.0″ N 3° 08′ 17″ E), depth 5–12 m, rocks, stones, collector T.A. Korshunova, A.V. Martynov, 10.09.2010, one specimen . Mediterranean Sea, Banyuls-sur-Mer, France (42° 28′ 53.0″ N 3° 08′ 17″ E), depth 5–12 m, rocks, stones, collector T.A. Korshunova, A.V. Martynov, 09.09.2010, one specimen . Mediterranean Sea, Catalonia, L’Estartit, Girona, Spain (42° 02′ 32″ N 3° 13′ 38″ E), depth 16 m, stones, collector M. Pontes, 22.04.2017, one specimen .urn:lsid:zoobank.org:act: D7DB7FFB-F6B1-4A67-8DF4-A1D0F05963A7.Trinchesia cuanensis which first revealed the presence of two species of this complex in the NE Atlantic.After Christine Morrow, co-author of “A Field Guide to the Nudibranchs of the British Isles” (1994), who sequenced a specimen of T. cuanensis sp. n., there is no narrow black band and towards the top of cerata there is broad orange band, three, rarely four anterior ceratal rows, radular formula 55–57 × 0.1.0, penial stylet short and considerably curved, seminal receptacle is oval without additional chamber, egg mass a short spiral.Body up to ca. 10 mm, white dorsal line, cerata with distinct colour zones, digestive gland basally light grayish to yellowish, then a usually broad distinct dotted orange band, then narrower black zone, then a blue broad band, then, compared to The length of the holotype is 9 mm  meadows. Feeds on Sertularella spp. hydroids, possibly on Sertularia perpusilla Stechow, 1919, and also Stylactis inermis Allman, 1872.Predominantly known from various locations in the Mediterranean Sea, from Greece to the Western basin, but may also reach the southern part of the UK. Occurs in all the Iberian Peninsula coastal areas, including both Portugal and Spain. Found in stony, relatively shallow areas, from 1 to 25 m depth, also in T. morrowae sp. n. can be distinguished from the partly sympatric (both are common in the North Atlantic and in the Mediterranean Sea) type species of the genus, T. caerulea, by this set of morphological data: 1). Light grayish- to yellow basis of the cerata, not greenish to light grayish as in T. caerulea; 2). Presence of a distinct lower orange band on the cerata, not a commonly reduced and diffuse one as in T. caerulea; 3). Presence of a thick white dorsal line and thin white lateral lines, which are always absent in T. caerulea; 4). Presence of commonly three, rarely four, anterior ceratal rows in T. morrowae sp. n., whereas there are commonly four in T. caerulea; 5). Angular anterior projections of the foot, not long foot corners as in T. caerulea; 6). Shape of the penial stylet, which is bent at the top in T. caerulea, but bent at the basis or middle in T. morrowae sp. n. 7). T. morrowae sp. n. has an adult body size up to half as large as T. caerulea.T. morrowae sp. n. can be distinguished from the partly sympatric (present only in the North Atlantic) T. cuanensis sp. n. by this set of morphological data: 1). Light grayish to yellowish basis of the cerata, not blackish to dark grayish as in T. cuanensis sp. n.; 2). Presence of a distinct lower orange band on the cerata, not a commonly diffuse reduced one as in T. cuanensis sp. n. 3). Presence of a thick white dorsal line and thin white lateral lines, which is always absent in T. cuanensis sp. n.; 4). Presence of commonly three, rarely four, anterior ceratal rows in T. morrowae sp. n., whereas there are commonly four in T. cuanensis sp. n.; 5). Angular anterior projections of the foot, not short foot corners as in T. cuanensis sp. n.; 6). Length of the penial stylet, which is short in T. morrowae sp. nov., but is extremely long in T. cuanensis. 7). T. morrowae sp. n. has an adult body size up to 2/3 that of T. cuanensis sp. n. T. morrowae sp. n. can be distinguished from the exclusively Black Sea species T. diljuvia sp. n. by this set of morphological data: 1). Presence of distinct colour zones on the cerata, which are absent in T. diljuvia sp. n.; 2). Presence of commonly three, rarely four, anterior ceratal rows inT. morrowae sp. n., whereas there are commonly two in T. diljuvia sp. n.; 3). Short anterior foot corners, which are completely absent in T. diljuvia sp. n.; 4). Shape and relative length of the penial stylet, which is short inT. morrowae sp. n. and relatively longer in T. diljuvia sp. n.T. morrowae sp. n. type specimen and T. caerulea., and T. cuanensis sp. n specimens are 11.27%, and 11.42% respectively. COI p-distances between T. morrowae sp. n. and T. diljuvia sp. n. ranged from 2.98–4.23%, whereas intraspecific divergence ranged from 0.16 - 2.18% in T. morrowae sp. n. and 0.16% in T. diljuvia sp. n. which is smaller than the interspecific differences between these species. Intraspecific divergence in T. morrowae sp. n. may indicate that T. morrowae sp. n. is still undergoing the process of evolutionary divergence. This supports the scenario of an extremely rapid evolution of the Mediterranean species T. morrowae sp. n.  in T. diljuvia sp. n. See also Discussion, Fig. Minimum uncorrected COI p-distances between the Figures –S5.Black Sea, Yalta region, Russia (44° 29′ N 34° 10′ E), depth 1–2 m, stones, collector T.A. Korshunova, A.V. Martynov, 24–26.07.2004, . Paratypes. Black Sea, Yalta region, Russia (44° 29′ N 34° 10′ E), depth 1–2 m, stones, collector T.A. Korshunova, A.V. Martynov, 28.07.2004, 1 specimen, dissected . Black Sea, Yalta region, Russia (44° 29′ N 34° 10′ E), depth 1–2 m, stones, collector T.A. Korshunova, A.V. Martynov, 31.07.2004, 1 specimen, dissected .urn:lsid:zoobank.org:act: C9228E8B-DF2C-46A0-9E78-038ED6B87D7B.Body up to 4.5 mm, white dorsal line, no colour zones on light brownish (with traces of bluish pigment) cerata, commonly two, maximum three, anterior ceratal rows, radular formula 27–34 × 0.1.0, penial stylet short slightly curved, seminal receptacle is rounded without any additional chamber, egg mass short semi-spiral.diluviim, deluge, inundation and juvenilis, youthful, alluding to the paedomorphic appearance of the new species and speciation during the formation of the modern Black Sea after the Holocene meltwater events (see Discussion).Combination of Latin, The length of the holotype is 4.5 mm Fig. . The lenThe basal colour is whitish; a distinct thick white line runs dorsally with median expansion Fig. . The cerThe jaws are triangularly ovoid Fig.  The mastFig. . The ampThe egg mass is a small semi-spiral cord with only a few eggs (ca. 20) Fig. .Sertularella spp. hydroids.Black Sea, Yalta region only, not found in the Mediterranean or other regions. Found in stony, shallow areas, around 1–2 m depth, on T. diljuvia sp. n. can be distinguished from the North Atlantic and Mediterranean species T. caerulea by this set of morphological data: 1). Absence of distinct colour zones on the cerata, which are present in T. caerulea; 2). Presence of a white dorsal line in T. diljuvia sp. n., which is absent in T. caerulea; 3). Presence of commonly two, rarely three, anterior ceratal rows inT. diljuvia sp. n., whereas there are commonly four in T. caerulea; 4). Absence of anterior foot corners inT. diljuvia sp. n., which are present and long in T. caerulea; 5). Shape and relative length of the penial stylet, which is relatively longer in T. diljuvia sp. n. and relatively shorter in T. caerulea. T. diljuvia sp. n. can be distinguished from the exclusively North Atlantic species T. cuanensis by this set of morphological data: 1). Absence of distinct colour zones on the cerata, which are present in T. cuanensis sp. n.; 2). Presence of a white dorsal line in T. diljuvia sp. n. which is absent in T. cuanensis sp. n.; 3). Presence of commonly two, rarely three, anterior ceratal rows in T. diljuvia sp. n., whereas there are commonly four in T. cuanensis sp. n.; 4). Absence of anterior foot corners in T. diljuvia sp. n., which are present and short in T. cuanensis sp. n.; 5). Shape and relative length of the penial stylet, which is relatively very short in T. diljuvia sp. n. compared to the extremely long stylet in T. cuanesis sp. n. T. diljuvia sp. n. can be distinguished from the predominantly Mediterranean species T. morrowae sp. n. by this set of morphological data: 1). Absence of distinct colour zones on the cerata, which are present in T. morrowae sp. n.; 2). Presence of commonly two, rarely three, anterior ceratal rows in T. diljuvia sp. n., whereas there are commonly three in T. morrowae sp. n.; 3). Absence of anterior foot corners in T. diljuvia sp. n., whereas