The studied material of the M. dotatus species group is preserved at the Institute of Zoology, Chinese Academy of Sciences, Beijing, China (IZAS) and the Museum of Hebei University, Baoding, China (MHBU).

We identified the species of the M. dotatus species group by relevant references (Kazantsev 1993; Li et al. 2012, 2015; Li 2015). The description format and terminology follow those of Li et al. (2012). Additionally, the male genitalia shape will be included in the description for the first time. In addition, the similar species in the male genitalia shapes shall be compared with the new species in discussing the parallax discrimination.

The specimens were softened in water, and the male genitalia were dissected, cleared in 10% NaOH solution, examined and photographed in glycerol, and finally glued on a paper card for permanent preservation. Images of adults were taken with a Canon EOS 80D digital camera and aedeagi by a Leica M205A stereomicroscope and then stacked in Helicon Focus 7. The final permutation was edited in Adobe Photoshop CS3.10.0.1. The measurements were taken with ImageJ 1.50i (NIH, USA). Body length was measured from the anterior margin of the head to the elytral apex, and the width was measured across the humeral part of the elytra. Pronotal length was measured from the middle of the anterior margin to the middle of the posterior margin and the width across the widest part of the pronotum. Eye diameter was measured at the widest point, and the interocular distance was taken at the point of minimum.

All of the species of the M. dotatus species group were included in the analysis. Digital photographs of male ­genitalia were annotated using TpsUtil 1.43 software (Rohlf 2008a, see http://life2.bio.sunysb.edu/morph). Two curves were extracted from the ventral and ­lateral contours of the median lobe to represent the external forms. The ventral cavity is neglected in the analysis due to its variation within some species (Li et al. 2012). The two curves both started from apices and ended at the same point and were resampled into 200 equally spaced semilandmarks (Fig. 1A, B). All curves and semilandmarks were digitized with TpsDig 2.12 software (Rohlf 2008b, see http://life2.bio.sunysb.edu/morph). The digitalization procedure was repeated three times by the same observer on different days to evaluate landmark measurement error (Zhao et al. 2023).

Then, we used TpsSmall (ver. 1.20, F. Rohlf, see http://life2.bio.sunysb.edu/ morph) to test whether the observed variation in shape was sufficiently small that the distribution of points in the tangent space could be used as a good approximation of the distribution in shape space. The coordinates were analyzed using TpsRelw (ver. 1.49, F. Rohlf, see http://life2.bio.sunysb.edu/morph) to calculate eigenvalues for each principal warp. The shape changes of different species implied by variation along the first two relative warp axes and shape changes were shown as transformation grids using thin-plate splines.

To examine shape variation, the digitized outline data were analyzed using MorphoJ 1.06d software (Klingenberg 2011, see http://life2.bio.sunysb.edu/morph). Principal component analysis (PCA) was employed to test how well the species could be distinguished by the shape of the median lobe. Frequently, the characters with high loading values in PCAs correspond to the observed variation patterns among species. The relative similarity and discrimination of the test groups was analyzed using canonical variates analysis (CVA). CVA finds shape values that maximize group means relative to variation within groups by assuming that covariate matrices are identical (Klingenberg 2010). Mahalanobis and Procrustes distances (the square root of the sum of squared differences between corresponding points) between the species were computed, and the matrix was produced by MorphoJ software (Klingenberg 2011).

The phylogenetic relationships among the species were based on the morphometric data of male genitalia considering UPGMA (unweighted pair group method using arithmetic averages), neighbor-joining (NJ) and maximum parsimony (MP) as the optimality criteria (Champakaew et al. 2021; Goloboff and Catalano 2016). Procrustes and Mahalanobis distance matrices were subjected to UPGMA and cluster analyses to determine the phenetic relationships among the species. In addition, neighbor-joining (NJ) trees (Sneath and Sokal 1973) were constructed to display the Mahalanobis and Procrustes distances between populations using PAST 2.17 with 1000 bootstrap replicates.

The tps files produced in tps-DIG were also used to perform MP analysis in TNT 1.5 (Goloboff and Catalano 2016). The search strategy followed a heuristic (traditional search) using random addition sequences and tree bisection reconnection (TBR) as the branch swapping algorithm, holding one tree per replicate and 1000 runs (mult = ras tbr hold 1 rep 1000) (Díaz-Cruz et al. 2021).