distinct angular projections are present inT. morrowae sp. n..; 4). Shape and relative length of the penial stylet, which is relatively longer in T. diljuvia sp. n. and relatively shorter in T. morrowae sp. n.T. diljuvia sp. n. type specimen and T. caerulea, T. cuanensis sp. n. and T. morrowae sp. n., specimens are 11.89%, 12.99%, and 2.98% respectively. See also Discussion, Fig. Minimum uncorrected COI p-distances between the T. caerulea complex from Britain and Ireland through continental Europe and the Mediterranean to the Black Sea, i.e., with a putative low degree of morphological disparity in the sense of Struck et al.9, in turn reveals both stable external and internal features , these putative morphs within the single T. caerulea species were always claimed to be “internally the same/similar”34, thus fulfilling the current definition9 of a ‘cryptic’ species.This case of a colourful nudibranch species that represents an apparently very cryptic a posteriori by the molecular data19 we specifically included the illustration from Thompson & Brown (1984)16 , it remained almost absolutely ‘cryptic’ until recently because smaller distinguishing taxonomic units were not defined at that time and researchers decided they could not plausibly grant them a separate species status under what, at the time, was a dominant morphological “lumping” taxonomic framework. Therefore, this species complex can be considered ‘cryptic’, ‘pseudocryptic’ and ‘non-cryptic’ at the same time. The novel data on multilevel diversity from a particular species complex presented here, therefore, confirm that the general ‘cryptic species’ concept is far from being a satisfying solution and that the commonly used ‘cryptic species’ concept needs to be reconsidered.To challenge this notion that ‘cryptic’ species can only be defined )16 Fig.  to show )16 Fig. , but werets Fig. ] which wet al.9 attempted to provide a stricter definition of cryptic species and proposed two main components of an updated definition: “diverged genotypic clusters of individuals (reflecting reproductive isolation) that do not form diagnostic morphological clusters” and the temporal dimension of “lower degrees of phenotypic  disparity than non-cryptic relatives”. The central proposal of the new updated ‘cryptic’ species definition9 has a deficiency in a heavy dependence on a detailed study of a species/organism and an existing taxonomic framework of a particular group. For example, most of the European nudibranch species of the genus Dendronotus were just a single, very complicated and non-diagnosable ‘cryptic’ species, even for experts, but a recent study revealed that it is possible to provide not only molecular values, but also morphological differences for every species in the complex8. Furthermore, the requirements9 for a cryptic species to be morphologically non-distinguishable but genetically isolated is also controversial, since there are many examples where genetically separate species either are similar morphologically (as is the case for the blue mussel species complex) or considerably different as is the case for dolphins and whales, but in both groups numerous cases of genetic introgression and/or presence of fertile hybrids have been demonstrated43. As an answer to a recent proposal to consider ‘cryptic’ species rather as a temporary term8 some authors continued to argue for validity of the cryptic species9 concept and mentioned previous studies of such different animal groups as lizards, annelids, molluscs, cnidarians, and mammals as examples of putatively “uniform” morphology among different species, which, however, under scrutiny may demonstrate diagnosable morphological taxa. Notably, in the example with an annelid species44 it was indicated that “the cryptic species complex of Stygocapitella subterranea is not as cryptic as assumed as the Australian populations are morphologically and genetically different”.Struck 3 can be formed only on the basis of zygote clones that automatically imply its identical genetic structure. If we instead discovered putative “species clones” but with some considerable genetic differences, this most likely suggests that we have missed some morphological differences during a study. Therefore, it is biologically impossible for species to be “physically indistinguishable from each other”19 since even clones can be different from each other because of epigenetic mechanisms48.If we claim that we cannot find any morphologically diagnosable structures in a ‘cryptic’ species complex, this would imply that we have exhaustively studied organism features and are able to unambiguously present all existing ‘macromorphological’ and ‘micromorphological’ features for a given organism. This is obviously impossible at the current level of our technology and knowledge. The putative strict distinction between morphological and molecular levels of organisms, on which the cryptic species concept is largely relying, loses clarity when we proceed to the tissue or cellular ‘micromorphological’ level. To the utmost degree, morphologically absolutely identical “body doubles”49, Japanese microsnails50, coryphellid nudibranchs of the genus Gulenia25 to species which are externally difficult to distinguish (but still possible) but internally demonstrate stable distinct characters, e.g., in the European nudibranch species of the genus Dendronotus8. This series continues with species which demonstrate some overall similarity and appear cryptic but under more detailed study turn out to demonstrate reliable and stable external and internal differences, like a polychaete species complex44 and the present case of the four Trinchesia species complex. Finally, there are the cases when the term ‘cryptic’ species was applied to externally diagnosable species (e.g. in the echinoderm ophiuroids13). Thus, a considerable amount of non-cryptic diversity is still currently included under the ‘cryptic species’ concept. It is therefore likely that if we really would like to make a distinction between ‘species’ and ‘cryptic’ species we will need a much more differentiated system of terminology than this simplistic pair ‘cryptic’ vs. ‘non-cryptic’. If we use the term ‘cryptic species’ conditionally and for the purpose of this discussion only, for example, additional terms might be ‘true cryptic species’ , ‘semi-cryptic species’ , ‘quasi-cryptic species’  and finally a ‘false cryptic species’ . However, while we can use such terminology for a preliminary sorting of multilevel diversity, quite obviously, the number of such various intermediate terms would grow exponentially, and it may be difficult to apply to other taxa since many cases may represent their own unique combination of genetic divergence/uniformity and morphological external and internal similarity/disparity. Remarkably, the last putative term in this series, ‘false cryptic species’ actually does not differ fundamentally from the basic term ‘species’, and the term ‘pseudocryptic species’ was previously applied to cases where it is possible to show at least some morphological differences18. It has already been noted that the line between cryptic and pseudocryptic “is not sharp”51, but these terms have been loosely applied until the meaning is lost52. Notably, the term ‘cryptic species’ has been applied53 to evaluate a nudibranch species revealed in a previous study54 to be “very similar to Limacia clavigera” yet with “consistent morphological and external differences between the two species examined” but without any corresponding molecular data for the morphologically-only defined “cryptic” Limacia iberica Caballer et al., 201654 species. Yet a previous proposal19 noted that cryptic species are, by definition, molecularly different species that can only turn out to be morphologically distinguishable ‘pseudocryptic’ species a posteriori. Thus, such highly inconsistent usage of the term ‘cryptic’ species confirms the most recent notion of Heethoff10 that the ‘cryptic’ species concept currently represents both conceptual and terminological chaos.In practice there is an array of various cases, from very highly similar external species, for which authors reported that they have not yet found confident morphological differences, e.g., in American lizards55, this in turn implies that any species at its origin is already completely ‘cryptic’. Indeed, many so called ‘cryptic’ species represent recently diverged lines and therefore their overall similarity may rely on significant similarity in the developmental genes responsible for the formation of the morphological structures, rather than on some mutations that may occur in the housekeeping genes which are commonly used for taxonomic purposes. More wide applications of full genomic/transcriptomic comparison may therefore potentially contribute to finding not only morphological but also high genetic similarity within recently diverged closely related lineages. Hence the term ‘super-cryptic’ species would be needed for the species without morphological, genetic or ecological differences which though probable, is only theoretically possible.Taking also into consideration that one of the united definitions of the term ‘species’ defines it as only being separately evolved metapopulations, which are not required to be morphologically different or even reproductively isolatedTrinchesia, so that what was a totally cryptic and non-diagnosable complex a few years ago is now four well-diagnosable and non-cryptic separate species. Even if complexes in other organism groups that are apparently even more ‘cryptic’ than the present case56 still exist, and potentially can be discovered further within that nudibranch species complex, this does not mean that after some time we will not be able to study their morphological structures using, for example, more advanced micro CT or a similar technique available to future generations, including potential detailed scanning of living animals, and also discovering fine details of their ecology, etc., and will be able therefore to elaborate and define well-diagnosable taxonomic units, as we have presented here for the British and Mediterranean Trinchesia species. Another nudibranch species that previously was incorrectly identified as “T. caerulea” from the Caribbean Sea was shown to be considerably different from the true T. caerulea both by morphological and molecular data57. Morphologically distinguishing characters, therefore, should not be identified only a posteriori18 but should have at least similar weight with the molecular ones. A molecular study may promote discovery of a hidden diversity within a group, but a robust taxonomic framework can be built only in an agreement with morphological data, even if such a task is difficult and requires a more detailed study such as those undertaken for the other nudibranchs58, when a considerable amount of external interspecific variability is present and some species were externally nearly identical to other related but different species. In turn, in a completely opposite situation, the presence of morphologically well-recognized species which have a very low degree of molecular divergence from related species60 clearly indicates the necessity of restoring the significance of morphology to the diagnoses of species in the form of detailed morphological data.Therefore, these apparent ‘cryptic’ species with “low morphological disparity” instead turned out to be a species which previously was “insufficiently studied” at different levels of morphological organisation. Thus, at a given time technological and scientific achievements allow us to understand some species and present their descriptions in more and more detail using the dominant paradigm at the time for species descriptions that may easily lead to some well-distinguishable features being missed. As a result, when a new study uncovers new details, a species can be easily considered as not ‘cryptic’ or ‘pseudocryptic’ anymore, but just a normally diagnosable species. This is the exact situation of the present discovery of well-diagnosable morphological patterns at different levels in the genus 61 there is a multilevel diversity in character evolution8, and correspondingly, further smaller taxonomically relevant morphological and molecular concordant units can be discovered within previously selected larger taxonomic groups. This process can be potentially quite endless, or at least take a considerable amount of time, while we set an increasingly narrower scale for such morphological and molecular taxonomic units , until we arrive at very small and narrowly defined species units, which may still include some amount of variability and the ability to hybridize with closely related, narrowly defined species. During the processes of decreasing the degree of disparity of morphological and molecular taxonomic units, the degree of their ‘crypticity’ is at first greatly increased because we are further attempting to find distinguishing features within increasingly smaller taxonomic units.When we discovered several new species within a complex traditionally assigned to a single species, we created a new morphological and molecular framework that defined much smaller taxonomically distinguishable units than were previously used. Because life is hierarchically organizedTherefore, instead of the very problematic division of this multilevel continuum into ‘non- cryptic’ and ‘cryptic’ components, we conclude that almost every species potentially hides numerous smaller and smaller units that need careful detection and description using an ever greater differentiating system of morphological and molecular characters, as was presented here for this case of ‘cryptic’ morphs within a nudibranch species complex . The problem was not in the absence of “physically distinguishable morphological characters”, but in the absence of enough finely differentiated units in the taxonomic framework that would have allowed species distinction at a much finer level.T. caerulea species complex  would be very ‘cryptic’ and would have inevitably been considered just small variations within the previous framework, but within the new morphological and molecular framework, they will be ‘less cryptic’ than before. This general consideration and the remarkable practical case in the present study clearly show that it is meaningless to use this simplistic ‘cryptic-pseudocryptic’ species pairing while dealing with the enormous continuum of highly differentiated diversity at smaller and smaller levels, each of which is notably more and more ‘cryptic’ than the previous one. Instead, we are proposing two interlinked central implications of the present study: “from ‘cryptic’ to obvious species” within more and more finely differentiated numerous taxonomic levels.Using the new framework established here for the lex Figs –S5, whic63. While we were analysing integrative morphological and molecular data for this nudibranch species complex we discovered a new Black Sea species, Trinchesia diljuvia sp. n., that is externally similar to the Mediterranean T. morrowae sp. n. (from which it is molecularly considerably diverged) and thus can be classified under the “low morphological disparity” general paradigm9 as morphologically uniform, but actually demonstrates stable and clear paedomorphic features 65.Furthermore, because underestimation of the epigenetic mechanisms in taxonomic practice, the ‘cryptic’ species label may prevent the discovery of such an important evolutionary phenomenon as paedomorphosis, which is now recognized in different groupsres Figs . The for5. A study on a polychaete family recently appeared which does not refute the possibility of finding morphologically distinguishing characters even within an apparent ‘mega-cryptic’ species complex66.Under this fine-scale multilevel species framework, morphological and molecular data, as well the other biological data, should equally contribute to the definition and description of any species. Most recent data show that taxonomists are gradually moving in this direction. Among 55 species of the putative ‘cryptic’ species of the amphipod crustacean which were recently investigated by integrative methods, biological differences (other than molecular differences) were not yet found for only four species10 but a serious theoretical and practical problem. Initially, the term ‘cryptic species’ has been applied when considerable molecular divergence was discovered within apparently morphologically similar species groups67. However, currently the term ‘cryptic species’ is greatly over used because researchers tend to firstly investigate molecular data and only secondly investigate morphology. Thus, for such studies all species are ‘cryptic’ before molecular study and afterwards they are named ‘pseudocryptic’ species52. Despite that, in our present study we show that previously recognized morphologically cryptic morphs in a nudibranch species complex are concordant with the newly obtained molecular differences and constitute well-defined morphological and molecular taxonomic units, and this species complex can therefore be termed simultaneously ‘cryptic’ and ‘non-cryptic’. Thus, the degree of ‘crypticity’ is a subjective and uncertain measure68.How to name morphologically difficult-to-distinguish species diversity is not just a terminological problemWe therefore propose to avoid the terms ‘cryptic’/’pseudocryptic’ species and in cases where taxonomy is not yet settled use the more neutral terms ‘hidden’ or ‘potentially unraveled/undiscovered’ diversity. The following scheme to explore hidden diversity is suggested: 1) Within a broader taxonomic framework, detect potential cases where species are difficult to distinguish by morphological data; 2) These difficult cases should be studied exhaustively at the current level of technological development; 3) Morphological and molecular methods should be applied in concordance, and ecological and any other relevant data can equally be primary sources to reveal fine but taxonomically reliable differences; 4) As a result of setting the ‘finer and finer taxonomic scale’ in a species complex, a new, more differentiated taxonomic framework will be established. Presumption of the ‘existence of morphological differences’ should be applied at every level of taxonomic study. Justification of such presumption is the biological impossibility of the existence of two genetically different but morphologically completely identical species. Accordingly, if in some cases we are unable to present definite morphological differences this means that we are just currently unable to detect them and need to postpone this unresolved question for a future study, but we cannot just state that morphological differences do not exist.70, we should concentrate on describing the patterns of this immense fine-scale multilevel diversity, rather than relying on attempts to merely roughly distinguish ‘cryptic’ species from ‘non-cryptic’ ones. Putative “body doubles”71 should, under scrutiny, always turn out to be neither doubles nor cryptic, but currently it has become fashionable to name any apparently taxonomically difficult group a ‘cryptic species’. Continued use of this term will only add ambiguity to the immense field of biodiversity, where an enormous number of species still need description, and the ‘cryptic’ concept is rather an obstacle than an aid. The term ‘cryptic species’ should only be regarded as a temporary state. Though the ‘cryptic species concept’ has played a role in emphasizing the importance of reviewing morphologically difficult to distinguish species, currently there is a necessity for a new framework for the species concept itself 72. The present study thus demands the establishment of such a new, fine-scale multilevel species paradigm through which can we approach a less subjective understanding of what ‘high’ and ‘low’ taxonomic disparity is, and is far from the simplistic ‘cryptic species’ notion which is currently dominant.Facing the rapid extinction of many organisms, including marine onesSupplementary Information


Pd doping was found to increase the electrical conductivity along with the electron carrier concentration. As a result, the effective mass and power factors also increased upon the Pd doping. While the bipolar thermal conductivity was reduced with the Pd doping due to the increased carrier concentration, the contribution of Pd to point defect phonon scattering on the lattice thermal conductivity was found to be very small. Consequently, Pd doping resulted in an enhanced thermoelectric figure of merit, zT, at a high temperature, due to the enhanced power factor and the reduced bipolar thermal conductivity.Doping is known as an effective way to modify both electrical and thermal transport properties of thermoelectric alloys to enhance their energy conversion efficiency. In this project, we report the effect of Pd doping on the electrical and thermal properties of  In fact, the zT of n-type Bi23 alloys remains below 1, while values significantly higher than 1 have often been reported for p-type 2Te3 alloys.Thermoelectric alloys have attracted attention in recent decades because these materials can convert a temperature gradient directly into electrical energy. Bismuth telluride 2Te3 alloys can easily be enhanced using substitutional dopants [n-type Bi23 alloys has not been investigated as much as that of doping on p-type 2Te3 alloys. It has been found that Cu intercalation in n-type Bi23 alloys is a very effective approach to reducing the lattice thermal conductivity (lattκ) by introducing additional point defect scattering centers [lattκ reduction may reduce the power factor, resulting in zT reduction.Doping is an effective approach to improving the  defects ,9,10,11. dopants ,5. Meanw centers . Howeverlattκ while enhancing the power factors in some other thermoelectric materials, such as SnTe and PbTe [p-type 2Te3 alloys, it was found that the co-doping of Ag and Ga reduced the lattκ further compared to that of single doped materials [Co-doping of two different substituents was also suggested to further decrease the and PbTe ,14,15,16aterials , while tn-type Bi23, Cu0.008Bi2Te2.7Se0.3. The Pd was anticipated to scatter phonons effectively due to the large mass and ionic radius differences between Pd and Bi . Pd doping increased the electron concentration, electrical conductivity, and power factors. However, the contribution of Pd to additional point defect scattering centers on the lattice thermal conductivity was found to be rather small. As a result, zT enhancement due to Pd doping was observed at high temperatures. To investigate the reason for the limited effectiveness of substitutional Pd doping in reducing the lattκ value in n-type Bi23 alloys, the electronic transport properties were analyzed using a single parabolic band model [lattκ was quantitatively predicted using the Debye–Callaway model [Herein, we investigated the effect of additional Pd substitutional doping on the electrical transport properties and thermal conductivities of Cu-doped nd model , and theay model .0.008Bi2Te2.7Se0.3 reference sample and a series of Pd-doped Cu0.008PdxBix2-Te2.7Se0.3  samples were synthesized by a conventional solid state reaction for 10 h at 1423 K, using high-purity (99.999%) raw materials. The synthesized ingots were ball-milled using a 8000M Mixer/Mill high-energy ball mill  for 10 min, and sieved powders under 45 µm were consolidated by spark plasma sintering at 723 K and 50 MPa for 2 min. Then, the temperature-dependent S and σ parameters were measured over the temperature range between room temperature and 480 K in a direction perpendicular to the pressing direction . The carrier concentrations were determined by Hall measurements in van der Pauw configuration, in a magnetic field of 0.5 T  in the same direction. The κ values of the samples were calculated from their theoretical density (ρs), heat capacity (Cp), and thermal diffusivity (λ) values (κ = ρs⋅Cp⋅λ), measured along the same direction.The Cu0.008PdxBix2-Te2.7Se0.3. All samples showed single phases without impurities. The lattice parameters a and c are shown in c parameter generally increased with the Pd doping, while a remained largely unchanged upon doping. The systematic change in the c parameter implies that substitutional doping was successfully achieved.