The distribution information was collected from the Global Biodiversity Information Facility (GBIF, https://www.gbif.org), relevant publications (Pic 1923, 1935, 1939; Kleine 1925, 1933, 1942; Nakane 1967, 1969; Kazantsev 1993, 2001, 2002, 2011; Li et al. 2012, 2015) and our material in the present study. The distribution map was prepared using ArcMap 10.8 and edited in Adobe Photoshop CS3.10.0.1.

Analyses of the datasets using TpsSmall indicated that excellent correlations between the tangent and the shape space in ventral and lateral views existed. The correlation (uncentered) between the tangent space (Y) regressed onto Procrustes distance (geodesic distances in radians) was 1.000000. There was little doubt on the basis of the result from TpsSmall, which supported the hypothesis that species within the M. dotatus species group can be analyzed by geometric morphometric methods because the results from the statistical test performed by TpsSmall proved the acceptability of the data for further statistical analysis (Pretorius and Scholtz 2001).

The first two principal components of the shape of the median lobe in lateral and ventral views explain 83.31% and 91.46% of the micromesh variation, respectively (­Tables S1, S2). They were plotted to indicate variation along the first two relative warp axes, which were shown as deformations of the least squares reference using thin-plate splines in lateral (Fig. 8A) and ventral (Fig. 8B) views.

Comparison of the tps configurations indicated that the average shape of the median lobe of the M. dotatus species group is almost even in width except for being slightly narrowed at apical one-seventh, bisinuate at basal nine- and three-fourteenths, respectively, and accordingly at an angle of ca. 30° and 150° with apical part in lateral view (Fig. 8a); nearly straight along whole length, subparallel-sided at basal four-sevenths, roundly and asymmetrically widened laterally at apical two-sevenths, gradually narrowed at apical one-seventh, feebly and triangularly emarginated at apex in ventral view (Fig. 8b).

The PCA and CVA scatter plots of shape differences of the shape of median lobe in lateral and ventral views (Figs S1–S4) showed that each species of M. dotatus species-group independently occupied an area and separated from one another.

The UPGMA phonograms based on both Procrustes and Mahalanobis distances of the shape of the median lobe in lateral view were completely consistent with each other (Fig. 9A). The species of the M. dotatus species group were divided into two branches, one of which was composed of M. atronotatimimussp. nov. + (M. unicolorsp. nov. + M. huoditangensissp. nov.), and the other consisted of (M. aemulus + M. dotatus) + (M. atronotatus + M. jianfenglingensis). In both NJ trees (Fig. 9B, C), the clade of M. atronotatus + M. jianfenglingensis was recovered, but it was clustered only with M. aemulus. In contrast to the UPGMA results, M. atronotatimimussp. nov. and M. huoditangensissp. nov. were always grouped into a clade in the NJ trees.

However, the produced topology of the MP analysis (Fig. 9D) is totally different from the aforementioned relationships among the species. The shape of the median lobe of M. atronotatimimussp. nov. is the most distinctive, which can also be reflected by its position in the relative warp axis. It occupies the top left position of the relative warp axis in the lateral view of the median lobe (Fig. 8A: tps configuration in red coloration). If M. atronotatimimussp. nov. was at the basal clade, the remaining species were grouped into two clusters, of which one was recovered as M. dotatus + (M. huoditangensissp. nov. + M. jianfenglingensis) and the other as M. aemulus + (M. atronotatus + M. unicolorsp. nov.).

Similar to the above, the clade of M. atronotatimimussp. nov. + M. huoditangensissp. nov. was recovered in both UPGMA phonograms (Fig. 10A) and NJ trees (Fig. 10B, C) based on the morphometric data of the shape of the median lobe in ventral view. Additionally, M. atronotatimimussp. nov. was the first to separate from all others in the phylogenetic tree of MP analysis (Fig. 10D) because it was located at the rightmost position in the ventral view (Fig. 8B: tps configuration in red coloration). In contrast, the clades of M. unicolorsp. nov. + M. jianfenglingensis and M. atronotatus + M. dotatus were clustered in both UPGMA phenograms (Fig. 10A) and the NJ tree of Mahalanobis distance (Fig. 10B). Meanwhile, the sister group of M. aemulus + dotatus was recovered in both the NJ tree of Procrustes distance (Fig. 10C) and the MP tree (Fig. 10D).

Similar to other net-winged beetles, the variability in the general appearance of Macrolycus sometimes prevents reliable identification (Li et al. 2012); therefore, the delineations of species are regularly based on the shape of the male genitalia and antennae, which are provided here in the following key. Although the shape of male genitalia is clearly defined in most cases, morphological interspecific divergence in quantitative variation is identified. Geometric morphometrics is a rigorous method (Gilchrist et al. 2000; Debat et al. 2003) to find and analyze shape variations between species (Walker 2000), thereby facilitating and stabilizing the taxonomy of Macrolycus. In addition, coloration patterns are rarely conspicuously variable within species (Li et al. 2012) due to their signaling function for unpalatability (Bocak and Bocakova 2008), so they will also be applied in the key.

In the present study, the statistical test performed by TpsSmall suggested that our obtained data of male genitalia are acceptable for the geometric morphometric analysis. Furthermore, the CVA analysis suggested that all species of the M. dotatus species group can be distinguished from one another by the shape of male genitalia, which is consistent with the preceding part in the key combined with some nongenital characteristics.

Male genitalia are undoubtedly among the most important and versatile morphological characteristics in insect taxonomy (Tuxen 1970; Song and Bucheli 2010). Male genitalia possess many traits that are unique to species, especially among closely related species, and their utility in species diagnosis has been thoroughly proven in many groups (Eberhard 1985; Hosken and Stockley 2004). A general consensus in the study of genital evolution is that male genitalia are under sexual selection (Eberhard 1985, 2001, 2004b; Huber and Eberhard 1997; Arnqvist 1998; Arnqvist and Danielsson 1999; Córdoba-Aguilar 2005; House and Simmons 2005). Because sexually selected characters tend to evolve rapidly (Lande 1981; Kirkpatrick 1982; West-Eberhard 1983; Gavrilets 2000), researchers generally agree that male genitalia evolve both rapidly and divergently (Eberhard 1985; Arnqvist 1997; Hosken and Stockley 2004; Mendez and Cordoba-Aguilar 2004). It is also a logical conclusion from the observation that male genitalia are consistently useful as a taxonomic character at the specific level, which suggests that they acquire a new form in each new species (Eberhard 1985). This assumption was verified in our study, and the species of the M. dotatus species group can be successfully delineated by the shape of male genitalia. In other words, the three new species discovered here have different median lobe shapes from the previously known species. Although only quantitative variations are exhibited, their differences are shown clearly in the tps configurations by GM methods. Moreover, the species that have no or only simple descriptions of male genitalia in previous publications (Pic 1923, 1935; Kleine 1925, 1933, 1942; Nakane 1967, 1969; Kazantsev 1993, 2001, 2002, 2011; Li et al. 2012, 2015) could be described in more detail. Therefore, we provide detailed descriptions of male genitalia for the M. dotatus species group in taxonomy Part 3.1, and combined with the results of Part 4.3, we could make comparisons between the new species and other similar species in this structure.

The clades of M. atronotatimimussp. nov. + M. huoditangensissp. nov. and M. aemulus + M. dotatus are frequently recovered based on the shape of the median lobe in both lateral (Figs 9B, C and 10A–C) and ventral (Figs 9A, 10C, D) views by either UPGMA or NJ analyses. These results suggest that the paired species have the most similar male genitalia. It is no doubt that this could be integrated in the description of taxonomy part.

Except for the common clades, there are some clades recovered solely in either lateral or ventral view. M. atronotatus + M. jianfenglingensis (Fig. 9A–C), which together are closer to M. aemulus (Fig. 9A, B), and M. unicolorsp. nov. + M. huoditangensissp. nov. (Fig. 9A) are recovered only in lateral view. In comparison, M. unicolorsp. nov. + M. jianfenglingensis (Fig. 10A, B) and M. atronotatus + M. dotatus (Fig. 10A, B) are solely produced in ventral view. These inconsistencies resulted from the independent analysis of the shape of the median lobe in different views. In the present study, only 2-dimensional visualization of the shape of the median lobe was analyzed. Although it provides a well-defined outline, the median lobe is actually a 3-dimensional structure, which demands data analysis to be conducted integrally. Therefore, more techniques are required to obtain and thoroughly analyze the 3-dimensional shape of the median lobe in the future, such as microcomputed tomography (or μ-CT) and computer-based 3D reconstruction techniques. Then, we can apply these comprehensive data in a phylogenetic context by combining GM and MP methods.