σ and S values of the Pd-doped Cu0.008PdxBix2-Te2.7Se0.3  are shown in σ value of the undoped sample was about 740 S/cm at 300 K, and substantially increased to 1320 S/cm for x = 0.02. On the other hand, the magnitude of the S values at 300 K decreased from −192 to −144 µV/K. As a result, the power factor (S2·σ) at 300 K remained unchanged (around 2.73 mW/m·K2) regardless of the Pd doping level (2.The measured ng level c. HowevenH) and mobility (µH) measured for the Cu0.008PdxBix2-Te2.7Se0.3 samples at 300 K. The nH gradually increased with the Pd doping, with nH values of 2.4, 2.8, 3.2, 3.4, and 4.2 × 1019 cm−3 for x = 0, 0.002, 0.004, 0.01, and 0.02, respectively. On the other hand, the µH values did not change significantly. Therefore, the increase in σ upon Pd doping is mainly due to the increased nH values. S of samples as a function of nH at 300 K. The solid lines were obtained for different effective masses  using Equation (1):e, h, and kB are the elementary charge, Planck’s constant, and Boltzmann constant, respectively. The m* values of all samples, deduced using Equation (1), are plotted in m* values, indicating that the electronic structure of the conduction band of Cu0.008Bi2Te2.7Se0.3 was slightly modified favorably for S.totκ of the Pd-doped Cu0.008Bi2Te2.7Se0.3 samples, revealing that the totκ values gradually increased with the doping level. In order to understand these changes, we analyzed the contributions to totκ, given by the following equation:elecκ and bpκ are the electronic and bipolar thermal conductivities, respectively. First, elecκ was calculated using the equation for the Lorenz number ) [ion (3)) , and theL and S in a simple function, based on a single parabolic band model [elecκ values increased as the electrical conductivity increased with Pd doping, straightforwardly with the increased carrier concentration (elecκ showed a significant increase from 0.4 to 0.7 W/m·K.Equation (3) describes the relationship between the nd model . The κelntration a. At 300bpκ parameter, related to the bipolar electronic transport properties, can be estimated based on a single parabolic band model and the Boltzmann transport equation (Equation (4)):pσ and nσ are the electrical conductivities of the valence (p) and conduction (n) bands , while pS and nS are the Seebeck coefficients for the VB and CB, respectively.The bpκ calculations are provided with the two-band model analysis in the bpκ value was gradually reduced from 0.36 to 0.23 W/m·K at 480 K, which represents a 36% decrease. The decrease in bpκ is also mostly related to the increased concentration of electron carriers, which are the majority carriers. Therefore, the influence of the minority carriers is reduced. The inset of bpκ and pσ values at 480 K [pσ values estimated from the two-band model are provided in the The details of the at 480 K . The σp lattκ were deduced by subtracting the elecκ and bpκ values from the measured totκ, and are shown as symbols in lattκ . Therefore, the determined totτ(z) values describe the theoretical lattκ, whereas totτ(z) can be estimated from the individual phonon relaxation times (iτ) for scattering mechanisms, based on Matthiessen’s equation (Equation (6)):Then, the lines in d using tPDτ, as shown in Equations (7) and (8):For scattering by point defects, which is the dominant mechanism in the present Pd doping case, the phonon relaxation time can be described using the scattering parameter (Г) within P and f are a fitting parameter and substituting fraction, respectively. In Equation (8), ΔM and Δa are the difference in mass and lattice constant between the two constituents of an alloy. The G and γ represent the ratio of the fractional change in the bulk modulus to the local bond length and the Grüneisen parameter, while r is the Poisson ratio. Further details of the calculation were not included here, because we found no differences in the lattκ values.In Equation (7), lattκ is shown as solid lines in lattκ (symbols). The experimental or theoretical lattκ values show rather small changes with the doping level, despite reaching a maximum at x = 0.02, implying that only minor additional scattering originated from the doped Pd. This is a peculiar result, as there is much evidence of additional point defect scattering upon substitutional doping. Due to the effect of the mass and lattice constant differences between two constituents of an alloy, described by Equation (8), we would expect a rather large additional contribution from phonon scattering, due to the large mass and ionic radius differences between Pd and Bi . Despite the rather large ΔM and Δa values, we did not observe significant additional scattering due to the Pd doping. A possible explanation would be that intercalated Cu and Te/Se disorder already provide enough point defect scattering, so that Pd substitution would not contribute further in reducing lattκ. Scattering from Cu is known to be rather effective [totκ value at 300 K showed a significant increase due to the increased elecκ, whereas that at 480 K increased only slightly, together with the decrease in bpκ, seen in The theoretical ffective . ConsequzT values of all samples. At low temperatures, the zT values were reduced, mainly due to the totκ increase. However, at higher temperatures (over 400 K), enhanced zT values were observed for intermediate Pd doping levels of x = 0.004 and 0.01. This is due to the enhanced power factors, along with the fact that totκ did not increase significantly despite the elecκ increase. For instance, the zT at 480 K increased from 0.70 to 0.79 in the x = 0.01 case. However, no clear Pd doping-induced enhancement in zT was observed at doping levels higher than x = 0.01, due to the simultaneous increase in elecκ and totκ, resulting from an excessive increase in electron carrier concentration. We found that moderate doping of Pd with levels of x = 0.004 to 0.01 in n-type Cu0.008Bi2Te2.7Se0.3 can be effective in enhancing the power factor. However, the Pd doping in Cu-doped n-type Bi23 did not further reduce κlatt despite the rather large ΔM and Δa values.n-type Cu-doped Bi2Te2.7Se0.3, Cu0.008Bi2Te2.7Se0.3, by analyzing the electrical and thermal properties of a series of n-type Cu0.008PdxBix2-Te2.7Se0.3 alloys  based on a single parabolic band and Debye-Callaway models. As the Pd doping increased, the electron carrier concentration and electrical conductivity increased simultaneously. The power factor was also enhanced, especially at higher temperatures. The bipolar conduction in the Pd-doped Cu0.008Bi2Te2.7Se0.3 samples was reduced; in particular, the bipolar thermal conductivity showed a significant decrease from 0.36 W/m·K in the undoped sample to 0.24 W/m·K in the x = 0.02 doped sample at 480 K. However, the analysis of the lattice thermal conductivity showed that substitutional Pd is not very effective in enhancing phonon scattering when interstitial Cu and Se/Te disorder are already present. Consequently, enhanced zT values at temperatures higher than 400 K were observed for the x = 0.004 and 0.01 doped samples.We studied the influence of Pd substitution in


C-reactive protein (CRP) is a powerful biomarker for inflammation, infection and sepsis. However, no reports have investigated canine CRP (c-CRP) concentration changes after orthopaedic procedures. If c-CRP changes were better characterized, it may be possible to identify postoperative complications more quickly. The purpose of this study was to clarify the characteristic changes in serum c-CRP after orthopaedic surgery in dogs. Blood samples were collected from 98 dogs on Day 0 (preoperatively), and then on Days 1, 4, 7, 10 and 13 postoperatively. Day 1 blood sampling was performed 12–24 h postoperatively. We classified the dogs into four groups based on changes in c-CRP pre- to postoperatively. Group 1 dogs showed a peak c-CRP concentration on Day 1, followed by decreases of ≥ 1 mg/dL. Group 2 dogs showed changes in c-CRP concentration by Day 4 that were within ± 1 mg/dL compared with Day 1. Dogs in Group 3 showed a peak c-CRP concentration on Day 4, followed by decreases of ≥ 1 mg/dL. Group 4 dogs showed an initial decrease in c-CRP, then an increase of ≥ 1 mg/dL. Group 1 was the largest group, with 63 dogs. c-CRP on Days 0, 1, 4, 7, 10 and 13 was 0.83 ± 1.03 mg/dL, 8.10 ± 3.15 mg/dL, 3.76 ± 1.94 mg/dL, 1.63 ± 0.92 mg/dL, 0.96 ± 0.70 mg/dL and 0.68 ± 0.51 mg/dL, respectively. Serum c-CRP concentration on Day 1 was significantly higher than at every other timepoint (P < 0.001). In Group 2, surgical site complications were confirmed in 9/15 dogs. In Group 3, surgical site complications were confirmed in 7/14 dogs. In Group 4, two surgical site problems and three surgical site infections were observed, and visceral disease was found in one dog. In Group 1, peak c-CRP was seen on Day 1 postoperatively in 63 dogs (64%), with c-CRP level decreasing by half at each subsequent measurement, which may describe a typical c-CRP change in orthopaedic patients. If deviation from this typical change is observed postoperatively, as in Groups 2–4, this may suggest possible complications. In small animal orthopaedic surgery, it is important to diagnose postoperative complications early. Overall, surgical site infection