In the molecular phylogeny of Li et al. (2015), four species of the M. dotatus species group were included in the analysis, and the phylogenetic relationships were recovered as (M. jianfenglingensis + M. dotatus) + (M. atronotatus + Macrolycus sp.). In the present study, we analyzed a total of seven species on the basis of the shape of the median lobe by combining the GM and MP methods. The phylogenetic relationships inferred from MP analyses (Figs 9D, 10D) are consistent with the above molecular phylogeny, with a closer relationship between M. jianfenglingensis and M. dotatus than M. atronotatus, but the converse (Figs 9A–C, 10C) or the latter two closer (Fig. 10A, B) in UPGMA and NJ analyses. The discrepancy in the topologies probably results from different analysis data and optimality criteria of the methods.

Currently, molecular phylogenetics has become the standard for inferring evolutionary relationships (Ziemert and Jensen 2012). Because numerous genes with fundamental biochemical functions are present in all species, they can be sequenced, aligned, and analyzed to study phylogenetic relationships at the deepest part of the tree of life (Hillis and Dixon 1991). In addition, this relationship appeared to be robust to tree-building methods. Therefore, the phylogenetic relationship inferred from the molecular data can be used as the standard reference (Zhao et al. 2023), and the study of Li et al. (2015) is no exception.

In morphological phylogenies, male genitalia have been broadly used across diverse arthropod lineages by systematists (Song and Bucheli 2010). Male genitalia provide excellent phylogenetic signals in higher-level classifications of several insect orders (Sharp and Muir 1912; Eyer 1924; Peck 1937; Michener 1944; Zumpt and Heinz 1950; Snodgrass 1957; Roth 1970). However, at the specific level, there is an idea that the rate of genital evolution is extremely rapid, to the point that there may not be observable phylogenetic inertia left in the structures (Arnqvist and Rowe 2002; Eberhard 2004a). In contrast, Song and Bucheli (2010) argued that rapid evolution does not necessarily equate to the lack of phylogenetic signal, and characters that evolve by a pattern of descent with modification make appropriate characters for a phylogenetic analysis, regardless of the rate of evolution, so they stated that male genitalia have phylogenetically conserved components at a deeper level (between families) as well as at a shallow level (between species).

Unexpectedly, there is still a gap between our obtained results of UPGMA and NJ analyses (Figs 9A–C, 10A–C) and the previous molecular phylogeny (Li et al., 2015). The most important advantage of using Procrustes and/or Mahalanobis distances to capture shape variation was that these distances were considered the best method for measuring shape differences among taxa (Goodall and Bose 1987; Chapman 1990; Rohlf 1990; Goodall 1991; Marcus et al. 1993; Pretorius and Scholtz 2001). Thus, the Procrustes and/or Mahalanobis distances can effectively indicate phenetic relationships, summarizing overall patterns of similarity (Pretorius and Scholtz 2001; Zhao et al. 2023). However, Losos (1999) argued that no relationship may exist between the degree of phylogenetic relationship and phenotypic similarity if rates of character evolution are high relative to the speciation rate. In this case, it is supposed that some nongenital characters of male (Song and Bucheli 2010) or female genitalia (Simmons and Fitzpatrik 2019) are also involved in the speciation of Macrolycus. Although the phenotypic similarity is different from those deepest in the molecular tree, it provides useful information for us to recognize morphologically similar species. Meanwhile, the tps configurations of GM analysis allow us to make quantitative comparisons among the species in terms of morphology.

Nevertheless, the phylogenetic relationships based on the geometric morphometric data of the shape of the median lobe by MP analysis are comparable to the molecular phylogenetic results, so it is possible to explore the relationships when DNA data are unavailable.