rates in small animals range from 2.83 to 5.8% –3. C-reaConcentrations of c-CRP begin to increase less than 6 h postoperatively, and maximum concentrations have been observed approximately 12–24 h postoperatively –11. If nThe purpose of the present study was to characterize the changes in c-CRP after orthopaedic surgery in dogs. We expected to see maximum c-CRP concentrations in the first 12–24 h after surgery, followed by a gradual decrease.This was a prospective study. Data were collected from 98 dogs treated for orthopaedic disorders at our institution between February 2014 and September 2016. The dog breeds varied, with a predominance of Toy Poodles (n = 30). Other breeds included Labrador Retriever (n = 8), mixed breed (n = 8), Miniature Dachshund (n = 6), Bernese Mountain Dog (n = 5), Pomeranian (n = 5), Chihuahua (n = 4), Border Collie (n = 3), Golden Retriever (n = 3), Italian Greyhound (n = 3), Jack Russell Terrier (n = 3), Shiba Inu (n = 3), Beagle (n = 2), Siberian Husky (n = 2), Welsh Corgi (n = 2), Yorkshire Terrier (n = 2) and English Bulldog, Cavalier King Charles Spaniel, French Bulldog, German Shorthaired Pointer, Great Dane, Maltese, Shetland Sheepdog, St. Bernard and White Shepherd (n = 1 each).g for 8 min . c-CRP levels were measured using a latex agglutination immunoassay method with an automatic analyser . The reagent used in the present study was the Canine CRP NEO . The assay range of this kit is 0.2–20 mg/dL [Blood samples were collected on Day 0 (before surgery), then on Days 1, 4, 7, 10 and 13 postoperatively. Day 1 blood sampling was performed 12–24 h postoperatively. Blood samples were collected slowly from the jugular vein or lateral saphenous vein into serum separating tubes . Serum samples were then centrifuged at 2000All dogs were cared for according to the perioperative care protocol of the Veterinary Medical Teaching Hospital, Nippon Veterinary and Life Science University for postorthopaedic patients Table . BandageThis research was approved by the ethics committee of the Veterinary Medical Teaching Hospital, Nippon Veterinary and Life Science University, Japan.We classified the dogs into one of four groups based on changes in c-CRP. Group 1 dogs showed a peak c-CRP on Day 1, and then levels continued to decrease during each subsequent measurement period. Group 2 dogs showed changes in c-CRP concentration by Day 4 that were within ± 1 mg/dL compared with Day 1. Group 3 dogs showed a peak c-CRP on Day 4 followed by decreasing levels during each subsequent measurement period. Group 4 dogs showed a peak c-CRP on Day 1 or Day 4, which decreased then increased again.Statistical analysis was performed between measurement days within Groups 1, 2 and 3 and between Groups 1, 2 and 3 for each measurement day. The normality of each c-CRP concentration in Group 1, 2 and 3 was confirmed using the Shapiro–Wilk’s test. The homoscedasticity of each value was then examined using Levene’s test. Homoscedasticity was confirmed for each value, then significant differences were confirmed using Tukey’s honestly significant difference test. When homoscedasticity was not observed for a value, significant differences were confirmed using the Games–Howell test. Data were expressed as the mean ± standard deviation, and P < 0.05 was considered statistically significant. The Statistical Package for the Social Sciences version 16.0.1  was used to perform all statistical analyses.The pre- and postoperative c-CRP concentrations, number of dogs, and the surgical procedures in Groups 1, 2 and 3 are shown in Table In Group 1, c-CRP concentration on Day 1 was significantly higher than at all other timepoints (P < 0.001). Additionally, c-CRP concentrations on Day 10 and Day 13 were not significantly different from those on Day 0 Table . There wGroup 4 included six dogs, numbered 2, 5, 10, 13, 59 and 64 (Table Sixty-three dogs (64%) showed a peak c-CRP concentration on Day 1 after surgery, consistent with previous studies of patients undergoing soft tissue surgery or spinal surgery –11. AddiStaphylococcus aureus was isolated from bone chips collected during surgery. In this dog, 25 mg/kg cefmetazole sodium (CMZ) was administered twice a day intravenously intra- and postoperatively, based on culture and sensitivity. The other dog, which had a radioulnar nonunion, received 25 mg/kg CMZ twice daily intravenously and 5 mg/kg enrofloxacin once daily subcutaneously. Pseudomonas aeruginosa was isolated from a bone chip collected during surgery, and the antibiotic was changed to ceftazidime hydrate 25 mg/kg three times a day intravenously over 1 h; however, the antibiotic sensitivity testing did not include CMZ and enrofloxacin, so it is unclear whether these antibiotic agents were effective for P. aeruginosa. Postoperative c-CRP levels in the two dogs in Group 1 may have decreased over time because of the dogs’ response to the intra- and postoperative antibiotics.A total of 35.7% (35/98) of the dogs did not belong to Group 1, and 86% (30/35) of these dogs had problems associated with changes in c-CRP. A previous study measured c-CRP in dogs undergoing ovariohysterectomy for pyometra . This prChanges in postoperative c-CRP are likely to be affected by the presence of surgical site infections; however, it was not possible to evaluate the influence of surgical site infection on postoperative c-CRP changes because of the small number of dogs, in our study. However, a recent study that measured c-CRP after tibial plateau levelling osteotomy reported that c-CRP levels in dogs with clinical signs of postoperative infection deviate from expected levels on postoperative Day 6 .Dogs with elevated c-CRP with concurrent marked swelling and/or heat at the surgical site were observed in Groups 2 and 3 in 60.0% and 35.7% of dogs, respectively, and visceral disease was observed in 20.0% and 28.6% of dogs, respectively. This suggests that if the Day 4 c-CRP concentration does not decrease compared with that on Day 1, clinicians should consider the presence of visceral disease, as well as contamination of the surgical site. In fact, c-CRP concentration on Day 4 in Group 1 was significantly lower compared with Group 2 and 3, in this study. In other words, we may be able to classify dogs regarding the presence or absence of complications by observing the pattern of c-CRP change between Day 0–1, and between Day 1–4, postoperatively. However, our results also indicate that it is difficult to identify the type of complication from the pattern of c-CRP change.1-acid glycoprotein, which are known to increase with inflammation, were not included in our evaluations, and it is unclear if these inflammatory markers change similarly to c-CRP concentration after orthopaedic surgery in dogs. Fifth, anti-inflammatory drugs such as nonsteroidal anti-inflammatory drugs and steroids were not permitted within the measurement period. Therefore, the number of dogs in our study was relatively small, and it was impossible to compare all procedures. Additionally, the effect on c-CRP of nonsteroidal anti-inflammatory drugs, which are often used in orthopaedic patients, could not be determined. However, one report suggests that carprofen or meloxicam administration in dogs undergoing elective ovariohysterectomy does not affect postoperative c-CRP concentrations [There are certain limitations in the present study. First, 22 dogs had preoperative c-CRP concentrations higher than the reference value, namely 14, 4, 1 and 3 dogs in Group 1, 2, 3 and 4, respectively. Events with a possible effect on preoperative c-CRP levels included five bone fractures, four infections and one revision surgery. However, in the other 12 dogs, the cause of the higher preoperative c-CRP concentration could not be identified. Second, we were not able to clarify how preoperative inflammation affects changes in c-CRP concentration after surgery. Third, we did not evaluate liver function, which is the organ that produces c-CRP. Fourth, we focused only on c-CRP concentration as an inflammatory marker, in this study; therefore, white blood cell counts, fibrinogen, serum amyloid A protein and αtrations .The present study showed a characteristic pattern of c-CRP changes after orthopaedic surgery. If deviation from this characteristic change is observed, clinicians should suspect the possibility of complications such as surgical site infections, and further assess the patient.


The fertilizer combination that resulted in the maximum yield was 62.98 kg ha−1 N, 47.04 kg ha−1 P2O5 and 59.95 kg ha−1 K2O (N:P2O5:K2O = 1:0.75:0.95), which produced the model-expected yield in trials at multiple sites. An economical fertilizer combination was determined on the basis of the best fertilizer measures in consideration of the cost of fertilizer and seed; this combination achieved yields of 2236.17 kg ha−1, the profit was 15,653.16 Yuan ha−1, and the corresponding rates were 57.60 kg ha−1 N, 47.03 kg ha−1 P2O5, and 31.64 kg ha−1 K2O (N:P2O5:K2O = 1:0.82:0.55).Nitrogen (N), phosphorus (P), and potassium (K) exert various effects on adzuki bean yields. Our research was conducted in a semi-arid area, and four test sites were established in environments that have chernozem or sandy loam soils. During a five-year period, the effects of N, P, and K fertilizers on yield were comprehensively investigated in field trials (2014–2016) and for model-implementation trials (2017–2018), with models established prior to the latter. In the field trials, 23 treatments comprising different N, P, and K combinations significantly affected both yield and yield components, and regression analysis indicated that the experimental results were suitable for model establishment. The model subsequently demonstrated that the yield and the yield components were more sensitive to N and K fertilizer than to P fertilizer. Moreover, the yield and yield components increased. These yield increases were intense in response to the 0.5 to 1.34 levels in terms of the single effects; interaction effects; and the effects of combinations of N, P, and K fertilizers. Moreover, the effects of combinations of N, P, and K fertilizers were more significant on yield than were the single or interaction effects of N, P, and K fertilizers. The optimal fertilizer combination that resulted in high yields (≥1941.53 kg ha Vigna angularis), which is cultivated in more than thirty countries worldwide, is a major leguminous crop species that is widely consumed and used for medicinal purposes2. Adzuki bean originated in China and is grown mainly in the temperate regions of East Asia, mainly China, Japan and South Korea. This legume is an important export product in China, where the planting area and total production each account for more than one-third of the corresponding global totals4. In China, the annual average adzuki bean planting area is approximately 250,000 ha. In addition, the total annual harvest in China is approximately 250,000–350,000 tons, and the export volume is approximately 50,000–80,000 tons. China’s total output and export volume of adzuki beans rank first worldwide. However, in China, soil quality, soil fertility and the quantity of arable soil have declined significantly because of an overdependence on fertilizer5. Therefore, the balanced uses of nitrogen (N), phosphorus (P), and potassium (K) fertilizers and proper combinations of N, P, and K fertilizers have become necessary.Adzuki bean  lower than that in the other treatments, and the yield in treatments 4, 11, 13 and 6–9 was highly significant (P < 0.01) lower than that in the other treatments. With respect to the number of pods per plant, treatments 4–9 and 11–14 yielded significantly (P < 0.05) lower values than did the other treatments, and with respect to the number of seeds per pod, treatments 1, 5, 8, 10 and 15–23 yielded significantly (P < 0.05) lower values than did the other treatments. Additionally, with respect to 100-seed weight, treatments 5–9 and 11–13 yielded significantly (P < 0.05) lower values than did the other treatments. The maximum yield was 2311.90 kg ha−1 and was attained in response to level 1 of each N, P2O5 and K2O fertilizer component. The maximum number of pods per plant was 28.10 and occurred in response to level 1 of each N, P2O5 and K2O component, and the maximum number of seeds per pod was 9.44 and occurred in response level −1 of N, level 1 of P2O5 and level −1 of K2O. The maximum 100-seed weight was 12.02 g and was attained in response to level 1.68 of N, level 0 of P2O5 and level 0 of K2O , number of pods per plant (2), number of seeds per pod (3), and 100-seed weight (4) in response to N, P, and K fertilizer.P-values of the above four equations were 0.0001, indicating significance (P < 0.01); thus, the mathematical models exhibit good adaptability. The P-values of the misfit for each equation were 0.2073 (1), 0.1437 (2), 0.1833 (3), and 0.2499 (4) and were not significant (P > 0.05); these results indicated that the influences of external factors on the experimental results could be ignored. Therefore, the four regression models were suitable for assessing the effects of N, P and K fertilizers on yield and yield components.The regression analysis results are shown in Table According to the absolute values of the regression coefficients of the above four equations, the relative magnitudes of the effects of N, P, and K fertilizers on yield, number of pods per plant, number of seeds per pod, and 100-seed weight were N > P > K (1), N > K > P (2), K > N > P (3), and N > K > P (4), respectively. The relative effect sizes of the interactions of N, P and K fertilizers on yield, number of pods per plant, number of seeds per pod and 100-seed weight were NK > NP > PK (1), NP >  = NK > PK (2), PK > NP > NK (3), and NK > NP > PK (4), respectively.P < 0.01) on both yield and number of pods per plant  effect on number of seeds per pod, whereas the N and P fertilizers had no significant (P > 0.05) effect on this variable (Table K fertilizer had a significant (le Table . As showP < 0.01) effects on 100-seed weight, whereas P fertilizer did not (P > 0.05) (Table N and K fertilizers had significant (5) Table . As showP < 0.05) effects on the yield, number of pods per plant and 100-seed weight. However, the interactions between P and K fertilizers had no significant (P > 0.05) effects on these variables, and the interactions between N and P fertilizers had no significant effect on yield or 100-seed weight (Table The interaction between N and K fertilizers had significant (ht Table . The N aht Table  and 3e.FP < 0.05) effects on the number of pods per plant and the number of seeds per pod. Moreover, the interaction between P and K had highly significant (P < 0.01) effects on the number of seeds per pod, whereas that between N and K did not (P > 0.05) (Table The interaction between N and P had significant (5) Table . The int5) Table . With re5) Table .−1) ranged from 57.23–68.43 kg ha−1, and the corresponding N fertilizer levels was 0.75 to 1.23, which lay within the range of the 0.5 to 1.34 levels. The P fertilizer interval was 36.04–47.32 kg ha−1, which corresponded to P fertilizer levels of 0.37 to 1.01 and was located within the range of the 0 to 1 levels, and the K fertilizer interval was 50.29–61.27 kg ha−1 and corresponded to K levels of 0.56 to 1.06, corresponding to the 0.5 to 1.34 levels  was achieved in response to levels of −0.31 to 0.31, corresponding to the −0.5 to 0.5 interval, and the K fertilizer amount needed (30.49–58.88 kg ha−1) was achieved in response to levels of −0.31 to 0.95, corresponding to levels of −0.5 to 1 , an N fertilizer amount of 59.24–70.35 kg ha−1, 23.33–31.78 kg ha−1, and 29.22–40.06 kg ha−1, respectively, corresponding to levels of −0.37 to 0.17, −0.35 to 0.12, and −0.37 to 0.11, respectively, which were within the levels of −0.5 to 0.5  were 32.13–43.61 kg ha−1) and 27 combinations for achieving high number of pods per plant ( > 24.13). Under these combinations, the effects of N, P, and K on the yield and number of pods per plant were apparent primarily at the 0 to 1.68 levels. The most influential fertilizer levels included level 1 for N (62.98 kg ha−1), P2O5 (47.04 kg ha−1), and K2O (59.95 kg ha−1) for yield and included level 1 for N (62.98 kg ha−1) and P2O5 (47.04 kg ha−1) but level 0 for K2O (37.60 kg ha−1) for number of pods per plant  and number of pods per plant (27.66) , a P2O5 at the 0 level (29.50 kg ha−1), and K2O at the 1 level (59.95 kg ha−1) ; for these combinations, the firm range for N and K fertilizers was 0 to 1.68 and that for P fertilizer was −1 to 1. The most influential fertilizer comprised N at the 1.68 level (78.99 kg ha−1) Fig. ; the gre−1) Fig. .−1) of N, the −1.68 level (0 kg ha−1) of K2O and the −1 level (15.25 kg ha−1) of K2O , and the results under the high fertilizer conditions and the no N, P, or K fertilizer conditions were similar , X2 (P), and X3 (K) were equal to zero, and the following equations were obtained:Partial equations of the above equations were obtained. The partial derivatives of the elements X1 = 0.7709, X2 = 0.9994, and X3 = −0.2666 and inserting these values into the formula, we obtained values of 57.60 kg/ha−1 N, 47.03 kg/ha−1 P2O5 and 31.64 kg/ha−1 K2O for the N:P2O5:K2O ratio = 1:0.82:0.55. The optimum fertilizer ratio was therefore 1:0.82:0.55, the resulting yield was 2236.17 kg/ha−1, and the profit was 15,653.16 Yuan.Under the conditions −1.68 ≤ xi ≤ 1.68, the most economically beneficial bean fertilizer combination was determined. By determining that X−1. Under the lower-fertility conditions of Zhenlai, Taonan and Tongyu, moderate yields were obtained; compared with that in response to normal fertilizer, the average yield (1762.40 kg/ha−1) of the three test points was 15.20% greater through optimal fertilizer combinations. Two-year multipoint tests determined an optimal fertilizer programme with an average yield of 1823.76 kg ha−1, which was 15.26% higher than that obtained with normal fertilizer  in the field research was at 1 level of N, P2O5 and K2O. These results constitute a reliable data foundation for model establishment. The fertilizer model was constructed via assessment of the comprehensive performance of single and interaction effects among the various fertilizers. Last, the optimal combination of N, P, and K fertilizer was ultimately obtained.The quadratic orthogonal rotation combination design applied in the field research was effective for determining the fertilizer combination that resulted in the greatest adzuki bean yield in our study. On the basis of the significant performance of the different combinations of N, P and K fertilizers in the field trail, and the fertilizer combination for achieving maximum yield  corresponded to the 0.5 to 1.34 levels of the N, P, and K fertilizers. Overall, the above results demonstrated that the high yields were achieved under the single and interaction effects and under the effects of optimal combinations of N, P, and K fertilizers at the same interval (0.5 to 1.34 levels). In particular, the combinations of N, P, and K fertilizers had a more significant effect on yield than did the single or interaction effects of N, P, and K fertilizers, which are also indicated in other articles36.Previous studies have shown that high numbers of pods per plant, numbers of seeds per pod and 100-seed weight are considered yield quality characteristics of adzuki bean−1; N:P2O5:K2O = 1:0.75:0.95), 62.98 kg ha−1 N, 47.04 kg ha−1 P2O5, and 59.95 kg ha−1 K2O, was approaching the upper limit of the optimal fertilizer combination. The maximum yields (1225–1750 kg ha−1) reported in the literature for subtropical humid regions were lower than our optimal yield37. In addition, the amounts of P fertilizer or K fertilizer applied in previous studies were greater than those applied in our study, with P > N > K or K > P > N39. These results demonstrate that regions with different soil environments or climates and varieties with different characteristics necessitate different fertilizer combinations. It was evident that the present study was conducted under relatively semi-arid and low-fertility conditions, and the results were obtained with early-maturing varieties. If rain is abundant, fertility is high, and mid–late-maturing varieties are used, the amount of P and K fertilizers applied should be appropriately increased, and the amount of N fertilizer should be reduced. Therefore, the yield response of different adzuki bean varieties in different regions to NPK fertilizer needs to be further explored.In our study, the optimal fertilizer combination for maximum yield  did not, as these sites were affected by sandy loam soils and low-moisture conditions; however, the yields were still significantly greater than those in response to normal fertilizer. Our optimal fertilizer combination resulted in increased yields at multiple production sites in the region and could serve as a reference for producing high-yield-inducing fertilizer in semi-arid areas of other regions. Optimal fertilizer models for high production in normal regions could be investigated on the basis of this reference.−1 of N, 47.03 kg ha−1 of P2O5, and 31.64 kg ha−1 of K2O, although less K fertilizer should be applied than the optimal amount because of the relatively high price of K fertilizer. This economical fertilizer combination could promote the use of profitable fertilizer in future production of adzuki bean.An economical fertilizer combination was established on the basis of the best fertilizer combination. In consideration of the market fluctuation with respect to the cost of fertilizer and seed, a fertilizer model inclusive of cost-effectiveness was constructed to obtain high yields and economic benefits. The corresponding amounts of fertilizer were 57.6 kg ha−1 N, 36.04–47.32 kg ha−1 P2O5 and 50.29–61.27 K2O. The fertilizer resulting in the maximum yield (N:P2O5:K2O = 1:0.75:0.95) comprised 62.98 kg ha−1 N, 47.04 kg ha−1 P2O5, and 59.95 kg ha−1 K2O; although this was the best combination, it approached the upper limit of the optimal fertilizer combination. The optimal fertilizer combination was successful in terms of production at multiple sites with chernozem and sandy loam soils. Thus, our research could provide a reference for producing high-yield-inducing fertilizer in semi-arid areas. The most economical fertilizer comprises 57.60 kg ha−1 N, 47.03 kg/ha−1 P2O5, and 31.64 kg ha−1 K2O, and its optimum ratio is N:P2O5:K2O = 1:0.82:0.55. The economical fertilizer combination could promote profitable fertilizer in the future production of adzuki bean.In our field research, the effects of various combinations of N, P, and K on yield and yield components were significant. According to the fertilizer model, K fertilization is an important strategy in the production of adzuki bean, as the yield and yield components were more sensitive to K fertilizer than to N and P fertilizers. The high yield achievements were intense at the 0.5 to 1.34 levels under the single and interaction effects and under the effects of the optimal combination of N, P, and K fertilizers. The effects of the combinations of N, P, and K fertilizers significantly influenced the yield more than the single or interaction effects of N, P, and K fertilizers did. The optimal fertilizer combination for achieving high yield comprised 57.23–68.43 kg haFive-year-long (2014–2018) trials were conducted around the Kerqin grassland square, and four test sites were established in Baicheng, Zhenlai, Taonan and Tongyu of Jilin Province, China (one site at each location). The territory is the main production region of China. The test region had two soil types with low soil fertility. The soil at Baicheng was a chernozem, and the other three locations had sandy loam soils. This area has a temperate semi-arid continental monsoon climate, and the longitude and latitude of the area are 123° E, 45° N, respectively. The region has a daily mean temperature of 20 °C (0.8 °C above the average for the area), an annual sunshine duration of 1243.2 h, and an annual mean rainfall of 404.9 mm.40. All treatments were repeated three times in completely randomized blocks for a total of 69 test plots. Each plot was 12 square metres in area and contained four rows, with ten seedlings metre−1 at a line spacing of 15 cm, and the row spacing was 60 cm. At the two-leaf stage, the plants were thinned to a uniform density of 180,000 plants ha−1. The fertilizers were mixed and sprayed as seed fertilizers to a depth of 5 cm before the seeds were sown during middle May. The N fertilizer (urea containing 46% N and diammonium phosphate containing 17% N), P fertilizer , and K fertilizer (potassium sulphate containing 50% K2O) used were obtained from Sinochem Jilin Changshan Fertilizer Co., Ltd. .Field trials were performed from 2014–2016 using the early-maturing adzuki bean variety Baihong 4 at the Baicheng Academy of Agricultural Sciences, Baicheng , Jilin Province, China. The field trial consisted of 23 treatments of various N, P, and K combinations using a three-factor and five-level quadratic orthogonal rotation combination design  was applied in the trails. This fertilizer comprised optimized components of 100 kg ha−1 of urea, 100 kg ha−1 of diammonium phosphate, and 120 kg ha−1 of potassium sulphate. Normal compound fertilizer (N:P2O5:K2O = 1:1:1) was applied at a rate of 300 kg ha−1 for comparison. The production trial areas were 0.5 ha in each location. The Zhenlai, Taonan, and Tongyu are affiliated to Baicheng, and the climate conditions are similar. At the growth periods of the trails in 2017–2018, the temperature and sunshine duration were not affected yield production, with the proper management  software  was used for designing the quadratic orthogonal rotation combination and for performing the variance analyses and regression analyses.